OpenLLM-France/wikimedia huggingface dataset:
# PlanetPhysics/Mikhail Gromov
## Mikhail Leonidovich Gromov

(b. December 23, 1943 in Boksitogorsk, Russia)
Currently at IHES, Mikhail Gromov is a French-Russian geometer with major contributions to modern mathematics over the last 25 years. Some of his most important contributions to modern geometry are in the following areas: Riemannian metrics, solutions of important problems in global Riemannian geometry, convergence of Riemannian manifolds, Gromov compactness principle, distance in abstract spaces, foundations of global symplectic geometry, J-holomorphic curves on symplectic manifolds, Gromov-Witten invariants (of significant interest in modern quantum field theory), groups of polynomial growth and immersion theory.

### Education

Masters degree in Mathematics in 1965, Doctorate in 1969 and a Post-doctoral Thesis in 1973 at Leningrad University.

### Academic career

* Assistant Professor from 1967 to 1974 at Leningrad University.
* Permanent Professor at the Institut des Hautes \'Etudes Scientifiques, Bures-sur-Yvette, France, since 1982. naturalized French citizen since 1992.
* Jay Gould Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University, (in addition to IHES)
* Elected Member of the US National Academy of Sciences.

### Major Awards

* Wolf Prize in 1993
* The Balzan Prize in 1999
* Leroy P. Steele Prize in 1997
* Lobatchewski Medal in 1997
* Kyoto Prize in Basic Sciences in 2002
* Abel Prize in 2009.
# PlanetPhysics/Minkowski's Four Dimensional Space World
## Minkowski's Four-Dimensional Space (``World")

(Supplementary to Section 17)} From Relativity: The Special and General Theory by Albert Einstein
We can characterise the Lorentz transformation still more simply if we introduce the imaginary ${\sqrt {-I}}\cdot ct$ in place of $t$, as time-variable. If, in accordance with this, we insert
   ${\begin{matrix}x_{1}&=&x\\x_{2}&=&y\\x_{3}&=&z\\x_{4}&=&{\sqrt {-I}}\cdot ct\end{matrix}}$
and similarly for the accented system $K^{1}$, then the condition which is identically satisfied by the transformation can be expressed thus:
    ${x'_{1}}^{2}+{x'}_{2}^{2}+{x'}_{3}^{2}+{x'}_{4}^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}\quad .\quad .\quad .\quad {\mbox{(12)}}.$
That is, by the afore-mentioned choice of ``coordinates," (11a) [see the end of Appendix II] is transformed into this equation.
We see from (12) that the imaginary time co-ordinate $x_{4}$, enters into the condition of transformation in exactly the same way as the space co-ordinates $x_{1},x_{2},x_{3}$. It is due to this fact that, according to the theory of relativity, the "time" $x_{4}$, enters into natural laws in the same form as the space co ordinates $x_{1},x_{2},x_{3}$.
A four-dimensional continuum described by the ``co-ordinates" $x_{1},x_{2},x_{3},x_{4}$, was called ``world" by Minkowski, who also termed a point-event a "world-point." From a ``happening" in three-dimensional space, physics becomes, as it were, an ``existence ``in the four-dimensional ``world."
This four-dimensional "world" bears a close similarity to the three-dimensional "space" of (Euclidean) analytical geometry. If we introduce into the latter a new Cartesian co-ordinate system ($x'_{1},x'_{2},x'_{3}$) with the same origin, then $x'_{1},x'_{2},x'_{3}$, are linear homogeneous functions of $x_{1},x_{2},x_{3}$ which identically satisfy the equation
    ${x'}_{1}^{2}+{x'}_{2}^{2}+{x'}_{3}^{2}=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}$
The analogy with (12) is a complete one. We can regard Minkowski's "world" in a formal manner as a four-dimensional Euclidean space (with an imaginary time coordinate); the Lorentz transformation corresponds to a "rotation" of the co-ordinate system in the four-dimensional ``world."
# PlanetPhysics/Methods of Solving ODE

There are many different methods of solving ordinary differential equations that occur in physics. These are tabulated here and divided into sections for linear and non-linear ODEs. These sections are further subdivided into exact, numerical and quantitative methods.

