Classical Mechanics, Mathematics and Numerical background
Contents
2. Classical Mechanics, Mathematics and Numerical background¶
2.1. Introduction¶
Classical mechanics is a topic which has been taught intensively over several centuries. It is, with its many variants and ways of presenting the educational material, normally the first real physics course many of us meet and it lays the foundation for further physics studies. Many of the equations and ways of reasoning about the underlying laws of motion and pertinent forces, shape our approaches and understanding of the scientific method and discourse, as well as the way we develop our insights and deeper understanding about physical systems.
There is a wealth of well-tested (from both a physics point of view and a pedagogical standpoint) exercises and problems which can be solved analytically. However, many of these problems represent idealized and less realistic situations. The large majority of these problems are solved by paper and pencil and are traditionally aimed at what we normally refer to as continuous models from which we may find an analytical solution. As a consequence, when teaching mechanics, it implies that we can seldomly venture beyond an idealized case in order to develop our understandings and insights about the underlying forces and laws of motion.
We aim at changing this here by introducing throughout the course what we will call a computational path, where with computations we mean solving scientific problems with all possible tools and means, from plain paper an pencil exercises, via symbolic calculations to writing a code and running a program to solve a specific problem. Mathematically this normally means that we move from a continuous problem to a discretized one. This appproach enables us to solve a much broader class of problems. In mechanics this means, since we often rephrase the physical problems in terms of differential equations, that we can in most settings reuse the same program with some minimal changes.
2.2. Reminder on vectors and other mathematical quantities¶
Our studies will start with the motion of different types of objects such as a falling ball, a runner, a bicycle etc etc. It means that an object’s position in space varies with time. In order to study such systems we need to define
choice of origin
choice of the direction of the axes
choice of positive direction (left-handed or right-handed system of reference)
choice of units and dimensions
These choices lead to some important questions such as
is the physics of a system independent of the origin of the axes?
is the physics independent of the directions of the axes, that is are there privileged axes?
is the physics independent of the orientation of system?
is the physics independent of the scale of the length?
Throughout this course we will use the standardized SI units. The standard unit for length is thus one meter 1m, for mass one kilogram 1kg, for time one second 1s, for force one Newton 1kgm/s\(^2\) and for energy 1 Joule 1kgm\(^2\)s\(^{-2}\).
We will use the following notations for various variables (vectors are always boldfaced in these lecture notes):
position \(\boldsymbol{r}\), in one dimention we will normally just use \(x\),
mass \(m\),
time \(t\),
velocity \(\boldsymbol{v}\) or just \(v\) in one dimension,
acceleration \(\boldsymbol{a}\) or just \(a\) in one dimension,
momentum \(\boldsymbol{p}\) or just \(p\) in one dimension,
kinetic energy \(K\),
potential energy \(V\) and
frequency \(\omega\).
More variables will be defined as we need them.
It is also important to keep track of dimensionalities. Don’t mix this up with a chosen unit for a given variable. We mark the dimensionality in these lectures as \([a]\), where \(a\) is the quantity we are interested in. Thus
\([\boldsymbol{r}]=\) length
\([m]=\) mass
\([K]=\) energy
\([t]=\) time
\([\boldsymbol{v}]=\) length over time
\([\boldsymbol{a}]=\) length over time squared
\([\boldsymbol{p}]=\) mass times length over time
\([\omega]=\) 1/time
2.3. Scalars, Vectors and Matrices¶
A scalar is something with a value that is independent of coordinate system. Examples are mass, or the relative time between events. A vector has magnitude and direction. Under rotation, the magnitude stays the same but the direction changes. Scalars have no spatial index, whereas a three-dimensional vector has 3 indices, e.g. the position \(\boldsymbol{r}\) has components \(r_1,r_2,r_3\), which are often referred to as \(x,y,z\).
There are several categories of changes of coordinate system. The observer can translate the origin, might move with a different velocity, or might rotate her/his coordinate axes. For instance, a particle’s position vector changes when the origin is translated, but its velocity does not. When you study relativity you will find that quantities you thought of as scalars, such as time or an electric potential, are actually parts of four-dimensional vectors and that changes of the velocity of the reference frame act in a similar way to rotations.
In addition to vectors and scalars, there are matrices, which have two indices. One also has objects with 3 or four indices. These are called tensors of rank \(n\), where \(n\) is the number of indices. A matrix is a rank-two tensor. The Levi-Civita symbol, \(\epsilon_{ijk}\) used for cross products of vectors, is a tensor of rank three.
In these lectures we will use boldfaced lower-case letters to label a vector. A vector \(\boldsymbol{a}\) in three dimensions is thus defined as
and using the unit vectors (see below) in a cartesian system we have
where the unit vectors have magnitude \(\vert\boldsymbol{e}_i\vert = 1\) with \(i=1=x\), \(i=2=y\) and \(i=3=z\). Some authors use letters \(\boldsymbol{i}=\boldsymbol{e}_1\), \(\boldsymbol{j}=\boldsymbol{e}_2\) and \(\boldsymbol{k}=\boldsymbol{e}_3\).
Alternatively, you may also encounter the above vector as
Here we have used that \(a_1=a_x\), \(a_2=a_y\) and \(a_3=a_z\). Such a notation is sometimes more convenient if we wish to represent vector operations in a mathematically more compact way, see below here. We may also find this useful if we want the different components to represent other coordinate systems that the Cartesian one. A typical example would be going from a Cartesian representation to a spherical basis. We will encounter such cases many times in this course.
We use lower-case letters for vectors and upper-case letters for matrices. Vectors and matrices are always boldfaced.
2.3.1. Polar Coordinates¶
As an example, consider a two-dimensional Cartesian system with a vector \(\boldsymbol{r}=(x,y)\). Our vector is then written as
Transforming to polar coordinates with the radius \(\rho\in [0,\infty)\) and the angle \(\phi \in [0,2\pi]\) we have the familiar transformations
and the inverse relations
We can rewrite the vector \(\boldsymbol{a}\) in terms of \(\rho\) and \(\phi\) as
and we define the new unit vectors as \(\boldsymbol{e}'_1=\cos{\phi}\boldsymbol{e}_1\) and \(\boldsymbol{e}'_2=\sin{\phi}\boldsymbol{e}_2\), we have
Below we will show that the norms of this vector in a Cartesian basis and a Polar basis are equal.
2.3.2. Unit Vectors¶
Also known as basis vectors, unit vectors point in the direction of the coordinate axes, have unit norm, and are orthogonal to one another. Sometimes this is referred to as an orthonormal basis,
Here, \(\delta_{ij}\) is unity when \(i=j\) and is zero otherwise. This is called the unit matrix, because you can multiply it with any other matrix and not change the matrix. The dot denotes the dot product, \(\boldsymbol{a}\cdot\boldsymbol{b}=a_1b_1+a_2b_2+a_3b_3=|a||b|\cos\theta_{ab}\). Sometimes the unit vectors are called \(\hat{x}\), \(\hat{y}\) and \(\hat{z}\).
Vectors can be decomposed in terms of unit vectors,
The vector components \(r_1\), \(r_2\) and \(r_3\) might be called \(x\), \(y\) and \(z\) for a displacement. Another way to write this is to define the vector \(\boldsymbol{r}=(x,y,z)\).
Similarly, for the velocity we will use in this course the components \(\boldsymbol{v}=(v_x, v_y,v_z\). The accelaration is then given by \(\boldsymbol{a}=(a_x,a_y,a_z)\).
As mentioned above, repeated indices infer sums. This means that when you encounter an expression like the one on the left-hand side here, it stands actually for a sum (right-hand side)
We will in our lectures seldom use this notation and rather spell out the summations. This inferred summation over indices is normally called Einstein summation convention.
2.4. Vector Operations, Scalar Product (or dot product)¶
For two vectors \(\boldsymbol{a}\) and \(\boldsymbol{b}\) we have
or with a norm-2 notation
Not of all of you are familiar with linear algebra. Numerically we will always deal with arrays and the dot product vector is given by the product of the transposed vector multiplied with the other vector, that is we have
The superscript \(T\) represents the transposition operations.
2.5. Digression, Linear Algebra Notation for Vectors¶
As an example, consider a three-dimensional velocity defined by a vector \(\boldsymbol{v}=(v_x,v_y,v_z)\). For those of you familiar with linear algebra, we would write this quantity as
and the transpose as
The norm is
as it should.
Since we will use Python as a programming language throughout this course, the above vector, using the package numpy (see discussions below), can be written as
import numpy as np
# Define the values of vx, vy and vz
vx = 0.0
vy = 1.0
vz = 0.0
v = np.array([vx, vy, vz])
print(v)
# The print the transpose of v
print(v.T)
[0. 1. 0.]
[0. 1. 0.]
Try to figure out how to calculate the norm with numpy. We will come back to numpy in the examples below.
As an example, consider our transformation of a two-dimensional Cartesian vector \(\boldsymbol{r}\) to polar coordinates. We had
Transforming to polar coordinates with the radius \(\rho\in [0,\infty)\) and the angle \(\phi \in [0,2\pi]\) we have
We can write this
The norm in Cartesian coordinates is \(\boldsymbol{r}\cdot\boldsymbol{r}=x^2+y^2\) and using Polar coordinates we have \(\rho^2(\cos{\phi})^2+\rho^2(\cos{\phi})^2=\rho^2\), which shows that the norm is conserved since we have \(\rho = \sqrt{x^2+y^2}\). A transformation to a new basis should not change the norm.
2.6. Vector Product (or cross product) of vectors \(\boldsymbol{a}\) and \(\boldsymbol{b}\)¶
Here \(\epsilon\) is the third-rank anti-symmetric tensor, also known as the Levi-Civita symbol. It is \(\pm 1\) only if all three indices are different, and is zero otherwise. The choice of \(\pm 1\) depends on whether the indices are an even or odd permutation of the original symbols. The permutation \(xyz\) or \(123\) is considered to be \(+1\). Its elements are
You may have met cross-products when studying magnetic fields. Because the matrix is anti-symmetric, switching the \(x\) and \(y\) axes (or any two axes) flips the sign. If the coordinate system is right-handed, meaning the \(xyz\) axes satisfy \(\hat{x}\times\hat{y}=\hat{z}\), where you can point along the \(x\) axis with your extended right index finger, the \(y\) axis with your contracted middle finger and the \(z\) axis with your extended thumb. Switching to a left-handed system flips the sign of the vector \(\boldsymbol{c}=\boldsymbol{a}\times\boldsymbol{b}\).
Note that \(\boldsymbol{a}\times\boldsymbol{b}=-\boldsymbol{b}\times\boldsymbol{a}\). The vector \(\boldsymbol{c}\) is perpendicular to both \(\boldsymbol{a}\) and \(\boldsymbol{b}\) and the magnitude of \(\boldsymbol{c}\) is given by
2.6.1. Pseudo-vectors¶
Vectors obtained by the cross product of two real vectors are called pseudo-vectors because the assignment of their direction can be arbitrarily flipped by defining the Levi-Civita symbol to be based on left-handed rules. Examples are the magnetic field and angular momentum. If the direction of a real vector prefers the right-handed over the left-handed direction, that constitutes a violation of parity. For instance, one can polarize the spins (angular momentum) of nuclei with a magnetic field so that the spins preferentially point along the direction of the magnetic field. This does not violate parity because both are pseudo-vectors. Now assume these polarized nuclei decay and that electrons are one of the products. If these electrons prefer to exit the decay parallel vs. antiparallel to the polarizing magnetic field, this constitutes parity violation because the direction of the outgoing electron momenta are a real vector. This is precisely what is observed in weak decays.
2.7. Differentiation of a vector with respect to a scalar¶
As an example, consider the acceleration \(\boldsymbol{a}\), which is given by the change in velocity per unit time, \(\boldsymbol{a}=d\boldsymbol{v}/dt\) with components
Here \(i=x,y,z\) or \(i=1,2,3\) if we are in three dimensions.
2.7.1. Gradient operator \(\nabla\)¶
