package math
The math
package contains classes, traits and objects for common mathematical
operations. Its package object defines exponentiation, logarithmic, trigonometric,
etc. operators and functions.
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case class
Complex
(re: Double, im: Double = 0.0) extends Fractional[Complex] with Ordered[Complex] with Product with Serializable
The
Complex
class is used to represent and operate on complex numbers.The
Complex
class is used to represent and operate on complex numbers. Internally, a complex number is represented as two double precision floating point numbers (Double). Externally, two forms are supported:a+bi = 2.1+3.2i via: Complex ("2.1+3.2i"), 'toString' (a, b) = (2.1, 3.2) via: create ("(2.1, 3.2)"), 'toString2'
Note: 'i * i = -1'. -------------------------------------------------------------------------
- re
the real part (e.g., 2.1)
- im
the imaginary part (e.g., 3.2)
-
final
class
Double_Exp
extends AnyVal
The
Double_Exp
value class adds an exponentiation operator 'x ~ y' and a 'near_eq' operator 'x =~ y' toDouble
. The '~' has higher precedence than '*' or '/'. -
type
FunctionS2S = (Double) ⇒ Double
The type definition for a function of a scalar (f: Double => Double)
-
type
Functions = Array[FunctionS2S]
The type definition for an array of scalar functions
-
final
class
Int_Exp
extends AnyVal
The
Int_Exp
value class adds an exponentiation operator 'x ~ y' and a 'near_eq' operator 'x =~ y' toInt
. The '~' has higher precedence than '*' or '/'. -
final
class
Long_Exp
extends AnyVal
The
Long_Exp
value class adds an exponentiation operator 'x ~ y' and a 'near_eq' operator 'x =~ y' toLong
. The '~' has higher precedence than '*' or '/'. -
case class
ProbNum
(x: Double, p: Double = 1.0) extends Numeric[ProbNum] with Ordered[ProbNum] with Error with Product with Serializable
The
ProbNum
class is used to represent probabilistic numbers '(x, p)' where 'x' is a real number and 'p' is its probability of occurrence.The
ProbNum
class is used to represent probabilistic numbers '(x, p)' where 'x' is a real number and 'p' is its probability of occurrence. FIX: Currently this class is half-baked!!!- x
the real number (double precision)
- p
the probability of its occurrence [0, 1]
- See also
http://okmij.org/ftp/Computation/monads.html#random-var-monad
-
case class
Rational
(num: Long, den: Long = 1l) extends Fractional[Rational] with Ordered[Rational] with Product with Serializable
The
Rational
class is used to represent and operate on rational numbers.The
Rational
class is used to represent and operate on rational numbers. Internally, a rational number is represented as two long integers. Externally, two forms are supported:a/b = 2/3 via: Rational ("2/3"), 'toString' (a, b) = (2, 3) via: create ("(2, 3)") 'toString2'
Rational number can be created without loss of precision using the constructor, 'apply', 'create' or 'fromBigDecimal' methods. Other methods may lose precision.
- num
the numerator (e.g., 2)
- den
the denominator (e.g., 3)
-
case class
Real
(hi: Double, lo: Double = 0.0) extends Fractional[Real] with Ordered[Real] with Product with Serializable
The
Real
class provides higher precision floating point numbers using the Double Double technique, which supports 106 bits of precision.The
Real
class provides higher precision floating point numbers using the Double Double technique, which supports 106 bits of precision. ----------------------------------------------------------------------------- Code adapted from DoubleDouble.java:- hi
the high portion of the real number
- lo
the low portion of the real number
- See also
oai.cwi.nl/oai/asset/9159/9159A.pdf -----------------------------------------------------------------------------
http://tsusiatsoftware.net/dd/main.html
Value Members
-
val
THRES: Double
The threshold used for near equality
-
def
cot(x: Double): Double
Return the cotangent of 'x'
-
def
csc(x: Double): Double
Return the cosecant of 'x'
-
implicit
def
double_exp(x: Double): Double_Exp
Implicit conversion from 'Double' to 'Double_Exp', which supports exponentiation and nearly equals.
Implicit conversion from 'Double' to 'Double_Exp', which supports exponentiation and nearly equals.
- x
the base parameter
-
implicit
def
int_exp(x: Int): Int_Exp
Implicit conversion from 'Int' to 'Int_Exp', which supports exponentiation and nearly equals.
Implicit conversion from 'Int' to 'Int_Exp', which supports exponentiation and nearly equals.
- x
the base parameter
-
def
log2(x: Double): Double
Compute the log of 'x' base 2.
Compute the log of 'x' base 2.
- x
the value whose log is sought
-
val
log_10: Double
The natural log of 10
-
val
log_2: Double
The natural log of 2
-
def
logb(b: Double, x: Double): Double
Compute the log of 'x' base 'b'.
Compute the log of 'x' base 'b'.
- b
the base of the logarithm
- x
the value whose log is sought
-
implicit
def
long_exp(x: Long): Long_Exp
Implicit conversion from 'Long' to 'Long_Exp', which supports exponentiation and nearly equals.
Implicit conversion from 'Long' to 'Long_Exp', which supports exponentiation and nearly equals.
- x
the base parameter
-
def
near_eq(x: Double, y: Double): Boolean
Determine whether two double precision floating point numbers 'x' and 'y' are nearly equal.
Determine whether two double precision floating point numbers 'x' and 'y' are nearly equal. Two numbers are considered to be nearly equal, if within '2 EPSILON'. A number is considered to be nearly zero, if within '2 MIN_NORMAL'. To accommodate round-off errors, may use 'TOL' instead of 'EPSILON'. --------------------------------------------------------------------------
- x
the first double precision floating point number
- y
the second double precision floating point number
- See also
http://stackoverflow.com/questions/10034149/why-is-nan-not-equal-to-nan --------------------------------------------------------------------------
stackoverflow.com/questions/4915462/how-should-i-do-floating-point-comparison -------------------------------------------------------------------------- If both 'x' and 'y' are NaN (Not-a-Number), the IEEE standard indicates that should be considered always not equal. For 'near_eq', they are considered nearly equal. Comment out the first line below to conform more closely to the IEEE standard.
BasicTest
-
def
nexp(x: Double): Double
Negative exponential function (e to the minus 'x').
Negative exponential function (e to the minus 'x').
- x
the argument of the function
-
def
oneIf(cond: Boolean): Int
Return 1 if condition 'cond' is true, else 0.
Return 1 if condition 'cond' is true, else 0.
- cond
the condition to evaluate
-
def
pow(x: Long, y: Long): Long
Power function for scala Longs 'x ~^ y'. Compute: 'math.pow (x, y).toLong' without using floating point, so as to not lose precision.
Power function for scala Longs 'x ~^ y'. Compute: 'math.pow (x, y).toLong' without using floating point, so as to not lose precision.
- x
the Long base parameter
- y
the Long exponent parameter
-
def
root(x: Long, y: Long): Long
Find the 'y'-th root of 'x', i.e., 'x ~ 1/y' for scala Longs. 'r = x ~ 1/y' is largest long integer 'r' such that 'r ~^ y <= x'.
Find the 'y'-th root of 'x', i.e., 'x ~ 1/y' for scala Longs. 'r = x ~ 1/y' is largest long integer 'r' such that 'r ~^ y <= x'.
- x
the Long base parameter
- y
the Long root level (reciprocal exponent) parameter
- See also
http://stackoverflow.com/questions/8826822/calculate-nth-root-with-integer-arithmetic
http://en.wikipedia.org/wiki/Shifting_nth_root_algorithm
-
def
sec(x: Double): Double
Return the secant of 'x'
-
def
sign(x: Double, y: Double): Double
Return the absolute value of 'x' with the sign of 'y'.
Return the absolute value of 'x' with the sign of 'y'.
- x
the value contributor
- y
the sign contributor
-
object
Combinatorics
extends Error
The
Combinatorics
object provides several common combinatorics functions, such as factorial permutations, combinations, gamma and beta functions. -
object
CombinatoricsTest
extends App
The
CombinatoricsTest
object tests the methods in theCombinatorics
object. -
object
CombinatoricsTest2
extends App
The
CombinatoricsTest2
object tests the Gamma and factorial methods in theCombinatorics
object. -
object
Complex
extends Serializable
The
Complex
companion object defines the origin (zero) and the fourth roots of unity as well as some utility functions. -
object
ComplexTest
extends App
The
ComplexTest
object is used to test theComplex
class.The
ComplexTest
object is used to test theComplex
class. > run-main scalation.math.ComplexTest -
object
ExtensionTest
extends App
The
ExtensionTest
object is used to test theInt_Exp
,Long_Exp
andDouble_Exp
classes.The
ExtensionTest
object is used to test theInt_Exp
,Long_Exp
andDouble_Exp
classes. > run-main scalation.math.ExtensionTest -
object
ExtremeD
The
ExtremeD
object contains constants representing extreme values for Double (IEEE 754 double precision floating point numbers).The
ExtremeD
object contains constants representing extreme values for Double (IEEE 754 double precision floating point numbers).- See also
en.wikipedia.org/wiki/Double-precision_floating-point_format ------------------------------------------------------------------------------ 64 bits: 1 sign-bit, 11 exponent-bits, 52 mantissa-bits + 1 implicit
http://docs.oracle.com/javase/8/docs/api/java/lang/Double.html
-
object
ExtremeDTest
extends App
The
ExtremeDTest
object is used to test theExtremeD
class.The
ExtremeDTest
object is used to test theExtremeD
class. > run-main scalation.math.ExtremeDTest -
object
MathTest
extends App
The
MathTest
object is used to test the supplemental exponential, logarithmic and trigonmetric functions defined in the 'scalation.math' package object.The
MathTest
object is used to test the supplemental exponential, logarithmic and trigonmetric functions defined in the 'scalation.math' package object. > run-main scalation.math.MathTest -
object
Primes
The
Primes
object provides an array of 1000 prime numbers as well as methods to generate prime numbers within a given range. -
object
PrimesTest
extends App
The
PrimesTest
object is use to perform timing test on thePrimes
object. -
object
ProbNumTest
extends App
The
ProbNumTest
object is used to test theProbNum
class.The
ProbNumTest
object is used to test theProbNum
class. > run-main scalation.math.ProbNumTest -
object
Rational
extends Serializable
The
Rational
companion object defines the origin (zero), one and minus one as well as some utility functions. -
object
RationalTest
extends App
The
RationalTest
object is used to test theRational
class. -
object
Real
extends Serializable
The
Real
companion object defines the origin (zero), one half and one as well as some utility functions. -
object
RealTest
extends App
The
RealTest
object is used to test theReal
class.The
RealTest
object is used to test theReal
class. > run-main scalation.math.RealTest -
object
StrNumTest
extends App
The
StrNumTest
object is used to test theStrNum
class.The
StrNumTest
object is used to test theStrNum
class. > run-main scalation.math.StrNumTest -
object
StrO
The
StrO
object is used to represent and operate on string numbers.The
StrO
object is used to represent and operate on string numbers. It contains an implicit class definition forStrNum
, which extends strings withNumeric
operations, it it can be used inVectorS
. The semantics ofStrNum
operators are similar those in Pike.- See also
http://docs.roxen.com/pike/7.0/tutorial/strings/operators.xml


Tyson Fury trains with UFC star Darren Till as boxer considers switch to MMA
Fury displayed his trademark power and slick movement as Till put the heavyweight bruiser through various training drills
by Matt Maltby, https://www.mirror.co.uk/authors/matt-maltby/Tyson Fury was put through his paces by UFC superstar Darren Till as the lineal world heavyweight boxing champion bids to transition to MMA.
Speculation has been rife in recent weeks that the British boxer had been eying a switch to the octagon following a successful, albeit brief, stint in wrestling with WWE.
Though he has a potential rematch with fellow undefeated boxing champ Deontay Wilder to look forward to in February next year, the Gypsy King remains keen to try his hand at another sport.
Indeed, Manchester boxer Fury met up with Liverpool fighter Till to showcase his MMA talents.
Fury displayed his trademark power and slick movement as Till put the heavyweight bruiser through a series training drills.
The boxer also posted a snap of the pair on Instagram, captioning his post: "The 2 baddest mofos in the fight game."
Francis Ngannou has been touted as a potential opponent for Fury should he make the move to MMA, with the Frenchman saying he would relish the chance to fight the boxer.
And speculation the pair will meet next year went into overdrive after the 31-year-old announced on his Instagram page that he would link up with Till.
"Good news everybody, I'm going to go training with Darren Till this weekend," said the Gypsy King in a video posted online.
"We're going to smash it and he's going to get me started on my MMA career. Get in there my boy."
Fury's latest revelation came a day after the lineal champ hit back at rival Wilder's claims that the Brit was running scared of a potential rematch between the duo.
The pair first met in the ring in Los Angeles in December last year, with Fury rising off the canvas as the bout ended in a draw following a monumental clash.
Speaking ahead of his WBC world title defence against Cuban Luis Ortiz, Wilder said he felt Fury was no longer as keen on the rematch as he once was, prompting an angry response from the Brit.
"The thing is with you Wilder, crack on with your own business and I'll see you February 22 to finish what I started. This time you're going to get smashed you big bum dosser," said Fury.