## Linear ODEs
### Exact methods

* General solution of linear differential equation
* Linear differential equation of first order
* Method of separation of variables
* Method of integrating factors
* Method of undetermined coefficients Frobenius' method Method of Green's functions

### Numerical methods

* Runge-Kutta method
* Heun method
* Rayleigh-Ritz method
* Monte Carlo methods
# PlanetPhysics/Moment of Inertia

The moment of inertia of a body about an axis equals the sum of the products of the masses of the particles of the body by the square of their distances from the axis. Thus if dm denotes an element of mass of the body and r its distance from the axis then the following is the analytical statement of the definition of moment of inertia:
   $I=\int _{0}^{m}r^{2}dm$
The integration which is involved in equation (1)is often simplified by a proper choice of the element of mass. The choice depends upon the bounding surfaces of the body and the position of the axis; therefore there is no general rule by which the most convenient element of mass may be selected. There is one important point, however, which the student should always keep in mind in selecting the element of mass, namely, \emph{the distances of the various parts of the element of mass from the axis must not differ by more than infinitesimal lengths}.
{\mathbf theorem I.}
\emph{The moment of inertia of a lamina about an axis which is perpendicular to its plane equals the sum of the moments of inertia with respect to two rectangular axes which lie in the plane of the lamina with their origin on the first axis.}
Suppose the lamina to be in the xy-plane, then the theorem states that the moment of inertia about the z-axis equals the sum of the moments of inertia about the other two axes, that is,
   $I_{x}=I_{x}+I_{y}$
The following analysis explains itself.
$I_{z}=\int _{0}^{m}r^{2}dm$ $I_{z}=\int _{0}^{m}\left(x^{2}+y^{2}\right)dm$ $I_{z}=\int _{0}^{m}x^{2}dm+\int _{0}^{m}y^{2}dm$ $I_{z}=I_{x}+I_{y}$
It is evident from this theorem that when the lamina is rotated about the z-axis $I_{x}$ and $I_{y}$ change, in general, but their sum remains constant.
{\mathbf Theorem II.}
\emph{The moment of inertia of a body about any axis equals its moment of inertia about a parallel axis through the center of mass plus the product of the mass of the body by the square of the distance between the two axes}.
Let the axis be perpendicular to the plane of the paper and pass through the point $O$, Fig. 86.
\begin{figure} \includegraphics[scale=.6]{Fig86.eps} \vspace{20 pt} \end{figure}
Further let $dm$ be any element of mass, $r$ its distance from the axis through $O$, and $r_{c}$ its distance from a parallel axis through the center of mass, $C$. We have
$I=\int _{0}^{m}r^{2}dm$ $I=\int _{0}^{m}\left(r_{c}^{2}+a^{2}-2ar_{c}\cos \theta \right)dm$ $I=\int _{0}^{m}r_{c}^{2}dm+\int _{0}^{m}a^{2}dm-2a\int _{0}^{m}r_{c}\cos \theta dm$ $I=I_{c}+ma^{2}-2a\int _{0}^{m}xdm$
But by the definition of the center of mass $\int _{0}^{m}xdm=m{\bar {x}}$ and in the present case the center of mass is at the origin therefore ${\bar {x}}$ and consequently the last integral vanishes. Thus we get
   $I=I_{c}+ma^{2}$
# PlanetPhysics/Metric Tensor

\setcounter{section}{1}
A metric tensor is a second rank tensor with a contravariant rank of zero and a covariant rank of two (0,2) with the conditions:
* symmetric tensor
* determinant does not equal zero
References
[1] Sean M. Carroll, "Lecture Notes on General Relativity.", Enrico Fermi Institute, 1997, Notes
[2] John Stewart, "Advanced General Relativity.", Cambridge University Press (1993)
[3] N.M.J. Woodhouse, "General Relativity.", Springer (2006).
# PlanetPhysics/Mircea Sabau
### Prof. Dr. Mircea N. Sabau

(b. August 24, 1934- d. June 15, 2009).
He was born at Turda, and became a Medical Physicist and Professor of Medical Physics and Health Physics, at the University of Chicago, IL, and until 2003 the Head of Radiology Dept. at Baylor Medical School of Dallas, TX.
He became an Emeritus Professor in 1998 and a Member of the American-Romanian Academy of Arts and Sciences in 1990.