This represents the derivatives \(\partial/\partial x\), \(\partial/\partial y\) and \(\partial/\partial z\). An often used shorthand is \(\partial_x=\partial/\partial_x\).
The gradient of a scalar function of position and time \(\Phi(x,y,z)=\Phi(\boldsymbol{r},t)\) is given by
with components \(i\)
Note that the gradient is a vector.
Taking the dot product of the gradient with a vector, normally called the divergence, we have
Note that the divergence is a scalar.
2.7.2. The curl¶
The curl of a vector is defined as \(\nabla\times\boldsymbol{a}\),
with components
2.7.3. The Laplacian¶
The Laplacian is referred to as \(\nabla^2\) and is defined as
Question: is the Laplacian a scalar or a vector?
2.7.4. Some identities¶
Here we simply state these, but you may wish to prove a few. They are useful for this class and will be essential when you study electromagnetism.
2.7.5. More useful relations¶
Using the fact that multiplication of reals is distributive we can show that
Similarly we can also show that (using product rule for differentiating reals)
We can repeat these operations for the cross products and show that they are distribuitive
We have also that
2.7.6. Gauss’s Theorem¶
For an integral over a volume \(V\) confined by a surface \(S\), Gauss’s theorem gives
For a closed path \(C\) which carves out some area \(S\),
2.7.7. and Stokes’s Theorem¶
Stoke’s law can be understood by considering a small rectangle, \(-\Delta x<x<\Delta x\), \(-\Delta y<y<\Delta y\). The path integral around the edges is
Here \(\Delta S\) is the area of the surface element.
2.8. Basic Matrix Features¶
Note: The material on matrices is optional and will not be used much (except for illustrations at the very end on garmonic oscillations) since most of you have not yet taken a course on linear algebra. The material is however included here for the sake of completeness.
The inverse of a matrix is defined by
| Relations | Name | matrix elements |
|---|---|---|
| $A = A^{T}$ | symmetric | $a_{ij} = a_{ji}$ |
| $A = \left (A^{T} \right )^{-1}$ | real orthogonal | $\sum_k a_{ik} a_{jk} = \sum_k a_{ki} a_{kj} = \delta_{ij}$ |
| $A = A^{ * }$ | real matrix | $a_{ij} = a_{ij}^{ * }$ |
| $A = A^{\dagger}$ | hermitian | $a_{ij} = a_{ji}^{ * }$ |
| $A = \left (A^{\dagger} \right )^{-1}$ | unitary | $\sum_k a_{ik} a_{jk}^{ * } = \sum_k a_{ki}^{ * } a_{kj} = \delta_{ij}$ |
2.8.1. Some famous Matrices¶
Diagonal if \(a_{ij}=0\) for \(i\ne j\)
Upper triangular if \(a_{ij}=0\) for \(i > j\)
Lower triangular if \(a_{ij}=0\) for \(i < j\)
Upper Hessenberg if \(a_{ij}=0\) for \(i > j+1\)
Lower Hessenberg if \(a_{ij}=0\) for \(i < j+1\)
Tridiagonal if \(a_{ij}=0\) for \(|i -j| > 1\)
Lower banded with bandwidth \(p\): \(a_{ij}=0\) for \(i > j+p\)
Upper banded with bandwidth \(p\): \(a_{ij}=0\) for \(i < j+p\)
Banded, block upper triangular, block lower triangular….
For an \(N\times N\) matrix \(\mathbf{A}\) the following properties are all equivalent
If the inverse of \(\mathbf{A}\) exists, \(\mathbf{A}\) is nonsingular.
The equation \(\mathbf{Ax}=0\) implies \(\mathbf{x}=0\).
The rows of \(\mathbf{A}\) form a basis of \(R^N\).
The columns of \(\mathbf{A}\) form a basis of \(R^N\).
\(\mathbf{A}\) is a product of elementary matrices.
\(0\) is not eigenvalue of \(\mathbf{A}\).
2.9. Rotations¶
Here, we use rotations as an example of matrices and their operations. One can consider a different orthonormal basis \(\hat{e}'_1\), \(\hat{e}'_2\) and \(\hat{e}'_3\). The same vector \(\boldsymbol{r}\) mentioned above can also be expressed in the new basis,
Even though it is the same vector, the components have changed. Each new unit vector \(\hat{e}'_i\) can be expressed as a linear sum of the previous vectors,
and the matrix \(U\) can be found by taking the dot product of both sides with \(\hat{e}_k\),
Thus, the matrix lambda has components \(U_{ij}\) that are equal to the cosine of the angle between new unit vector \(\hat{e}'_i\) and the old unit vector \(\hat{e}_j\).
Note that the matrix is not symmetric, \(U_{ij}\ne U_{ji}\). One can also look at the inverse transformation, by switching the primed and unprimed coordinates,
The definition of transpose of a matrix, \(M^{t}_{ij}=M_{ji}\), allows one to state this as
2.9.1. Tensors¶
A tensor obeying Eq. (8) defines what is known as a unitary, or orthogonal, transformation.
The matrix \(U\) can be used to transform any vector to the new basis. Consider a vector
This is the same vector expressed as a sum over two different sets of basis vectors. The coefficients \(r_i\) and \(r'_i\) represent components of the same vector. The relation between them can be found by taking the dot product of each side with one of the unit vectors, \(\hat{e}_i\), which gives
Using Eq. (7) one can see that the transformation of \(r\) can be also written in terms of \(U\),
Thus, the matrix that transforms the coordinates of the unit vectors, Eq. (7) is the same one that transforms the coordinates of a vector, Eq. (9).
As a small exercise, find the rotation matrix \(U\) for finding the components in the primed coordinate system given from those in the unprimed system, given that the unit vectors in the new system are found by rotating the coordinate system by and angle \(\phi\) about the \(z\) axis.
In this case
By inspecting Eq. (5), we get
Under a unitary transformation \(U\) (or basis transformation) scalars are unchanged, whereas vectors \(\boldsymbol{r}\) and matrices \(M\) change as
Physical quantities with no spatial indices are scalars (or pseudoscalars if they depend on right-handed vs. left-handed coordinate systems), and are unchanged by unitary transformations. This includes quantities like the trace of a matrix, the matrix itself had indices but none remain after performing the trace.
Because there are no remaining indices, one expects it to be a scalar. Indeed one can see this,
A similar example is the determinant of a matrix, which is also a scalar.
2.10. Numerical Elements¶
Numerical algorithms call for approximate discrete models and much of the development of methods for continuous models are nowadays being replaced by methods for discrete models in science and industry, simply because much larger classes of problems can be addressed with discrete models, often by simpler and more generic methodologies.
As we will see throughout this course, when properly scaling the equations at hand, discrete models open up for more advanced abstractions and the possibility to study real life systems, with the added bonus that we can explore and deepen our basic understanding of various physical systems
Analytical solutions are as important as before. In addition, such solutions provide us with invaluable benchmarks and tests for our discrete models. Such benchmarks, as we will see below, allow us to discuss possible sources of errors and their behaviors. And finally, since most of our models are based on various algorithms from numerical mathematics, we have a unique oppotunity to gain a deeper understanding of the mathematical approaches we are using.
With computing and data science as important elements in essentially all aspects of a modern society, we could then try to define Computing as solving scientific problems using all possible tools, including symbolic computing, computers and numerical algorithms, and analytical paper and pencil solutions. Computing provides us with the tools to develope our own understanding of the scientific method by enhancing algorithmic thinking.
The way we will teach this course reflects this definition of computing. The course contains both classical paper and pencil exercises as well as computational projects and exercises. The hope is that this will allow you to explore the physics of systems governed by the degrees of freedom of classical mechanics at a deeper level, and that these insights about the scientific method will help you to develop a better understanding of how the underlying forces and equations of motion and how they impact a given system.
Furthermore, by introducing various numerical methods via computational projects and exercises, we aim at developing your competences and skills about these topics.
These competences will enable you to
understand how algorithms are used to solve mathematical problems,
derive, verify, and implement algorithms,
understand what can go wrong with algorithms,
use these algorithms to construct reproducible scientific outcomes and to engage in science in ethical ways, and
think algorithmically for the purposes of gaining deeper insights about scientific problems.
All these elements are central for maturing and gaining a better understanding of the modern scientific process per se.
The power of the scientific method lies in identifying a given problem as a special case of an abstract class of problems, identifying general solution methods for this class of problems, and applying a general method to the specific problem (applying means, in the case of computing, calculations by pen and paper, symbolic computing, or numerical computing by ready-made and/or self-written software). This generic view on problems and methods is particularly important for understanding how to apply available, generic software to solve a particular problem.
However, verification of algorithms and understanding their limitations requires much of the classical knowledge about continuous models.
2.11. A well-known example to illustrate many of the above concepts¶
Before we venture into a reminder on Python and mechanics relevant applications, let us briefly outline some of the abovementioned topics using an example many of you may have seen before in for example CMSE201. A simple algorithm for integration is the Trapezoidal rule. Integration of a function \(f(x)\) by the Trapezoidal Rule is given by following algorithm for an interval \(x \in [a,b]\)
where \(h\) is the so-called stepsize defined by the number of integration points \(N\) as \(h=(b-a)/(n)\). Python offers an extremely versatile programming environment, allowing for the inclusion of analytical studies in a numerical program. Here we show an example code with the trapezoidal rule. We use also SymPy to evaluate the exact value of the integral and compute the absolute error with respect to the numerically evaluated one of the integral \(\int_0^1 dx x^2 = 1/3\). The following code for the trapezoidal rule allows you to plot the relative error by comparing with the exact result. By increasing to \(10^8\) points one arrives at a region where numerical errors start to accumulate.
%matplotlib inline
from math import log10
import numpy as np
from sympy import Symbol, integrate
import matplotlib.pyplot as plt
# function for the trapezoidal rule
def Trapez(a,b,f,n):
h = (b-a)/float(n)
s = 0
x = a
for i in range(1,n,1):
x = x+h
s = s+ f(x)
s = 0.5*(f(a)+f(b)) +s
return h*s
# function to compute pi
def function(x):
return x*x
# define integration limits
a = 0.0; b = 1.0;
# find result from sympy
# define x as a symbol to be used by sympy
x = Symbol('x')
exact = integrate(function(x), (x, a, b))
# set up the arrays for plotting the relative error
n = np.zeros(9); y = np.zeros(9);
# find the relative error as function of integration points
for i in range(1, 8, 1):
npts = 10**i
result = Trapez(a,b,function,npts)
RelativeError = abs((exact-result)/exact)
n[i] = log10(npts); y[i] = log10(RelativeError);
plt.plot(n,y, 'ro')
plt.xlabel('n')
plt.ylabel('Relative error')
plt.show()
2.11.1. Analyzing the above example¶
This example shows the potential of combining numerical algorithms with symbolic calculations, allowing us to
Validate and verify their algorithms.
Including concepts like unit testing, one has the possibility to test and test several or all parts of the code.
Validation and verification are then included naturally and one can develop a better attitude to what is meant with an ethically sound scientific approach.
The above example allows the student to also test the mathematical error of the algorithm for the trapezoidal rule by changing the number of integration points. The students get trained from day one to think error analysis.
With a Jupyter notebook you can keep exploring similar examples and turn them in as your own notebooks.
2.12. Python practicalities, Software and needed installations¶
We will make extensive use of Python as programming language and its myriad of available libraries. You will find Jupyter notebooks invaluable in your work.
If you have Python installed (we strongly recommend Python3) and you feel pretty familiar with installing different packages, we recommend that you install the following Python packages via pip as
pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow
For Python3, replace pip with pip3.
For OSX users we recommend, after having installed Xcode, to install brew. Brew allows for a seamless installation of additional software via for example
brew install python3
For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution, you can use pip as well and simply install Python as