The <phenote-configuration> tag ...
| Name | Description | Legal Values | Required | Default |
|
name |
This is a short descriptive name given to the Configuration to be displayed in the "chooser" window. This does not have to be the same as the filename. If it is not specified, the filename will be displayed instead. |
any text value | no | |
|
xmlns |
This line is required. Please include as specified: |
"phenote/config/xml" | yes | |
|
author |
The name of the author of the configuration file. It might be nice to include an email address in case if there are questions. |
any text value | no | |
|
version |
A version number for the configuration. This should indicate which version of Phenote it is compatible with, and something about the revision history itself. Use the format: 1.3.1 (first two numbers indicate Phenote version, last number is the revision number for the configuration) | any text value | yes | |
|
description |
This is a general description of the purpose of the configuration. The author might list the general target community, the overall use of the data, a repository where the data might be stored, or other important information. | any text value | no |
All other tags should be included within the <phenote-configuration> tag, including:
<ns:phenote-configuration version="1.3.1" xmlns:ns="phenote/config/xml">
<!--Enter your configuration options here -->
</ns:phenote-configuration>


Format Used in Proposal¶
USDA requirements are formatted as follows:
-
:USDA #12:
¶ Support capture/documentation of metadata for food composition and non-composition data.
Ontology terms are formatted as follows:
schema:sameAs
(the schema.org facet term meaning that A is the same as B)ncit:C46090
(the NIH NCI facet term code for the facet term “Glycemic Index”)agrontology:isUsedToMake
(the UN FAO term meaning that A is used to make B)
A word or phrase that is a link to a URL is formatted as follows: food labeling services for the USDA community
A term that is defined in the glossary is formatted as follows: application services
A bibliographic references is formatted as follows: See :cite:`5002` for more information about ...
Discussion about a design or approach.
- point 1
- point 2
- point 3
- point 4
Illustration of a REST conversation
See also
Reference to a related section of the Proposal
Tip
Advice based on experience with managing similar issues
Attention
Warning that an alternative approach may produce an ineffective result
Danger
Advice that an alternative approach will produce a poor or unintended outcome


|
DESERT
3.0
|
#include <uwpolling_AUV.h>
Public Member Functions | |
| ProbeTimer (Uwpolling_AUV *m) | |
| virtual | ~ProbeTimer () |
| Public Member Functions inherited from Uwpolling_AUV::Uwpolling_AUV_Timer | |
| Uwpolling_AUV_Timer (Uwpolling_AUV *m) | |
| virtual | ~Uwpolling_AUV_Timer () |
| virtual void | freeze () |
| virtual void | unFreeze () |
| virtual void | stop () |
| virtual void | schedule (double val) |
| bool | isIdle () |
| bool | isRunning () |
| bool | isExpired () |
| bool | isFrozen () |
| bool | isActive () |
| void | resetCounter () |
| void | incrCounter () |
| int | getCounter () |
| double | getDuration () |
Protected Member Functions | |
| virtual void | expire (Event *e) |
Additional Inherited Members | |
| Protected Attributes inherited from Uwpolling_AUV::Uwpolling_AUV_Timer | |
| double | start_time |
| double | left_duration |
| int | counter |
| Uwpolling_AUV * | module |
| UWPOLLING_TIMER_STATUS | timer_status |
Class (inherited from Uwpolling_AUV_Timer) used to handle the Probe Timer.
The duration of this timer is the time in which the nodes can transmit their PROBE packets to "book" the possibility to transmit data packets to the AUV
Definition at line 427 of file uwpolling_AUV.h.
|
inline |
Conscructor of ProbeTimer class.
Definition at line 433 of file uwpolling_AUV.h.
|
inlinevirtual |
Destructor of ProbeTimer class.
| Uwpolling_AUV* | Pointer of an object of type Uwpolling_AUV |
Definition at line 442 of file uwpolling_AUV.h.
|
protectedvirtual |
Method call when the timer expire.
| Event* | pointer to an object of type Event |
Definition at line 215 of file uwpolling_AUV.cpp.


Song uploads are currently capped at %{ maxFilesize }MB per file. Only MP3s are supported at this time.


{% extends "layout.html" %} {% block page_title %} Money Claims Prototype {% endblock %} {% block content %} {% include "includes/phase_banner_beta.html" %} {{formData | safe}} Some useful information about Help with Fees Making an application for Help with Fees does not guarantee that you will get your fee covered. You may still have to pay some or all of your court fee to get the claim issued (for the court system to officially start the claim and send details to the other side). When you apply for Help with Fees, you should receive an update from us within 5 working days, giving you the result of your application. If you want to apply for Help with Fees, you will complete an online form in a new window. This will give you a reference number. Please note the number and keep it safe, as you will need it later in the claim process. (NB: if you have more than one claim going on, each claim must have a separate Help with Fees application and reference number). You can send in your claim as soon as you have the Help with Fees reference number, but the claim will not be issued until the Help with Fees application has been processed by the court. This is so that you will know what fees are covered and what you still have to pay. If you choose not to pay, the claim will not be issued. The claim will stop here unless you change your mind within 95 days. You may be asked by the court to email evidence in support of your application before your claim is issued. Do you wish to continue to make a Help with Fees Application? Yes No {% if data.return_page and data.return_page.includes('check-and-send') or data.return_page and data.return_page.includes('check-your-answers')%} Cancel {% else %} {% endif %} {% include 'prototypes/features-to-be-built/includes/contact.html' %} {% endblock %}
Making an application for Help with Fees does not guarantee that you will get your fee covered. You may still have to pay some or all of your court fee to get the claim issued (for the court system to officially start the claim and send details to the other side). When you apply for Help with Fees, you should receive an update from us within 5 working days, giving you the result of your application.
If you want to apply for Help with Fees, you will complete an online form in a new window. This will give you a reference number. Please note the number and keep it safe, as you will need it later in the claim process. (NB: if you have more than one claim going on, each claim must have a separate Help with Fees application and reference number). You can send in your claim as soon as you have the Help with Fees reference number, but the claim will not be issued until the Help with Fees application has been processed by the court. This is so that you will know what fees are covered and what you still have to pay. If you choose not to pay, the claim will not be issued. The claim will stop here unless you change your mind within 95 days.
You may be asked by the court to email evidence in support of your application before your claim is issued.


--- layout: archive title: Zulip Chat Archive permalink: /stream/116395-maths/topic/Bayes.20theorem.20.2B.20future.20directions.html ---
hello,
I have just completed a formalization of Bayes theorem building on top of the measure theory library. this was my first formalization effort so it is a bit rough around the edges and needs cleaning up. https://github.com/kodyvajjha/mathlib/commit/54639f16ec9e6a646fe43d870131a6099e8a550c
i had set this target as a first milestone in formalizing the (G)ARCH time series models, and I wanted to ask the community if they had any tips/suggestions on getting there. as i understand it - matrices aren't yet formalized, are there any plans on getting to matrices in the near future?
Matrices are in ring_theory/matrix
Last updated: Apr 24 2020 at 19:02 UTC


use your mind
use your strength
use your words
use your imagination
what are your tools? don't forget to put them back in your toolbox when you're done.


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Receives information to ship to the user after done is called.
The status code used to close the Reply.
An Array of event Arrays to be emitted on the client.
A JSON-serializable Object compiled from calls to content.
Typically empty but may be manually set.


