In order to get the ESP8266 to send and receive data, the next task is to make it listen to incoming requests and answer back with messages So, to make it behave like this, let's set up a web server. The web server will listen to any incoming request to the device, and if the request matches a specific pre-defined address, will answer back with a pre-defined answer.
First, include the webserver module
#include <ESP8266WebServer.h>
Next, need to add a server object
ESP8266WebServer server(80);
and 2 functions: one for the default answer, and one for addresses the server doesn't recognize.
void handleRoot(){
server.send(200, "text/plain", "Hooray!, your ESP8266 server is alive!");
}
void handleNotFound(){
server.send(404, "text/plain", "unknown address");
}
as part of the setup - you need to add the functions above as callbacks for specific server route or unknown address and start the server
server.on("/", handleRoot);
server.onNotFound(handleNotFound);
server.begin();
You also need to check for incoming requests so place the following inside your loop
server.handleClient();
#include <ESP8266WiFi.h>
#include <ESP8266WebServer.h>
const char* ssid = "intel makers";
const char* password = "1234567890";
#define ONBOARD_LED_PIN D4
ESP8266WebServer server(80);
void handleRoot(){
server.send(200, "text/plain", "Hooray!, your ESP8266 server is alive!");
}
void handleNotFound(){
server.send(404, "text/plain", "Error 404 - ESP8266 server could not find the page you were looking for");
}
void setup() {
// setup the on-board pin (D4) to output mode
pinMode(ONBOARD_LED_PIN, OUTPUT);
// start serial connection
Serial.begin(115200);
Serial.println("");
Serial.print("Connecting to ");
Serial.println(ssid);
// set WiFi to STA mode
WiFi.mode(WIFI_STA);
// set static IP
IPAddress ip(192,168,1, );
IPAddress gateway(192,168,1,254);
IPAddress subnet(255,255,255,0);
WiFi.config(ip, gateway, subnet);
// connect to AP
WiFi.begin(ssid, password);
// wait until connection is complete
while (WiFi.status() != WL_CONNECTED) {
delay(500);
Serial.print(".");
}
Serial.println("");
Serial.println("WiFi connected");
Serial.println("IP address: ");
Serial.println(WiFi.localIP());
server.on("/", handleRoot);
server.onNotFound(handleNotFound);
server.begin();
}
void loop()
{
// toggle the LED each 0.1 second
digitalWrite(ONBOARD_LED_PIN, HIGH);
delay(100);
digitalWrite(ONBOARD_LED_PIN, LOW);
delay(100);
server.handleClient();
}
browse to 192.168.1.
you should see a similar message
and if you browse to some random address, like 192.168.1.
you should get to your 404 (error) message
Click "Test me" when you are ready.


Multiple Languages
Support for multiple languages has now been added. For now only French and German translations are available. If you wish to translate WebPlotDigitizer to other languages, then feel free to send me an email.
Export All Data
You can now export data from all datasets to a combined CSV file in one single operation. All this requires is clicking the 'Export Data' option in the 'Data' menu.
Extraction Algorithm Improvements
X step with interpolation and X step algorithms have been extended to work with log-scale XY plots.


GET image
Retrieve an image that has been previously stored on the server.
Resource
http://dev5:8888/image/51f973830d861c2c5c626910.jpg
HTTP Request: Headers
The request method is GET so there is no body that needs to be described.
Only the basic headers are sent.
For example:
GET /image/51f973830d861c2c5c626910.jpg HTTP/1.1
Host: dev5:8888
HTTP Request: Headers: Request Method Parameters
Expected Format:
GET /image/[filename]
fileName (required) |
See the sample URL above.
The filename will always be a 24 character hexidecimal string followed by ".jpg" or ".png".
Only JPEG and PNG file formats are currently supported. |
HTTP Request: Body
The request method is GET.
So the body does not exist.
HTTP Response: Headers
The following response codes are possible from this service.
(Client code must handle each of them.):
200 Success
400 Bad Request
500 Server Error
If successful (Status Code = 200 Success),
the content of the body of the HTTP Response will always be an image.
Therefore, the following header will always be sent:
Content-Type: image/jpeg
OR
Content-Type: image/png
If unsuccessful (Status Code = 400 or 500),
the content of the body will be JSON.
Therefore, the following header will always be sent:
Content-Type: application/json
HTTP Response: Headers: Caching
This service instructs the client and proxy servers to cache the image.
Clients of this service should obey the instruction to cache the image in a local data store.
Clients should not re-request the image until the cache expires -
unless, of course, the user explicitly asks to refresh the image.
The headers to pay attention to here are:
Cache-Control: public; max-age=770875895
If Cache-Control is public or private, the client must cache the content.
The "max-age" directive specifies how many seconds that the content must be cached for.
You can use this to calculate a specific expiry date for the image in your cache.
Expires: Tue, 19 Jan 2038 15:14:06 GMT
Alternatively, you can use the pre-calculated date & time in the Expires header
to do the same thing.
Example Headers:
Cache-Control: public; max-age=770875895
Content-Type: image/jpeg
Date: Thu, 15 Aug 2013 23:02:32 GMT
Expires: Tue, 19 Jan 2038 15:14:06 GMT
Server: Apache-Coyote/1.1
Transfer-Encoding: chunked
HTTP Response: Body
If the service executed successfully (Response Code = 200 Created)
the response body will contain the unencoded binary image in the format you requested.
If the service failed (Response Code = 400 or 500)
the standard JSON describing the error will be returned in the body of the response:
{
"errorCode": 2,
"errorMessage": "INVALID PARAMS",
"data" : "specified image does not exist"
}
HTTP Request Example
http://dev5:8888/image/51f973830d861c2c5c626916.jpg
HTTP Response Example (Success)
HTTP Response Example (Failure)
{
"errorCode": 2,
"errorMessage": "INVALID PARAMS",
"data" : "file name must be a 24 character hexadecimal string followed by '.jpg' or '.png'"
}
{
"errorCode": 2,
"errorMessage": "INVALID PARAMS",
"data" : "the file specified does not exist"
}


Hello there!
I'm Holden Clark --
Student at Epicodus
Projects
About Me
Experience
Japanese Melons
Wikipedia Rebuild
Favorite Restaurants


Hi, I've a system in the local school and it uses an XP desktop machine running IIS so I ran into an port conflict issue when using XAMPP . I changed the listen directive for xampp, to use port 85, and thereby avoid the conflict.
From the nanode5 base I'm using though, I can't post data to the local emoncms server....
I can post to vis.openenergymonitor.org
I can access emoncms from my laptop which is external to the server.
I can ping the Nanode.
The Nanode is posting data to it's serial port.
I can post data using the API string on the emoncms server just to verify I can write to the db and see it on emoncms.
Even though all this is working, I am failing to post to the local emoncms server... So, I set hisport =85; in the sketch to try to correct the port conflict issue.
I know that the ethercard library specifies port 80 in the ethercard.cpp file explicitly, but thought if I assigned 85 to the hisport variable in the sketch it should work.
Does anyone have experience of this - I'm not too sure how to debug from here - great learning in it though but need to get it nailed soon...
Thanks, Eamonn
Re: Specifing a different port on the http server [ e.g. using hisport ]
I can only conclude that specifying "ether.hisport = 85; " in the sketch isn't actually directing my nanode to use port 85 at al. I'm going to try stopping the IIS webserver and reconfgure Xampp to use port 80. That may confirm it for me
Eamonn
Re: Specifing a different port on the http server [ e.g. using hisport ]
I have experience with a setup using a different port for the web connection on EmonBase. I've added the ether.hisport = 8808 code to the setup part of the sketch just above the rf12_initialize line.
Did you check the access logs of the webserver to see if any requests are coming in at all? (other issues could be API key or different URL).
Re: Specifing a different port on the http server [ e.g. using hisport ]
Afs, thanks for that ; code is the same as you've described and when I check the access logs I get ;
<IP_ADDRESS> - - [04/May/2012:09:21:35 +0100] "GET /emoncms3/input/list.json HTTP/1.1" 200 82 "http://localhost:85/emoncms3/input/list" "Mozilla/5.0 (Windows NT 5.1; rv:12.0) Gecko/20100101 Firefox/12.0"
MySQL or Apache error logs are empty for today, and the Apache access log above looks ok to me though I'm not 100% sure if the 1st line of the request is right "GET /emoncms3/input/list.json HTTP/1.1".
But 'm getting an 'ok' response so it is confirming I am successfully reaching the server.
I'll try a new API, but thanks for making me check the logs again.
Eamonn
Re: Specifing a different port on the http server [ e.g. using hisport ]
Environment is as follows
Re: Specifing a different port on the http server [ e.g. using hisport ]
I've no errors being logged, but am not writing to the db. Assuming the Apache access log is healthy above, this means that it must be an environment issue - i.e. I'm not even getting to the db.
I've checked my user account is set correctly[ settings.php and mysql account are in sync and has full db priviliges]. I've set up the environment in c:/xampp
Has anyone else a different installation on XP that I could correlate against?
thanks,Eamonn
Re: Specifing a different port on the http server [ e.g. using hisport ]
I had an issue with privileges: In settings.php it would only accept access as root with a null password (not even an empty password!), even though the user ID I wanted to use had exactly (as far as I could tell) the same privileges as root.
(This was with Windows XP and WampServer - I've still not got it going).
Re: Specifing a different port on the http server [ e.g. using hisport ]
very interesting. Thanks for that....
Re: Specifing a different port on the http server [ e.g. using hisport ]
very interesting. Thanks for that....
Re: Specifing a different port on the http server [ e.g. using hisport ]
Tried variations of root passwords to no avail. However, it was a useful workshop for understanding how phpmyadmin is configured..........
I created a new database called Scoil [This is Irish for school, by the way], and setup the username as 'root' and password as 'demo' (in my settings.php file). Once I had set up and went to me URL, I saw the setup complete and clicked the 'continue to emoncms' link. I couldn't generate any API, and when I logged out, I couldn't log back in[ using root/demo].
any ideas? I know this is a slight tangent, but I want to make sure I've a clean db and have eliminated the username/password problems.
Eamonn
Re: Specifing a different port on the http server [ e.g. using hisport ]
Just getting back to this now.....
I can access the server from a standalone laptop as well as the server; using the 'IPv4address:8808/emoncms3' as the URL.
I have changed the tcpip.cpp file in the ethercard library to explicitly look for 8808 instead of using hisport.
I've changed the xampp/conf/https.conf file to Listen on port 8808 using 'Listen 8808'
The apache error log is clear except for a warning that the ....
"pid file C:/xampp/apache/logs/httpd.pid overwritten -- Unclean shutdown of previous Apache run?"
The acces log shows me no record of the GET from the emonbase.....so my requests are not reaching the server.
I'll have a talk with some folks this evening on this and post my resolution here. Environment is windows XP pro. IIS is running on the same machine. I'd like to turn it off and confirm I can post using the default port assignments.
Eamonn.