sudo apt-get install python3 (or python for pyhton2.7)
etc etc.
2.12.1. Python installers¶
If you don’t want to perform these operations separately and venture into the hassle of exploring how to set up dependencies and paths, we recommend two widely used distrubutions which set up all relevant dependencies for Python, namely
which is an open source distribution of the Python and R programming languages for large-scale data processing, predictive analytics, and scientific computing, that aims to simplify package management and deployment. Package versions are managed by the package management system conda.
is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.
Furthermore, Google’s Colab is a free Jupyter notebook environment that requires no setup and runs entirely in the cloud. Try it out!
2.13. Useful Python libraries¶
Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)
NumPy is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays
The pandas library provides high-performance, easy-to-use data structures and data analysis tools
Xarray is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun!
Scipy (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering.
Matplotlib is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.
Autograd can automatically differentiate native Python and Numpy code. It can handle a large subset of Python’s features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives
SymPy is a Python library for symbolic mathematics.
scikit-learn has simple and efficient tools for machine learning, data mining and data analysis
TensorFlow is a Python library for fast numerical computing created and released by Google
Keras is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano
Your jupyter notebook can easily be converted into a nicely rendered PDF file or a Latex file for further processing. For example, convert to latex as
pycod jupyter nbconvert filename.ipynb --to latex
And to add more versatility, the Python package SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) and is entirely written in Python.
2.14. Numpy examples and Important Matrix and vector handling packages¶
There are several central software libraries for linear algebra and eigenvalue problems. Several of the more popular ones have been wrapped into ofter software packages like those from the widely used text Numerical Recipes. The original source codes in many of the available packages are often taken from the widely used software package LAPACK, which follows two other popular packages developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly here.
LINPACK: package for linear equations and least square problems.
LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK’s website http://www.netlib.org it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available.
BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from http://www.netlib.org.
Numpy provides an easy way to handle arrays in Python. The standard way to import this library is as
import numpy as np
Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution,
n = 10
x = np.random.normal(size=n)
print(x)
[-1.83408226 -0.4118334 -1.21071409 -0.59684054 0.70333963 0.0289105
0.75626664 -1.48393448 0.76111648 0.37006943]
We defined a vector \(x\) with \(n=10\) elements with its values given by the Normal distribution \(N(0,1)\). Another alternative is to declare a vector as follows
import numpy as np
x = np.array([1, 2, 3])
print(x)
[1 2 3]
Here we have defined a vector with three elements, with \(x_0=1\), \(x_1=2\) and \(x_2=3\). Note that both Python and C++ start numbering array elements from \(0\) and on. This means that a vector with \(n\) elements has a sequence of entities \(x_0, x_1, x_2, \dots, x_{n-1}\). We could also let (recommended) Numpy to compute the logarithms of a specific array as
import numpy as np
x = np.log(np.array([4, 7, 8]))
print(x)
[1.38629436 1.94591015 2.07944154]
In the last example we used Numpy’s unary function \(np.log\). This function is highly tuned to compute array elements since the code is vectorized and does not require looping. We normaly recommend that you use the Numpy intrinsic functions instead of the corresponding log function from Python’s math module. The looping is done explicitely by the np.log function. The alternative, and slower way to compute the logarithms of a vector would be to write
import numpy as np
from math import log
x = np.array([4, 7, 8])
for i in range(0, len(x)):
x[i] = log(x[i])
print(x)
[1 1 2]
We note that our code is much longer already and we need to import the log function from the math module. The attentive reader will also notice that the output is \([1, 1, 2]\). Python interprets automagically our numbers as integers (like the automatic keyword in C++). To change this we could define our array elements to be double precision numbers as
import numpy as np
x = np.log(np.array([4, 7, 8], dtype = np.float64))
print(x)
[1.38629436 1.94591015 2.07944154]
or simply write them as double precision numbers (Python uses 64 bits as default for floating point type variables), that is
import numpy as np
x = np.log(np.array([4.0, 7.0, 8.0])
print(x)
Input In [9]
print(x)
^
SyntaxError: invalid syntax
To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the itemsize functionality (the array \(x\) is actually an object which inherits the functionalities defined in Numpy) as
import numpy as np
x = np.log(np.array([4.0, 7.0, 8.0])
print(x.itemsize)
2.14.1. Matrices in Python¶
Having defined vectors, we are now ready to try out matrices. We can define a \(3 \times 3 \) real matrix \(\hat{A}\) as (recall that we user lowercase letters for vectors and uppercase letters for matrices)
import numpy as np
A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))
print(A)
If we use the shape function we would get \((3, 3)\) as output, that is verifying that our matrix is a \(3\times 3\) matrix. We can slice the matrix and print for example the first column (Python organized matrix elements in a row-major order, see below) as
import numpy as np
A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))
# print the first column, row-major order and elements start with 0
print(A[:,0])
We can continue this was by printing out other columns or rows. The example here prints out the second column
import numpy as np
A = np.log(np.array([ [4.0, 7.0, 8.0], [3.0, 10.0, 11.0], [4.0, 5.0, 7.0] ]))
# print the first column, row-major order and elements start with 0
print(A[1,:])
Numpy contains many other functionalities that allow us to slice, subdivide etc etc arrays. We strongly recommend that you look up the Numpy website for more details. Useful functions when defining a matrix are the np.zeros function which declares a matrix of a given dimension and sets all elements to zero
import numpy as np
n = 10
# define a matrix of dimension 10 x 10 and set all elements to zero
A = np.zeros( (n, n) )
print(A)
or initializing all elements to
import numpy as np
n = 10
# define a matrix of dimension 10 x 10 and set all elements to one
A = np.ones( (n, n) )
print(A)
or as unitarily distributed random numbers (see the material on random number generators in the statistics part)
import numpy as np
n = 10
# define a matrix of dimension 10 x 10 and set all elements to random numbers with x \in [0, 1]
A = np.random.rand(n, n)
print(A)
2.14.2. Meet the Pandas¶
Another useful Python package is pandas, which is an open source library providing high-performance, easy-to-use data structures and data analysis tools for Python. pandas stands for panel data, a term borrowed from econometrics and is an efficient library for data analysis with an emphasis on tabular data.
pandas has two major classes, the DataFrame class with two-dimensional data objects and tabular data organized in columns and the class Series with a focus on one-dimensional data objects. Both classes allow you to index data easily as we will see in the examples below. pandas allows you also to perform mathematical operations on the data, spanning from simple reshapings of vectors and matrices to statistical operations.
The following simple example shows how we can, in an easy way make tables of our data. Here we define a data set which includes names, place of birth and date of birth, and displays the data in an easy to read way. We will see repeated use of pandas, in particular in connection with classification of data.
import pandas as pd
from IPython.display import display
data = {'First Name': ["Frodo", "Bilbo", "Aragorn II", "Samwise"],
'Last Name': ["Baggins", "Baggins","Elessar","Gamgee"],
'Place of birth': ["Shire", "Shire", "Eriador", "Shire"],
'Date of Birth T.A.': [2968, 2890, 2931, 2980]
}
data_pandas = pd.DataFrame(data)
display(data_pandas)
In the above we have imported pandas with the shorthand pd, the latter has become the standard way we import pandas. We make then a list of various variables and reorganize the above lists into a DataFrame and then print out a neat table with specific column labels as Name, place of birth and date of birth. Displaying these results, we see that the indices are given by the default numbers from zero to three. pandas is extremely flexible and we can easily change the above indices by defining a new type of indexing as
data_pandas = pd.DataFrame(data,index=['Frodo','Bilbo','Aragorn','Sam'])
display(data_pandas)
Thereafter we display the content of the row which begins with the index Aragorn
display(data_pandas.loc['Aragorn'])
We can easily append data to this, for example
new_hobbit = {'First Name': ["Peregrin"],
'Last Name': ["Took"],
'Place of birth': ["Shire"],
'Date of Birth T.A.': [2990]
}
data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin']))
display(data_pandas)
Here are other examples where we use the DataFrame functionality to handle arrays, now with more interesting features for us, namely numbers. We set up a matrix of dimensionality \(10\times 5\) and compute the mean value and standard deviation of each column. Similarly, we can perform mathematial operations like squaring the matrix elements and many other operations.
import numpy as np
import pandas as pd
from IPython.display import display
np.random.seed(100)
# setting up a 10 x 5 matrix
rows = 10
cols = 5
a = np.random.randn(rows,cols)
df = pd.DataFrame(a)
display(df)
print(df.mean())
print(df.std())
display(df**2)
Thereafter we can select specific columns only and plot final results
df.columns = ['First', 'Second', 'Third', 'Fourth', 'Fifth']
df.index = np.arange(10)
display(df)
print(df['Second'].mean() )
print(df.info())
print(df.describe())
from pylab import plt, mpl
plt.style.use('seaborn')
mpl.rcParams['font.family'] = 'serif'
df.cumsum().plot(lw=2.0, figsize=(10,6))
plt.show()
df.plot.bar(figsize=(10,6), rot=15)
plt.show()
We can produce a \(4\times 4\) matrix
b = np.arange(16).reshape((4,4))
print(b)
df1 = pd.DataFrame(b)
print(df1)
and many other operations.
The Series class is another important class included in pandas. You can view it as a specialization of DataFrame but where we have just a single column of data. It shares many of the same features as DataFrame. As with DataFrame, most operations are vectorized, achieving thereby a high performance when dealing with computations of arrays, in particular labeled arrays. As we will see below it leads also to a very concice code close to the mathematical operations we may be interested in. For multidimensional arrays, we recommend strongly xarray. xarray has much of the same flexibility as pandas, but allows for the extension to higher dimensions than two.
2.15. Introduction to Git and GitHub/GitLab and similar¶
Git is a distributed version-control system for tracking changes in any set of files, originally designed for coordinating work among programmers cooperating on source code during software development.
The reference document and videos here give you an excellent introduction to the git.
We believe you will find version-control software very useful in your work.
All teaching material related to this course is open and freely available via the GitHub site of the course. The video here gives a short intro to GitHub.
See also the overview video on Git and GitHub.
2.15.1. Useful Git and GitHub links¶
These are a couple references that we have found useful (git commands, markdown, GitPages):
When dealing with homeworks, at some point you would need to use an editor, or an integrated development envinroment (IDE). As an IDE, we would like to recommend anaconda since we end up using jupyter-notebooks. anaconda runs on all known operating systems.
If you prefer editing Python codes, there are several excellent cross-platform editors. If you are in a Windows environment, word is the classical text editor.
There is however a wealth of text editors and/ord IDEs that run on all operating systems and functions well with Python. Some of the more popular ones are


