OpenLLM-France/wikimedia huggingface dataset:
# On 2D Inverse Problems/Blaschke products

Let {b$_k$} be a set of n points in the complex unit disc D. The corresponding Blaschke product is defined as
    $B_{b}(z)=\prod _{k}{\frac {|b_{k}|}{b_{k}}}({\frac {b_{k}-z}{1-{\overline {b_{k}}}z}}).$
If the set of points is finite, the function defines the n-to-1 map of the unit disc onto itself,
    $B_{b}:\mathbb {D} {\xrightarrow[]{n\leftrightarrow 1}}\mathbb {D} .$
If the set of points is infinite, the product converges and defines an automorphism of the complex unit disc, given the Blaschke condition
    $\sum _{k}(1-|b_{k}|)<\infty .$
The Cayley transform
    $\tau (z)={\frac {1-z}{1+z}}$
provides a link between the Stieltjes continued fractions and Blaschke products and the Pick-Nevanlinna interpolation problem for the complex unit disc and the half-space.
Exercise(**). Prove that
    $\tau \circ \tau =Id$
and every Stieltjes continued fraction is the conjugate of a Blaschke product w/real b$_k$'s:
    $\beta =\tau \circ (\pm B_{b})\circ \tau .$
and
$\prod _{\beta (\mu _{k})=1}{\frac {1-\mu _{k}}{1+\mu _{k}}}=\pm B_{b}(0)=\prod _{l}b_{l}=\pm {\frac {1-\beta (1)}{1+\beta (1)}}.$
(Hint.) Cayley transform is a 1-to-1 map between the complex unit disc and the half-space.
# On 2D Inverse Problems/Classics

The following classical inverse problems have motivated the typing:
# On 2D Inverse Problems/About the author

On 2D Inverse Problems/redial Daviddaved (discuss • contribs) 01:23, 13 January 2013 (UTC)
# On 2D Inverse Problems/About the book

This book is about the inverse problems that take its roots in medical imaging such as electrical impedance tomography (EIT) and similar imaging methods from geophysics with applications to the oil & gas production industry. The study was motivated by the practical needs of non-destructive and non-intrusive methods for imaging of hidden objects such as internal human/animal organs or Earth's natural resources.
The inverse problems are formulated as the mathematical problems of recovering the coefficients of systems of differential/difference equations from their solutions. These problems are opposite in some sense to the forward problems of evaluating functions. The study of the inverse problems is well suited for computer simulations and many fundamental mathematical problems can be naturally restated as inverse problems.
# On 2D Inverse Problems/Algorithm for solution

The Dirichlet-to-Neumann operator of a rotation invariant network is diagonal in Fourier coordinates. The direct calculation shows that, its eigenvalues are given by the values of the Stieltjes continued fraction at the eigenvalues of the discrete boundary Laplacian -L.
    $\Lambda (G)={\sqrt {-L}}\beta ({\sqrt {-L}}),$
where
    $\beta _{\gamma }(z)=\gamma _{n}z+{\cfrac {1}{\gamma _{n-1}z+{\cfrac {\ldots }{\ldots +{\cfrac {1}{\gamma _{1}z}}}}}}.$
Therefore, one can reduce the layered inverse problem to a Pick-Nevanlinna interpolation problem, since given the Dirichlet-to-Neumann operator of a layered network, one can find its eigenvalues and the interpolating rational function. The conductivities of the network are given then by the coefficients of continued fraction and their reciprocals and can be found by the Eucledian algorithm.
The continuous analog of the inverse problem can be transformed to the inverse problem of Krein for a string.
# On 2D Inverse Problems/Cauchy matrices

    $\det(C_{x})={\frac {\prod _{1\leq k<l\leq n}(x_{l}-x_{k})^{2}}{\prod _{1\leq ,k,l\leq n}(x_{k}+x_{l})}}.$
    Exercise (*). Prove that for any positive numbers $x_{k}$ there is a Stieltjes continued fraction, interpolating the constant unit function at these numbers, $\beta _{x}(x_{k})=1$.
(Hint.) Use the solution of the Pick-Nevanlinna interpolation problem w/the appropriate Cauchy matrix.
    Exercise (**). Prove that for any positive definite matrix M there is a Stieltjes continued fraction, such that $\beta _{M}(M)={\sqrt {M}}$.
# Programming Fundamentals/Conditional Compilation

An introduction and example of conditional compilation as used within the C++ programming language.