The path to health is a personal one that is grounded in the cell. Fully functional cells make it possible to experience the comprehensive health that you and your patients are after. Our thoughtful approach to cellular health starts with ProOmega 2000—pure, triglyceride-form omega-3 EPA+DHA, formulated for high potency and maximum absorption.
Therapeutic Levels of EPA+DHA
An integral part of the cell membrane, omega-3 EPA+DHA play a significant role in modulating nearly every cellular activity.* These critical nutrients need to be continually replenished to help keep our cells functioning properly.* Our ProOmega® 2000 family of omega-3 concentrates packs up to 2000 mg EPA+DHA into two soft gels, making it easy for patients to achieve therapeutic amounts with a single serving.
Triglyceride Form for Easy Uptake
We take the extra step to formulate our concentrates in a highly absorbable, 90+% triglyceride form—the form naturally found in fish, and the form our bodies most easily recognize. Research shows that these omega-3s are absorbed up to 70% better than ethyl ester omega-3s. Our triglyceride fish oils also demonstrate nearly 20% better uptake into the body than other brands’ low-concentration oils.
Now with Vitamin D3
Vitamin D receptors are found in virtually every cell and tissue in the body. In fact, the presence of vitamin D3 has been shown to directly influence the cell’s production and release of critical proteins.* Combined, omega-3 EPA+DHA and vitamin D3 offer synergistic support for optimal cellular health.*


Real Court Televisionby Michael Asimow, UCLA Law School (September 1998) Here come the judges. Judge Judy, Peoples Court, and Judge Mills Lane are gaveling their way right through daytime TV with two more real court television shows about to debut. And then theres the spoof of Judge Judy now running on the Playboy Channel. Leading the pack is Judge Judy with the acerbic Judge Judy Scheindlin on the bench. This show is now in its fourth season. Judge Scheindlin was a New York family court judge for many years before becoming a TV star. The revival of Peoples Court is into its second season with former New York City mayor Ed Koch wielding the gavel. This fall Judge Mills Lane joined the pack. Judge Lane is a former Nevada state judge and boxing referee who labels himself "Americas judge." According to the Los Angeles Times, in a few weeks Judge Joe Brown (starring a Memphis judge) will debut. And, for a trip down memory lane, the beloved Judge Wapner (the old star of Peoples Court) is about to resurface in Animal Court on the Animal Planet cable network. As strange as this sounds, it will probably differ little from the other shows, which frequently feature disputes about pets. Earlier plans for former LA prosecutor Vince Bugliosi to host another real court show have apparently been scrapped. Judge Judy has received the ultimate tributeshes being spoofed by "Judge Julie" whose Sex Court is now running on the Playboy Channel. Judge Julie dresses in a much more provocative manner than her competition. According to Playboys website , one of Judge Julies cases concerns a woman whose boyfriend has a video of her between the sheets. Shes trying to prevent him from marketing the video. As a dedicated nonsubscriber to this premium channel, however, I cant give you any more information on Judge Julie. Real court shows involve actual, unscripted disputes between real people. A judge hears the testimony; after a commercial break, the judge hands down a decision. The judge handles the trial in an inquisitorial manner. There are no lawyers. The judge fires questions at the litigants (or the occasional non-party witness) in an attempt to get at the truth. The parties dont get to ask any questions. Typically the cases center on sharp disputes about credibility with each litigant calling the other a liar. The cases concern relatively small matters which can be easily understood but the litigants are passionately involved. Watching all three shows, I saw an assortment of the kinds of cases one would expect to see in small claims court.
The parties are compensated for their appearance on the shows in a way that preserves their incentives. Peoples Court explains that the litigants will share a fund (the size of which depends on the size of the amount in dispute). Depending on the judges decision, either the plaintiff or the defendant will get a larger share of the fund. Thus the defendant doesnt really have to pay the damages and the plaintiff gets paid something for her trouble even though she loses the case. Nevertheless the parties have a definite financial stake in the decision because the division of the fund depends on the judges decision.
There are substantial differences between the shows. Judge Judy is
extremely strict and maintains careful control of the trial. She does not allow the
litigants to interrupt one another. She feels free to lecture the parties, especially if
she senses that someone has acted irresponsibly. Indeed, she often tells them off. Judge Koch lets the parties mix it up morethey frequently get into shouting matches with each other and seem close to coming to blows on screen. However, he tries to joke around with the parties and renders his decision without berating them. Peoples Court is into gimmicks. You can email your opinion of how the trial is going and who should win. Thus we have a currently updated guide to the publics reaction. Attorney Harvey Levin views the trial in shopping malls with a dozen or so shoppers who are invited to express their opinions about the litigants and about the judges decision after its handed down. He also dispenses legal advice suggested by the dispute ("always get a receipt if you pay your rent in cash ") The litigants also have a chance to express their opinions about the verdict after its handed down.
Judge Lane is still developing his style; he seems more strict
than Koch but less strict than Scheindlin. His show is pretty plain vanilla and lacks
gimmicks. He does look very tough however, as befits a former Marine, boxer, and boxing
referee. (Lane was the referee in the infamous Mike Tyson-Evander Holyfield ear biting
fight). The question is why so many viewers are tuning into these shows. Personally, I find them both annoying and tedious. What am I missing? Judge Judy is whacking the competition in Los Angeles and appears twice each weekday. People are watching and there are plenty of sponsors. From the point of view of producers and local stations, obviously the shows are relatively cheap to stage, at least as compared to a soap opera. Yet whats the explanation for their appeal to viewers? I can think of several theories.
People seem obsessed with law and are fascinated by judges and trials; perhaps they feel that they will learn something useful for their own lives by watching the shows. Perhaps this curiosity was stoked by the endless TV coverage of the OJ trial. Peoples Court recognizes the function of the shows as self-help manuals by dispensing little dollops of legal advice after each case. Unlike talk shows, the real court shows have resolution. The judge always decides the case before our eyes. Somebody wins, somebody loses. But on a talk show, bad people can walk away without any consequences and victims dont get any redress. I think viewers hunger for quick, definitive resolutions to big messy problems. Another theory is that real court shows should be viewed as game shows. When you watch Jeopardy you match wits with the contestants. Here you match wits with the judge. Will the judge resolve the credibility dispute the same way you did? Did you know the law before the judge stated it? Will he/she apply the law the same way you would have applied it? In this sense, the court shows can be viewed as participatory. Peoples Court recognizes this important point by making itself interactive. You can actually register your opinion by sending an email and ordinary shoppers in the mall get to sound off about how they would have decided the case. A taste for verbal violence is also involved. The litigants get really nasty toward each other. And Judge Judy gets really nasty to them. Judge Koch doesnt abuse the litigants but he allows the litigants to yell at each other. Thus the same people who like professional wrestling or Jerry Springer may be attracted to real court shows. Its a bit like the pleasure of watching a barroom brawl when you dont have to get punched yourself. But something else is at work here. A key point is that real people are airing real disputes in an unscripted hearing. Viewers seem to have a hunger for this sort of realityto see the problems of people just like themselves.  More fundamentally, though, I think many people today are quite isolated. Daytime TV viewers may feel stuck at homeperhaps unemployed or retired, perhaps watching small kids. They may be lonely. They may not know anyone on their street, may have nobody to talk to on the phone, may be far from family. If they have a partner at all, that person is away for the day. As you watch the commercials on daytime TV for vocational schools or lawyers to help in your workers comp case, you get the feeling that a lot of people who are watching wish they could go to work. Real court shows offer a vicarious relationship with real people. This may be more enticing than watching actors play roles in fictitious stories on soap operas. How else to explain the enormous success of jennicam.org? For those who havent heard of it, this is one of the most popular sites on the internet. Its said to receive half a million hits per day. A young woman named Jenni works at home as a website designer. Cameras are running in her apartment 24 hours a day. And you just watch whatever shes doing; she may be sleeping, eating pizza, dressing, hanging out with her boyfriend, or playing with her cat. If you subscribe ($15 per year) you get a new picture two minutes. There are said to be ten to fifteen thousand "members." But you can pop in as a "guest" for free and get a picture thats updated every twenty minutes. Why are people interested in Jennis humdrum life? To me, it seems inexpressibly boring. I really cant say, but it must have something to do with the fact that Jenni is a real person who has opened up her life to anyone who cares to visit. And, people seem to have a hunger for human contacteven contact of this third-rate variety. In interviews, Jenni says that she gets a great amount of mail from people telling her their life story. Evidently, these people have decided that they really know her. [Warning: if you visit this site, avoid jennicam.com which is a hard-core pornography site free-riding on Jennis success. The correct address is jennicam.org] And then theres The Truman Show, one of this years truly outstanding films. As everyone must know, the premise of the film is that Truman Burbank (superbly played by Jim Carrey) is the star of a 24-hour a day soap opera but doesnt know it. Everyone else on the show, including his wife and boss, are acting but Truman goes about his life (on a gigantic set) thinking it is real. Personally, I found this one of the scariest movies I have ever seenbecause the premise is so horribly plausible. Especially the part about the huge worldwide audience that follows avidly every trivial detail of Trumans life. At this point, after watching the real court TV shows and pondering the success of jennicam.org, it is entirely believable that billions of people would actually care about watching Truman get up in the morning, eat his breakfast, chat with his "wife," greet his neighbors, and go to work. I would like to acknowledge the work of my student Samantha Slipock, whose excellent paper "Judge Judy and The Peoples Court: The Phenomenon of the Real Court Television Genre," drew my attention to these shows and furnished some of the material in this article. Her take on the popularity of the genre is that it feeds off of the unpopularity of lawyerspeople approve of a justice system without lawyers in which litigants and the judge come up with justice on their own. She also believes that the shows allow people to keep an eye on the court system which they distrust. Anyone who wants a copy of Ms. Slipocks paper can email me at<EMAIL_ADDRESS>and Ill send you a copy.
|