Blog grid
There are many variations of pas-
sages of Lorem Ipsum.
It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout..
Read MoreThere are many variations of pas-
sages of Lorem Ipsum.
It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout..
Read MoreThere are many variations of pas-
sages of Lorem Ipsum.
It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout..
Read MoreThere are many variations of pas-
sages of Lorem Ipsum.
It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout..
Read MoreThere are many variations of pas-
sages of Lorem Ipsum.
It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout..
Read MoreThere are many variations of pas-
sages of Lorem Ipsum.
It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout..
Read More


When contributing to the pyhole project, please be sure to read over the following information.
import re
import urllib
from BeautifulSoup import BeautifulSoup
from pyhole import plugin
from pyhole import utils
"""This is a single-line docstring"""
"""This is a multi-line docstring
Second paragraph goes like this. Ending quotes are on their own line.
"""
Should a line flow over 79 characters, you will indent as such:
log = logging.handlers.TimedRotatingFileHandler("%s/%s.log" % (log_dir,
name.lower()), "midnight")
Make note of the double indent (8 characters in length).
Every new piece of code must be covered by a unit test. One must also ensure that all tests pass before submitting code. Testing examples can be found in the tests directory.


React Essentials
by
Nick Payne
&
Florin Senoner
01 Intro
About this Course
A quick overview
A Simple React Component
02 App Setup
Create an App
JSX & Typescript
npm scripts
03 Your first Components
Separation of Concerns
Styling
Props & State
Testing
04 Building the Quiz
Tools
Routing
Asynchronous API Requests
Custom Hooks
05 Pokedex
TDD
Rendering a list
Change detection
Sharing state
06 Registration Form
Form State
Validations
Localstorage
Libraries
07 Optimizing
Code Splitting & Suspense
Concurrent Mode
08 (legacy) API
lifecyles
class Components


7.17 psb_rcv — Receive data
call psb_rcv(ctxt, dat, src, m)
This subroutine receives a packet of data to a destination.
-
Type:
- Synchronous: see usage notes.
-
On Entry
-
-
ctxt
- the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable.
-
src
- Source process.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer value 0 <= src <= np - 1.
-
m
- Number of rows.
Scope: global.
Type: Optional.
Intent: in.
Specified as: an integer value 0 <= m <= size(dat,1).
When dat is a rank 2 array, specifies the number of rows to be sent
independently of the leading dimension size(dat,1); must have the same
value on sending and receiving processes.
-
On Return
-
-
dat
- The data to be received.
Scope: local.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar,
or a rank 1 or 2 array, or a character or logical scalar. Type, kind and
rank must agree on sender and receiver process; if m is not specified, size
must agree as well.
Notes
- This subroutine implies a synchronization, but only between the calling
process and the source process src.


Tempter of the Bone
Time Limit: 2 Seconds
Memory Limit: 65536 KB
The doggie found a bone in an ancient maze, which fascinated him a lot. However,
when he picked it up, the maze began to shake, and the doggie could feel the
ground sinking. He realized that the bone was a trap, and he tried desperately
to get out of this maze.
The maze was a rectangle with sizes N by M. There was a door in the maze. At
the beginning, the door was closed and it would open at the T-th second for
a short period of time (less than 1 second). Therefore the doggie had to arrive
at the door on exactly the T-th second. In every second, he could move one block
to one of the upper, lower, left and right neighboring blocks. Once he entered
a block, the ground of this block would start to sink and disappear in the next
second. He could not stay at one block for more than one second, nor could he
move into a visited block. Can the poor doggie survive? Please help him.
Input
The input consists of multiple test cases. The first line of each test case
contains three integers N, M, and T (1 < N, M < 7; 0 < T < 50),
which denote the sizes of the maze and the time at which the door will open,
respectively. The next N lines give the maze layout, with each line containing
M characters. A character is one of the following:
'X': a block of wall, which the doggie cannot enter;
'S': the start point of the doggie;
'D': the Door; or
'.': an empty block.
The input is terminated with three 0's. This test case is not to be processed.
Output
For each test case, print in one line "YES" if the doggie can survive,
or "NO" otherwise.
Sample Input
4 4 5
S.X.
..X.
..XD
....
3 4 5
S.X.
..X.
...D
0 0 0
Sample Output
NO
YES
Author:
ZHANG, Zheng
Source:
Zhejiang Provincial Programming Contest 2004
Submit
Status


| in.out {mgcv} | R Documentation |
Tests whether each of a set of points lie within a region defined by one or more (possibly nested) polygons. Points count as ‘inside’ if they are interior to an odd number of polygons.
in.out(bnd,x)
bnd |
A two column matrix, the rows of which define the vertices of polygons defining the boundary of a region.
Different polygons should be separated by an |
x |
A two column matrix. Each row is a point to test for inclusion in the region defined by |
The algorithm works by counting boundary crossings (using compiled C code).
A logical vector of length nrow(x)
. TRUE
if the corresponding row of x
is inside
the boundary and FALSE
otherwise.
Simon N. Wood<EMAIL_ADDRESS>http://www.maths.bris.ac.uk/~sw15190/
library(mgcv) data(columb.polys) bnd <- columb.polys[[2]] plot(bnd,type="n") polygon(bnd) x <- seq(7.9,8.7,length=20) y <- seq(13.7,14.3,length=20) gr <- as.matrix(expand.grid(x,y)) inside <- in.out(bnd,gr) points(gr,col=as.numeric(inside)+1)


quota -s- Verbose output (also display quotas on filesystems where no storage is allocated):
quota -v- Quiet output (only display quotas on filesystems where usage is over quota):
quota -q- Print quotas for the groups of which the current user is a member:
quota -g- Show disk quotas for another user:
sudo quota -u username


MANTIS
HOME
ABOUT
TEAM
Hello, this is the screening questions service
Send URL
Server status: Disconnected


About Me
About Me
My name is Hayley Schultz. I'm a senior at Western Reserve Academy. I like to play tennis and sail. Follow me on instagram @hayleyyschultz. I wanted to take the class because I had no clue how to use any of the machines. I had another class slot to fill and I thought I would learn useful skills in this class. I wanted to be more familiar with the machines and be knowledgable on how to use them.