[1]
input to box to use for other things like a security camera , or dvd player .
[2]
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<plugin>
<groupId>org.openapitools</groupId>
<artifactId>openapi-generator-maven-plugin</artifactId>
<version>4.2.3</version>
</plugin>
23 March 2020
Implementing JAX/RS REST APIs with Swagger/OpenAPI, the language agnostic interface to RESTful APIs, following an API Design-First approach starts with the formal specification of the REST API. Then OpenAPI generators are used to create server stubs. These code generators create specific problems, that may require customization of templates or the whole generator. This article describes several solutions that are related to the JAX/RS context objects.
But, before starting the discussion of the JAX/RS context object related issues,
I shortly describe the setup of the openapi-jaxrs
sample project, you’ll find
on the
code branch
of the Blog repository.
The prerequisites to run the demo project are Java of version equal or higher 8 and a current version of Maven. The code samples shown in this Blog post use the OpenAPI Maven plugin:
<plugin>
<groupId>org.openapitools</groupId>
<artifactId>openapi-generator-maven-plugin</artifactId>
<version>4.2.3</version>
</plugin>
This plugin integrates very well with Eclipse: Updating the Maven project executes the generator. In addition, the output directory of generated code is automatically added as source folder to the Eclipse project.
The generator places the output directory into the target
folder of the
project. This ensures that the code generation is executed for every build
and generated code is never put under version control.
The OpenAPI generator plugin supports several kinds of JAX/RS generators, eg.
jaxrs-spec
, jaxrs-resteasy
, jaxrs-cxf
. For this Blog post, we’ll use
the jaxrs-spec
generator, which produces code that is compliant to the
Jakarta EE standard, but does not depend on a particular implementation of
this standard. Nowadays the standard APIs support all features typically
required in application development, so that implementation specific
extensions are rarely required.
The documentation of the jaxrs-spec
generator’s options can be found on
the OpenAPITools/openapi-generator
Github repo at
JAX/RS Spec Generator.
The demo project is configured for the Thorntail
framework, which allows
convenient start of the sample application from the command-line by
mvn thorntail:run
But the classical packaging as war
file and deployment to an Jakarta EE
compliant application server is equally possible.
The following list enumerates all JAX/RS context objects of the JAX-RS
2.1 specification, ie. types that can be injected using the @Context
annotation:
javax.ws.rs.core.Application
javax.ws.rs.core.HttpHeaders
javax.ws.rs.core.Request
javax.ws.rs.core.SecurityContext
javax.ws.rs.core.UriInfo
javax.ws.rs.core.Configuration
javax.ws.rs.container.ResourceContext
javax.ws.rs.ext.Providers
javax.ws.rs.sse.Sse
javax.ws.rs.sse.SseEventSink
In addition, the following types are available when the application in deployed to a servlet container:
javax.servlet.HttpServletRequest
javax.servlet.HttpServletResponse
javax.servlet.ServletConfig
javax.servlet.ServletContext
What makes JAX/RS context objects special is that they can only injected into JAX/RS resources itself, but not into CDI beans, that are injected into the JAX/RS resource objects. If the JAX/RS resources reside in generated code, the context objects are available only if the generator takes them into account.
The easiest solution to make JAX/RS context objects available is to generate interfaces of the JAX/RS resources only. This can achieved by setting the generator’s option
<interfaceOnly>true</interfaceOnly>
in the OpenAPI generator plugin of Maven’s pom.xml
file.
The resulting generated code of a simple greeting service looks then like this:
Path("/greeting")
@Api(description = "the greeting API")
@javax.annotation.Generated(value = "org.openapitools.codegen.languages.JavaJAXRSSpecServerCodegen", date = "2020-03-23T19:02:54.718784+01:00[Europe/Zurich]")
public interface GreetingApi {
@GET
@ApiOperation(value = "", notes = "", tags={ "misc" })
@ApiResponses(value = {
@ApiResponse(code = 200, message = "Returns greeting on success", response = Void.class),
@ApiResponse(code = 405, message = "Invalid input", response = Void.class) })
Response greet(@QueryParam("name") @ApiParam("Optional name of person to greet") String name);
}
Since only interfaces are generated, the actual implementation must be coded manually, eg.:
public class GreetingApiImpl implements GreetingApi {
private static final Logger LOGGER = LoggerFactory.getLogger(GreetingApiImpl.class);
@Context
HttpHeaders headers;
@Context
UriInfo uriInfo;
public Response greet(@QueryParam("name") @ApiParam("Optional name of person to greet") String name) {
StringBuilder headersBuilder = new StringBuilder("Headers:\n");
for (Map.Entry<String, List<String>> header : headers.getRequestHeaders().entrySet()) {
headersBuilder.append("\t").append(header.getKey()).append(": ").append(header.getValue()).append("\n");
}
LOGGER.info(headersBuilder.toString());
LOGGER.info("UriInfo: {}", uriInfo);
return Response.ok("Hello world").build();
}
}
Because the JAX/RS resource implementation is hand-written, you are free to
inject any context object. In the example above, HttpHeaders
and
UriInfo
have been added for demo purposes, but any others is possible, too.
For some projects it might not be desired or possible to work with interfaces of JAX/RS resource objects. Let’s see what happens when we change the OpenAPI generator to
<interfaceOnly>false</interfaceOnly>
First difference to interface only generation is that the RestApplication
object is now generated and must not longer provided with the application code.
The generate JAX/RS resource now looks like:
@Path("/greeting")
@Api(description = "the greeting API")
@javax.annotation.Generated(value = "org.openapitools.codegen.languages.JavaJAXRSSpecServerCodegen", date = "2020-03-23T19:06:40.010561+01:00[Europe/Zurich]")
public class GreetingApi {
@GET
@ApiOperation(value = "", notes = "", response = Void.class, tags={ "misc" })
@ApiResponses(value = {
@ApiResponse(code = 200, message = "Returns greeting on success", response = Void.class),
@ApiResponse(code = 405, message = "Invalid input", response = Void.class)
})
public Response greet(@QueryParam("name") @ApiParam("Optional name of person to greet") String name) {
return Response.ok().entity("magic!").build();
}
}
The API method of the generated class provides an implementation already. You might be tempted to change this implementation to your needs and add the application’s business logic here. However, the class is generated and the next build would overwrite any manual change.
What can we do about that? Moving the generated class to the developer managed code-base is not an option, because it violates the principle that the code is generated on each build and generated code is never taken under version control. The best would be to customize the generation in a way that the actual business logic gets injected and the JAX/RS API methods just delegate to the injected business services. This idea is based on the integration of JAX/RS and CDI, which allows to inject arbitrary CDI beans into JAX/RS resources.
The OpenAPITools/openapi-generator Github repository includes comprising documentation about the customization of Templates or even the entire Generators.
For our purposes the customization of templates is sufficient. After adding the configuration
<templateDirectory>${project.basedir}/src/main/templates</templateDirectory>
to the OpenAPI generator plugin, customized Mustache templates can be provided in defined folder.
| The OpenAPI generator processes many template files in a generation run, but only the customized templates need to be hosted in the project’s template directory. The remaining templates will still be retrieved from the set of standard templates of the generator, ie. the custom teplates shadow the equally named templates of the generator. |
For our use case the injection of the service class need to be added in the
api.mustache
template file:
@Inject {{package}}.services.{{classname}}Impl delegatee;
And the delegation to the injected business service need to be added
in the apiMethod.mustache
template file:
public Response {{nickname}}({{#allParams}}{{>queryParams}}{{>pathParams}}{{>headerParams}}{{>bodyParams}}{{>formParams}}{{#hasMore}},{{/hasMore}}{{/allParams}}) {
return delegatee.{{nickname}}({{#allParams}}{{paramName}}{{#hasMore}}, {{/hasMore}}{{/allParams}});
}
The delegatee, ie. the CDI bean hosting the business logic, looks in its simplest form like:
package net.gunther.blog.codegen.api.services;
import javax.ws.rs.core.Response;
public class GreetingApiImpl {
public Response greet(String name) {
return Response.ok("Hello world").build();
}
}
At this point we achieved that the generated JAX/RS resource classes delegate each call to a hand-written service class, that host the actual business logic. The JAX/RS context objects are still unavailable to the application. To solve this last challenge, we introduce a request scoped holder object of the JAX/RS context:
@RequestScoped
public class JAXRSContext {
private UriInfo uriInfo;
private HttpHeaders httpHeaders;
public UriInfo getUriInfo() {
return uriInfo;
}
public void setUriInfo(UriInfo uriInfo) {
this.uriInfo = uriInfo;
}
public HttpHeaders getHttpHeaders() {
return httpHeaders;
}
public void setHttpHeaders(HttpHeaders httpHeaders) {
this.httpHeaders = httpHeaders;
}
}
For sake of simplicity, the sample code limits to HttpHeaders and UriInfo ,
but any other JAX/RS context object can be easily added. Import statements
are also omitted.
|
Then we add the injection of the JAX/RS context objects and our new holder
object to the customized api.mustache
template file:
...
@Context UriInfo uriInfo;
@Context HttpHeaders httpHeaders;
@Inject JAXRSContext context;
...
The injected objects can then be used in the generated API methods, ie. the
template apiMethod.mustache
file can further customized by adding:
public Response {{nickname}}({{#allParams}}{{>queryParams}}{{>pathParams}}{{>headerParams}}{{>bodyParams}}{{>formParams}}{{#hasMore}},{{/hasMore}}{{/allParams}}) {
context.setUriInfo(uriInfo);
context.setHttpHeaders(httpHeaders);
return delegatee.{{nickname}}({{#allParams}}{{paramName}}{{#hasMore}}, {{/hasMore}}{{/allParams}});
}
You may have noted, that we do not add the JAX/RS holder object to the
signature of the delegatee’s method.
The JAX/RS holder context
is a CDI bean, which is just populated with the
JAX/RS context in the generated resource class. Because the bean of type
JAXRSContext
is request scoped, every request processing (thread) gets its
own instance of the bean.
The JAXRSContext
is a regular CDI bean which can be injected into any other
CDI bean, eg. the delegatee’s service implementation:
public class GreetingApiImpl {
private static final Logger LOGGER = LoggerFactory.getLogger(GreetingApiImpl.class);
@Inject JAXRSContext context;
public Response greet(String name) {
StringBuilder headersBuilder = new StringBuilder("Headers:\n");
for (Map.Entry<String, List<String>> header : context.getHttpHeaders().getRequestHeaders().entrySet()) {
headersBuilder.append("\t").append(header.getKey()).append(": ").append(header.getValue()).append("\n");
}
LOGGER.info(headersBuilder.toString());
LOGGER.info("UriInfo.absolutePath: {}", context.getUriInfo().getAbsolutePath());
return Response.ok("Hello world").build();
}
}
When now calling the application the HTTP headers and the absolute path of the requested JAX/RS resource are logged, for example:
2020-03-24 20:45:02,834 INFO [net.gunther.blog.codegen.api.services.GreetingApiImpl] (default task-1) Headers:
DNT: [1]
Accept-Language: [en-US,en;q=0.5]
Host: [localhost:8080]
Accept: [text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,*/*;q=0.8]
User-Agent: [Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:74.0) Gecko/20100101 Firefox/74.0]
Accept-Encoding: [gzip, deflate]
Upgrade-Insecure-Requests: [1]
Connection: [keep-alive]
Cache-Control: [max-age=0]
2020-03-24 20:45:02,836 INFO [net.gunther.blog.codegen.api.services.GreetingApiImpl] (default task-1) UriInfo.absolutePath: http://localhost:8080/greeting
Implementing the JAXRSContext
as request scoped CDI bean has several
benefits:
The technical JAX/RS context does not pollute the business interfaces implemented by the service delegates.
The JAXRSContext
can hold any number of context objects, you can start
with just one and add more if you need more in later stages of the development.
Adding more context objects means extending the template, but does not break
a single line of existing code.
The JAXRSContext
can be injected into business logic of any level in the
call hierarchy, not only in the directly called delegatee.
The JAXRSContext
is only injected into CDI beans that actually need the
context.
The simplest approach when it comes to OpenAPI and its generators is to limit the generated code to interfaces. This approach does not require customization of templates and nevertheless leaves any implementation option in your hands.
If you already generate JAX/RS resource implementations or need to customize the generator’s templates anyway, then the described JAX/RS holder object may be an option for you. Implementing the JAX/RS holder as request scoped CDI bean offers several benefits as listed above.