Instead of throwing waste you can do tons of things with waste like if you are throwing a ladder then instead of throwing it you can make it into a bookshelf.
There are tons tons of things that you can do with plastic bottles like create a broom with it or create a flower pot with it or even create wrist bands that you can wear. Some things like paper you can't really make things much out of that so instead oof throwing paper in the rubbish bin, throw it in the recycling bin.
Some people might have some old clothes that you didn't use and you want to throw it away. Then instead of throwing it away you can just give to poor people on the streets or donate it to charities which collect clothes, charities like crossroads in HK or any other charity you know then just contact them and tell them that you are donating something then 99.99% they will want your old clothes.


Adorable Indie Games
Made With ♥
Made With ♥
About
Hi there! We're Dovetail, a (very) tiny team of game designers and developers based in Vancouver, BC.
Our studio loves creating NES-inspired applications that are both a joy to watch as they are to play.
Games
Interested in what we're working on?
Since our soft launch in December 2018, our first title is still in the works. That being said, we're documenting the journey on our Dovetail Medium space. Follow along with us as we fumble (gracefully, hopefully) towards our first release!


| Synchronizing |
This feature is an original idea from a user of an older version of PopUp Killer.
With this feature you will be able to share your PopUp's with others as well as to download all the PopUp's that others have made available.To open the Synchronize dialog, simply select the Synchronize option from PUK's main menu.
To begin either the download or upload process, simply:
- Check the boxes for the operation(s) you would like to perform.
- Make sure you're connected to the Internet.
- And click the Start button.
- The rest of the process will run just automatically...
When clicking the Upload my PopUp's checkbox you'll receive a warning dialog.
This warning alerts you that PUK will upload your popups under a file with the name under which your copy of Windows was registered when it was installed.Your name, will NOT be used for anything.
Actually, the server automatically deletes PUK's uploads everyday.Anyway, if you don't like this, simply do not upload your popups.
NOTE: Uploading your black list to the server is no longer available.


Sai Baba, one of the foremost saints of modern India, lived in the small village of Shirdi in the state of Maharashtra for sixty years. Due to his presence there even after his Samadhi, today the small village has transformed itself as a great spiritual center to people from all religions. Shri Sai Baba, inspite of his great spiritual stature, never publicized himself through discoursing, touring and preaching unlike todays many so-called saints. Rather, he discouraged unnecessary publicity. But still, his spiritual perfection is still drawing innumerable devotees to him from all over the world. Even after his Samadhi in 1918, Sai Baba still continues to be a dynamic spiritual force which invokes countless devotees for their spiritual and material progress. Sai Baba did never reveal his original name, time and place of birth, especially his religion and caste, and even the names of his parents. Through this, he has emerged as a solution to all the religious and communal differences that are destroying the world today. He preaches that God is Almighty and he has given all the souls on earth equal opportunity to reach him, whichever is the religion they belong to. Sai Baba is the name given to him by his first devotee, Mahalsapathi Sai means Saint and Baba means Father. The name is just an expression of love, reverence and devotion. Sai Baba never discriminated between the rich and the poor. He was equally indifferent to honour or dishonour shown to him by the people. He used to utter the name of Allah frequently.


Goal Progress #{{$index + 1}} I am easily going to {{goal.name}} no later then {{goal.completeBy | date:'longDate' }}. Subgoals Progress I am easily going to {{subGoal.name}} no later then {{subGoal.completeBy | date:'longDate' }}.


This is the most simple example. Take a look at this page's source and the javascript source, to see how it works.
There is a hidden easter egg, see if you can figure it out :-).
Adding a watch field will give you better performance because it will only execute the computed expression when one of the watched properties has changed. In our trivial example below it will give you very little performance benefit, but for more complicated expressions it can give a significant speedup.
You can also do computed setters.
You can also combine getters and setters, make sure you add a watch array or you might get some unexpected behaviour.


{{ selectedStorage?.name }} of cloud storage and able to add more space
Can add and manage Sub Account
You'll be charged monthly including application taxes until you cancel your subscription.
Previous charges won't be refunded when you canceled unless it's legally required.
Your payment data is encrypted and secure. All amounts shown are in USD
Not refunds for subscription canceled between billing cycles.
I agree to the WTHApps Terms of Services and the Automatic Renewal terms above


---
layout: post
title: Rough storyboards tv series
date: '2018-06-01T13:17:48+02:00'
categories:
- Storyboards
picture_url: https://film-Storyboards.tumblr.com/post/174473079526/rough-Storyboards-tv-series
---
rough Storyboards, stunt sequence for The Crimson Rivers, TV series episode directed by Olivier Barma.