#### Education

He studied at the School of Physics at the University of Bucharest between 1952 and 1957. After he obtained his M.S. in nuclear physics in Bucharest he worked for 18 years on nuclear reactors at the Institute of Atomic Physics. Then, he continued with High energy physics studies and earned his Pd.D. degree in 1970 with a thesis on high energy physics.

### Research and Publications

He was then able to study at the Institute of Nuclear Physics at Dubna, in the former USSR, at the time the only foreign country where postdoctoral research was allowed from Romania.
In 1975 he succeeded to travel with his family to Chicago and transferred to the Argonne Laboratory where he studied high energy physics until the late 1970's when funding for high energy physics at Argonne was drastically reduced. Since 1980 until his retirement in 1998 he worked at the University of Chicago as a Professor of Medical Physics, specialized in Nuclear Medicine, with a 4-year appointment at the Baylor Medical Center of Dallas University since 1999 as the Head of the Department of Radiology. He published over 150 scientific papers in peer-reviewed journals and participated at over 50 International Conferences and meetings.
He has also contributed for 10 years numerous documents for Human Rights that were presented to the United Nations Council.

#### Selected Publications

Gerald L. Buchel, Mircea N. Sabau, T. Lyle Wilson, John J. Sadler. 1998. Evaluation of a test device to assess X-ray phototimers Radiologic Technology, July-August, 1998.
# Survey research and design in psychology/Readings/Textbooks/HowittCramer/2014b

Howitt, D. & Cramer, D. (2014b). Introduction to SPSS in psychology (6th ed.). Harlow, UK: Pearson. ISBN 1292000694 | RR AU$59.40 | Co-op: AU$47.52 | Publisher site | Companion site | Educator resources
# Survey research and design in psychology/Readings/Textbooks/HowittCramer/2017a

Howitt, D. & Cramer, D. (2017a). Understanding Statistics in Psychology with SPSS (7th ed.). Harlow, UK: Pearson. ISBN 1292134216 | eBook | Educator resources
# Survey research and design in psychology/Readings/Textbooks/HowittCramer/2017b

Howitt, D. & Cramer, D. (2017b). Introduction to SPSS in psychology (7th ed.). Harlow, UK: Pearson. ISBN 1292186666 | Publisher site
# Survey research and design in psychology/Readings/Textbooks/Pallant/2010

Pallant, J. (2010). SPSS survival manual (4th ed.). London: Open University Press. (Download 1st ed. online - no cost)
# Survey research and design in psychology/Readings/Textbooks/Pallant/2013

Pallant, J. (2013). SPSS survival manual (5th ed.). London: Open University Press. ISBN 9781743314005. AU$45. Publisher site
# Survey research and design in psychology/Readings/Textbooks/HowittCramer/2011b

Howitt, D. & Cramer, D. (2011). Introduction to SPSS statistics in psychology. For version 19 and earlier (5th ed.). Harlow, UK: Pearson. ISBN 9780273734260 | RR AU$56.84 Co-op member AU$51.15 | Publisher site | UC Library: HA32.F72 2011
# Survey research and design in psychology/Readings/Textbooks/HowittCramer/2014a

Howitt, D. & Cramer, D. (2014a). Introduction to statistics in psychology (6th ed.). Harlow, UK: Pearson. ISBN 1292000740 | RR: AU$87.95 | Co-op member: AU$70.36 | Publisher site | Companion site | Educator resources | UC library
# Survey research and design in psychology/Readings/Textbooks/Pallant/2007