A process for treating used absorbent sanitary products by providing a rotary cylindrical autoclave having an inner surface and two ends, at least one of which terminates in a hatch that can be opened to enable access to the autoclave and sealably closed to enable pressurization of the autoclave; loading the autoclave with closed absorbent sanitary products; heating to a sterilization temperature and pressurizing the autoclave and at the same time driving the autoclave in rotation about a longitudinal axis thereof; and providing inside the autoclave a load of high-density tearing elements designed to facilitate thermal and physical destructuring of the absorbent sanitary products.
This application claims benefit of Italian Patent Application No. TO2011A001090, filed Nov. 28, 2011, which is herein incorporated by reference.
1. Field of the Invention
The present invention relates to a process for recycling used absorbent sanitary products.
By the term “absorbent sanitary products” is meant in general disposable absorbent products, such as: baby diapers, incontinence absorbent pads, ladies sanitary pads, bed mats, etc.
2. Description of the Related Art
Absorbent sanitary products are generally made up of a wide range of different materials, amongst which sheets of plastic material, cellulose fluff, superabsorbent polymers, sheets of non-woven fabric, etc.
Absorbent sanitary products contain high-quality materials such as plastic and cellulose, and it would be desirable to recover said materials to use them in a new production cycle or else for the production of energy.
Currently, used absorbent sanitary products are disposed of as undifferentiated waste to be sent to rubbish dumps. The component materials of used absorbent sanitary products are not recovered in the first place because the various materials (cellulose fibres, superabsorbent polymers, sheets of plastic material, etc.) are intimately interconnected, and to obtain separation of the materials it would be necessary to carry out a complete destructuring of the products. In addition, used absorbent sanitary products contain organic excretions and bacteria, and it would be necessary to carry out a sterilization of the products prior to recycling of the materials.
For the above reasons, used absorbent sanitary products are not included amongst recyclable waste products for which differentiated collection is carried out.
It is estimated that absorbent sanitary products constitute approximately 2-3% of the total of urban solid waste. However, where a differentiated collection is carried out with a high percentage of differentiation of the waste (with a percentage of differentiated waste higher than 60% of the total) the percentage of absorbent sanitary products with respect to the remaining part constituted by the undifferentiated residual fraction rises to approximately 20%.
The high percentage of absorbent sanitary products with respect to the residual fraction of non-recyclable waste renders highly desirable the availability of equipment and processes that enable a treatment of absorbent sanitary products to be carried out aimed at recycling their component materials in an efficient and economically convenient way.
Currently known techniques for treatment of used absorbent sanitary products are not satisfactory. A first known technique envisages carrying out washing of the used absorbent products with water, alkalis, and soap and separating the cellulose from the plastic during the washing operation. Examples of this technique are disclosed in the documents Nos. WO 94/20668 and WO 96/27045.
The document No. U.S. Pat. No. 5,292,075 describes a process in which the dirty absorbent sanitary products are preliminarily shredded. The shredded material is then washed in a washing machine comprising a perforated cylindrical drum that withholds the plastic material inside it. The material containing the cellulose pulp is then dehydrated.
These techniques of treatment of absorbent sanitary products are in actual practice problematical to implement since the washing water would contain a high amount of pollutants, such as gelified superabsorbent polymers and organic residue, which renders problematical disposal thereof. Drying of the cellulose after washing moreover entails a high expenditure of energy.
A further difficulty derives from the fact that used absorbent sanitary products are normally thrown away folded and closed to form a pack, with the outer plastic layer of the products that forms an impermeable barrier. If the products are treated in the form in which they have been thrown away, the outer impermeable layer prevents an effective sterilization of the products. On the other hand, a preliminary treatment as described in U.S. Pat. No. 5,292,075 entails the need to shred articles with a high content of organic excretions, bacteria, and contaminants.
The document No. JP<PHONE_NUMBER> describes a process for treating diapers that contain absorbent polymers, whereby the used diapers are set in a pressurized closed vessel together with sawdust. Inside the vessel the diapers are treated with steam at high temperature and high pressure for a pre-set time. Steam treatment is carried out at a pressure of 15-25 atm and at a temperature of 150-250° C. This document envisages use of the absorbent sanitary products, after said treatment, as fertilizers following upon fermentation.
The document No. WO 2010/065088 describes an autoclave for the treatment of urban solid waste that envisages drying of the waste using steam. The apparatus described in the document WO 2010/065088 comprises a rotary cylindrical autoclave provided with at least one hatch that can be opened to enable access to the autoclave and sealably closed to enable pressurization of the autoclave, an inlet for contact steam that comes into direct contact with the waste contained inside the autoclave, a plurality of straight hollow blades, which are designed to conduct non-contact steam, project from the inner surface of the autoclave, and are supplied with non-contact steam. This apparatus enables sterilization of urban solid waste and drying of the waste during treatment in the autoclave. The apparatus described in the document WO 2010/065088 has been developed for treatment of undifferentiated urban solid waste and does not contains specific teachings to obtain sterilization, drying, and separation of the component materials of absorbent sanitary products.
The object of the present invention is to provide a process for treating used absorbent sanitary products that will enable sterilization, drying, and destructuring of used absorbent sanitary products in order to carry out recovery of the constituent materials.
According to the present invention, the above object is achieved by a process having the characteristics forming the subject of Claims 1.
The claims form an integral part of the teaching provided herein in relation to the invention.
So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments.
figref[FIG. 1] is a perspective view of a rotary-autoclave apparatus for treating waste; and
figref[FIG. 2] is a schematic cross-sectional view of the autoclave of figref[FIG. 1] .
With reference to figref[FIG. 1] , designated by 10 is a rotary-autoclave apparatus for treating used absorbent sanitary products. The apparatus 10 comprises a stationary structure 12, which carries a cylindrical autoclave 14 that turns about its longitudinal axis A. The apparatus 10 comprises a driving device (not illustrated), which drives the autoclave 14 in rotation about the axis A. The supporting structure 12 may be provided with actuators 16 for varying the inclination of the autoclave 14 with respect to a horizontal axis, which enables tilting of the autoclave 14 between a loading/unloading position and a working position. The autoclave 14 has two ends, at least one of which terminates in a hatch that can be opened to enable access to the internal space of the autoclave and sealably closed to enable pressurization of the internal space. In the example illustrated two openable hatches 18, 20 are provided, which can be used, for example, for loading the autoclave with the products to be treated and for unloading the treated products. Alternatively, a single openable hatch could be provided, which can be used both for loading and for unloading.
The apparatus 10 comprises a circuit for heating and pressurizing the autoclave 14 in order to heat the absorbent sanitary products to a sterilization temperature.
The hatches 18, 20 are provided with respective rotary connectors 34, 36 for inlet and outlet of heating steam coming from a steam generator 38. The flow of heating steam can be divided into a flow of non-contact steam 42 that traverses ducts located on the inner wall of the autoclave 14 and a flow of contact steam 44 that comes into direct contact with the products to be treated and pressurizes the internal volume of the autoclave 14. On the outlet connector 36 the flow of non-contact steam 42 and the flow of contact steam 44 are divided and treated separately, for example as described in the document No. WO 2010/065088.
Typically, absorbent sanitary products comprise an absorbent core of cellulose fibres and of superabsorbent polymers. The absorbent core is usually enclosed between two sheets of plastic material joined together. Typically, the backsheet is impermeable, whereas the topsheet is porous. Used absorbent sanitary products are normally folded up so as to enclose the product in the form of a pack within the impermeable backsheet. Usually adhesive tabs are provided for closing the folded product. The organic excretions are thus enclosed within a sealed sheet of impermeable plastic material.
The present invention envisages carrying out the treatment of absorbent sanitary products just as they are collected, i.e., in the form where they are closed to form a pack, and without any preliminary treatment for opening the products.
To obtain an effective action of drying and sterilization during treatment in the autoclave 14 it is necessary to obtain destructuring of the products so as to expose all the organic substances to the sterilization temperature in every point inside the autoclave 14. Destructuring of the absorbent sanitary products is absolutely essential to achieve a complete sterilization and to separate the plastic from the cellulose fibres.
 The autoclave 14 is then sealably closed and pressurized by the contact steam. At the same time, the autoclave is heated by the non-contact steam. The autoclave, once heated and pressurized, is driven in rotation about the axis A. Inside the autoclave 14 there may be provided radial blades 50 projecting from the inner wall of the autoclave.
The high-density tearing elements 48 facilitate transfer of heat and destructuring of the absorbent sanitary products 46. The tearing elements 48 are made of a thermally conductive material, preferably metal material. The tearing elements 48 may be small and sharp objects such as for example stones or objects coming from metalwork such as screws, bolts, lengths of L-sectional steel, etc.
The tearing elements 48 absorb heat by conduction from the heated walls of the autoclave 14. During rotation of the autoclave 14 the mass of absorbent sanitary products 46 is entrained upwards by the walls of the autoclave and then drops towards the centre. Then, the tearing elements drop on top of the mass of absorbent sanitary products 46.
Given that the tearing elements 48 are heavy, they penetrate into the mass of absorbent sanitary products that has accumulated on the bottom of the autoclave 14 and reach the wall of the autoclave 14.
As the tearing elements 48 traverse the mass of absorbent sanitary products 46, they yield heat by conduction, convection, and radiation. In this way, the energy available on the wall of the autoclave 14 is effectively transferred within the mass of waste significantly increasing the effective surface of thermal exchange.
The tearing elements 48 are at the temperature of the wall of the autoclave or at a temperature close to the temperature of the wall of the autoclave, which is set at a value higher than the temperature for melting the enveloping plastic material of the absorbent sanitary products. As the tearing elements 48 pass through the mass of absorbent sanitary products 46, they weaken, tear, and form holes in the plastic envelopes thus destructuring the absorbent sanitary products and releasing the fibrous contents of the waste.
The amount in weight of tearing elements 48 necessary to obtain destructuring of the absorbent sanitary products 46 is between 0.25 and 5 times the dry weight of the load of products to be treated. The preferred amount is between 0.5 and 1.5 times the dry weight of the products 46.
In tests that have been conducted a successful destructuring of absorbent sanitary products has been obtained with steel bolts having a unit weight comprised between 0.25 and 1 kg, and with flat pieces of steel of the same weight.
The mass of tearing elements 48 in combination with the temperature and pressure inside the autoclave 14 enable a complete destructuring of the absorbent sanitary products inside the autoclave 14. In this way, there is avoided the need for a preliminary treatment of shredding of the products, which would expose the operators and the surrounding environment to evil odours and to the contaminating elements contained in the absorbent sanitary products.
Complete destructuring of the products during treatment in the autoclave enables drying and sterilization of the products in shorter times. After treatment in the autoclave a dried and sterile destructured mass is obtained, basically formed by plastic and cellulose fibres. Next, the dried and sterile destructured mass is passed through a sieve in which the plastic and the cellulose fibres are separated.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.


JIN-ROH: THE WOLF BRIGADE A film review by Rachel Gordon Copyright 2001 filmcritic.com
Anyone growing up on Disney animation would be shocked by Japanese Anime, a genre now famous for giving human experience a different look. It does what family-enticing animation has refused to, including violence, sex, and other adult motifs normally reserved for live-action big blockbusters.
Jin-Roh takes Anime another courageous step forward. Its beginning is chock-full of useful information, adding a documentary feel by establishing the cultural setup in black and white with voiceover. It may sound like a high school lecture, but the images never get boring. Not to mention that without this necessary information, you'd be lost when the key story starts to roll.
The setting is Tokyo, but if Japan had lost World War II to Nazi Germany instead of the United States.  Another faction adding to the mess is "The Wolf Brigade," a rumored extremist sect of the Capital Police that can't be pinned down.
We follow Kazuki Fuse (Michael Dobson), a young member of the elite counterintelligence force.  As he tries to continue on with his duties, he begins to obsess over her, dreaming of her. He contacts her older sister, Kei (Moneca Stori), and they spend time together, finding a tenuous connection in the oppressive society.
As time goes on, the fight between personal needs and duty to his command increases in Kazuki. He is talented and therefore allowed to continue training, but he is constantly being watched and even plotted against with one mental test after another. His times with Kei are pleasant, but there is always an underlying tension as to just how much is really possible.
Like many Anime films, Jin-Roh is brutally honest. The storyline mimics real human interaction, and none of the subplots are easily solved because the terrorists' motivations are complex. Blood, sweat, and tears aren't covered up to save shock. And even if the animation isn't always as minutely detailed as the ever-popular CGI, this is made up for in realistic bodily movements. When a character gets hurt, his limp is real.
The dialogue can be predictable, mimicking almost any other political jargon heard in the average American blockbuster. This could be from a language gap in the translation from Japanese or simply a case of rushing things. It can be annoying but doesn't affect the overall quality of the film.
More depressing than enjoyable, Jin-Roh demands respect because the story is compelling and it's difficult not to be emotionally engaged with the characters. A far cry from something to show the kiddies, but fascinating for those who appreciate an original gem.