In our angular momentum lectures on the Wigner-Eckart theorem we developed two equations. One for the general expectation value that depends also on the magnetic quantum numbers $$ \langle \Phi^J_M|T^{\lambda}_{\mu}|\Phi^{J'}_{M'}\rangle\equiv(-1)^{J-M}\left(\begin{array}{ccc} J & \lambda & J' \\ -M & \mu & M'\end{array}\right)\langle \Phi^J||T^{\lambda}||\Phi^{J'}\rangle, $$ and one for the reduced matrix elements in terms of $$ \langle \Phi^J||T^{\lambda}||\Phi^{J'}\rangle\equiv\sum_{M,\mu,M'}(-1)^{J-M}\left(\begin{array}{ccc} J & \lambda & J' \\ -M & \mu & M'\end{array}\right)\langle \Phi^J_M|T^{\lambda}_{\mu}|\Phi^{J'}_{M'}\rangle. $$
Unless we have observables which depend on the magnetic quantum numbers, the degeneracy given by these quantum numbers is not seen experimentally. The typical situation when we perform shell-model calculations is that the results depend on the magnetic quantum numbers. The reason for this is that it is easy to implement the Pauli principle for many particles when we work in what we dubbed for \( m \)-scheme.
A resulting state in a shell-model calculations will thus depend on the total value of \( M \) defined as $$ M=\sum_{i=1}^{A}m_{j_i}. $$ A shell model many-body state is given by a linear combination of Slater determinants \( \vert \Phi_i\rangle \). That is, for some conserved quantum numbers \( \lambda \) we have $$ \vert Psi_{\lambda}\rangle = \sum_{i} C_i \vert \Phi_i\rangle, $$ where the coefficients are the overlaps between the many-body basis sets \( \Psi \) and \( \Phi \) and are the resulting eigenvectors from the shell-model calculations.
In second quantization, our ansatz for a state like the ground state is $$ \vert \Phi_0\rangle = \left(\prod_{i\le F}\hat{a}_{i}^{\dagger}\right)|0\rangle, $$ where the index \( i \) defines different single-particle states up to the Fermi level. We have assumed that we have \( N \) fermions. A given one-particle-one-hole (\( 1p1h \)) state can be written as $$ |\Phi_i^a\rangle = \hat{a}_{a}^{\dagger}\hat{a}_i|\Phi_0\rangle, $$ while a \( 2p2h \) state can be written as $$ |\Phi_{ij}^{ab}\rangle = \hat{a}_{a}^{\dagger}\hat{a}_{b}^{\dagger}\hat{a}_j\hat{a}_i|\Phi_0\rangle, $$ and a general \( NpNh \) state as $$ |\Phi_{ijk\dots}^{abc\dots}\rangle = \hat{a}_{a}^{\dagger}\hat{a}_{b}^{\dagger}\hat{a}_{c}^{\dagger}\dots\hat{a}_k\hat{a}_j\hat{a}_i|\Phi_0\rangle. $$
A general shell-model many-body state $$ \vert Psi_{\gamma}\rangle = \sum_{i} C_i \vert \Phi_i\rangle, $$ can be expanded as $$ |\Psi_{\gamma}\rangle=C_0|\Phi_0\rangle+\sum_{ai}C_i^a|\Phi_i^a\rangle+\sum_{abij}C_{ij}^{ab}|\Phi_{ij}^{ab}\rangle+\dots. $$
A one-body operator represented by a spherical tensor of rank \( \lambda \) is given as $$ O_{\mu}^{\lambda} = \sum_{pq} \langle p \vert O_{\mu}^{\lambda} \vert q \rangle a^{\dagger}_pa_q, $$ meaning that when we compute a transition amplitude $$ \langle \Psi_{\delta} \vert O_{\mu}^{\lambda} \vert \Psi_{\gamma} \rangle = \sum_{ij} C^{*}_{\delta i} C_{\gamma j} \langle \Phi_i \vert O_{\mu}^{\lambda} \vert \Phi_j\rangle, $$ we need to compute $$ \langle \Phi_i \vert O_{\mu}^{\lambda} \vert \Phi_j\rangle. $$
We want to rewrite $$ \langle \Phi_i \vert O_{\mu}^{\lambda} \vert \Phi_j\rangle, $$ in terms of the reduced matrix element only. Let us introduce the relevant quantum numbers for the states \( \Phi_i \) and \( \Phi_j \). We include only the relevant ones. We have then in \( m \)-scheme $$ \langle \Phi_i \vert O_{\mu}^{\lambda} \vert \Phi_j\rangle = \sum_{pq} \langle p \vert O_{\mu}^{\lambda} \vert q \rangle \langle \Phi_{M}^{J} \vert a^{\dagger}_pa_q \vert \Phi_{M'}^{J'}\rangle. $$ With a shell-model \( m \)-scheme basis it is straightforward to compute these amplitudes. However, as mentioned above, if we wish to related these elements to experiment, we need to use the Wigner-Eckart theorem and express the amplitudes in terms of reduced matrix elements.
We can rewrite the above transition amplitude using the Wigner-Eckart theorem. Our first step is to rewrite the one-body operator in terms of reduced matrix elements. Since the operator is a spherical tensor we need that the annihilation operator is rewritten as (where \( q \) represents \( j_q \), \( m_q \) etc) $$ \tilde{a}_q=\left(-1\right)^{j_q-m_q}a_{j_q,m_q}. $$ The operator $$ O_{\mu}^{\lambda} = \sum_{pq} \langle p \vert O_{\mu}^{\lambda} \vert q \rangle a^{\dagger}_pa_q, $$ is rewritten using the Wigner-Eckart theorem as $$ O_{\mu}^{\lambda} = \sum_{pq} \langle p \vert \vert O^{\lambda}\vert \vert q \rangle (-1)^{j_p-m_p}\left(\begin{array}{ccc} j_p & \lambda & j_q \\ -m_p & \mu & m_q\end{array}\right)a^{\dagger}_pa_q. $$
We have $$ O_{\mu}^{\lambda} = \sum_{pq} \langle p \vert \vert O^{\lambda}\vert \vert q \rangle (-1)^{j_p-m_p}\left(\begin{array}{ccc} j_p & \lambda & j_q \\ -m_p & \mu & m_q\end{array}\right)a^{\dagger}_pa_q. $$ We then single out the sum over \( m_p \) and \( m_q \) only and define the recoupled one-body part of the operator as $$ \lambda^{-1}\left[ a_{j_p}^{\dagger}\tilde{a}_{j_q}\right]^{\lambda}_{\mu} = \sum_{m_p,m_q} (-1)^{j_p-m_p}\left(\begin{array}{ccc} j_p & \lambda & j_q \\ -m_p & \mu & m_q\end{array}\right)a^{\dagger}_pa_q, $$ with \( \lambda=\sqrt{2\lambda+1} \). This gives the following expression for the one-body operator $$ O_{\mu}^{\lambda} = \sum_{j_pj_q} \langle p \vert \vert O^{\lambda}\vert \vert q \rangle \lambda^{-1}\left[ a_{j_p}^{\dagger}\tilde{a}_{j_q}\right]^{\lambda}_{\mu}. $$
With $$ O_{\mu}^{\lambda} = \sum_{j_pj_q} \langle p \vert \vert O^{\lambda}\vert \vert q \rangle \lambda^{-1}\left[ a_{j_p}^{\dagger}\tilde{a}_{j_q}\right]^{\lambda}_{\mu}, $$ we can write $$ \langle \Phi^J_M|O^{\lambda}_{\mu}|\Phi^{J'}_{M'}\rangle = \sum_{pq} \langle p \vert O_{\mu}^{\lambda} \vert q \rangle \langle \Phi_{M}^{J} \vert a^{\dagger}_pa_q \vert \Phi_{M'}^{J'}\rangle, $$ as $$ \langle \Phi^J_M|O^{\lambda}_{\mu}|\Phi^{J'}_{M'}\rangle = \sum_{j_pj_q} \langle p \vert \vert O^{\lambda} \vert\vert q \rangle \langle \Phi_{M}^{J}\vert \lambda^{-1}\left[ a_{j_p}^{\dagger}\tilde{a}_{j_q}\right]^{\lambda}_{\mu} \vert \Phi_{M'}^{J'}\rangle. $$ We have suppressed the summation over quantum numbers like \( n_p,n_q \) etc.
Using the Wigner-Eckart theorem $$ \langle \Phi^J_M|O^{\lambda}_{\mu}|\Phi^{J'}_{M'}\rangle\equiv(-1)^{J-M}\left(\begin{array}{ccc} J & \lambda & J' \\ -M & \mu & M'\end{array}\right)\langle \Phi^J||O^{\lambda}||\Phi^{J'}\rangle, $$ we can then define $$ \langle \Phi^J||O^{\lambda}||\Phi^{J'}\rangle = \lambda^{-1}\sum_{j_pj_q} \langle p \vert \vert O^{\lambda} \vert\vert q \rangle \langle \Phi_{M}^{J}\vert\vert \left[ a_{j_p}^{\dagger}\tilde{a}_{j_q}\right]^{\lambda}\vert \vert \Phi_{M'}^{J'}\rangle. $$ The quantity to the left in the last equation is normally called the transition amplitude or in case of a decay process, simply the decay amplitude. The quantity \( \langle \Phi_{M}^{J}\vert \lambda^{-1}\left[ a_{j_p}^{\dagger}\tilde{a}_{j_q}\right]^{\lambda}_{\mu} \vert \Phi_{M'}^{J'}\rangle \) is called the one-body transition density while the corresponding reduced one is simply called the reduced one-body transition density. The transition densities characterize the many-nucleon properties of the initial and final states. They do not carry information about the transition operator beyond its one-body character. Finally, note that in a shell-model calculation it is actually \( \langle \Phi^J_M|O^{\lambda}_{\mu}|\Phi^{J'}_{M'}\rangle \) which is calculated.
The reduced transition probability \( B \) is defined in terms of reduced matrix elements of a one-body operator by $$ B(i \rightarrow f)= \frac{\langle J_{f}||{\cal O}(\lambda )||J_{i}\rangle^{2}}{(2J_{i}+1)}. $$ With our definition of the reduced matrix element, $$ \langle J_{f}||{\cal O}(\lambda )||J_{i}\rangle^{2} =\langle J_{i}||{\cal O}(\lambda )||J_{f}\rangle^{2}, $$ the transition probability \( B \) depends upon the direction of the transition by the factor of \( (2J_{i}+1) \). For electromagnetic transitions \( J_{i} \) is that for the higher-energy initial state. But in Coulomb excitation the initial state is usually taken as the ground state, and it is normal to use the notation \( B(\uparrow) \) for transitions from the ground state.
The one-body operators \( {\cal O}(\lambda) \) represent a sum over the operators for the individual nucleon degrees of freedom \( i \) $$ {\cal O}(\lambda ) = \sum_{i} O(\lambda ,i). $$
The electric transition operator is given by $$ O(E\lambda ) = r^{\lambda } \; Y^{\lambda }_{\mu }(\hat{r}) \; e_{q} e, $$ were \( Y^{\lambda }_{\mu } \) are the spherical harmonics and \( q \) stands for proton \( q=p \) or neutron \( q=n \).
Gamma transitions with \( \lambda=0 \) are forbidden because the photon must carry off at least one unit of angular momentum. The \( e_{q} \) are the electric charges for the proton and neutron in units of \( e \). For the free-nucleon charge we would take \( e_{p}=1 \) and \( e_{n}=0 \), for the proton and neutron, respectively. Although the bare operator acts upon the protons, we will keep the general expression in terms of \( e_{q} \) in order to incorporate the effective charges for the proton and neutron, which represent the center-of-mass corrections and the average effects of the renormalization from wavefunction admixtures outside the model space.
The magnetic transition operator is given by: $$ O(M\lambda)=\left[\mathbf{l}\frac{2g^{l }_{q}}{(\lambda +1)}+ \mathbf{s}g^{s}_{q}\right]\mathbf{\nabla}[r^{\lambda }Y^{\lambda }_{\mu }(\hat{r})]\mu _{N} $$ $$ = \sqrt{\lambda (2\lambda +1)}\left[[Y^{\lambda -1}(\hat{r})\otimes \mathbf{l}\,]^{\lambda }_{\mu }\frac{2g^{l}_{q}}{(\lambda +1)} + [Y^{\lambda -1}(\hat{r})\otimes \mathbf{s}\,]^{\lambda }_{\mu }g^{s}_{q}\right]r^{\lambda -1}\mu _{N}, $$ where \( \mu_{N} \) is the nuclear magneton, $$ \mu _{N}=\frac{e\hbar }{2m_{p}c} = 0.105 \; e {\rm fm}, $$ and where \( m_{p} \) is the mass of the proton.
The g-factors \( g^{l}_{q} \) and \( g^{s}_{q} \) are the orbital and spin g-factors for the proton and neutron, respectively. The free-nucleon values for the g-factors are \( g^{l}_{p}=1 \), \( g^{l}_{n}=0 \), \( g^{s}_{p}=5.586 \) and \( g^{s}_{n}=-3.826 \). We may use effective values for these g-factors to take into account the truncation of the model space.
The most common types of transitions are \( E1 \), \( E2 \) and \( M1 \). The \( E1 \) transition operator is given by \( \lambda=1 \) $$ O(E1) = rY^{(1)}_{\mu }(\hat{r})e_{q} e= \sqrt{\frac{3}{4\pi }}\mathbf{r}e_{q} e. $$ The \( E2 \) transition operator with \( \lambda=2 \) $$ O(E2) = r^{2}Y^{(2)}_{\mu }(\hat{r})e_{q} e, $$
The \( M1 \) transition operator with \( \lambda=1 \) and with $$ Y^{0}=1/\sqrt{4\pi }, $$ we have $$ O(M1)=\sqrt{\frac{3}{4\pi }}[\mathbf{l}g^{l }_{q}+\mathbf{s} \; g^{s}_{q}]\mu _{N}. $$
The selection rules are given by the triangle condition for the angular momenta, \( \Delta(J_{i},J_{f},\lambda) \).
The electromagnetic interaction conserves parity, and the elements of the operators for \( E\lambda \) and \( M\lambda \) can be classified according to their transformation under parity change $$ \hat{P}\hat{O}\hat{P}^{-1}=\pi_{O}\hat{O}, $$ where we have \( \pi _{O}=(-1)^{\lambda } \) for \( Y^{\lambda } \), \( \pi _{O}=-1 \) for the vectors \( \mathbf{r} \), \( \mathbf{\nabla} \) and \( \mathbf{p} \), and \( \pi _{O}=+1 \) for the pseudo vectors \( \mathbf{l}=\mathbf{r}\times\mathbf{p} \) and \( \mathbf{\sigma} \). For a given matrix element we have: $$ \langle\Psi _{f}\vert {\cal O}\vert \Psi _{i}\rangle =\langle\Psi _{f}\vert P^{-1}P{\cal O}P^{-1}P\vert \Psi _{i}\rangle=\pi _{i}\pi _{f}\pi _{O} \langle\Psi _{f}\vert {\cal O}\vert \Psi _{i}\rangle. $$ The matrix element will vanish unless \( \pi _{i}\pi _{f}\pi _{O}=+1 \).