GET https://apis.wso2.com/api/am/store/v1/apis/{apiId}/asyncapi
You can use this operation to retrieve the AsyncAPI definition of an API. `X-WSO2-Tenant` header can be used to retrive the AsyncAPI definition an API of a different tenant domain. If not specified super tenant will be used. If Authorization header is present in the request, the user's tenant associated with the access token will be used. **NOTE:** * This operation does not require an Authorization header by default. But in order to see a restricted API's swagger definition, you need to provide Authorization header.
Not required
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Path |
apiId required |
**API ID** consisting of the **UUID** of the API. |
String | |
| Query |
labelName optional |
Name of the API microgateway labels |
String | |
| Query |
environmentName optional |
Name of the API gateway environment. |
String | |
| Query |
clusterName optional |
Name of the container managed cluster name. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String | |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. Requested AsyncAPI document of the API is returned |
string |
304 |
Not Modified. Empty body because the client has already the latest version of the requested resource. |
|
404 |
NotFound. Requested API does not exist. |
Error |
406 |
Not Acceptable. The requested media type is not supported |
Error |
GET https://apis.wso2.com/api/am/store/v1/apis/{apiId}
Using this operation, you can retrieve complete details of a single API. You need to provide the Id of the API to retrive it. `X-WSO2-Tenant` header can be used to retrieve an API of a different tenant domain. If not specified super tenant will be used. If Authorization header is present in the request, the user's tenant associated with the access token will be used. **NOTE:** * This operation does not require an Authorization header by default. But if it is provided, it will be validated and checked for permissions of the user, hence you may be able to see APIs which are restricted for special permissions/roles. \n
Not required
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Path |
apiId required |
**API ID** consisting of the **UUID** of the API. |
String | |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. Requested API is returned |
API |
304 |
Not Modified. Empty body because the client has already the latest version of the requested resource. |
|
404 |
Not Found. The specified resource does not exist. |
Error |
406 |
Not Acceptable. The requested media type is not supported. |
Error |
GET https://apis.wso2.com/api/am/store/v1/apis/{apiId}/graphql-schema
You can use this operation to retrieve the swagger definition of an API. `X-WSO2-Tenant` header can be used to retrieve the swagger definition an API of a different tenant domain. If not specified super tenant will be used. If Authorization header is present in the request, the user's tenant associated with the access token will be used. **NOTE:** * This operation does not require an Authorization header by default. But in order to see a restricted API's swagger definition, you need to provide Authorization header.
Not required
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Path |
apiId required |
**API ID** consisting of the **UUID** of the API. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String | |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. Requested swagger document of the API is returned |
|
304 |
Not Modified. Empty body because the client has already the latest version of the requested resource. |
|
404 |
Not Found. The specified resource does not exist. |
Error |
406 |
Not Acceptable. The requested media type is not supported. |
Error |
GET https://apis.wso2.com/api/am/store/v1/apis/{apiId}/subscription-policies
This operation can be used to retrieve details of the subscription throttling policy of an API by specifying the API Id. `X-WSO2-Tenant` header can be used to retrive API subscription throttling policies that belongs to a different tenant domain. If not specified super tenant will be used. If Authorization header is present in the request, the user's tenant associated with the access token will be used.
Not required
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Path |
apiId required |
**API ID** consisting of the **UUID** of the API. |
String | |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. Throttling Policy returned |
ThrottlingPolicy |
304 |
Not Modified. Empty body because the client has already the latest version of the requested resource. |
|
404 |
Not Found. The specified resource does not exist. |
Error |
406 |
Not Acceptable. The requested media type is not supported. |
Error |
GET https://apis.wso2.com/api/am/store/v1/apis/{apiId}/swagger
You can use this operation to retrieve the swagger definition of an API. `X-WSO2-Tenant` header can be used to retrieve the swagger definition an API of a different tenant domain. If not specified super tenant will be used. If Authorization header is present in the request, the user's tenant associated with the access token will be used. **NOTE:** * This operation does not require an Authorization header by default. But in order to see a restricted API's swagger definition, you need to provide Authorization header.
Not required
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Path |
apiId required |
**API ID** consisting of the **UUID** of the API. |
String | |
| Query |
labelName optional |
Name of the API microgateway labels |
String | |
| Query |
environmentName optional |
Name of the API gateway environment. |
String | |
| Query |
clusterName optional |
Name of the container managed cluster name. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String | |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. Requested swagger document of the API is returned |
string |
304 |
Not Modified. Empty body because the client has already the latest version of the requested resource. |
|
404 |
Not Found. The specified resource does not exist. |
Error |
406 |
Not Acceptable. The requested media type is not supported. |
Error |
GET https://apis.wso2.com/api/am/store/v1/apis/{apiId}/thumbnail
This operation can be used to download a thumbnail image of an API. `X-WSO2-Tenant` header can be used to retrive a thumbnail of an API that belongs to a different tenant domain. If not specified super tenant will be used. If Authorization header is present in the request, the user's tenant associated with the access token will be used. **NOTE:** * This operation does not require an Authorization header by default. But in order to see a restricted API's thumbnail, you need to provide Authorization header.
Not required
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Path |
apiId required |
**API ID** consisting of the **UUID** of the API. |
String | |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. Thumbnail image returned |
|
304 |
Not Modified. Empty body because the client has already the latest version of the requested resource. |
|
404 |
Not Found. The specified resource does not exist. |
Error |
406 |
Not Acceptable. The requested media type is not supported. |
Error |
GET https://apis.wso2.com/api/am/store/v1/apis
This operation provides you a list of available APIs qualifying under a given search condition. Each retrieved API is represented with a minimal amount of attributes. If you want to get complete details of an API, you need to use **Get details of an API** operation. This operation supports retrieving APIs of other tenants. The required tenant domain need to be specified as a header `X-WSO2-Tenant`. If not specified super tenant's APIs will be retrieved. If you used an Authorization header, the user's tenant associated with the access token will be used. **NOTE:** * By default, this operation retrieves Published APIs. In order to retrieve Prototyped APIs, you need to use **query** parameter and specify **status:PROTOTYPED**. * This operation does not require an Authorization header by default. But if it is provided, it will be validated and checked for permissions of the user, hence you may be able to see APIs which are restricted for special permissions/roles.
Not required
GET https://localhost:9443/api/am/store/v1/apis HTTP 1/1
Authorization: Bearer ae4eae22-3f65-387b-a171-d37eaa366fa8
HTTP 1/1 200 OK
Content-Type: application/json
{
"count" : 1,
"list" : [ {
"id" : "ae4eae22-3f65-387b-2323-d37eaa366fa8",
"name" : "CalculatorAPI",
"description" : "A calculator API that supports basic operations",
"context" : "CalculatorAPI",
"version" : "1.0.0",
"provider" : "admin",
"lifeCycleStatus" : "CREATED",
"workflowStatus" : "APPROVED",
"hasThumbnail" : true,
"securityScheme" : [ "oauth2" ]
} ],
"pagination" : {
"offset" : 0,
"limit" : 1,
"total" : 1,
"next" : "",
"previous" : ""
}
}
curl -k -v -X GET 'https://localhost:9443/api/am/store/v1/apis' -H 'Authorization: Bearer ae4eae22-3f65-387b-a171-d37eaa366fa8'
GET https://localhost:9443/api/am/store/v1/apis HTTP/1.1
Authorization: Bearer ae4eae22-3f65-387b-a171-d37eaa366fa8
HTTP/1.1 200 OK
Content-Type: application/json
{
"count":2,
"list":[
{
"id":"43537569-b701-4f3f-a989-e1b6f42ebcf0",
"name":"PizzaShackAPI",
"description":"This is a simple API for Pizza Shack online pizza delivery store.",
"context":"/pizzashack",
"version":"1.0.0",
"provider":"admin",
"lifeCycleStatus":"PUBLISHED",
"workflowStatus":null,
"hasThumbnail":true,
"securityScheme":[
]
},
{
"id":"740aeb01-2d3f-4721-afac-4324988a2e0b",
"name":"PizzaShackAPI",
"description":"This is a simple API for Pizza Shack online pizza delivery store.",
"context":"/pizzashack",
"version":"2.0.0",
"provider":"admin",
"lifeCycleStatus":"CREATED",
"workflowStatus":null,
"hasThumbnail":true,
"securityScheme":[
]
}
],
"pagination":{
"offset":0,
"limit":25,
"total":2,
"next":"",
"previous":""
}
}
curl -k -H "Authorization: Bearer ae4eae22-3f65-387b-a171-d37eaa366fa8" https://localhost:9443/api/am/store/v1/apis
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Query |
limit optional |
Maximum size of resource array to return. |
Integer |
25 |
| Query |
offset optional |
Starting point within the complete list of items qualified. |
Integer |
0 |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String | |
| Query |
query optional |
**Search condition**. You can search in attributes by using an **"<attribute>:"** modifier. Eg. "provider:wso2" will match an API if the provider of the API is exactly "wso2". Additionally you can use wildcards. Eg. "provider:wso2*" will match an API if the provider of the API starts with "wso2". Supported attribute modifiers are [**version, context, status, description, subcontext, doc, provider, tag**] If no advanced attribute modifier has been specified, search will match the given query string against API Name. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. List of qualifying APIs is returned. |
APIList |
406 |
Not Acceptable. The requested media type is not supported. |
Error |
GET https://apis.wso2.com/api/am/store/v1/apis/{apiId}/wsdl
This operation can be used to retrieve the swagger definition of an API.
Not required
GET https://localhost:9443/api/am/store/v1/apis/db8566ee-6260-47f1-a15f-e71bd2ecb68f/wsdl?environmentName=Production%20and%20Sandbox HTTP 1/1
Authorization: Bearer 6cc80644-dd9b-3213-a3ca-0037da5caae7
HTTP/1.1 200
Content-Type: application/wsdl
Content-Disposition: attachment; filename="admin-IP2Geo-1.0.0.zip"
Content-Length: 7670
<?xml version="1.0" encoding="UTF-8"?>
<wsdl:definitions targetNamespace="http://ws.cdyne.com/" xmlns:s="http://www.w3.org/2001/XMLSchema" xmlns:wsdl="http://schemas.xmlsoap.org/wsdl/" xmlns:mime="http://schemas.xmlsoap.org/wsdl/mime/" xmlns:tns="http://ws.cdyne.com/" xmlns:http="http://schemas.xmlsoap.org/wsdl/http/" xmlns:tm="http://microsoft.com/wsdl/mime/textMatching/" xmlns:soap12="http://schemas.xmlsoap.org/wsdl/soap12/" xmlns:soap="http://schemas.xmlsoap.org/wsdl/soap/" xmlns:soapenc="http://schemas.xmlsoap.org/soap/encoding/">
<wsdl:documentation xmlns:wsdl="http://schemas.xmlsoap.org/wsdl/">Our system uses a multiple sources for resolution. Including a host database, trace route information, and other systems. Resolves IP addresses to Organization, Country, City..
...
...
<wsdl:port name="IP2GeoHttpGet" binding="tns:IP2GeoHttpGet">
<http:address location="https://localhost:8243/ip2geo/1.0"/>
</wsdl:port>
<wsdl:port name="IP2GeoHttpPost" binding="tns:IP2GeoHttpPost">
<http:address location="https://localhost:8243/ip2geo/1.0"/>
</wsdl:port>
</wsdl:service>
</wsdl:definitions>
curl -k -v -X GET 'https://localhost:9443/api/am/store/v1/apis/db8566ee-6260-47f1-a15f-e71bd2ecb68f/wsdl?environmentName=Production%20and%20Sandbox' -H 'Authorization: Bearer 6cc80644-dd9b-3213-a3ca-0037da5caae7'
GET https://localhost:9443/api/am/store/v1/apis/7369e7ba-ac2e-4492-9fa5-9d2cd6029db4/wsdl?environmentName=Production%20and%20Sandbox HTTP 1/1
Authorization: Bearer 6cc80644-dd9b-3213-a3ca-0037da5caae7
HTTP/1.1 200
Content-Disposition: attachment; filename="admin-StockQuoteArchiveAPI-1.0.0.zip"
Content-Type: application/zip
Content-Length: 1493
<binary-data>
curl -k -v -X GET 'https://localhost:9443/api/am/store/v1/apis/7369e7ba-ac2e-4492-9fa5-9d2cd6029db4/wsdl?environmentName=Production%20and%20Sandbox' -H 'Authorization: Bearer 6cc80644-dd9b-3213-a3ca-0037da5caae7'
| Type | Name | Description | Schema | Default |
|---|---|---|---|---|
| Path |
apiId required |
**API ID** consisting of the **UUID** of the API. |
String | |
| Query |
labelName optional |
Name of the API microgateway labels |
String | |
| Query |
environmentName optional |
Name of the API gateway environment. |
String | |
| Header |
If-None-Match optional |
Validator for conditional requests; based on the ETag of the formerly retrieved variant of the resourec. |
String | |
| Header |
X-WSO2-Tenant optional |
For cross-tenant invocations, this is used to specify the tenant domain, where the resource need to be retrieved from. |
String |
| HTTP Code | Description | Schema |
|---|---|---|
200 |
OK. Requested WSDL document of the API is returned |
|
304 |
Not Modified. Empty body because the client has already the latest version of the requested resource (Will be supported in future). |
|
404 |
Not Found. The specified resource does not exist. |
Error |
406 |
Not Acceptable. The requested media type is not supported. |
Error |