Pallant, J. (2007). SPSS survival manual (3rd ed.). London: Open University Press. ISBN 9781742373928 | AU$45.00 Co-op member AU$41.85 | Publisher site | Download 1st ed. | New 6th edition due March, 2016. ISBN 9781760291952
# Survey research and design in psychology/Readings/Textbooks/HowittCramer/2011a

Howitt, D. & Cramer, D. (2011). Introduction to statistics in psychology (5th ed.). Harlow, UK: Pearson. ISBN 9780273734307 | RR: AU$105.05 Co-op member: AU$97.70 | Publisher site | Companion site | Instructor resources | UC library: BF39.H69 2011
# Survey research and design in psychology/Readings/Textbooks/Pallant

Pallant, J. (2007). SPSS survival manual (3rd ed.). London: Open University Press. ISBN 9781742373928 | AU$45.00 Co-op member AU$41.85 | Publisher site | Download 1st ed. | New 6th edition due March, 2016. ISBN 9781760291952
Pallant, J. (2013). SPSS survival manual (5th ed.). London: Open University Press. ISBN 9781743314005. AU$45. Publisher site
Pallant, J. (2016). SPSS survival manual (6th ed.). Sydney: Allen and Unwin. ISBN 9781760291952. RRP AU$49.99. Publisher site
# Status of education system in the Philippines

Status of Education System in The Philippines
There are three agencies that have been created through various republic acts that comprises the education system in the Philippines. They are the Department of Education (DepEd) for basic education from Kinder to senior high school, the Commission on Higher Education (CHED) for college and graduate education and the Technical Education and Skills Development Authorities (TESDA0 for various technical and vocational education and training.
Due to Covid-19 pandemic, face to face classes were suspended and the schools were closed all over the Philippines. But this must not be a reason to stop the department from giving quality education to pupils. To continue with the learning, the education sector recommended a new way of learning which is the online learning. But there are many problems that occur in online learning. Poor students do not have the money to constantly have access to the internet. Another problem is for those who live in remote places where internet signal is too weak or completely absent. Because of these problems another learning modality was introduced. It is the printed modular learning modality which is commonly used modality in remote areas like ours. In this kind of modality, the parents or guardians of the pupils is scheduled to go to school to get the printed modules and other activity sheets to be accomplish by the pupils at home. The teacher's duty is to monitor them and help them in accomplishing their tasks using different platforms. The teacher can also send video lessons for their better understanding or they can call or text the pupils or the guardians for monitoring. Others use radio or television as their learning modality. Some are using the blended learning modality which is the combination of all the other modalities mentioned.
Our education sector really find ways to continue the education of our pupils even in this difficult time of pandemic. Whatever learning modality we are using the most important thing is that we always find ways to help our pupils and their parents in coping with this new modality of teaching and learning in our country. We must not stop praying that this pandemic ends so that we could go back to our normal lives.
# Statistics in plain view
## Descriptive Statistics
### Univariate Data

* Data Vectors (pdf)
* Numeric Summaries (pdf)

### Bivariate Data

* Independent Samples (pdf)

### Central Tendency and Variability

* Expected Value (D.pdf)

### Linear Regression
## Inferential Statistics
### Overview

* Overview (pdf)

### Random Sampling

* Random Sampling (pdf)

### Binomial Distribution

* Binomial Distribution (pdf)

### Hypothesis Test

* Hypothesis Testing (pdf)

### Sampling Distribution and z-Test

* z Test (pdf)

### t-Test for Single Samples

* t Test - I (pdf)

### t-Test for Correlated and Independent Groups

* t Test - II (pdf)

### Analysis of Variance

* ANOVA (pdf)

### Chi-Square Test

* Chi-Square Test (pdf)
* Monte Carlo Algorithms (C.pdf)
go to [ Electrical_&_Computer_Engineering_Studies ]
# Statistics/OpenStat/Research projects/Formatting rules and function for importing into R