The transitions are divided into two classes, those which do not change parity change \( \pi _{i}\pi _{f}=+1 \) which go by the operators with \( \pi _{O}=+1 \): $$ \pi _{i}\pi _{f}=+1 \; \mathrm{for} \; M1, E2, M3, E4 \dots, $$ and the ones which do change parity change \( \pi _{i}\pi _{f}=-1 \) which go by the operators with \( \pi _{O}=-1 \): $$ \pi _{i}\pi _{f}=-1 \; \mathrm{for} \; E1, M2, E3, M4 \dots. $$
The electromagnetic moment operator can be expressed in terms of the electromagnetic transition operators. By the parity selection rule of the moments are nonzero only for \( M1 \), \( E2 \), \( M3 \), \( E4,\ldots \). The most common are: $$ \mu =\sqrt{\frac{4\pi }{3}}\langle J,M=J\vert {\cal O}(M1)\vert J,M=J\rangle= \sqrt{\frac{4\pi }{3}}\left\{\begin{array}{ccc} J & 1 &J \\ -J & 0 & J \end{array}\right\} \langle J\vert \vert {\cal O}(M1)\vert \vert J\rangle, $$ and $$ Q = \sqrt{\frac{16\pi }{5}}\langle J,M=J\vert {\cal O}(E2)\vert J,M=J\rangle= \sqrt{\frac{16\pi }{5}}\, \left(\begin{array}{ccc} {J}& {2} & {J}\\ {-J} & {0}& {J}\end{array}\right)\langle J\vert\vert {\cal O}(E2)\vert\vert J\rangle. $$
Electromagnetic transitions and moments depend upon the reduced nuclear matrix elements \( \langle f\vert\vert {\cal O}(\lambda )\vert\vert i\rangle \). These can be expressed as a sum over one-body transition densities (OBTD) times single-particle matrix elements $$ \langle f\vert\vert {\cal O}(\lambda )\vert\vert i\rangle =\sum _{k_{\alpha } k_{\beta }}\mathrm{OBTD}(f i k_{\alpha } k_{\beta } \lambda ) \langle k_{\alpha }\vert\vert O(\lambda )\vert\vert k_{\beta }\rangle, $$ where the OBTD is given by $$ \mathrm{OBTD}(f i k_{\alpha} k_{\beta}\lambda)= \frac{\langle f\vert\vert [a^{+}_{k_{\alpha }}\otimes \tilde{a}_{k_{\beta }}]^{\lambda }\vert\vert i\rangle}{\sqrt{(2\lambda +1)}}. $$ The labels \( i \) and \( f \) are a short-hand notation for the initial and final state quantum numbers \( (n \omega _{i}J_{i}) \) and \( (n\omega_{f}J_{f}) \), respectively. Thus the problem is divided into two parts, one involving the nuclear structure dependent one-body transition densities OBTD, and the other involving the reduced single-particle matrix elements (SPME).
The SPME for the \( E\lambda \) operator is given by $$ \langle k_{a}\vert\vert O(E\lambda )\vert\vert k_{b}\rangle=(-1)^{j_{a}+1/2}\frac{[1+(-1)^{l_{a}+\lambda +l_{b}}]}{2} $$ $$ \times\sqrt{ {(2j_{a}+1)(2\lambda +1)(2j_{b}+1)\over4\pi }}\left(\begin{array}{ccc} {j_{a}}& {\lambda} & {j_{b}}\\ {1/2} & {0}& {-1/2}\end{array}\right)\langle k_{a}\vert r^{\lambda }\vert k_{b}\rangle e_{q} e. $$
The SPME for the spin part of the magnetic operator is $$ \langle k_{a}\vert\vert O(M\lambda ,s)\vert\vert k_{b}\rangle = $$ $$ =\sqrt{\lambda (2\lambda +1)}< j_{a}\vert\vert [Y^{\lambda -1}(\hat{r})\otimes\mathbf{s}\,]^{\lambda }\vert\vert j_{b}> < k_{a}\vert r^{\lambda -1}\vert k_{b}>g^{s}_{q}\mu _{N}, $$ $$ = \sqrt{\lambda (2\lambda +1)}\, \sqrt{(2j_{a}+1)(2j_{b}+1)(2\lambda +1)}\left\{\begin{array}{ccc} {l _{a}}& {1/2} & {j_{a}}\\ {l _{b}}& {1/2} & {j_{b}}\\ {\lambda -1} & {1} & {\lambda}\end{array}\right\} $$ $$ \times \langle l _{a}\vert\vert Y^{\lambda -1}(\hat{r})\vert\vert l _{b}\rangle\langle\vert\vert \mathbf{s}\vert\vert s\rangle\langle k_{a}\vert r^{\lambda -1}\vert k_{b}\rangle g^{s}_{q}\mu _{N}, $$ where $$ \langle\vert\vert \mathbf{s}\vert\vert s\rangle = \sqrt{3/2}. $$
The SPME for the orbital part of the magnetic operator is: $$ \langle k_{a}\vert\vert O(M\lambda ,l )\vert\vert k_{b}\rangle= $$ $$ = \frac{\sqrt{\lambda (2\lambda +1)}\, }{\lambda +1} \langle j_{a}\vert\vert [Y^{\lambda -1}(\hat{r})\otimes\mathbf{l}\,]^{\lambda }\vert\vert j_{b}\rangle \langle k_{a}\vert r^{\lambda -1}\vert k_{b}\rangle g^{l }_{q}\mu _{N} $$ $$ =\frac{\sqrt{\lambda (2\lambda +1)}\, }{\lambda +1}(-1)^{l _{a}+1/2+j_{b}+\lambda } \sqrt{(2j_{a}+1)(2j_{b}+1)} $$ $$ \times\left\{\begin{array}{ccc} {l _{a}} & {l _{b}} & {\lambda} \\ {j_{b}}& {j_{a}}& {1/2}\end{array}\right\} \langle l _{a}\vert\vert [Y^{\lambda -1}(\hat{r})\otimes\mathbf{l}\,]^{\lambda }\vert\vert l _{b}\rangle \langle k_{a}\vert r^{\lambda -1}\vert k_{b}\rangle g^{l }_{q}\mu _{N}, $$
where we have defined $$ \langle l _{a}\vert\vert [Y^{\lambda -1}(\hat{r})\otimes\mathbf{l}]^{\lambda }\vert\vert l _{b}\rangle=(-1)^{\lambda +l _{a}+l _{b}} \sqrt{(2\lambda +1)l _{b}(l _{b}+1)(2l _{b}+1)} $$ $$ \times\left\{\begin{array}{ccc} {\lambda -1} & {1}& {\lambda}\\ {l _{b}}& {l _{a}} & {l _{b}} \end{array}\right\} \langle l _{a}\vert\vert Y^{\lambda -1}(\hat{r})\vert\vert l _{b}\rangle, $$ with $$ \langle l _{a}\vert\vert Y^{\lambda -1}(\hat{r})\vert\vert l _{b}\rangle=(-1)^{l _{a}} \sqrt{\frac{(2l _{a}+1)(2l _{b}+1)(2\lambda -1)}{4\pi }}\left(\begin{array}{ccc} {l _{a}} & {\lambda -1} & {l _{b}}\\ {0} & {0}& {0}\end{array}\right) . $$
For the \( M1 \) operator the radial matrix element is $$ < k_{a}\vert r^{0}\vert k_{b}>\, = \delta _{n_{a},n_{b}}, $$ and the SPME simplify to: $$ \langle k_{a}\vert\vert O(M1,s)\vert\vert k_{b}\rangle=\sqrt{ \frac{3}{4\pi }}\langle j_{a}\vert\vert \mathbf{s}\,\vert\vert j_{b}\rangle \delta _{n_{a},n_{b}}g^{s}_{q}\mu_{N} $$ $$ =\sqrt{ \frac{3}{4\pi }}(-1)^{l _{a}+j_{a}+3/2} \sqrt{(2j_{a}+1)(2j_{b}+1)}\left\{\begin{array}{ccc} {1/2}& {1/2} & {1} \\ {j_{b}} & {j_{a}}& {l _{a}}\end{array}\right\} $$ $$ \times\langle s\vert\vert \mathbf{s}\vert\vert s\rangle \delta _{l _{a},l _{b}} \delta _{n_{a},n_{b}}g^{s}_{q}\mu _{N}, $$
where we have $$ < s\vert\vert \mathbf{s}\,\vert\vert s>\, = \sqrt{3/2}\, , $$ and $$ < k_{a}\vert\vert O(M1,l )\vert\vert k_{b}>\, = \sqrt{ \frac{3}{4\pi }}\, < j_{a}\vert\vert \mathbf{l}\,\vert\vert j_{b}> \delta _{n_{a},n_{b}} \; g^{l }_{q} \; \mu _{N} $$ $$ =\sqrt{ \frac{3}{4\pi }}\, (-1)^{l _{a}+j_{b}+3/2} \sqrt{(2j_{a}+1)(2j_{b}+1)}\, \left\{\begin{array}{ccc} {l _{a}}& {l _{b}} & {1}\\ {j_{b}}& {j_{a}}& {1/2}\end{array}\right\} $$ $$ \times\langle l _{a}\vert\vert \mathbf{l}\,\vert\vert l _{b}\rangle \delta _{n_{a},n_{b}}g^{l }_{q}\mu _{N} , $$ where $$ \langle l _{a}\vert\vert \mathbf{l}\,\vert\vert l _{b}\rangle = \delta _{l _{a},l _{b}} \sqrt{l _{a}(l_{a}+1)(2l _{a}+1)}. $$ Thus the \( M1 \) operator connects only those orbitals which have the same \( n \) and \( l \) values.
We will now focus on allowed \( \beta \)-decay. Suhonen's chapter 7 and Alex Brown's chapter 29 cover much of the material to be discussed on \( \beta \)-decay.
The allowed beta decay rate \( W \) between a specific set of initial and final states is given by $$ W_{i,f} = (f/K_{o}) \left[ g_{V}^{2} \; B_{i,f}(F_{\pm})+ g_{A}^{2}B_{i,f}(GT_{\pm})\right], $$ where \( f \) is dimensionless three-body phase-space factor which depends upon the beta-decay \( Q \) value, and \( K_{o} \) is a specific combination of fundamental constants $$ K_{o}=\frac{2\pi^{3}\hbar^{7}}{ m_{e}^{5} c^{4}}= 1.8844 \times 10^{-94}\mathrm{erg}^{2}\mathrm{cm}^{6}\mathrm{s}. $$ The \( \pm \) signrefer to \( \beta_{\pm} \) decay of nucleus \( (A_{i},Z_{i}) \) into nucleus \( (A_{i},Z_{i} \mp 1) \). The weak-interaction vector (\( V \)) and axial-vector (\( A \)) coupling constants for the decay of neutron into a proton are denoted by \( g_{V} \) and \( g_{A} \), respectively.
The total decay rate for a given initial state is obtained by summing the partial rates over all final states $$ W = \displaystyle\sum _{f} W_{if}, $$ with the branching fraction to a specific final state given by $$ b_{if} = \frac{W_{if}}{W}. $$ Beta decay lifetime are usually given in terms of the half-life with a total half-life of $$ T_{1/2} = \frac{{\rm ln}(2)}{W}. $$ The partial half-life for a particular final state will be denoted by \( t_{1/2} \) $$ t_{1/2} = \frac{T_{1/2}}{b_{if}}. $$
Historically one combines the partial half-life for a particular decay with the calculated phase-space factor \( f \) to obtain an ft value given by $$ f t_{1/2}=\frac{C }{\left[B(F_{\pm})+(g_{A}/g_{V})^{2} B(GT_{\pm}) \right] } $$ where $$ C = \frac{{\rm ln}(2)K_{o}}{(g_{V})^{2}}. $$
One often compiles the allowed beta decay in terms of a logft which stands for log$_{10}$ of the \( ft_{1/2} \) value.
The values of the coupling constants for Fermi decay, \( g_{V} \), and Gamow-Teller decay, \( g_{A} \) are obtained as follows. For a \( 0^{+} \rightarrow 0^{+} \) nuclear transition \( B(GT)=0 \), and for a transition between \( T=1 \) analogue states with \( B(F)=2 \) we find $$ C = 2 t_{1/2} f. $$ The partial half-lives and \( Q \) values for several \( 0^{+} \rightarrow 0^{+} \) analogue transitions have been measured to an accuracy of about one part in 10000. With phase space factors one obtains $$ C = 6170(4) $$ This result, together with the value of \( K_{o} \) can be used to obtain \( g_{V} \).
At the quark level \( g_{V}=-g_{A} \). But for nuclear structure we use the value obtained from the neutron to proton beta decay $$ \vert g_{A}/g_{V}\vert = 1.261(8). $$
The operator for Fermi beta decay in terms of sums over the nucleons is $$ {\cal O}(F_{\pm}) = \displaystyle\sum _{k} t_{k\pm}. $$ The matrix element is $$ B(F) =\, \vert \langle f\vert T_{\pm} \vert i\rangle\vert ^{2}, $$ where $$ T_{\pm} = \sum _{k} t_{\pm} $$ is the total isospin raising and lowering operator for total isospin constructed out of the basic nucleon isospin raising and lowering operators $$ t_{-}\vert n\rangle=\vert p\rangle \hspace{1cm} t_{-}\vert p\rangle= 0, $$ and $$ t_{+}\vert p\rangle=\vert n\rangle, \;\; t_{+}\vert n\rangle= 0. $$
The matrix elements obey the triangle conditions \( J_{f}=J_{i} \) (\( \Delta J=0 \)). The Fermi operator has \( \pi _{O}=+1 \), and thus the initial and final nuclear states must have \( \pi _{i}\pi _{f}=+1 \) for the matrix element to be nonzero under the parity transform.
When isospin is conserved the Fermi matrix element must obey the isospin triangle condition \( T_{f}=T_{i} \) $(\Delta T=0)$, and the Fermi operator can only connect isobaric analogue states.
For \( \beta_{-} \) decay $$ T_{-}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}\rangle $$ $$ = \sqrt{(T_{i}(T_{i}+1)-T_{zi}(T_{zi}-1)}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}-1\rangle, $$ and $$ B(F_{-}) =\, \vert \langle \omega _{f},J_{f},M_{f},T_{f},T_{zi}-1\vert T_{-}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}\rangle\vert ^{2} $$ $$ = [T_{i}(T_{i}+1)-T_{zi}(T_{zi}-1)] \delta _{\omega _{f},\omega }\;\delta _{J_{i},J_{f}}\;\delta _{M_{i},M_{f}}\;\delta _{T_{i},T_{f}}. $$
For \( \beta_{ + } \) we have $$ B(F_{+}) =\, \vert \langle \omega _{f},J_{f},M_{f},T_{f},T_{zi}+1\vert T_{+}\vert \omega _{i},J_{i},M_{i},T_{i},T_{zi}\rangle\vert ^{2} $$ $$ = [T_{i}(T_{i}+1)-T_{zi}(T_{zi}+1)] \delta _{\omega _{f},\omega }\;\delta _{J_{i},J_{f}}\delta _{M_{i},M_{f}}\delta _{T_{i},T_{f}}. $$ For neutron-rich nuclei (\( N_{i}> Z_{i} \)) we have \( T_{i}=T_{zi} \) and thus $$ B(F_{-})(N_{i}> Z_{i}) = 2T_{zi} = (N_{i}-Z_{i})\delta _{\omega _{f},\omega }\delta _{J_{i},J_{f}}\;\delta _{M_{i},M_{f}}\;\delta _{T_{i},T_{f}}, $$ and $$ B(F_{+})(N_{i}> Z_{i}) = 0. $$
The reduced single-particle matrix elements are given by $$ \langle k_{a},p\vert\vert \sigma t_{-}\vert\vert k_{b},n\rangle=\langle k_{a},n\vert\vert \sigma t_{+}\vert\vert k_{b},p\rangle= 2\langle k_{a}\vert\vert \mathbf{s}\vert\vert k_{b}\rangle, $$ where the matrix elements of \( \mathbf{s} \) are given by $$ \langle k_{a}\vert\vert \mathbf{s}\vert\vert k_{b}\rangle=\langle j_{a}\vert\vert \mathbf{s}\vert\vert j_{b}\rangle \delta_{n_{a},n_{b}} $$ $$ =(-1)^{l_{a}+j_{a}+3/2} \sqrt{(2j_{a}+1)(2j_{b}+1)}\left\{\begin{array}{ccc} {1/2}& {1/2}& {1} \\ {j_{b}}& {j_{a}}& {l_{a}}\end{array}\right\} \langle s\vert\vert \mathbf{s}\,\vert\vert s\rangle \delta _{\ell _{a},\ell _{b}} \delta_{n_{a},n_{b}} , $$ with $$ \langle s\vert\vert \mathbf{s}\vert\vert s\rangle= \sqrt{3/2}. $$