Visit filmcritic.com on the Web at http://www.filmcritic.com
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
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to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


| Modifier and Type | Field and Description |
|---|---|
(package private) Question |
IntSiteManagerMember.QuestionsAndAnswers.java1 |
(package private) Question |
IntSiteManagerMember.QuestionsAndAnswers.node1 |
(package private) Question |
IntSiteManagerMember.QuestionsAndAnswers.node2 |
private Question |
Answer.question |
(package private) Question |
IntSiteManagerMember.QuestionsAndAnswers.sql1 |
(package private) Question |
IntSiteManagerMember.QuestionsAndAnswers.sql2 |
| Modifier and Type | Field and Description |
|---|---|
private java.util.ArrayList<Question> |
Membership.questions |
private java.util.ArrayList<Question> |
Group.questions |
| Modifier and Type | Method and Description |
|---|---|
private Question |
IntMemberTest.generateFakeQuestion(java.lang.String emailAddress,
int index)
Deprecated.
|
Question |
Answer.getQuestion()
Return the question that this class is answering
|
| Modifier and Type | Method and Description |
|---|---|
protected java.util.ArrayList<Question> |
Membership.getQuestions()
Returns the list of questions from Membership
|
java.util.List<Question> |
Group.getQuestions()
Returns a List of questions that have been added to this group
|
java.util.List<Question> |
Member.getQuestions(Group group)
Returns all questions asked by this member in the group passed in as
parameters
|
java.util.List<Question> |
Member.getQuestions(Group group,
int n)
Returns the n most recent questions asked by this member in this group sorted
on the order they were asked, most recent first.
|
java.util.List<Question> |
Group.getQuestions(int n)
Returns the n most recent questions asked in this group sorted on the order
they were asked, most recent first.
|
java.util.List<Question> |
Member.getQuestionsByPoints(int n)
Returns a list of n length of questions for this member sorted by points,
highest to lowest.
|
java.util.List<Question> |
Group.getQuestionsByPoints(int n)
Returns a list of n length of questions for this member sorted by points,
highest to lowest.
|
| Modifier and Type | Method and Description |
|---|---|
void |
Member.addAnswer(Group group,
Question question,
Answer answer,
java.time.LocalDateTime date)
Adds this member's answer to this question which is in this group and records
the date answered.
|
void |
Member.addQuestion(Group group,
Question question,
java.time.LocalDateTime date)
Adds the question to the group by this member and records the date the
question was asked.
|
protected void |
Membership.addQuestion(Question question)
Adds a question to the questions array that pertains to this member to this
group
|
protected void |
Group.addQuestion(Question question)
Adds a Question to the List of questions in this Group
|
private Answer |
IntMemberTest.generateFakeAnswer(Question q,
java.lang.String screenName,
int index)
Deprecated.
|
java.util.List<Answer> |
Member.getAnswersByPoints(int n,
Question q)
Returns a list of n length of answers by question for this member sorted by
points, highest to lowest.
|
java.util.List<Answer> |
Group.getAnswersByPoints(int n,
Question q)
Returns a list of n length of answers by question for this member sorted by
points, highest to lowest.
|
java.util.List<Answer> |
Member.getAnswersByPoints(Question q)
Returns a list of all answers by question for this member sorted by points,
highest to lowest.
|
java.util.List<Answer> |
Group.getAnswersByPoints(Question q)
Returns a list of all answers by question for this member sorted by points,
highest to lowest.
|
| Constructor and Description |
|---|
Answer(Question q,
java.lang.String text,
java.time.LocalDateTime date)
Constructor for the Answer Class that takes in a question, text(answerTest),
and a date(created)
|


CorrosiveTeam
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5.3 The Data and Control Flow Dictionary
Function APPLY
Macro DEFUN
Accessor FDEFINITION
Function FBOUNDP
Function FMAKUNBOUND
Special Operator FLET, LABELS, MACROLET
Function FUNCALL
Special Operator FUNCTION
Function FUNCTION-LAMBDA-EXPRESSION
Function FUNCTIONP
Function COMPILED-FUNCTION-P
Constant Variable CALL-ARGUMENTS-LIMIT
Constant Variable LAMBDA-LIST-KEYWORDS
Constant Variable LAMBDA-PARAMETERS-LIMIT
Macro DEFCONSTANT
Macro DEFPARAMETER, DEFVAR
Macro DESTRUCTURING-BIND
Special Operator LET, LET*
Special Operator PROGV
Special Form SETQ
Macro PSETQ
Special Operator BLOCK
Special Operator CATCH
Special Operator GO
Special Operator RETURN-FROM
Macro RETURN
Special Operator TAGBODY
Special Operator THROW
Special Operator UNWIND-PROTECT
Constant Variable NIL
Function NOT
Constant Variable T
Function EQ
Function EQL
Function EQUAL
Function EQUALP
Function IDENTITY
Function COMPLEMENT
Function CONSTANTLY
Function EVERY, SOME, NOTEVERY, NOTANY
Macro AND
Macro COND
Special Operator IF
Macro OR
Macro WHEN, UNLESS
Macro CASE, CCASE, ECASE
Macro TYPECASE, CTYPECASE, ETYPECASE
Macro MULTIPLE-VALUE-BIND
Special Operator MULTIPLE-VALUE-CALL
Macro MULTIPLE-VALUE-LIST
Special Operator MULTIPLE-VALUE-PROG1
Macro MULTIPLE-VALUE-SETQ
Accessor VALUES
Function VALUES-LIST
Constant Variable MULTIPLE-VALUES-LIMIT
Macro NTH-VALUE
Macro PROG, PROG*
Macro PROG1, PROG2
Special Operator PROGN
Macro DEFINE-MODIFY-MACRO
Macro DEFSETF
Macro DEFINE-SETF-EXPANDER
Function GET-SETF-EXPANSION
Macro SETF, PSETF
Macro SHIFTF
Macro ROTATEF
Condition Type CONTROL-ERROR
Condition Type PROGRAM-ERROR
Condition Type UNDEFINED-FUNCTION
Copyright 1996, The Harlequin Group Limited. All Rights Reserved.