What is the most easyiest and consintent way defining timedependet datasets and importing into R?
Data structures as the MAMEU example can be imported e.g. with the following R-script (click edit to conserve formating):
library(XML) wikiurl <- 'http://en.wikiversity.org/w/index.php?title=Topic:Statistics:OpenStat:MAMEU&action=edit' page <- htmlTreeParse( readLines( url(wikiurl),encoding='UTF-8' ), asText=TRUE ) part <- (page$children$html$children$body$children$div$children$div$children$div['div',all=TRUE][2]$div$children) textfeld <- part$form$children$textarea$children$text$value #split by main titles textfeld <- strsplit(as.character(textfeld),'==')[[1]] dataname <- gsub('=','',as.character(textfeld[1])) dataname <- gsub('\n','',as.character(dataname[1])) dataname <- gsub('Data ','',as.character(dataname[1])) dataname description <-textfeld[3] description ### make dataframe eval(parse(text=paste(dataname,' <- data.frame(year=1:2100)'))) ### make dataframe comment eval(parse(text=paste('comment(',dataname,') <-\"',description,'\"'))) # ### descripion of the structure variablestructure <- textfeld[5] ### referenceslist references <- textfeld[7] ### the folloing variables counter <- (1:length(textfeld))[-c(1:7)] counter <- seq(from=counter[1],to=counter[length(counter)],by=2) ### for each variable
for (count in counter) { variablename <- gsub('^ *= *','',textfeld[count]) variablename <- gsub(' ','_',variablename) variablename <- gsub('\\(','',variablename) variablename <- gsub('\\)','',variablename) variablename <- gsub('/','_',variablename) ### variablename print(variablename) #eval(parse(text=paste(variablename,' <- numeric',sep=''))) #print(ls) vardatalist <- unlist(strsplit(textfeld[count+1],'\n')) missing <- c(grep('^=$',vardatalist),grep('^-*$',vardatalist)) missing vardatalist <- vardatalist[-missing] varlist <- strsplit(vardatalist,'\\|') varrefyear <- lapply(1:length(varlist),function(number){ varlist[[number]][1] }) varrefyear <- as.numeric(gsub(' *','',varrefyear)) vardata <- lapply(1:length(varlist),function(number){ varlist[[number]][2] }) vardata <- as.numeric(gsub(' *','',vardata)) varsource<- lapply(1:length(varlist),function(number){ varlist[[number]][3] }) varcomment <- paste(lapply(1:length(varlist),function(number){ varlist[[number]][4] }),lapply(1:length(varlist),function(number){ varlist[[number]][5] })) #varcomment varsource eval(parse(text=paste(dataname,'$',variablename,'[',dataname,'$','year==',varrefyear,'] <- ',vardata,sep=''))) } print(eval(parse(text=dataname)))
# Statistics for Business Decisions
## Statistics in Marketing

Marketing uses a number of statistical techniques both to better understand and target materials to certain groups of customers as well as to measure the effectiveness of various marketing efforts. Some of these techniques are listed below...

### Basic Statistics
#### Indexing

The use of indexes can be used to help identify that certain subgroups of data are different from an established benchmark. For a simplified example, let's compare the population of a hypothetical country and the population of a hypothetical school by age group.
| Table A |
| Age Group | Country | School |
| 0 - 10 | 20% | 40% |
| 11 - 20 | 20% | 40% |
| 21 - 40 | 20% | 10% |
| 41 - 60 | 20% | 10% |
| 61 + | 20% | 0% |
| Total | 100% | 100% |
Let's call the percentage distribution for the country the benchmark (this serves as a ruler to compare other groups too). In this case we will take the school percentage distribution column and divide it by the benchmark's percentage distribution. This establishes a new column which we will call the index.
| Table B |
| Age Group | Country | School | Index |
| 0 - 10 | 20% | 40% | 2.0 |
| 11 - 20 | 20% | 40% | 2.0 |
| 21 - 40 | 20% | 10% | 0.5 |
| 41 - 60 | 20% | 10% | 0.5 |
| 61 + | 20% | 0% | 0.0 |
| Total | 100% | 100% | 1.0 |
The index column in table B can identify that the age distribution in the school differs significantly from the benchmark (the population of the country). The index indicates how much more or less likely it is to encounter a given group.
Applying Indexes
Indexes can be applied against multiple groups of people and multiple variables. This can aid in understanding how customers differ in certain geographical areas. It can also be used as a basic tool to find if customers you are wanting to target are more likely to live in certain areas.

