text:
The role of universities in the "open content" world

Introduction
Universities are still the major place in society where, worldwide, millions of people create, process, use, adapt and distribute knowledge, in various forms and types. In their mission statements universities often underline their public role in terms of the responsibility for active  knowledge sharing between academics and the dissemination of knowledge to the society in general. The ‘public’ role of the university can also be connected to its being a kind of “refuge” for research and education (K.U.Leuven speaks about vrijplaats) which obviously refers to its particular (academic) freedom. In this contribution, however, public refers to the open character of generated knowledge and technology, though one could argue that current policies at the K.U.Leuven also limit  academic freedom and the notion of public that is implied.

Our aim is to focus on the tension between the overall ambition of an increased number of universities for active knowledge sharing and the fact that their concrete policy practices rather discourage knowledge sharing, even encourage knowledge privatization. This tension will be illustrated by focusing on some concrete policy practices of the K.U.Leuven. More in particular we will clarify that the performance indicators that are formulated by the K.U.Leuven encourages researchers to generate knowledge and technology only under proprietary licenses, that is, licensed under exclusive legal right of the copyright holder. In opposition to this, we will elaborate in the second part of our contribution on several methods to publish knowledge and technology under open licenses and open standards. These methods are not valorized and, as a result, discouraged by current policy practices at the K.U.Leuven also limit academic freedom and the notion of public that is implied.

Performance Indicators
In order for an organization to valorize its performance, the K.U.Leuven underlines that performance indicators are required. These indicators are formulated for research, academic service, education, internationalization, … etc. We focus here on the first two elements: research and academic service (wetenschappelijke dienstverlening). The complete mission statement (only in Dutch) summarizes Key performance indicators (KPI) that are used to monitor the input, process and result.

K.U.Leuven performance indicators for research
It is important to underline that the K.U.Leuven, by taking the number of published papers together with their impact factor and number of citations as indicators for the valorization of research performance, imposes a policy that discourages active knowledge sharing. Researchers are stimulated to distribute their work in journals that come with high impact factors, yet proprietary license. Open knowledge sharing through open software, open content or the development of open standards simply do not count (no valorization) as publications. Most Open access journals, being only recently set up, are hardly valorized as they come with a very low impact (taking the citations of the last two to five years into account). As a consequence, these journals do not attract the best articles and there the viscous circle starts. In other words, the use of the K.U.Leuven performance indicators discourages people to openly exchange knowledge and technology and cultivates its privatization. This might sound strange in the context of a publication policy.

K.U.Leuven performance indicators for academic service (wetenschappelijke dienstverlening)
Here again, we want to underline that, taking the number of generated patents or spin-offs as performance indicators, the K.U.Leuven discourages active knowledge sharing and supports knowledge privatization. Here as well, in view of the expectation to maximize patenting opportunities, researchers are stimulated to generate knowledge and technology under proprietary licenses. In this context, K.U.Leuven has set up a technology transfer office (TTO), the K.U.Leuven Research & Development (LRD) that supports researchers in their interaction with industry and society (covering contract and collaborative research, patenting and licensing and spin-off creation) and in the valorization of their research results. The third indicator, industrial revenue, discourages researchers to use (mainly free) open source software as they are rewarded for spending a lot of money (for example on software licenses).

Open licenses and open standards
In this short exploration of active knowledge sharing and open knowledge construction, we make a distinction between open software, open content, open access and open standards.

Open software licenses
In contrast to proprietary software licenses that imply that certain rights regarding the software - inspection of code, modification and distribution - are reserved by the software publisher, open software licenses make software free for inspection of its code, modification, and distribution. These initiatives have the intention to maximise the distribution of knowledge that is collected in the software code. We will focus here on three distinct types of software licenses:

 * 1) GNU General Public License (GPL)
 * 2) Berkeley Software Distribution (BSD) license
 * 3) GNU Lesser General Public License (LGPL)

Roughly speaking, the GPL forces users to release all their changes to GPLed software, including the software they added "externally". The BSD does not impose any release of changes, but does not allow you to call the software your own. The LGPL is somewhere in between: it expects release of improvements, but allows linking  with the software without the obligation to release it.