## Overview

As you proceed in your programming career, the problems/tasks that need solving become more complex. The documentation of the algorithm done in pseudo code (or some other method) will still need to be converted into a programming solution. Inevitably, when writing that source code mistakes will be introduced. When learning the syntax of a new programming language, programmers sometimes automatically think in their old language syntax, and make mistakes that are sometimes hard to detect.
The concept of using a flag to either activate or have remain dormant certain lines of code designed solely to help with the debugging of a program has existed since almost the beginning of modern computer programming (1950's). One of the debugging tools available within C++ is conditional compilation. For our flag, we would use a defined constant like:
Then using another compiler directive pair, the #if and #endif, we can have the compiler during the pre-processor either include or not include one or more lines of code.
Of course saying "Hi mom!" is not very useful for debugging your code. However, you can use test data with conditional compilation. A series of input data values and a series of output predictors can be placed in the program. Then you can turn on the debug feature or turn them off with your debugging flag.
You should study the demonstration program in conjunction with this module.

## Demonstration Program in C++
### Creating a Folder or Sub-Folder for Source Code Files

Depending on your compiler/IDE, you should decide where to download and store source code files for processing. Prudence dictates that you create these folders as needed prior to downloading source code files. A suggested sub-folder for the Bloodshed Dev-C++ 5 compiler/IDE might be named:
* Demo_Programs
If you have not done so, please create the folder(s) and/or sub-folder(s) as appropriate.

### Download the Demo Program

Download and store the following file(s) to your storage device in the appropriate folder(s). Following the methods of your compiler/IDE, compile and run the program(s). Study the source code file(s) in conjunction with other learning materials. You may need to right click on the link and select "Save Target As" in order to download the file.
Download from Connexions: Demo_Conditional_Compliation.cpp

## Definitions
### conditional compilation

    A compiler directive that includes or excludes lines of code based on a Boolean expression.
# Programming Fundamentals/Condition Examples Python
## References

* Wikiversity: Computer Programming
# Programming Fundamentals/Condition Examples Swift
## References

* Wikiversity: Computer Programming
# Programming Fundamentals/Condition Examples Java
## References

* Wikiversity: Computer Programming
# Programming Fundamentals/Conditional Operator

An introduction to the conditional operator as used within the C++ programming language.

## Overview

The conditional operator is unique in that it has three operands separated by two unconnected operator symbols. All other C++ operators are either unary (one operator and one operand) or binary (one operator and two operands). On the "Abbreviated Precedence Chart for C++ Operators" the conditional operator has the word "trinary" in the comments column. This prefix "tri" means three, thus three operands.
TABLE 1 :
| C++ Operator | Meaning | Comments |
| ? : | conditional | trinary – three operands with two operators |
As an operator it produces a value for the expression. An easy way to explain the conditional operator is to convert an "if then else" control structure to an expression using the conditional operator.

### Example 3: conditional = option 2
#### NOTE:

The use of parenthesizes is needed because of the precedence of operators. The conditional expression is of lower precedence than the insertion (writing) operator.
The first operand is a test expression similar to those that control program flow in control structures. This type of expression is also known as a Boolean expression because they create a Boolean answer of true or false. If the test is true the second operand becomes the value of the expression. If false, the third operand becomes the value of the expression. The operators of the question mark and colon separate the three operands.

### Example 4: general format
## Definitions
### conditional

    A trinary C++ operator that acts like an if then else control structure.
# Programming Fundamentals/Condition Examples
## References

* Wikiversity: Computer Programming
# Programming Fundamentals/Condition Examples C++
## References

* Wikiversity: Computer Programming
# Programming Fundamentals/Condition Examples CSharp
## References

* Wikiversity: Computer Programming
# Programming Fundamentals/Condition Examples JavaScript
## References

* Wikiversity: Computer Programming
# Programming Fundamentals/Conditions
## Overview

This chapter introduces conditions and selection control structures.