### Advanced Statistics
#### Data Mining
## See Also

* https://openstax.org/details/books/introductory-business-statistics OpenStax: Introductory Business Statistics]]
# Stem cells

Welcome to the Stem Cells Study Project.

## Content summary

Stem cells are undifferenciated cells that can be found in bone marrow, aborted fetuses, menstrual blood, exc. They have shown potential to replace damaged body tissue and repair spinal cord injuries. Parkinson's Disease is also a subject in stem cell research and has show some progress. Some countries have banned stem cell research since the embryonic stem cell type involves the disposal of fertilized female embryo (Zygote) in order to retrieve a mass of 30 stem cells the eighth day of life.
Scientists have recently developed a method to transform normal human somatic cells into pluripotent cells via the introduction of four different factors. The converted cells are called induced pluripotent stem cells (iPSCs).

## Goals

Help Wikiversity participants understand what stem cells are and how they can be used in medical treatments. This interdisciplinary project also investigates why and how some governments regulate stem cell research.

## Learning materials

Learning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the lesson (lessons are independent pages in the main namespace) and start writing!
You should also read about the Wikiversity:Learning model. Lessons should center on learning activities for Wikiversity participants. Learning materials and learning projects can be used by multiple projects. Cooperate with other departments that use the same learning resource.

### Texts

* b:__Textbook Name___

### Lessons

* Lesson 1: ...

### Assignments
#### Activities

* Activity 1.
* etc.

#### Readings

Each activity has a suggested associated background reading selection.
* Reading 1:
   * Study guide:
   * Wikipedia article: Stem Cells
* Reading 2 (howto example):
   * Study guide:
   * Wikipedia article: w: __Article Name__
* etc.
# Student Projects/Radioactivity

Radioactivity
Radioactivity was first discovered by Henry Becquerel in the year 1896. The natural phenomenon in which heavy nuclei disintegrates (decays) spontaneously with the emission of certain radiations is called as Natural Radioactivity. It is also known as radioactive decay.
Types of Radioactive Decay:
α – decay: The radioactive decay where a helium nucleus is emitted with positive charge is called as α – decay. In α – decay, the atomic number (A) of product (daughter) nucleus decreases by 2 and mass number (Z) decreases by 4 than that of the parent.
The α – decay can be written as,
* $_Z$X$^A$         ----→                         $_{Z-2}$Y$^{A-4}$     +       $_2$He$^4$     +    Q
* (Parent)                   (Daughter)     (α - particle)
β – decay: The radioactive decay where electrons or positrons are emitted is called as β – decay. In β – decay, the mass number (Z) of the product nucleus remains the same but its atomic number changes by 1 than that of the parent.
The β – decay can be written as,
* $_Z$X$^A$    –––––→               $_{Z±1}$Y$^A$     +     e$^{-1}$    or   e$^{+1}$
* (Parent)                  (Daughter)     (electron)   (positron)
γ – decay: The radioactive decay where high energy photons are emitted is called as γ – decay. The emission of γ – ray dischanges the nucleus i.e., no change in A or Z. After emission of α or β particle, the nucleus is in excited energy state. The excited nucleus returns to lower energy state or ground state by emitting γ – rays.
All radioactive nuclei emit either α –rays or β – rays, followed by the emission of γ – rays. α –rays and β – rays are never simultaneously emitted. During disintegration of radioactive material both energy and charge are conserved.
References:
http://www.ncert.nic.in/ncerts/l/leph205.pdf