Eurojackpot results for Friday 30th November 2018
The winning numbers for the 48th Eurojackpot draw in 2018 that took place on Friday 30th November at 21:00 CEST (20:00 GMT) were:
Winners
Winners
Amount
Slovenian Prize Breakdown
View prize breakdowns for other countries| Numbers Matched | Prize Per Winner | Winners from Slovenia | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | 0 | €0 | 45 |
|
Match 4 and 1 Euro Number |
€254.70 | 5 | €1,273.50 | 749 |
|
Match 4 |
€121.80 | 15 | €1,827 | 1,218 |
|
Match 3 and 2 Euro Numbers |
€66.50 | 23 | €1,529.50 | 1,912 |
|
Match 2 and 2 Euro Numbers |
€23 | 329 | €7,567 | 28,461 |
|
Match 3 and 1 Euro Number |
€17.40 | 486 | €8,456.40 | 36,370 |
|
Match 3 |
€16.70 | 717 | €11,973.90 | 54,385 |
|
Match 1 and 2 Euro Numbers |
€10.70 | 2,025 | €21,667.50 | 153,245 |
|
Match 2 and 1 Euro Number |
€7.70 | 6,619 | €50,966.30 | 525,796 |
|
Total |
- | 10,219 | €105,261.10 | 802,185 |
Eurojackpot prizes in Slovenia must be claimed within 90 days of the draw date, so tickets purchased for this draw were valid until Thursday 28th February 2019.
Additional Draw Information
In total there were 21,197,792 entries into this draw from all participating countries.
Draw Number: 48
European Prize Breakdown
| Numbers Matched | Prize Per Winner | Winners from Croatia | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
kn163,000,000 | 0 | kn0 | 0 |
|
Match 5 and 1 Euro Number |
kn4,519,581.69 | 0 | kn0 | 3 |
|
Match 5 |
kn4,519,581.69 | 0 | kn0 | 1 |
|
Match 4 and 2 Euro Numbers |
kn34,933.81 | 0 | kn0 | 45 |
|
Match 4 and 1 Euro Number |
kn1,888.86 | 13 | kn24,555.18 | 749 |
|
Match 4 |
kn903.27 | 27 | kn24,388.29 | 1,218 |
|
Match 3 and 2 Euro Numbers |
kn493.16 | 36 | kn17,753.76 | 1,912 |
|
Match 2 and 2 Euro Numbers |
kn170.57 | 434 | kn74,027.38 | 28,461 |
|
Match 3 and 1 Euro Number |
kn129.04 | 734 | kn94,715.36 | 36,370 |
|
Match 3 |
kn123.85 | 1,029 | kn127,441.65 | 54,385 |
|
Match 1 and 2 Euro Numbers |
kn79.35 | 2,506 | kn198,851.10 | 153,245 |
|
Match 2 and 1 Euro Number |
kn57.10 | 9,691 | kn553,356.10 | 525,796 |
|
Total |
- | 14,470 | kn1,115,088.82 | 802,185 |
Eurojackpot prizes in Croatia must be claimed within 60 days of the draw date, so tickets purchased for this draw were valid until Tuesday 29th January 2019.
The estimated jackpot advertised in Croatia prior to the draw was kn163,000,000.
| Numbers Matched | Prize Per Winner | Winners from Czech Republic | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
Kc580,000,000 | 0 | Kc0 | 0 |
|
Match 5 and 1 Euro Number |
Kc15,817,924 | 0 | Kc0 | 3 |
|
Match 5 |
Kc15,817,924 | 0 | Kc0 | 1 |
|
Match 4 and 2 Euro Numbers |
Kc122,263 | 0 | Kc0 | 45 |
|
Match 4 and 1 Euro Number |
Kc6,610 | 19 | Kc125,590 | 749 |
|
Match 4 |
Kc3,161 | 20 | Kc63,220 | 1,218 |
|
Match 3 and 2 Euro Numbers |
Kc1,726 | 32 | Kc55,232 | 1,912 |
|
Match 2 and 2 Euro Numbers |
Kc596 | 438 | Kc261,048 | 28,461 |
|
Match 3 and 1 Euro Number |
Kc451 | 555 | Kc250,305 | 36,370 |
|
Match 3 |
Kc433 | 927 | Kc401,391 | 54,385 |
|
Match 1 and 2 Euro Numbers |
Kc277 | 2,649 | Kc733,773 | 153,245 |
|
Match 2 and 1 Euro Number |
Kc199 | 8,637 | Kc1,718,763 | 525,796 |
|
Total |
- | 13,277 | Kc3,609,322 | 802,185 |
Eurojackpot prizes in Czech Republic must be claimed within 35 days of the draw date, so tickets purchased for this draw were valid until Friday 4th January 2019.
The estimated jackpot advertised in Czech Republic prior to the draw was Kc0.
| Numbers Matched | Prize Per Winner | Winners from Denmark | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
kr.0 | 0 | kr.0 | 0 |
|
Match 5 and 1 Euro Number |
kr.3,885,187 | 0 | kr.0 | 3 |
|
Match 5 |
kr.3,885,187 | 0 | kr.0 | 1 |
|
Match 4 and 2 Euro Numbers |
kr.30,060 | 3 | kr.90,180 | 45 |
|
Match 4 and 1 Euro Number |
kr.1,653 | 56 | kr.92,568 | 749 |
|
Match 4 |
kr.806 | 95 | kr.76,570 | 1,218 |
|
Match 3 and 2 Euro Numbers |
kr.453 | 151 | kr.68,403 | 1,912 |
|
Match 2 and 2 Euro Numbers |
kr.172 | 2,295 | kr.394,740 | 28,461 |
|
Match 3 and 1 Euro Number |
kr.130 | 2,551 | kr.331,630 | 36,370 |
|
Match 3 |
kr.125 | 4,342 | kr.542,750 | 54,385 |
|
Match 1 and 2 Euro Numbers |
kr.80 | 12,115 | kr.969,200 | 153,245 |
|
Match 2 and 1 Euro Number |
kr.57 | 37,433 | kr.2,133,681 | 525,796 |
|
Total |
- | 59,041 | kr.4,699,722 | 802,185 |
Eurojackpot prizes in Denmark must be claimed within a set period of time depending on how much you have won. Visit the How to Claim page to find specific claim periods, with some prizes needing to be claimed within 90 days of the draw (valid until Thursday 28th February 2019).
The estimated jackpot advertised in Denmark prior to the draw was kr.63,000,000.
| Numbers Matched | Prize Per Winner | Winners from Estonia | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | 1 | €4,710.60 | 45 |
|
Match 4 and 1 Euro Number |
€254.70 | 9 | €2,292.30 | 749 |
|
Match 4 |
€121.80 | 12 | €1,461.60 | 1,218 |
|
Match 3 and 2 Euro Numbers |
€66.50 | 15 | €997.50 | 1,912 |
|
Match 2 and 2 Euro Numbers |
€23 | 191 | €4,393 | 28,461 |
|
Match 3 and 1 Euro Number |
€17.40 | 244 | €4,245.60 | 36,370 |
|
Match 3 |
€16.70 | 347 | €5,794.90 | 54,385 |
|
Match 1 and 2 Euro Numbers |
€10.70 | 1,063 | €11,374.10 | 153,245 |
|
Match 2 and 1 Euro Number |
€7.70 | 3,337 | €25,694.90 | 525,796 |
|
Total |
- | 5,219 | €60,964.50 | 802,185 |
Eurojackpot prizes in Estonia must be claimed within 90 days of the draw date, so tickets purchased for this draw were valid until Thursday 28th February 2019.
The estimated jackpot advertised in Estonia prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Finland | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 2 | €1,218,873 | 3 |
|
Match 5 |
€609,436.50 | 1 | €609,436.50 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | At present this information is not released by the lottery operator of Finland | 45 | |
|
Match 4 and 1 Euro Number |
€254.70 | 749 | ||
|
Match 4 |
€121.80 | 1,218 | ||
|
Match 3 and 2 Euro Numbers |
€66.50 | 1,912 | ||
|
Match 2 and 2 Euro Numbers |
€23 | 28,461 | ||
|
Match 3 and 1 Euro Number |
€17.40 | 36,370 | ||
|
Match 3 |
€16.70 | 54,385 | ||
|
Match 1 and 2 Euro Numbers |
€10.70 | 153,245 | ||
|
Match 2 and 1 Euro Number |
€7.70 | 525,796 | ||
|
Total |
- | 802,185 |
Eurojackpot prizes in Finland must be claimed within 365 days of the draw date, so tickets purchased for this draw are valid until Saturday 30th November 2019.
The estimated jackpot advertised in Finland prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Germany | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 1 | €609,436.50 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | At present this information is not released by the lottery operator of Germany | 45 | |
|
Match 4 and 1 Euro Number |
€254.70 | 749 | ||
|
Match 4 |
€121.80 | 1,218 | ||
|
Match 3 and 2 Euro Numbers |
€66.50 | 1,912 | ||
|
Match 2 and 2 Euro Numbers |
€23 | 28,461 | ||
|
Match 3 and 1 Euro Number |
€17.40 | 36,370 | ||
|
Match 3 |
€16.70 | 54,385 | ||
|
Match 1 and 2 Euro Numbers |
€10.70 | 153,245 | ||
|
Match 2 and 1 Euro Number |
€7.70 | 525,796 | ||
|
Total |
- | 802,185 |
Eurojackpot prizes in Germany must be claimed within 3 years of the draw date, so tickets purchased for this draw are valid until Tuesday 30th November 2021.
The estimated jackpot advertised in Germany prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Hungary | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
Ft176,127,150 | 0 | Ft0 | 1 |
|
Match 4 and 2 Euro Numbers |
Ft1,361,365 | 0 | Ft0 | 45 |
|
Match 4 and 1 Euro Number |
Ft73,610 | 11 | Ft809,710 | 749 |
|
Match 4 |
Ft35,200 | 24 | Ft844,800 | 1,218 |
|
Match 3 and 2 Euro Numbers |
Ft19,220 | 35 | Ft672,700 | 1,912 |
|
Match 2 and 2 Euro Numbers |
Ft6,645 | 612 | Ft4,066,740 | 28,461 |
|
Match 3 and 1 Euro Number |
Ft5,030 | 894 | Ft4,496,820 | 36,370 |
|
Match 3 |
Ft4,825 | 1,155 | Ft5,572,875 | 54,385 |
|
Match 1 and 2 Euro Numbers |
Ft3,090 | 3,594 | Ft11,105,460 | 153,245 |
|
Match 2 and 1 Euro Number |
Ft2,225 | 14,567 | Ft32,411,575 | 525,796 |
|
Total |
- | 20,892 | Ft59,980,680 | 802,185 |
Eurojackpot prizes in Hungary must be claimed within 180 days of the draw date, so tickets purchased for this draw were valid until Wednesday 29th May 2019.
The estimated jackpot advertised in Hungary prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Iceland | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
kr.3,138,405,090 | 0 | kr.0 | 0 |
|
Match 5 and 1 Euro Number |
kr.84,699,480 | 0 | kr.0 | 3 |
|
Match 5 |
kr.84,699,480 | 0 | kr.0 | 1 |
|
Match 4 and 2 Euro Numbers |
kr.654,670 | At present this information is not released by the lottery operator of Iceland | 45 | |
|
Match 4 and 1 Euro Number |
kr.35,390 | 749 | ||
|
Match 4 |
kr.16,920 | 1,218 | ||
|
Match 3 and 2 Euro Numbers |
kr.9,240 | 1,912 | ||
|
Match 2 and 2 Euro Numbers |
kr.3,190 | 28,461 | ||
|
Match 3 and 1 Euro Number |
kr.2,410 | 36,370 | ||
|
Match 3 |
kr.2,320 | 54,385 | ||
|
Match 1 and 2 Euro Numbers |
kr.1,480 | 153,245 | ||
|
Match 2 and 1 Euro Number |
kr.1,070 | 525,796 | ||
|
Total |
- | 802,185 |
Eurojackpot prizes in Iceland must be claimed within 1 year of the draw date, so tickets purchased for this draw are valid until Saturday 30th November 2019.
The estimated jackpot advertised in Iceland prior to the draw was kr.0.
| Numbers Matched | Prize Per Winner | Winners from Italy | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | 0 | €0 | 45 |
|
Match 4 and 1 Euro Number |
€254.70 | 15 | €3,820.50 | 749 |
|
Match 4 |
€121.80 | 27 | €3,288.60 | 1,218 |
|
Match 3 and 2 Euro Numbers |
€66.50 | 34 | €2,261 | 1,912 |
|
Match 2 and 2 Euro Numbers |
€23 | 586 | €13,478 | 28,461 |
|
Match 3 and 1 Euro Number |
€17.40 | 713 | €12,406.20 | 36,370 |
|
Match 3 |
€16.70 | 1,145 | €19,121.50 | 54,385 |
|
Match 1 and 2 Euro Numbers |
€10.70 | 3,397 | €36,347.90 | 153,245 |
|
Match 2 and 1 Euro Number |
€7.70 | 11,704 | €90,120.80 | 525,796 |
|
Total |
- | 17,621 | €180,844.50 | 802,185 |
Eurojackpot prizes in Italy must be claimed within a set period of time depending on how much you have won. Visit the How to Claim page to find specific claim periods, with some prizes needing to be claimed within 30 days of the draw (valid until Sunday 30th December 2018).
The estimated jackpot advertised in Italy prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Latvia | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | At present this information is not released by the lottery operator of Latvia | 45 | |
|
Match 4 and 1 Euro Number |
€254.70 | 749 | ||
|
Match 4 |
€121.80 | 1,218 | ||
|
Match 3 and 2 Euro Numbers |
€66.50 | 1,912 | ||
|
Match 2 and 2 Euro Numbers |
€23 | 28,461 | ||
|
Match 3 and 1 Euro Number |
€17.40 | 36,370 | ||
|
Match 3 |
€16.70 | 54,385 | ||
|
Match 1 and 2 Euro Numbers |
€10.70 | 153,245 | ||
|
Match 2 and 1 Euro Number |
€7.70 | 525,796 | ||
|
Total |
- | 802,185 |
Eurojackpot prizes in Latvia must be claimed within 30 days of the draw date, so tickets purchased for this draw were valid until Sunday 30th December 2018.
The estimated jackpot advertised in Latvia prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Lithuania | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | 0 | €0 | 45 |
|
Match 4 and 1 Euro Number |
€254.70 | 2 | €509.40 | 749 |
|
Match 4 |
€121.80 | 4 | €487.20 | 1,218 |
|
Match 3 and 2 Euro Numbers |
€66.50 | 16 | €1,064 | 1,912 |
|
Match 2 and 2 Euro Numbers |
€23 | 147 | €3,381 | 28,461 |
|
Match 3 and 1 Euro Number |
€17.40 | 106 | €1,844.40 | 36,370 |
|
Match 3 |
€16.70 | 118 | €1,970.60 | 54,385 |
|
Match 1 and 2 Euro Numbers |
€10.70 | 717 | €7,671.90 | 153,245 |
|
Match 2 and 1 Euro Number |
€7.70 | 1,265 | €9,740.50 | 525,796 |
|
Total |
- | 2,375 | €26,669 | 802,185 |
Eurojackpot prizes in Lithuania must be claimed within 60 days of the draw date, so tickets purchased for this draw were valid until Tuesday 29th January 2019.
The estimated jackpot advertised in Lithuania prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Netherlands | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | At present this information is not released by the lottery operator of Netherlands | 45 | |
|
Match 4 and 1 Euro Number |
€254.70 | 749 | ||
|
Match 4 |
€121.80 | 1,218 | ||
|
Match 3 and 2 Euro Numbers |
€66.50 | 1,912 | ||
|
Match 2 and 2 Euro Numbers |
€23 | 28,461 | ||
|
Match 3 and 1 Euro Number |
€17.40 | 36,370 | ||
|
Match 3 |
€16.70 | 54,385 | ||
|
Match 1 and 2 Euro Numbers |
€10.70 | 153,245 | ||
|
Match 2 and 1 Euro Number |
€7.70 | 525,796 | ||
|
Total |
- | 802,185 |
Eurojackpot prizes in Netherlands must be claimed within 365 days of the draw date, so tickets purchased for this draw are valid until Saturday 30th November 2019.
The estimated jackpot advertised in Netherlands prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Norway | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
kr.214,000,000 | 0 | kr.0 | 0 |
|
Match 5 and 1 Euro Number |
kr.5,935,910 | 0 | kr.0 | 3 |
|
Match 5 |
kr.5,935,910 | 0 | kr.0 | 1 |
|
Match 4 and 2 Euro Numbers |
kr.45,880 | At present this information is not released by the lottery operator of Norway | 45 | |
|
Match 4 and 1 Euro Number |
kr.2,480 | 749 | ||
|
Match 4 |
kr.1,185 | 1,218 | ||
|
Match 3 and 2 Euro Numbers |
kr.645 | 1,912 | ||
|
Match 2 and 2 Euro Numbers |
kr.220 | 28,461 | ||
|
Match 3 and 1 Euro Number |
kr.165 | 36,370 | ||
|
Match 3 |
kr.160 | 54,385 | ||
|
Match 1 and 2 Euro Numbers |
kr.100 | 153,245 | ||
|
Match 2 and 1 Euro Number |
kr.70 | 525,796 | ||
|
Total |
- | 802,185 |
Eurojackpot prizes in Norway must be claimed within 3 months of the draw date, so tickets purchased for this draw were valid until Thursday 28th February 2019.
The estimated jackpot advertised in Norway prior to the draw was kr.214,000,000.
| Numbers Matched | Prize Per Winner | Winners from Poland | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
zł95,000,000 | 0 | zł0 | 0 |
|
Match 5 and 1 Euro Number |
zł0 | 0 | zł0 | 3 |
|
Match 5 |
zł0 | 0 | zł0 | 1 |
|
Match 4 and 2 Euro Numbers |
zł197,552.60 | 3 | zł592,657.80 | 45 |
|
Match 4 and 1 Euro Number |
zł1,092.70 | 36 | zł39,337.20 | 749 |
|
Match 4 |
zł522.60 | 35 | zł18,291 | 1,218 |
|
Match 3 and 2 Euro Numbers |
zł285.30 | 62 | zł17,688.60 | 1,912 |
|
Match 2 and 2 Euro Numbers |
zł98.70 | 905 | zł89,323.50 | 28,461 |
|
Match 3 and 1 Euro Number |
zł74.70 | 1,382 | zł103,235.40 | 36,370 |
|
Match 3 |
zł71.70 | 2,082 | zł149,279.40 | 54,385 |
|
Match 1 and 2 Euro Numbers |
zł45.90 | 5,021 | zł230,463.90 | 153,245 |
|
Match 2 and 1 Euro Number |
zł33.10 | 18,583 | zł615,097.30 | 525,796 |
|
Total |
- | 28,109 | zł1,855,374.10 | 802,185 |
Eurojackpot prizes in Poland must be claimed within 3 years of the draw date, so tickets purchased for this draw are valid until Tuesday 30th November 2021.
The estimated jackpot advertised in Poland prior to the draw was zł95,000,000.
| Numbers Matched | Prize Per Winner | Winners from Slovakia | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | 2 | €9,421.20 | 45 |
|
Match 4 and 1 Euro Number |
€254.70 | 15 | €3,820.50 | 749 |
|
Match 4 |
€121.80 | 12 | €1,461.60 | 1,218 |
|
Match 3 and 2 Euro Numbers |
€66.50 | 44 | €2,926 | 1,912 |
|
Match 2 and 2 Euro Numbers |
€23 | 555 | €12,765 | 28,461 |
|
Match 3 and 1 Euro Number |
€17.40 | 697 | €12,127.80 | 36,370 |
|
Match 3 |
€16.70 | 897 | €14,979.90 | 54,385 |
|
Match 1 and 2 Euro Numbers |
€10.70 | 2,958 | €31,650.60 | 153,245 |
|
Match 2 and 1 Euro Number |
€7.70 | 8,968 | €69,053.60 | 525,796 |
|
Total |
- | 14,148 | €158,206.20 | 802,185 |
Eurojackpot prizes in Slovakia must be claimed within 35 days of the draw date, so tickets purchased for this draw were valid until Friday 4th January 2019.
The estimated jackpot advertised in Slovakia prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Spain | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
€22,582,415.42 | 0 | €0 | 0 |
|
Match 5 and 1 Euro Number |
€609,436.50 | 0 | €0 | 3 |
|
Match 5 |
€609,436.50 | 0 | €0 | 1 |
|
Match 4 and 2 Euro Numbers |
€4,710.60 | 0 | €0 | 45 |
|
Match 4 and 1 Euro Number |
€254.70 | 29 | €7,386.30 | 749 |
|
Match 4 |
€121.80 | 38 | €4,628.40 | 1,218 |
|
Match 3 and 2 Euro Numbers |
€66.50 | 69 | €4,588.50 | 1,912 |
|
Match 2 and 2 Euro Numbers |
€23 | 1,079 | €24,817 | 28,461 |
|
Match 3 and 1 Euro Number |
€17.40 | 1,194 | €20,775.60 | 36,370 |
|
Match 3 |
€16.70 | 1,967 | €32,848.90 | 54,385 |
|
Match 1 and 2 Euro Numbers |
€10.70 | 5,490 | €58,743 | 153,245 |
|
Match 2 and 1 Euro Number |
€7.70 | 17,291 | €133,140.70 | 525,796 |
|
Total |
- | 27,157 | €286,928.40 | 802,185 |
Eurojackpot prizes in Spain must be claimed within 30 days of the draw date, so tickets purchased for this draw were valid until Sunday 30th December 2018.
The estimated jackpot advertised in Spain prior to the draw was €22,000,000.
| Numbers Matched | Prize Per Winner | Winners from Sweden | Prize Fund Amount | Total Winners |
|---|---|---|---|---|
|
Match 5 and 2 Euro Numbers |
kr.227,000,000 | 0 | kr.0 | 0 |
|
Match 5 and 1 Euro Number |
kr.6,281,644 | 0 | kr.0 | 3 |
|
Match 5 |
kr.6,281,644 | 0 | kr.0 | 1 |
|
Match 4 and 2 Euro Numbers |
kr.164,763 | 2 | kr.329,526 | 45 |
|
Match 4 and 1 Euro Number |
kr.15,054 | 34 | kr.511,836 | 749 |
|
Match 4 |
kr.7,017 | 66 | kr.463,122 | 1,218 |
|
Match 3 and 2 Euro Numbers |
kr.3,665 | 78 | kr.285,870 | 1,912 |
|
Match 2 and 2 Euro Numbers |
kr.237 | 1,307 | kr.309,759 | 28,461 |
|
Match 3 and 1 Euro Number |
kr.179 | 1,592 | kr.284,968 | 36,370 |
|
Match 3 |
kr.172 | 2,504 | kr.430,688 | 54,385 |
|
Match 1 and 2 Euro Numbers |
kr.110 | 6,831 | kr.751,410 | 153,245 |
|
Match 2 and 1 Euro Number |
kr.79 | 22,324 | kr.1,763,596 | 525,796 |
|
Total |
- | 34,738 | kr.5,130,775 | 802,185 |
Eurojackpot prizes in Sweden must be claimed within 3 months of the draw date, so tickets purchased for this draw were valid until Thursday 28th February 2019.
The estimated jackpot advertised in Sweden prior to the draw was kr.227,000,000.
Associated Draw Results
- 9
- 8
- 3
- 2
- 8
- 4
| Numbers Matched | Prize Per Winner | Total Winners |
|---|---|---|
| Match 6 in Exact Order | €50,000 | 0 |
| Match Last 5 in Exact Order | €5,000 | 0 |
| Match Last 4 in Exact Order | €500 | 10 |
| Match Last 3 in Exact Order | €50 | 118 |
| Match Last 2 in Exact Order | €5 | 905 |
| Match Last 1 in Exact Order | €3 | 9,401 |
- 2
- 1
- 8
- 4
- 2
- 5
| Numbers Matched | Prize Per Winner | Total Winners |
|---|---|---|
| Match 6 | CZK0 | 0 |
| Match 5 | CZK200,000 | 1 |
| Match 4 | CZK20,000 | 3 |
| Match 3 | CZK2,000 | 62 |
| Match 2 | CZK200 | 660 |
| Match 1 | CZK120 | 6,691 |
- 1
- 5
- 3
- 5
- 5
- 9
- 3
| Numbers Matched | Prize Per Winner | Total Winners |
|---|---|---|
| Match 7 in Exact Order | €1,000,000 | 0 |
| Match Any 6 in the Right Spot | €20,000 | 3 |
| Match Any 5 in the Right Spot | €500 | 23 |
| Match Any 4 in the Right Spot | €50 | 463 |
| Match Any 3 in the Right Spot | €6 | 4,322 |
| Match Any 2 in the Right Spot | €3 | 22,986 |
- Oslo
- 97
| Numbers Matched | Prize Per Winner | Total Winners |
|---|---|---|
| City and Number | €1,000 | 14 |
| City | €5 | 1,205 |
- 9
- 0
- 3
- 8
- 8
| Numbers Matched | Prize Per Winner | Total Winners |
|---|---|---|
| Match 5 in Exact Order | kr2,000,000 | 0 |
| Match First/Last 4 in Exact Order | kr100,000 | 0 |
| Match First/Last 3 in Exact Order | kr10,000 | 7 |
| Match First/Last 2 in Exact Order | kr2,000 | 119 |
- Moss
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Subject guides are repositories of information that relate to your course. This will include information and reading lists you can use to pass your course, as well as additional knowledge that will be required for you to reach the higher mark boundaries and succeed. For HE students, you will be expected to access your subject guides regularly.