## Chapter Outline

* Structured Programming
* Selection Control Structures
* If Then Else
* Code Blocks
* Relational Operators
* Assignment vs Equality
* Logical Operators
* Nested If Then Else
* Case Control Structure
* Condition Examples
* Code Examples
** C++
** C#
** Java
** JavaScript
** Python
** Swift
* Practice: Conditions

## Learning Objectives

* Understand key terms and definitions.
* Given example pseudocode, flowcharts, and source code, create a program that uses conditions and selection control structures to solve a given problem.
# Radiation Oncology/Prostate/Hormones/Drugs

| Front Page: Radiation Oncology | RTOG Trials | Randomized Trials | Edit this |
| Prostate: Main Page | Prostate Overview | Screening and Prevention | Workup | Natural History | External Beam RT | IMRT | Androgen Suppression Therapy | Brachytherapy | Protons | Prostatectomy | Adjuvant RT after Prostatectomy | Salvage RT | Chemotherapy | Localized prostate cancer | Node Positive | Advanced disease | Recurrence after RT | Cryotherapy | RTOG Prostate Trials | Randomized Evidence | |
Classes of Androgen Suppressive Agents
* (Bilateral orchiectomy)
* Estrogens
** Diethyl stilbestrol (DES)
** Estramustine - derivative of estradiol with nitrogen mustard, an alkylating agent with estrogen-induced specificity
* Progestins
** Medroxyprogesterone acetate (Provera)
** Megestrol acetate (Megace) - synthetic progestin, able to lower testosterone and LH/FSH, and block binding of testosterone and dihydrotestosterone to androgen receptor
* Adrenal enzyme inhibitors
** Ketoconazole (works in the testis and adrenal glands) - weak antiandrogen, can reduce levels of androgens produced in testicles and adrenal glands
** Aminoglutethimide (first generation aromatase inhibitor)
* 5-Alpha reductase inhibitors - prevent conversion of testosterone into dihydrotestosterone (DHT)
** Finasteride (Proscar, Propecia) - inhibits only type II
** Dutasteride (Avodart) - inhibits both type I and II
** FCE 28260 (Experimental)
* Gonadotropin-releasing hormone inhibition (Injectable)
** Gonadotropin-releasing hormone agonists
*** Leuprolide acetate (Lupron)
*** Goserelin acetate (Zoladex)
** Gonadotropin-releasing hormone antagonists
*** Abarelix (Plenaxis)- withdrawn
*** Cetrorelix (Cetrotide)
*** Degarelix (Firmagon)
*** Ganirelix (Antagon)
* Non-steroidal anti-androgens (Oral) - androgen receptor blockers
** Flutamide (Eulexin) - 250 mg TID
** Nilutamide (Nilandron)
** Bicalutamide (Casodex) - 50 mg QD - appears to have least side effects
* Steroid anti-androgens - androgen receptor blockers
** Cyproterone acetate (Androcur) - also has weak progestational and glucocorticoid activity
* Abiraterone:
** Medication used in Castration Resistant Prostate Ca
** Increase OS 4m
** Inhibits biosynthesis of testosterione
*** By inhibiting CYP17
**** A hydroxylase enzyme
**** Produced in
***** testis
***** tumor
***** adrenal
**** Action
***** Pregnolonone --> hydroxy-pregnolone
***** Hydroxy-P --> DHEA
*** Side effects:
**** HTN
**** Hypokalemia
**** Fluid retention
*** Required reduced dose in patients with liver disease
Physiology Overview
* GnRH is released by hypothalamus in a pulsatile fashion, and acts on pituitary gland
* Anterior pituitary releases LH and FSH. LH acts on testes to produce testosterone
* Testosterone is metabolized to DHT by 5-alpha reductase
* DHT (and to much smaller extent testosterone) stimulate prostate cancer cells
Side-effects Overview
# Parallel Spectral Numerical Methods/Style Guide and Authors

Please follow the style guide. Changes to the guide should be proposed on the discussion page for agreement of consensus between contributors.

## Style Guide

* This books is written in American English
* While the book tries to be self-contained, references and links outside of wikibooks are encouraged for lengthy explanations, alternative explanations and papers
* The book is primarily about collocation methods
* Equations and figures that are referenced in the text should be labelled
* Example programs are strongly recommended. The primary languages used thus far are Matlab, Python and Fortran; however additions in other languages such as UPC, C, C++, Chapel, OpenCL are welcome

## Authors and Contributors

If you've made a contribution and wish to be recognized, add your name below:
* Gong Chen
* Brandon Cloutier
* Ning Li
* Benson K. Muite
* Paul Rigge
* Sudarshan Balakrishnan
* Andre Souza
* Jeremy West
* Dmalicke
# Parallel Spectral Numerical Methods/Maxwell's Equations