◆ generateGraph
Convert UserData into graphable data, create a GraphView.
◆ moralOrderButton
| - (IBOutlet UIButton*) moralOrderButton |
|
protected |
button to toggle order type (Asc/Des)
◆ moralSortButton
| - (IBOutlet UIButton*) moralSortButton |
|
protected |
button to toggle sort type (Name/Weight)
◆ moralType
| - (IBOutlet UIImageView*) moralType |
|
protected |
image to depict current status of view (Virtue/Vice)
◆ moralTypeButton
| - (IBOutlet UIButton*) moralTypeButton |
|
protected |
button to switch between Virtue/Vice
◆ moralTypeLabel
| - (IBOutlet UILabel*) moralTypeLabel |
|
protected |
◆ previousButton
| - (IBOutlet UIButton*) previousButton |
|
protected |
◆ reportTableView
| - (IBOutlet UITableView*) reportTableView |
|
protected |
◆ thoughtModalArea
| - (IBOutlet UIView*) thoughtModalArea |
|
protected |
◆ isAlphabetical
◆ isAscending
◆ isGood
is current view for Virtues or Vices
◆ previousScreen
| - (IBOutlet UIImageView*) previousScreen |
|
readwritenonatomicassign |
◆ reportPieModel
The documentation for this category was generated from the following file:


Zlatan Ibile excited as he hugs rapper Cardi B (photos)
- Indigenous rap star Zlatan Ibile recently got to meet rapper Cardi B
- The excited music star flooded his social media page with photos
- Zlatan’s followers flooded his comment section with remarks on the pictures
The entertainment and nightlife scene in Lagos, Nigeria, was recently set abuzz, following the arrival of international rapper, Cardi B, for her concert in the country.
Cardi B had made her presence felt through posts on her official Instagram page, and the several appearances she made at media houses and clubs.
As expected, Nigerian celebrities were not left out of thousands of people that wanted a one-on-one artist to fan moment with the rapper, and indigenous rapper Zlatan Ibile, was among those that got his wish granted.
PAY ATTENTION: Read best news on Nigeria's #1 news app
Zlatan flooded his official Instagram page with photos he took with the international rapper, during her time at a popular nightclub in Lagos.
In the photos, Zlatan and Cardi B were seen exchanging pleasantries.
Check out the pictures below:
PAY ATTENTION: Get your daily relationship tips and advice on Africa Love Aid group
Read some reactions to the photos below:
oyemykke: "The way this man is looking at you fam "
deotheplug: "You teach her that thing?"
healthertainer: "Three of my favs in one picture! Zlatan, Cardi and Burna"
fullstop_man: "Omo, this your hair na million dollar hair"
adedolafunmi01: "She's so humble and jovial"
manias_art: "Leave her waist na @zlatan_ibile bolanle ma binu naw"
Meanwhile Legit.ng previously reported that Cardi B during her visit to Nigeria took to her social media page, and disclosed that she is tired of her hotel room. The Money crooner said she would like to experience the real country, eat jollof rice and fish.
Photos of embattled Mompha all smiles as he appears in court, Nigerians react
PAY ATTENTION: NAIJ.com upgrades to Legit.ng: a letter from our Editor-in-Chief Bayo Olupohunda
NAIJ.com (naija.ng) -> Legit.ng We have upgraded to serve you better
Cardi B full performance in Lagos | Legit TV


Separation Key:
In an excel sheet a separation key is needed to separate the azimuth of dip and the angle of dip. The separation key can be any ASCII-sign.