The matrix elements of \( \mathbf{s} \) has the selection rules \( \delta_{ \ell_{a} , \ell_{b} } \) and \( \delta_{n _{a} ,n _{b} } \). Thus the orbits which are connected by the GT operator are very selective; they are those in the same major oscillator shell with the same \( \ell \) value. The matrix elements such as \( 1s_{1/2}-0d_{3/2} \) which have the allowed \( \Delta j \) coupling but are zero due to the \( \Delta\ell \) coupling are called \( \ell \)-forbidden matrix elements.
Sum rules for Fermi and Gamow-Teller matrix elements can be obtained easily.
The sum rule for Fermi is obtained from the sum $$ \sum _{f} \left[ B_{fi}(F_{-}) - B_{fi}(F_{+}) \right] =\sum _{f} \left[ \vert \langle f\vert T_{-} \vert i\rangle\vert ^{2} - \vert \langle f\vert T_{+} \vert i\rangle\vert ^{2} \right] $$ The final states \( f \) in the \( T_{-} \) matrix element go with the \( Z_{f}=Z_{i}+1 \) nucleus and those in the \( T_{+} \) matrix element to with the \( Z_{f}=Z_{i}-1 \) nucleus. One can explicitly sum over the final states to obtain $$ \sum _{f} \left[ \langle i\vert T_{+} \vert f\rangle \langle f\vert T_{-}\vert i\rangle - \langle i\vert T_{-} \vert f\rangle \langle f\vert T_{+}\vert i\rangle \right] $$ $$ = \langle i\vert T_{+} T_{-} - T_{-} T_{+}\vert i\rangle =\langle i\vert 2T_{z}\vert i\rangle = (N_{i}-Z_{i}). $$
The sum rule for Gamow-Teller is obtained as follows $$ \sum_{f,\mu} \vert \langle f\vert \sum_{k} \sigma_{k,\mu} t_{k-} \vert i\rangle\vert^{2} - \sum_{f,\mu} \vert \langle f\vert \sum_{k} \sigma_{k,\mu } t_{k+} \vert i\rangle\vert^{2} $$ $$ = \sum_{f,\mu}\langle i\vert \sum_{k} \sigma_{k,\mu} t_{k+} \vert f\rangle\langle f\vert \sum_{k'} \sigma_{k',\mu} t_{k'-} \vert i\rangle $$ $$ - \sum_{f,\mu} \langle i\vert \sum_{k} \sigma_{k,\mu } t_{k-} \vert f\rangle\langle f\vert\sum_{k'} \sigma_{k',\mu } t_{k'+} \vert i\rangle $$ $$ = \sum_{\mu} \left[\langle i\vert \left(\sum _{k} \sigma_{k,\mu} t_{k+} \right) \left( \sum_{k'} \sigma_{k',\mu} t_{k'-}\right) - \left( \sum_{k} \sigma_{k,\mu} t_{k-} \right) \left( \sum_{k'} \sigma_{k',\mu} t_{k'+} \right) \vert i\rangle \right] $$ $$ = \sum_{\mu } \langle i\vert \sum_{k} \sigma ^{2}_{k,\mu } \left[ t_{k+} t_{k-} - t_{k-} t_{k+} \right] \vert i\rangle = 3 \langle i\vert \sum_{k} \left[ t_{k+} t_{k-} - t_{k-} t_{k+} \right] \vert i\rangle $$ $$ = 3\langle i\vert T_{+} T_{-} - T_{-} T_{+}\vert i\rangle= 3\langle i\vert 2T_{z}\vert i\rangle = 3(N_{i}-Z_{i}). $$
We have used the fact that \( \sigma ^{2}_{x} = \sigma ^{2}_{y}=\sigma ^{2}_{z}=1 \). When \( k \neq k' \) the operators commute and cancel. Thus $$ \sum_{f} \left[B_{fi}(F_{-}) - B_{fi}(F_{+}) \right] = (N_{i}-Z_{i}), $$ and $$ \sum_{f} \left[ B_{fi}(GT_{-}) - B_{fi}(GT_{+}) \right] = 3(N_{i}-Z_{i}). $$
The sum-rule for the Fermi matrix elements applies even when isospin is not conserved.
For \( N > Z \) we usually have \( T_{i}=T_{zi} \) which means that \( B(F_{+})=0 \).
For \( N=Z (T_{zi}=0) \) and \( T_{i}=0 \) we get \( B(F_{+})=B(F_{-})=0 \), and for \( T_{i}=1 \) we have \( B(F_{+}) = B(F_{-}) = 2 \). Fermi transitions which would be zero if isospin is conserved are called isospin-forbidden Fermi transitions.
When \( N > Z \) there are some situations where one has \( B(GT_{+})=0 \), and then we obtain \( B(GT_{-}) = 3(N_{i}-Z_{i}) \). In particular for the \( \beta_{-} \) decay of the neutron we have \( B(F_{-})=1 \) and \( B(GT_{-})=3 \).
We need to say something about so-called core-polarization effects. To do this, we have to introduce elements from many-body perturbation theory.
We assume here that we are only interested in the ground state of the system and expand the exact wave function in term of a series of Slater determinants $$ \vert \Psi_0\rangle = \vert \Phi_0\rangle + \sum_{m=1}^{\infty}C_m\vert \Phi_m\rangle, $$ where we have assumed that the true ground state is dominated by the solution of the unperturbed problem, that is $$ \hat{H}_0\vert \Phi_0\rangle= W_0\vert \Phi_0\rangle. $$ The state \( \vert \Psi_0\rangle \) is not normalized, rather we have used an intermediate normalization \( \langle \Phi_0 \vert \Psi_0\rangle=1 \) since we have \( \langle \Phi_0\vert \Phi_0\rangle=1 \).
The Schroedinger equation is $$ \hat{H}\vert \Psi_0\rangle = E\vert \Psi_0\rangle, $$ and multiplying the latter from the left with \( \langle \Phi_0\vert \) gives $$ \langle \Phi_0\vert \hat{H}\vert \Psi_0\rangle = E\langle \Phi_0\vert \Psi_0\rangle=E, $$ and subtracting from this equation $$ \langle \Psi_0\vert \hat{H}_0\vert \Phi_0\rangle= W_0\langle \Psi_0\vert \Phi_0\rangle=W_0, $$ and using the fact that the both operators \( \hat{H} \) and \( \hat{H}_0 \) are hermitian results in $$ \Delta E=E-W_0=\langle \Phi_0\vert \hat{H}_I\vert \Psi_0\rangle, $$ which is an exact result. We call this quantity the correlation energy.
This equation forms the starting point for all perturbative derivations. However, as it stands it represents nothing but a mere formal rewriting of Schroedinger's equation and is not of much practical use. The exact wave function \( \vert \Psi_0\rangle \) is unknown. In order to obtain a perturbative expansion, we need to expand the exact wave function in terms of the interaction \( \hat{H}_I \).
Here we have assumed that our model space defined by the operator \( \hat{P} \) is one-dimensional, meaning that $$ \hat{P}= \vert \Phi_0\rangle \langle \Phi_0\vert , $$ and $$ \hat{Q}=\sum_{m=1}^{\infty}\vert \Phi_m\rangle \langle \Phi_m\vert . $$
We can thus rewrite the exact wave function as $$ \vert \Psi_0\rangle= (\hat{P}+\hat{Q})\vert \Psi_0\rangle=\vert \Phi_0\rangle+\hat{Q}\vert \Psi_0\rangle. $$ Going back to the Schr\"odinger equation, we can rewrite it as, adding and a subtracting a term \( \omega \vert \Psi_0\rangle \) as $$ \left(\omega-\hat{H}_0\right)\vert \Psi_0\rangle=\left(\omega-E+\hat{H}_I\right)\vert \Psi_0\rangle, $$ where \( \omega \) is an energy variable to be specified later.
We assume also that the resolvent of \( \left(\omega-\hat{H}_0\right) \) exits, that is it has an inverse which defined the unperturbed Green's function as $$ \left(\omega-\hat{H}_0\right)^{-1}=\frac{1}{\left(\omega-\hat{H}_0\right)}. $$
We can rewrite Schroedinger's equation as $$ \vert \Psi_0\rangle=\frac{1}{\omega-\hat{H}_0}\left(\omega-E+\hat{H}_I\right)\vert \Psi_0\rangle, $$ and multiplying from the left with \( \hat{Q} \) results in $$ \hat{Q}\vert \Psi_0\rangle=\frac{\hat{Q}}{\omega-\hat{H}_0}\left(\omega-E+\hat{H}_I\right)\vert \Psi_0\rangle, $$ which is possible since we have defined the operator \( \hat{Q} \) in terms of the eigenfunctions of \( \hat{H} \).
These operators commute meaning that $$ \hat{Q}\frac{1}{\left(\omega-\hat{H}_0\right)}\hat{Q}=\hat{Q}\frac{1}{\left(\omega-\hat{H}_0\right)}=\frac{\hat{Q}}{\left(\omega-\hat{H}_0\right)}. $$ With these definitions we can in turn define the wave function as $$ \vert \Psi_0\rangle=\vert \Phi_0\rangle+\frac{\hat{Q}}{\omega-\hat{H}_0}\left(\omega-E+\hat{H}_I\right)\vert \Psi_0\rangle. $$ This equation is again nothing but a formal rewrite of Schr\"odinger's equation and does not represent a practical calculational scheme. It is a non-linear equation in two unknown quantities, the energy \( E \) and the exact wave function \( \vert \Psi_0\rangle \). We can however start with a guess for \( \vert \Psi_0\rangle \) on the right hand side of the last equation.
The most common choice is to start with the function which is expected to exhibit the largest overlap with the wave function we are searching after, namely \( \vert \Phi_0\rangle \). This can again be inserted in the solution for \( \vert \Psi_0\rangle \) in an iterative fashion and if we continue along these lines we end up with $$ \vert \Psi_0\rangle=\sum_{i=0}^{\infty}\left\{\frac{\hat{Q}}{\omega-\hat{H}_0}\left(\omega-E+\hat{H}_I\right)\right\}^i\vert \Phi_0\rangle, $$ for the wave function and $$ \Delta E=\sum_{i=0}^{\infty}\langle \Phi_0\vert \hat{H}_I\left\{\frac{\hat{Q}}{\omega-\hat{H}_0}\left(\omega-E+\hat{H}_I\right)\right\}^i\vert \Phi_0\rangle, $$ which is now a perturbative expansion of the exact energy in terms of the interaction \( \hat{H}_I \) and the unperturbed wave function \( \vert \Psi_0\rangle \).
In our equations for \( \vert \Psi_0\rangle \) and \( \Delta E \) in terms of the unperturbed solutions \( \vert \Phi_i\rangle \) we have still an undetermined parameter \( \omega \) and a dependecy on the exact energy \( E \). Not much has been gained thus from a practical computational point of view.
In Brilluoin-Wigner perturbation theory it is customary to set \( \omega=E \). This results in the following perturbative expansion for the energy \( \Delta E \) $$ \Delta E=\sum_{i=0}^{\infty}\langle \Phi_0\vert \hat{H}_I\left\{\frac{\hat{Q}}{\omega-\hat{H}_0}\left(\omega-E+\hat{H}_I\right)\right\}^i\vert \Phi_0\rangle= $$ $$ \langle \Phi_0\vert \left(\hat{H}_I+\hat{H}_I\frac{\hat{Q}}{E-\hat{H}_0}\hat{H}_I+ \hat{H}_I\frac{\hat{Q}}{E-\hat{H}_0}\hat{H}_I\frac{\hat{Q}}{E-\hat{H}_0}\hat{H}_I+\dots\right)\vert \Phi_0\rangle. $$
$$ \Delta E=\sum_{i=0}^{\infty}\langle \Phi_0\vert \hat{H}_I\left\{\frac{\hat{Q}}{\omega-\hat{H}_0}\left(\omega-E+\hat{H}_I\right)\right\}^i\vert \Phi_0\rangle=$$ $$ \langle \Phi_0\vert \left(\hat{H}_I+\hat{H}_I\frac{\hat{Q}}{E-\hat{H}_0}\hat{H}_I+ \hat{H}_I\frac{\hat{Q}}{E-\hat{H}_0}\hat{H}_I\frac{\hat{Q}}{E-\hat{H}_0}\hat{H}_I+\dots\right)\vert \Phi_0\rangle. $$ This expression depends however on the exact energy \( E \) and is again not very convenient from a practical point of view. It can obviously be solved iteratively, by starting with a guess for \( E \) and then solve till some kind of self-consistency criterion has been reached.
Actually, the above expression is nothing but a rewrite again of the full Schr\"odinger equation.
Inserted in the expression for \( \Delta E \) leads to $$ \Delta E= \langle \Phi_0\vert \hat{H}_I+\hat{H}_I\hat{Q}\frac{1}{E-\hat{H}_0-\hat{Q}\hat{H}_I\hat{Q}}\hat{Q}\hat{H}_I\vert \Phi_0\rangle. $$ In RS perturbation theory we set \( \omega = W_0 \) and obtain the following expression for the energy difference $$ \Delta E=\sum_{i=0}^{\infty}\langle \Phi_0\vert \hat{H}_I\left\{\frac{\hat{Q}}{W_0-\hat{H}_0}\left(\hat{H}_I-\Delta E\right)\right\}^i\vert \Phi_0\rangle= $$ $$ \langle \Phi_0\vert \left(\hat{H}_I+\hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}(\hat{H}_I-\Delta E)+ \hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}(\hat{H}_I-\Delta E)\frac{\hat{Q}}{W_0-\hat{H}_0}(\hat{H}_I-\Delta E)+\dots\right)\vert \Phi_0\rangle. $$
Recalling that \( \hat{Q} \) commutes with \( \hat{H_0} \) and since \( \Delta E \) is a constant we obtain that $$ \hat{Q}\Delta E\vert \Phi_0\rangle = \hat{Q}\Delta E\vert \hat{Q}\Phi_0\rangle = 0. $$ Inserting this results in the expression for the energy results in $$ \Delta E=\langle \Phi_0\vert \left(\hat{H}_I+\hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}\hat{H}_I+ \hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}(\hat{H}_I-\Delta E)\frac{\hat{Q}}{W_0-\hat{H}_0}\hat{H}_I+\dots\right)\vert \Phi_0\rangle. $$
We can now this expression in terms of a perturbative expression in terms of \( \hat{H}_I \) where we iterate the last expression in terms of \( \Delta E \) $$ \Delta E=\sum_{i=1}^{\infty}\Delta E^{(i)}. $$ We get the following expression for \( \Delta E^{(i)} \) $$ \Delta E^{(1)}=\langle \Phi_0\vert \hat{H}_I\vert \Phi_0\rangle, $$ which is just the contribution to first order in perturbation theory, $$ \Delta E^{(2)}=\langle\Phi_0\vert \hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}\hat{H}_I\vert \Phi_0\rangle, $$ which is the contribution to second order.
$$ \Delta E^{(3)}=\langle \Phi_0\vert \hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}\hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}\hat{H}_I\Phi_0\rangle- \langle\Phi_0\vert \hat{H}_I\frac{\hat{Q}}{W_0-\hat{H}_0}\langle \Phi_0\vert \hat{H}_I\vert \Phi_0\rangle\frac{\hat{Q}}{W_0-\hat{H}_0}\hat{H}_I\vert \Phi_0\rangle, $$ being the third-order contribution.
I hope this is not the case