Maxwell’s equations are a set of hyperbolic partial differential equations that describe the propagation of electric and magnetic fields. They can be numerically approximated by several different methods, common methods include: finite element, finite differences, and spectral methods. In this section, we wish to explain how to develop a spectral method scheme to solve Maxwell's equations. To do so, we first introduce Maxwell's equations.
Maxwell’s equations for an observer in the laboratory frame, where no free charges and currents are present, can be written as:
    ${\vec {D}}_{t}-\nabla \times {\vec {H}}=0$         ( 1)
    ${\vec {B}}_{t}+\nabla \times {\vec {E}}=0$         ( 2)
with the relation between the electromagnetic components given by the constitutive relations:
    ${\vec {D}}={\vec {\zeta }}_{e}({\bar {\varepsilon }},{\vec {E}})=\varepsilon _{o}{\vec {E}}+\varepsilon _{o}{\vec {\Phi }}_{e}({\bar {\varepsilon }},{\vec {E}})+{\vec {\upsilon }}\times {\vec {H}}$         ( 3)
    ${\vec {B}}={\vec {\zeta }}_{h}({\bar {\mu }},{\vec {H}})=\mu _{o}{\vec {H}}+\mu _{o}{\vec {\Phi }}_{h}({\bar {\mu }},{\vec {H}})+{\vec {\upsilon }}\times {\vec {E}}$         ( 4)
where ${\bar {\varepsilon }}$ and ${\bar {\mu }}$ are the electromagnetic material properties, analytically they are symmetrical second rank tensors with non zero off-diagonal entries; $\varepsilon _{o}$ and $\mu _{o}$ are the vacuum’s permittivity and permeability, respectively; the functions ${\vec {\Phi }}_{e}$ and ${\vec {\Phi }}_{h}$ are the polarization and magnetization, respectively, material’s response to the incident field; and ${\vec {\upsilon }}$ is known as the dichroic response of the material ..
# Parallel Spectral Numerical Methods/Motivation for Numerical Methods

Many partial differential equations do not have exact closed-form solutions for all choices of initial conditions - an example is the Navier-Stokes equation which is thought to describe the motion of an incompressible viscous fluid. Irregular boundary conditions can also make finding an analytic solution difficult for many partial differential equation. In these cases, finding an approximate solution with a numerical method can be helpful either for physical purposes, engineering purposes or for mathematical investigations of the behavior of solutions to these partial differential equations.
There are also cases where the partial differential equations have explicitly known exact solutions, but the formulae used to express the exact solutions require a large number of computations to evaluate them - an example is the sine-Gordon equation. In this case we are interested in making numerical approximations that result in accurate and cost-efficient solutions.
Numerical methods allows us to use a computer to calculate approximate solutions to partial differential equations. The accuracy of the solution will depend on which numerical method is used and usually more accurate numerical methods tend to be more complicated than less accurate methods. We will therefore start with some simple numerical methods to familiarize ourselves with how numerical methods work. We encourage the reader to take a full course on the numerical solution of partial differential equations as well as reading the references to find out about numerical techniques not discussed here.
# Parallel Spectral Numerical Methods/Style Guide and Contributors

Please follow the style guide. Changes to the guide should be proposed on the discussion page for agreement of consensus between contributors.

## Style Guide

* This books is written in American English.
* While the book tries to be self-contained, references and links outside of wikibooks are encouraged for lengthy explanations, alternative explanations and papers.
* The book is primarily about collocation methods.
* Equations and figures that are referenced in the text should be labelled.
* Each chapter of the book should have its own reference section.
* Example programs are strongly recommended. The primary languages used thus far are Matlab, Python and Fortran; however additions in other languages such as UPC, C, C++, Chapel, OpenCL are welcome.
* Equations, figures and example programs are numbered using templates which are documented here. Equations are numbered with Hindu-Arabic European numerals, figures are numbered with Roman numerals and code is numbered with letters.

## Contributors

If you've made a contribution and wish to be recognized, add your name below:
* Sudarshan Balakrishnan
* Abdullah H. Bargash
* Gong Chen
* Brandon Cloutier
* Ning Li
* Benson K. Muite
* Michael Quell
* Paul Rigge
* Mamdouh Solimani
* Andre Souza
* Abdulaziz S.Thiban
* Jeremy West
* Dave Malicke
* Mark Van Moer
* Damian San Roman Alerigi
This wikibook was originally based on the text Parallel Spectral Numerical Methods The original text (including LaTeX source code and programs) is available at
https://open.umich.edu/find/open-educational-resources/literature-science-arts/parallel-spectral-numerical-methods
# Screen Printing/Making the Stencil

The stencil, which is created on polyester mesh, defines the art to be printed. The stencil consists of a solid area that will not allow the ink to pass and an open area that will allow the ink to be deposited on the substrate.
There are a variety of ways to create stencils suitable for screenprinting. The following sections briefly summarize some of these processes, and the associated sub pages go into more elaborate detail and how-to information.