Security Engineering
In the age where most devices have an IP address, Security Engineering in Hardware Design and Product Development is more critical than ever. It is important therefore to ensure robustness from the ground up.
In today's interconnected world, safeguarding hardware design and product development is crucial to maintaining integrity across all aspects of your business. With our expertise in security engineering, we help you create secure products that protect sensitive information while adhering to industry standards.
Services Offered as a Security Engineer
Secure Hardware Design: collaborate with your team to develop robust hardware designs that incorporate built-in security features such as encryption modules, tamper detection mechanisms, and secure boot processes – effectively mitigating potential threats at the hardware level.
Supply Chain Protection: evaluate your supply chain for vulnerabilities and implement risk mitigation strategies; ensuring components remain untampered throughout the manufacturing process while minimizing exposure to counterfeit or compromised parts.
Firmware Security: review firmware code for potential vulnerabilities using static analysis tools; identify weaknesses within embedded software that could be exploited by malicious actors seeking unauthorized access or control over devices.
Compliance with Industry Standards: ensure all aspects of product design align with relevant industry standards (e.g., FIPS 140-2, ISO/IEC 15408) for enhanced credibility and customer trust; maintain compliance through regular audits or certifications where necessary.
End-to-end Encryption & Secure Communication Protocols: implement strong end-to-end encryption methods on data transmitted between devices preventing eavesdropping or interception further bolstering privacy protection during data transfers interactions within connected ecosystems.
Regular Hardware Security Audits & Updates: conduct periodic security audits on implemented solutions monitoring any emerging threats adjusting defense mechanisms accordingly provide ongoing support to ensure sustained levels of resilience against evolving cyber attacks and enhancing firmware by providing updates and patches to mitigate newly discovered vulnerabilities in order to maximize longevity of deployed systems.
Supply Chain Protection: evaluate your supply chain for vulnerabilities and implement risk mitigation strategies; ensuring components remain untampered throughout the manufacturing process while minimizing exposure to counterfeit or compromised parts.
Firmware Security: review firmware code for potential vulnerabilities using static analysis tools; identify weaknesses within embedded software that could be exploited by malicious actors seeking unauthorized access or control over devices.
Compliance with Industry Standards: ensure all aspects of product design align with relevant industry standards (e.g., FIPS 140-2, ISO/IEC 15408) for enhanced credibility and customer trust; maintain compliance through regular audits or certifications where necessary.
End-to-end Encryption & Secure Communication Protocols: implement strong end-to-end encryption methods on data transmitted between devices preventing eavesdropping or interception further bolstering privacy protection during data transfers interactions within connected ecosystems.
Regular Hardware Security Audits & Updates: conduct periodic security audits on implemented solutions monitoring any emerging threats adjusting defense mechanisms accordingly provide ongoing support to ensure sustained levels of resilience against evolving cyber attacks and enhancing firmware by providing updates and patches to mitigate newly discovered vulnerabilities in order to maximize longevity of deployed systems.
Security Engineering / Cybersecurity Consultant
Having secure hardware and systems is only a part of the puzzle, those systems also exist and are used in the world, by real people and on the public internet. Together we can create personalized security strategies, reliable network or hardware designs or custom-made employee training programs that reinforce your business against cyberattacks. Don't leave the safety of your digital domain to chance – let's collaborate, tell me about the needs of your organisation and I will provide exceptional service to bring you peace of mind and guide you towards a secure future!
Background
With a strong background in technology and engineering and over 13 years of experience actively participating in the hacker scene, from grassroots and the underground to industry including involvement with groundbreaking movements such as the Cryptoparty Movement and the Chaos Computer Club (CCC), I am well-equipped to offer my expertise as a Cybersecurity Expert/Consultant. My primary goal is to utilize my extensive knowledge of security to help orginisations engaged in social change and ethical businesses to protect their digital assets from cyber threats effectively.
The Cryptoparty Movement has been empowering individuals around the world by teaching them how to use encryption tools and techniques that enhance privacy protection. As an active participant in this movement, I have witnessed firsthand its tremendous impact on raising awareness about data privacy and fostering a culture where people prioritize their online safety.
Chaos Computer Club (CCC) As one of Europe's largest hacker organizations, CCC has played a crucial role in advocating for transparency, freedom of information, and personal privacy through various initiatives including conferences, workshops, publications and projects that address relevant issues within society. My experience with CCC has provided me with valuable insights into critical aspects of cybersecurity while exposing me to state-of-the-art methods employed by ethical hackers worldwide.
The Cryptoparty Movement has been empowering individuals around the world by teaching them how to use encryption tools and techniques that enhance privacy protection. As an active participant in this movement, I have witnessed firsthand its tremendous impact on raising awareness about data privacy and fostering a culture where people prioritize their online safety.
Chaos Computer Club (CCC) As one of Europe's largest hacker organizations, CCC has played a crucial role in advocating for transparency, freedom of information, and personal privacy through various initiatives including conferences, workshops, publications and projects that address relevant issues within society. My experience with CCC has provided me with valuable insights into critical aspects of cybersecurity while exposing me to state-of-the-art methods employed by ethical hackers worldwide.
Services Offered as a Cybersecurity Expert/Consultant
Security Risk Assessment: conduct comprehensive assessments on your company's digital infrastructure using advanced threat modeling methodologies; identifying vulnerabilities or weaknesses susceptible to potential cyber attacks.
Secure Network Design: robust network architecture tailored specifically for your business needs; utilizing best practices such as DMZs, VPNs, firewalls configuration optimization while adhering to industry standards ensuring maximum protection against cyber threats.
Penetration Testing Perform rigorous penetration testing simulating real-world hacking scenarios uncovering potential attack vectors before malicious actors exploit them effectively safeguarding your organization from costly data breaches or downtime incidents.
Employee Training & Awareness Programs: develop customized training programs aimed at educating employees about current cybersecurity risks, phishing schemes, social engineering tactics and so on thereby cultivating responsible behavior fostering a security-conscious culture within the workplace.
Incident Response Planning: preparing comprehensive incident response plans outlining procedures to follow in case of cybersecurity breaches, ensuring quick containment and minimal damage to your business operations.
Regulatory Compliance Assistance: provide guidance on staying compliant with industry-specific regulations such as GDPR, HIPAA, PCI-DSS; guaranteeing that your organization meets all legal requirements minimizing potential fines or penalties due to non-compliance.
With my background in Cryptoparty Movement, Chaos Computer Club (CCC), and extensive hands-on experience in cybersecurity, I am confident about assisting businesses in safeguarding their digital assets from ever-evolving cyber threats through strategic planning and effective implementation of robust security practices.
Secure Network Design: robust network architecture tailored specifically for your business needs; utilizing best practices such as DMZs, VPNs, firewalls configuration optimization while adhering to industry standards ensuring maximum protection against cyber threats.
Penetration Testing Perform rigorous penetration testing simulating real-world hacking scenarios uncovering potential attack vectors before malicious actors exploit them effectively safeguarding your organization from costly data breaches or downtime incidents.
Employee Training & Awareness Programs: develop customized training programs aimed at educating employees about current cybersecurity risks, phishing schemes, social engineering tactics and so on thereby cultivating responsible behavior fostering a security-conscious culture within the workplace.
Incident Response Planning: preparing comprehensive incident response plans outlining procedures to follow in case of cybersecurity breaches, ensuring quick containment and minimal damage to your business operations.
Regulatory Compliance Assistance: provide guidance on staying compliant with industry-specific regulations such as GDPR, HIPAA, PCI-DSS; guaranteeing that your organization meets all legal requirements minimizing potential fines or penalties due to non-compliance.
With my background in Cryptoparty Movement, Chaos Computer Club (CCC), and extensive hands-on experience in cybersecurity, I am confident about assisting businesses in safeguarding their digital assets from ever-evolving cyber threats through strategic planning and effective implementation of robust security practices.
Image Gallery


{% load crowdsourcing %} {#{% load bootstrap %}#}
{{ report.get_summary }}
Thanks for your submission.


dcp - distributed file copy program
dcp [cCdfhpRrUv][--] source_file target_file dcp [cCdfhpRrUv][--] source_file ... target_directory
dcp is a file copy tool in the spirit of cp(1) that evenly distributes work across a large cluster without any centralized state. It is designed for copying files which are located on a distributed parallel file system. The method used in the file copy process is a self-stabilization algorithm which enables per-node autonomous processing and a token passing scheme to detect termination.
When copying a source directory to a destination directory, copy the source directory over the destination directory. The default behavior is to copy the source directory inside the destination directory.
Skip the compare operation to confirm file integrity. When using this option, a file integrity check, such as md5sum, should be performed after the file(s) have been copied.
Specify the level of debug information to output. Level may be one of: fatal, err, warn, info, or dbg. Increasingly verbose debug levels include the output of less verbose debug levels.
Remove existing destination files if creation or truncation fails. If the destination filesystem is specified to be unreliable (-U
, --unreliable-filesystem
), this option may lower performance since each failure will cause the entire file to be invalidated and copied again.
Print a brief message listing the dcp(1) options and usage.
Preserve the original files' owner, group, permissions (including the setuid and setgid bits), time of last modification and time of last access. In case duplication of owner or group fails, the setuid and setgid bits are cleared.
Copy directories recursively, and do the right thing when objects other than ordinary files or directories are encountered.
Copy directories recursively, and ignore objects other than ordinary files or directories.
If the filesystem is very unreliable, this option may be used to always retry an operation when a failure occurs. If failures are permanent, this option will cause an infinite loop. Specifying this option when force is enabled (-f
, --force
) may lower performance.
Print version information and exit.
When the force option is specified and truncation fails, the copy and truncation will be stuck in an infinite loop until the truncation operation returns with success.
The maximum supported filename length for any file transfered is approximately 4068 characters. This may be less than the number of characters that your operating system supports.
dcmp
(1). dcp
(1). dfilemaker
(1). dfind
(1). dgrep
(1). dparallel
(1). drm
(1). dtar
(1). dwalk
(1).
The FileUtils source code and all documentation may be downloaded from http://fileutils.io


How to use
Toggle Control panel windown
Controls
Timeline Showing:
Analytics
Scagnostics Viewer
Historical Data
RealTime
Control panel
Visualizing:
Sort
Normalization per plot:
max
min
Apply
reset
User Info


Most good programmers do programming not because they expect to get paid or get adulation by the public, but because it is fun to program.
While I’ve never done anything thing amazing like Linus and invent an operating system, I do love programming. It’s not often you have an opportunity to do what you love, but I’ve been privileged to have that opportunity. Listed below are a few of the projects I’ve worked on over the years.


Enter Title:
Enter Text to translate:
Enter instructions for learner:
Correct Answer:
Add more possible Answers


Method to reorder a large number of cards containing images and some text.
Method to sequentially edit multiple images.


Chattanoogan: Marie House - Painter Of Vivid Colors
by Ralph Petty
posted March 12, 2007
Follow me!
[
mariesartwork
]
Connect with us on Skype [mariesartwork]! We're usually on during our shows! See video of the festivities!


| fkGraphics reference pages |
h=POLARSCATTER h=POLARSCATTER(theta,rho) h=POLARSCATTER(theta,rho,size) h=POLARSCATTER(theta,rho,size,color)
h=POLARSCATTER plots a polar scatter plot of random data. A handle to a polar scatter graphics object is returned.
h=POLARSCATTER(theta,rho) plots a polar scatter plot in the current axes using the angle and radius data. Theta and rho should be vector of the same length.
h=POLARSCATTER(theta,rho,size) sets size data for each marker, which can either be a scalar or a vector the same size as theta and rho.
h=POLARSCATTER(theta,rho,size,color) sets color for each marker, which can either be an index into the colormap, a rgb color vector or a color string. The color argument can be a scalar or should be the same length as theta and rho.
h=POLARBAR(hax,...) will plot in axes with handle hax.
h=POLARBAR(...,param1,val1,...) sets polar scatter properties through parameter/value pairs. Execute set(h) to see a list of valid properties that can be modified.
| additime | Toolbox page | line2patch |


NFL: Eleven teams confirmed for Kaepernick workout
LOS ANGELES, Nov 15 — At least 11 NFL teams will send representatives to a private workout arranged for Colin Kaepernick this weekend, the league confirmed yesterday.
Kaepernick has been unemployed since the end of the 2016-2017 season, when he ignited controversy by kneeling during the pre-game playing of the US national anthem to protest racial injustice.
In an unexpected move on Tuesday, the NFL announced it had arranged a workout for Kaepernick on Saturday and invited all teams to send scouts to watch and interview the ex-San Francisco 49ers star.
Although the timing and details of the workout have been greeted with scepticism in some quarters, Kaepernick welcomed the league move on Tuesday.
“I’ve been in shape and ready for this for three years, can’t wait to see the head coaches and GMs on Saturday,” said Kaepernick, who earlier this year reached a settlement with the NFL after alleging in a legal action he had been “blackballed” by the league.
The NFL yesterday said in a statement 11 teams had committed to attend the session, and more were expected.
“We are looking forward to Saturday’s workout with Colin,” the league said in a statement.
“Eleven teams — Arizona, Atlanta, Cleveland, Denver, Detroit, Miami, New England, New York Giants, New York Jets, Tampa Bay, and Washington — have already committed to attend, and it’s only Thursday.
“With two days remaining until the workout, we expected additional teams to commit.”
Former Oakland Raiders and Cleveland Browns head coach Hue Jackson would be responsible for running drills with Kaepernick, the NFL said.
The league added that video of the workout and an interview with Kaepernick would be sent to the head coaches and general managers of all 32 NFL teams.
Yesterday’s NFL statement came after Kaepernick’s former team-mate Eric Reid and several commentators questioned whether the NFL’s workout was a sincere attempt to find the quarterback a team.
Many sceptics have pointed out that most head coaches and GMs will be busy preparing teams for Sunday fixtures, while team scouts are also more likely to be at college football games.
“It feels like the same play from the NFL,” Reid said on Wednesday.
“It feels disingenuous. At this point it feels like a PR stunt.” — AFP


Beta This is a test version of the layout of this page. Take the survey to help us improve it
Guidance
This document sets out some things you can do if you are concerned about a state-maintained school or academy.
Please also read Complain about a school or childminder .
If you are concerned about your child’s school, you should start by talking directly to the teachers or headteacher or, if necessary, the governing body or the local authority.
If you are not satisfied with the responses you have received, Ofsted may be able to help.
There are a number of things we can do, and in exceptional cases we can arrange an immediate inspection of the school.