Jason Vorhees
How could anyone write about Slasher films and not mention the destructive mommas boy? Terrorizing Crystal lake ever since he grew up in the wilderness after witnessing his mom die to the hands of a counselor she was trying to kill.  That is one ki ki ki-lling story!
Ghostface
The prepare for trouble, and make it double slasher of the more modern-day screens! Instead of the usual ridiculous psycho that's seen in the genre, Ghostface brought a little realism, as much as a slasher can, by employing a double killer aspect to the antagonist. Always a different duo in every movie of the franchise, how all of them know what I did last Summer? I'll never know.
Chucky
Bad dude, immortal inside of a doll after almost dying, and then going around like Stewie with free-reign causing multiples of murders. Now after a boy that has been instutionalized after trying to report this black magic criminals new found body, this killer's like a horror based Freaky Friday that can't not be mentioned for its silly tone and comedic kills.


Share Your Interest
We've made it even easier to share your interests with your friends! Whether you’ve moved to a new town, started a hobby, entered a new phase of life or just want to make some new friends, My Top Nine makes it easy to connect with people who have similar passions to your own.


Michelle Obama Recruits Selena Gomez, Megan Rapinoe for Voter Outreach Drive
NEW YORK (AP) — Election Day is over, but Michelle Obama is still trying to get out the vote.
by Breitbart NewsThe former first lady announced that Selena Gomez, Liza Koshy, Shonda Rhimes, Megan Rapinoe, Tracee Ellis Ross and Kerry Washington have signed on as co-chairs of the national organization When We All Vote.
Obama is already a co-chair, along with Lin-Manuel Miranda, Faith Hill, Tom Hanks and wife Rita Wilson, and basketball star Chris Paul.
When We Vote bills itself as a nonpartisan group dedicated to increasing voter participation. The announcement Thursday marks a year until the date of the 2020 elections, which includes the presidential race.
The organization was founded in 2018.
Hanks said “registering new voters is an act of hope and taking part in the American idea.” He added that voting guarantees the blessings of “liberty for the grandkids.”