## Photo Emulsion

The use of a photo emulsion allows the creation of a stencil with near photographic quality. It is perhaps the easiest way in which to make a stencil at a very low cost of approximately USD$0.25 per square foot of stencil area.
Learn How
# Scribbling On Regardless/Making Stickers

Fun & easy stickers using simple materials!

### Materials you'll need

* Sticker paper
* Pens or pencils
* Scissors

### Instructions

Watch our video for a step-by-step guide
* Sketch out your sticker design – what do you want it to be? Maybe use your Art Dice to help you decide…
* Do you want to make one big sticker? Or lots of little ones?
* Draw your design onto the paper
* What shape do you want your stickers to be? Round? Square? Curvy?
* Now decide where it’s going to go… on your sketchbook maybe?

## Next Project

Making a Shrinkie

## Previous Project

3 colour drawing
# Scribbling On Regardless/Making a BoomBuddy

In this tutorial we'll show you how to make and decorate your very own BOOM buddy. If you've got a printer, you can print out the template below. If you don't have a printer, then you can also trace the template by placing a piece of paper up against the screen - but be very careful not to damage the screen! (You might need an adult to help with that. If you are an adult, don't get pen on the screen...)

### Materials you'll need for your BOOM buddy

* Boom buddy template (see below)
* Glue
* Scissors
* Coloured pens or pencils

### Instructions

Watch our video for a step-by-step guide
* Print out your BOOM buddy - we've got 2 sizes to choose from...
* Colour in your BOOM buddy - decorate them however you'd like! They could have rainbows & smiley faces, or maybe they're a robot or a friendly monster?
* Cut out along the solid lines. (Not the dotted ones!)
* Fold along the dotted lines.
* Glue the tabs to the inside of the BOOM buddy.
* Glue the arm pieces to the sides
* Decorate! Does your BOOM buddy need a hat? Are they carrying anything? What are they called?
BOOM buddy templates - click to expand
* Big BOOM buddy
* Regular BOOM buddy

## Next Project

Making ArtDice

## Previous Project

Making a sketchbook
# Scribbling On Regardless
## Preface

This Wikibook was created in March 2020 with input from artists & volunteers at Boom! Community Arts, to help provide arts & crafts activities that can be done at home, with basic materials, during the COVID-19 lockdown in the UK.
Boom! Community Arts usually provides face-to-face art workshops for adults and young people in the North of Glasgow, Scotland, but due to the Coronavirus pandemic, this was no longer possible. We decided to create free-to-access arts & crafts resources to help combat the boredom and social isolation that lockdown and school closures would create.
We'll be Scribbling On Regardless.

## Table of contents

* Materials you will need
* Making a sketchbook
* Making a BoomBuddy
* Making ArtDice
* 3 Colour Drawing
* Making Stickers
* Making a Shrinkie
# Screen Printing/Planning and Executing your Project
## A Brief Overview

In screenprinting, you use a fine mesh material, stretched over a frame, to produce a stencil by blocking parts of the screen with filler material. One of the most popular and effective methods is by using a photo-sensitive material called photo emulsion which hardens when exposed to light. We will describe the process of using this substance to make stencils suitable for screenprinting in the section "Making the Stencil". Once you have a stencil, you use it as a pattern for transfering ink onto your printing surface. The screen helps to prevent you from using too much ink and allows a very sharp edged design to be printed, with a little practice. The screen also allows you to deposit the ink more evenly, and more easily, over the printing surface to help create consistent prints.
The process of creating the stencil can take a few days, but once it's created, printing is fast and easy. You can also save stencils indefinitely for reuse, so those few days are a one time deal for each stencil.

## Materials
### Fabric/Paper

* Keep in mind, when transferring to different materials, different ink will be necessary

### Inks

Many inks available for different materials. Brand list:
* Speedball
** $20 for pack of six

### Printing Frame

* Making one
* Buying one
* Makeshift frames
** Embroidery hoops
*** Usually under two dollars

### Screen Material

What to keep in mind
* Nylon
* Tulle
* Silk