Copy .obj file just before loading, to replace dataRefs and texture.
These routines make a copy of an .obj
file just before it gets loaded by X-Plane. This way we can replace dataRefs and textures.
xsb_aircraft.txt
formats vary by now out in the wild. For example, X-CSL/X-IvAp used to defined texture on the OBJ8
line. X-Plane, especially for instancing, cannot replace textures on the fly. The solution is to copy the .obj
file, replacing the up to two lines defining the texture to use, and then only have it loaded by X-Plane.
- CSL-Models might not use correct dataRefs as supported by XPMP2. For example are the widely used Bluebell models known to have translated only a limited set of dataRefs from their World Traffic origin into the libxplanemp world. XPMP2 now supports a lot more dataRefs. Replacing dataRef names in those models unlocks a number of feature like rotating props/rotors, turning wheels, or reversers.
- See also
- https://twinfan.github.io/XPMP2/XSBAircraftFormat.html for the
xsb_aircraft.txt
format definition as supported by XPMP2.
-
https://twinfan.github.io/XPMP2/CSLdataRefs.html for a list of animation dataRefs supported by XPMP2. And beyond that you can add even more using the XPMPAddModelDataRef() function.
- Author
- Birger Hoppe
- Copyright
- (c) 2020 Birger Hoppe
-
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
 IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.