AMAZING PEOPLE ARE MAKING AMAZING DESIGNS IN A FUN ENVIRONMENT
When you work with us you are part of a team of committed collaborators. All aspects of our software development process are integrated,interactive and agile
Our approach unifies design, development and product management to create exceptional products
We start each project by understanding your business goals,the user's needs and the product requirements
Then we help translate them into effective elegant solutions
Before we sign a contract or even write a line of code our team will spend the necessary time needed to understand your product vision
The outcome of this scoping session is a proposals or high-levle statement of work.
Based on your requirements, we can provide a complete offering or just the pieces you need
Our design practice offers a full range of services including brand strategy, interaction and visual design and user experience testing. Throughout your project, our designers create and implement visual design and workflows, solicit user feedback and work with you to make sure what gets built is what is needed.
All engineers are fluent in the latest enterprise, mobile and web development technologies. They collaborate with your team to write, and improve code on a daily basis, using proven practices such as test-driven development and pair programming.
Planning and development is iterative. Because we are constantly coding and testing, the products we build are always ready to go live. This iterative process allows for changes as business requirements evolve.
DELANI STUDIO
2020


Instead of packing to a buffer, and subsequently storing data to a
file, you can directly pack to a file by passing the filename and
openmode arguments to pack or xdr_pack
's constructor. The arguments
are identical to that of fopen:
{ pack_t checkpoint("foo.ckpt","w"); checkpoint << bar; }The advantage here is large checkpoints can be written to disk without intermediate buffering in memory. The file is closed when the
pack_t
object is destroyed.


| HYTOOL Function Reference |
Non Linear List Square Curve fitting
[p,ci] = nli_fit( F, p0, x, y) F = name of the function to fit F should be of the form F(p,x) p = vector of the optimal parameters of the function p0 = inital guess for vector of the parameters x = vector of input value y = vector of response
This function is an internal function that allows to make the interface between hytool and the various implementations of non linear optimization within matlab. It allows to change only one file to make hytool compatible with different versions of matlab. NLI_FIT is looking for p that minimizes y - F(p,x)
p = nli_fit('ths_dim',[1,1e-2],t,s) See also : lin_fit
| Hytool |
© 1998-2007 Philppe Renard and Co. Terms of Use Acknowledgments


{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph.name }}
{{ paragraph.affiliation }}
{{ paragraph.country }}
{{ paragraph }}
{% endfor %}{{ paragraph.name }}
{{ paragraph.affiliation }}
{{
paragraph.country }}
{{ paragraph }}
{% endfor %}{{ paragraph }}
{% endfor %}