--- layout: default layout_grid: true home: true angularjs: true title: EasyNode home sitemap: priority: 1.0 lastmod: 2016-04-17T00:00:00-00:00 ---
Easynode is a framework for microservice written with es6 and integrated a light web service based on koa and a light tcp servic based on native socket. You can utilize all feature characters of ES6 in the framework.
Our general purpose is to code with a synchronized way but run in an asynchronous way for the web project written Node.JS.


We are presented with a video made up of three second clips. The majority of the clips have Yakety Sax playing, but a few do not. Notably, these clips are the first and last clips, and a number of clips that are simply of a stump with a sign that says "I'm John".
The John Stump clips clue, well, John Stump, a satirical composer. In particular, this puzzle refers to his work Faerie's Aire and Death Waltz, as indicated by the first and last clips.
Once we have identified the work that this video is referring to, we find the clips match with the strange and amusing markings of the piece. Tracing a path from marking to marking in the order of the clips in the video spells a letter, with letter breaks indicated by the John Stump clip.
| Music? | Description of Clip | Marking |
|---|---|---|
| No | Faeries playing music. | Faerie's Aire |
| Yes | A bowl of rigatoni pasta. | Rigatoni |
| Yes | A man sitting in a chair balanced on a tightrope on two legs before he falls off of it. | balance your chair on 2 legs |
| Yes | Mute Punk Key for sale on eBay. | sell mute |
| Yes | A woman daydreaming of an armrest. | rests are imaginary |
| Yes | Oil being poured on a gift bow. | oil bow here |
| No | A tree stump with a sign that says "I'm John". | John Stump |
| Yes | A pair of feet being taped together. | Keep both feet together |
| Yes | NBA team Lakers celebrating. | Lakers in 6. |
| Yes | Jon Stewart kicking off the Late Show with "Play ball!" | Play ball! |
| Yes | Someone slapping their thigh. | slap thigh |
| Yes | Someone drops a deck of cards and is excited to see that the diamonds are sorted. | Arranged by Accident |
| Yes | Nighttime driving on a road. | Drive it! |
| No | A tree stump with a sign that says "I'm John". | John Stump |
| Yes | Doctors Without Borders/Medicins Sans Frontieres logo | msf |
| Yes | A couple are walking, then suddenly they duck to avoid a duck. | duck |
| Yes | A timpani with "deal with it" sunglasses and a fan. | Cool Timpani with small fan |
| Yes | A couple are walking, then suddenly they duck to avoid a duck. | duck |
| Yes | Some people release penguins from an enclosure. | release the penguins |
| No | A tree stump with a sign that says "I'm John". | John Stump |
| Yes | Bicycles get added to a pot. | add bicycle |
| Yes | Peanuts are dumped into a slow cooker. | insert peanuts |
| Yes | Someone stares at his phone and becomes frustrated. | gradually become agitated |
| Yes | A man runs quickly across the screen. | Go fast |
| Yes | A cow walks off of a stage. | remove cattle from stage |
| No | A tree stump with a sign that says "I'm John". | John Stump |
| Yes | A cornet casts an Ice spell. | Cornet use ice |
| Yes | A valve is removed from a tank. | remove valve |
| Yes | A mouse cursor clicks a plus icon next to "The Sopranos" logo. | add Sopranos |
| Yes | A string unties from in front of the Slipknot logo. | untie slip knot |
| Yes | A mouse cursor clicks a plus icon next to "The Sopranos" logo. | add Sopranos |
| Yes | Someone does the moonwalk. | Moon-walk |
| Yes | A swimmer does a butterfly stroke. | continue "swimming" motion |
| No | Death, the character from SMITE, appears in a circle of people waltzing. | Death Waltz |
The answer to this puzzle is WHY ME.


Browse all posts published on the website by tags.
Sorted list of all posts published on the website.


--- title: Vector Operations sidebar: documentation_sidebar permalink: VectorsOperations.html folder: documentation toc: false ---
In MTEX, one can calculate with three dimensional directions as with ordinary numbers, i.e. we can use the predefined vectors vector3d.X, vector3d.Y, and vector3d.Z and set
{% highlight matlab %} v = vector3d.X + 2*vector3d.Y {% endhighlight %} {% highlight plaintext %} v = vector3d {% endhighlight %}Moreover, all basic vector operations as "+", "-", "*", inner product, cross product are implemented in MTEX.
{% highlight matlab %} u = dot(v,vector3d.Y) * vector3d.Y + 2 * cross(v,vector3d.Z) {% endhighlight %} {% highlight plaintext %} u = vector3d {% endhighlight %}Besides the standard linear algebra operations, there are also the following functions available in MTEX.
|
angle between two specimen directions |
|
|
inner product |
|
|
cross product |
|
|
length of the specimen directions |
|
|
normalize length to 1 |
|
|
sum over all specimen directions in v |
|
|
mean over all specimen directions in v |
|
|
conversion to spherical coordinates |
A simple example for applying the norm function is to normalize a set of specimen directions
{% highlight matlab %} u = u ./ norm(u) {% endhighlight %} {% highlight plaintext %} u = vector3d {% endhighlight %}As any other MTEX variable you can combine several vectors to a list of vectors. Additionally, all the operators operations mentioned before will work elementwise on a list of vectors. See Working with lists on how to manipulate lists in Matlab.
Using the brackets v = [v1,v2]
two lists of vectors can be joined to a single list. Now each single vector is accesable via v(1)
and v(2)
.
When calculating with concatenated specimen directions all operations are performed componentwise for each specimen direction.
{% highlight matlab %} w = w + v; {% endhighlight %}A list of vectors can be indexed directly by specifying the ids of the vectors one is interested in, e.g.
{% highlight matlab %} % import many vectors from a file fname = fullfile(mtexDataPath,'vector3d','vectors.txt'); v = vector3d.load(fname,'ColumnNames',{'polar angle','azimuth angle'}) % extract vectors 1 to 5 v(1:5) {% endhighlight %} {% highlight plaintext %} v = vector3d size: 1000 x 1 ans = vector3d size: 5 x 1 {% endhighlight %}gives the first 5 vectors from the list, or by logical indexing. The following command plots all vectors with an polar angle smaller then 60 degree
{% highlight matlab %} scatter(v(v.theta<60*degree),'grid','on') {% endhighlight %}


The 2020 Grammy Nominations Are Here
by Morgan BailaIt's nearly the holidays which means one thing: The Grammy nominations are here.
This year, the new Recording Academy President/CEO Deborah Dugan presented the nominees alongside the Chair of the Board of Trustees Harvey Mason Jr.. Alicia Keys, who hosted the 2019 Grammys and is returning — despite her own promise not to — as a host for the 2020 ceremony. Keys popped by the announcements after being introduced by Gayle King to help share the rest of the nominees.
Follow along as we find out whose music is being honoured at the 62nd Annual Grammy Awards on 26th January.
Record of the Year
"Hey Ma," Bon Iver
"Bad Guy," Billie Eilish
"7 rings," Ariana Grande
"Hard Place," H.E.R
"Talk," Khalid
"Old Town Road," Lil Nas X Ft. Billy Ray Cyrus
"Truth Hurts," Lizzo
"Sunflower," Post Malone feat. Swae Lee
Album of the Year
thank u next, Ariana Grande
I Used To Know Her, H.E.R.
Cuz I Love You, Lizzo
Father of the Bride, Vampire Weekend
Norming F***ing Rockwell, Lana del Rey
I,I, Bon Iver
When We All Fall Asleep, Where Do We Go, Billie Eilish
7, Lil Nas X
Song of the Year
"bad guy," performed by Billie Eilish
"Lover," performed by Taylor Swift
"Truth Hurts," performed by Lizzo
"Always Remember Us This Way," performed by Lady Gaga
"Bring My Flowers Now," performed by Tanya Taylor
"Hard Place," performed by H.E.R
"Norman F***ing Rockwell," performed by Lana del Rey
"Someone I Loved," performed by Lewis Capaldi
Best New Artist
Black Pumas
Billie Eilish
Lil Nas X
Maggie Rogers
Rosalia
Tank and the Bangas
Yola
Lizzo
Best Pop Solo Performance
"Spirit," Beyoncé
"7 rings," Ariana Grande
"Truth Hurts," Lizzo
"You Need to Calm Down," Taylor Swift
"Bad Guy," Billie Eilish
Best Pop Vocal Album
The Lion King: The Gift, Beyoncé
When We All Fall Asleep, Where Do We Go?, Billie Eilish
Thank U, Next, Ariana Grande
Lover, Taylor Swift
No. 6 Collaborations Project, Ed Sheeran
Best Rap Album
Revenge of the Dreamers, Dreamville
Championships, Meek Mill
i am > i was, 21 Savage
IGOR, Tyler the Creator
The Lost Boy, YBN Cordae
Best Country Album
Desperate Man, Eric Church
Stronger than the Truth, Reba McEntire
Interstate Gospel, Pistol Annies
Center Point Road, Thomas Rhett
While I'm Livin', Tanya Tucker
Best R&B Performance
"Could've Been" (Performed by H.E.R. Featuring Bryson Tiller)
"Love Again" (Performed by Daniel Caesar & Brandy)
"Exactly How I Feel" (Performed by Lizzo Featuring Gucci Mane)
"Roll Some Mo" (Performed by Lucky Daye)
"Come Home" (Performed by Anderson .Paak Featuring André 3000)
Find the rest of the nominees in the 84 categories, here.