Kim and Ken had a bet. Ten bucks if you get to the top of the hill. Ken and Kim shook hands. Who will win the ten bucks" Kim began to run up the hill. Ken went plod, plod, plod. It is a steep hill. Kim got hot. He was huffing and puffing! He had to stop. Ken went on, tramp, tramp, tramp! Kim had to rest. He fell asleep. Ken went on slog, slog, slog up to the summit! He did not look back. Who got the ten bucks"
in-context


--- layout: archive title: Zulip Chat Archive permalink: /stream/113488-general/topic/forward.20implication.20from.20an.20.60iff.60.2C.20with.20typeclasses.html ---
I've discovered a gap in library_search
, and am having trouble fixing it.
The essential problem is that many library lemmas are iff
, and we have to construct the forward and backward implications separately, so they can be apply
d.
It's very important that this construction step is fast, because we're repeating this step over every relevant imported lemma in the library.
My current approach is to use
iff_mp_core
in tactic/basic.lean
. This takes an expression along with its known type, and builds the corresponding .mp
after dropping down through all the arguments.
As an example, on le_mul_iff_one_le_left
this creates the expression
λ {α : Type u} [_inst_1 : linear_ordered_semiring α] {a b : α} (hb : b > 0), (le_mul_iff_one_le_left hb).mp
and at this point you can see my problem... The instance [_inst_1]
is not available in the later arguments or body of the lambda, so we get errors:
e.g.
failed to synthesize type class instance for α : Type u, _inst_1 : linear_ordered_semiring α, a b : α ⊢ has_zero αLean
at b > 0
.
... help?!
Why don't you skip the apply
altogether and use unify
instead?
actually I can't see the problem as you have articulated it. The iff_mp_core
expression already has the instances filled in
The problem is that the expression that iff_mp_core
produces doesn't even typecheck
Because when we put all the lambdas back in place, the instances don't enter the instance cache
Note that iff_mp_core
is not using to_expr
or anything, it's just building expr
objects by hand.
Sorry, I'll try to make a MWE.
It is exactly because it is building exprs by hand that it doesn't have to worry about typeclass inference or to_expr or anything
it's just a fully elaborated and type correct expression
Okay, I agree, my diagnosis of the problem was completely wrong. Nevertheless, I can't get apply
to work here. Here's a self-contained instance of the problem:
import algebra.ordered_ring #print le_mul_iff_one_le_left -- theorem le_mul_iff_one_le_left : ∀ {α : Type u} [_inst_1 : linear_ordered_semiring α] {a b : α}, b > 0 → (b ≤ a * b ↔ 1 ≤ a) := -- This works fine: def oom {a b : ℕ} (h : 0 < b) (w : 1 ≤ a) : b ≤ a * b := (le_mul_iff_one_le_left h).mpr w open tactic meta def f : tactic unit := do d ← get_decl `le_mul_iff_one_le_left, let n := d.to_name, let t := d.type, e ← mk_const n, mp ← iff_mpr_core e t, apply mp, skip example {a b : ℕ} : b ≤ a * b := begin f, /- invalid apply tactic, failed to unify b ≤ a * b with ?m_3 ≤ ?m_4 * ?m_3 -/ end
oh, crap, it's universes:
set_option pp.all true example {a b : ℕ} : b ≤ a * b := begin f, /- invalid apply tactic, failed to unify @has_le.le.{0} nat nat.has_le b (@has_mul.mul.{0} nat nat.has_mul a b) with @has_le.le.{u} ?m_1 (@preorder.to_has_le.{u} ?m_1 (@partial_order.to_preorder.{u} ?m_1 (@ordered_comm_monoid.to_partial_order.{u} ?m_1 (@ordered_cancel_comm_monoid.to_ordered_comm_monoid.{u} ?m_1 (@ordered_semiring.to_ordered_cancel_comm_monoid.{u} ?m_1 (@linear_ordered_semiring.to_ordered_semiring.{u} ?m_1 ?m_2)))))) ?m_3 (@has_mul.mul.{u} ?m_1 (@mul_zero_class.to_has_mul.{u} ?m_1 (@semiring.to_mul_zero_class.{u} ?m_1 (@ordered_semiring.to_semiring.{u} ?m_1 (@linear_ordered_semiring.to_ordered_semiring.{u} ?m_1 ?m_2)))) ?m_4 ?m_3) -/ end
Or is it? I guess I don't know how apply
deals with those u
s.
Oooh... I think I see. The type coming out of d.type
has a fixed universe already plugged in. The type for e
coming out of mk_const
(correctly) has fresh universe metavariables.
Wah!
I think this means I have to run infer_type e
instead of just using d.type
.
:+1:
Unfortunately this is slow, and will kill library_search
, I think. :-(
just create a bunch of metavariables for the declaration's universe variables and substitute
It seems infer_type
is not actually a problem (this is strange, as previously it seemed it was).
Let me actually profile before deciding whether to do the universe substitution.
In any case:
example {a b : ℕ} (h : a ≥ 1): b ≤ a * b := by library_search -- exact le_mul_of_ge_one_left' (by norm_num) h
(well, not quite --- it does run norm_num
to discharge the arithmetic goals, but for now it prints the term norm_num
produces, which is no good)
the expr
substitution functions should be very fast, faster than apply
since apply
does that among many other things
I know how to fix this, but need to work out how to do substring replacement. :-)
what's the issue / what are you aiming for?
The problem has just been the library_search
has to date been failing to apply any iff
lemmas that involved universes!
Which is a lot of them
you shouldn't be running norm_num
as part of a library search, that will kill your performance
hmm..
it seems okay on my example set
I'm really confused on your goals now though
oh, sorry
the norm_num issue is separate
It should be a really simple dumb search to be performant on the whole library
okay... let's now change topics to norm_num. :-)
if you can't afford to substitute metavariables you certainly can't afford norm_num
I really want to be able to solve problems like this:
example {a b : ℕ} (h : a * 2 ≤ b) : a ≤ b / 2 := by library_search -- exact (nat.le_div_iff_mul_le a b XXX).mpr h
where XXX
should be dec_trivial
or (by norm_num)
The problem is that too many library lemmas have arithmetic side conditions.
You should note the initial success to shortlist it and come back to it later
Or just give them back as subgoals
no, giving back subgoals won't work --- there are way too many lemmas that successfully apply
, but the hypotheses are just completely irrelevant to the problem you're actually working on
I think a useful and general approach is to try to rank successes by how similar they are to the goal
i.e. don't necessarily close the goal outright but give some possible matching lemmas
Sorry -- do you mean how similar the newly generated goals (after the initial apply) are to the original goal?
The problem is there are many lemmas whose conclusion is just a \leq b
, and they only really differ in their hypotheses.
I mean how "deeply" the goal and hypotheses match with the target and things in the context
Ok.
So at the moment I only report lemmas that match so deeply that solve_by_elim
can solve all the newly generated goals, from local hypotheses
I'm still thinking one step proofs here, but it's not an immediate fail if some hypotheses can't be found in the context
Okay.
If you like, you could try splitting into two tactics, one that finds likely candidates and another more tidy
-like tactic that tries to kill the subgoals of the candidates
Even just: "Apply a library lemma, and then as many as possible local hypotheses. Return the library lemma for which some combination of [number of applied hypotheses]/[number of remaining goals] is 'best'".
This follows your description of trying to get good "matching" with the local goals/hypotheses
Especially if you can't close the goal, though, I think you should consider reporting multiple matches. If you can display the subgoals for each case I could quickly look through them to see things like "this one needs 0 > 2, no good, that one needs 2 | x, no good, that one says x < x + 1, ok let's try that"
Hmm... this sounds great, but realistically I can't work on that anytime soon.
I will PR a fix that deals with the universe issue.
okay, just thought I would give some ideas
No, they are great ideas. I will attempt to write up a description of some things someone should do, and shop it around here/to students. :-)
(on that note, we should keep thinking about how to make/maintain lists of "things someone should do")
The metamath IDE I use has a "step search" function that allows you to type a statement and then it searches the library and reports all matches. Many are silly matches but they are mostly organized in groups so you can still scroll through them to find the one you are after
that feature would be much improved if the matches were organized by relevance in terms of number of matched constants in the unify, so that things like "\all p, bla -> bla -> p" don't appear in every match
So... in copying the universe metavariables over from e <- mk_const n
into d.type
... how do I know which universes correspond to which?
I can call expr.collect_univ_params d.type
to collect universes out of the type I get from the declaration, but I have no idea what order this list is in.
Is it certain to be in the same order as in ls
when I match mk_const n
against expr.const _ ls
?
declaration
has a list name
field for this
it lists the universe names used in d.type
in the order they appear in expr.const
It looks like running infer_type
costs about a 10% increase in runtime in the library_search
tests, so I'll avoid it, I guess.
@Mario Carneiro I never got this working, but I've made a [WIP] PR that shows the problem I ran into. #967 I'm attempt to update the universe levels in d.type
use the new universes from e <- mk_const d.to_name
, but apparently I'm not getting them all.


| parameter_trans {pomp} | R Documentation |
Equipping models with parameter transformations to facilitate searches in constrained parameter spaces.
parameter_trans(toEst, fromEst, ...)
## S4 method for signature ''NULL','NULL''
parameter_trans(toEst, fromEst, ...)
## S4 method for signature 'pomp_fun,pomp_fun'
parameter_trans(toEst, fromEst, ...)
## S4 method for signature 'Csnippet,Csnippet'
parameter_trans(toEst, fromEst, ..., log, logit, barycentric)
## S4 method for signature 'character,character'
parameter_trans(toEst, fromEst, ...)
## S4 method for signature ''function','function''
parameter_trans(toEst, fromEst, ...)
toEst , fromEst |
procedures that perform transformation of model parameters to and from the estimation scale, respectively. These can be furnished using C snippets, R functions, or via procedures in an external, dynamically loaded library. |
... |
ignored. |
log |
names of parameters to be log transformed. |
logit |
names of parameters to be logit transformed. |
barycentric |
names of parameters to be collectively transformed according to the log barycentric transformation. Important note: variables to be log-barycentrically transformed must be adjacent in the parameter vector. |
When parameter transformations are desired, they can be integrated into the ‘pomp’ object via the partrans
arguments using the parameter_trans
function.
As with the other basic model components, these should ordinarily be specified using C snippets.
When doing so, note that:
The parameter transformation mapping a parameter vector from the scale used by the model codes to another scale, and the inverse transformation, are specified via a call to
parameter_trans(toEst,fromEst)
.
The goal of these snippets is the transformation of the parameters from the natural scale to the estimation scale, and vice-versa.
If p
is the name of a variable on the natural scale, its value on the estimation scale is T_p
.
Thus the toEst
snippet computes T_p
given p
whilst the fromEst
snippet computes p
given T_p
.
Time-, state-, and covariate-dependent transformations are not allowed. Therefore, neither the time, nor any state variables, nor any of the covariates will be available in the context within which a parameter transformation snippet is executed.
These transformations can also be specified using R functions with arguments chosen from among the parameters.
Such an R function must also have the argument ‘...
’.
In this case, toEst
should transform parameters from the scale that the basic components use internally to the scale used in estimation.
fromEst
should be the inverse of toEst
.
Note that it is the user's responsibility to make sure that the transformations are mutually inverse.
If obj
is the constructed ‘pomp’ object, and coef(obj)
is non-empty, a simple check of this property is
x <- coef(obj, transform = TRUE) obj1 <- obj coef(obj1, transform = TRUE) <- x identical(coef(obj), coef(obj1)) identical(coef(obj1, transform=TRUE), x)
One can use the log
and logit
arguments of parameter_trans
to name variables that should be log-transformed or logit-transformed, respectively.
The barycentric
argument can name sets of parameters that should be log-barycentric transformed.
Note that using the log
, logit
, or barycentric
arguments causes C snippets to be generated.
Therefore, you must make sure that variables named in any of these arguments are also mentioned in paramnames
at the same time.
The logit transform is defined by
\mathrm{logit}(\theta)=\log\frac{\theta}{1-\theta}.
The log barycentric transformation of variables \theta_1,\dots,\theta_n
is given by
\mathrm{logbarycentric}(\theta_1,\dots,\theta_n)=\left(\log\frac{\theta_1}{\sum_i \theta_i},\dots,\log\frac{\theta_n}{\sum_i \theta_i}\right).
Some Windows users report problems when using C snippets in parallel computations.
These appear to arise when the temporary files created during the C snippet compilation process are not handled properly by the operating system.
To circumvent this problem, use the cdir
and cfile
options to cause the C snippets to be written to a file of your choice, thus avoiding the use of temporary files altogether.
More on implementing POMP models:
Csnippet
,
accumvars
,
basic_components
,
betabinomial
,
covariates
,
dinit_spec
,
dmeasure_spec
,
dprocess_spec
,
emeasure_spec
,
eulermultinom
,
pomp-package
,
pomp_constructor
,
prior_spec
,
rinit_spec
,
rmeasure_spec
,
rprocess_spec
,
skeleton_spec
,
transformations
,
userdata
,
vmeasure_spec