GNU General Public License (GPL): Free speech as a moral duty
Richard Matthew Stallman was the first important American 'software freedom activist. In September 1983, he launched the GNU Project to create a free Unix-like operating system, and has been the project's lead architect and organizer. With the launch of the GNU Project, he initiated the free software movement; in October 1985 he founded the Free Software Foundation.

Stallman pioneered the concept of copyleft and he is the main author of several copyleft licenses including the GNU General Public License, the most widely used free software license.

Copyleft is a play on the word copyright to describe the practice of using copyright law to offer the right to distribute copies and modified versions of a work and requiring that the same rights be preserved in modified versions of the work. In other words, copyleft is a general method for making a program (or other work) free, and requiring all modified and extended versions of the program to be free as well.

Copyleft licenses are sometimes referred to as "viral licenses" because any works derived from a copyleft work must themselves be copyleft when distributed (and thus they exhibit a viral phenomenon). The term 'General Public Virus', or 'GNU Public Virus' (GPV), has a long history on the Internet, dating back to shortly after the GPL was first conceived.

Stallman argues that software users should have the freedom to share with their neighbour and to be able to study and make changes to the software that they use. He maintains that attempts by proprietary software vendors to prohibit these acts are antisocial and unethical. The phrase "software wants to be free" is often incorrectly attributed to him, and Stallman argues that this is a misstatement of his philosophy. He argues that freedom is vital for the sake of users and society as a moral value, and not merely for pragmatic reasons such as possibly developing technically superior software.

Berkeley Software Distribution (BSD) license: Free speech as a pragmatic choice
BSD licenses are a family of permissive free software licenses. The original license was used for the Berkeley Software Distribution (BSD), a Unix-like operating system after which it is named. The licenses have fewer restrictions on distribution compared to other free software licenses such as the GNU General Public License or even the default restrictions provided by copyright, putting them relatively closer to the public domain.

In distinction to viral license, BSD licenses are open source, that is, they allow inspection of source code in order to improve unlimited redistribution. Yet, there is no obligation of distribution under copyleft terms. One of the initial BSD licenses is shown below.

Copyright (c) , All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of the nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL  BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

The permissive nature of the BSD license allows companies to distribute derived products as proprietary software without exposing source code and sometimes intellectual property to competitors. Searching for strings containing "University of California, Berkeley" in the documentation of products, in the static data sections of binaries and ROMs, or as part of other information about a software program, will often show BSD code has been used. This permissiveness also makes BSD code suitable for use in open source products, and the license is compatible with many other open source licenses. The permissive nature of the BSD license also allows derivative works of code released originally under the BSD license to become less permissive with time.

GNU Lesser General Public License (LGPL) : A compromise between GPL and BSD
The GNU Lesser General Public License (formerly the GNU Library General Public License) or LGPL is a free software license published by the Free Software Foundation (FSF). It was designed as a compromise between the strong-copyleft GPL and permissive licenses such as the BSD licenses. The GNU Library General Public License (as the LGPL was originally named) was published in 1991, and was the version number 2 for parity with GPL version 2. The LGPL was revised in minor ways in the 2.1 point release, published in 1999, when it was renamed the GNU Lesser General Public License to reflect the FSF's position that not all libraries should use it.

The LGPL places copyleft restrictions on the program itself but does not apply these restrictions to other software that merely links with the program. There are, however, certain other restrictions on this software.

The LGPL is primarily used for computer science software libraries, although it is also used by some stand-alone applications, most notably Mozilla and Openoffice.org and sometimes media as well.

Open content licenses
Open content involves any kind of creative work, or content, published under an open content license (OPL) that explicitly allows copying and/or modification of the information by anyone. Hence, it includes the right to modify the work. Open content therefore is an alternative paradigm to the use of copyright that ultimately creates a monopoly over the knowledge. One of the largest open content project is Wikipedia. It is interesting to notice that the K.U.Leuven runs a WikiServer that provides WikiSpace for educational purposes. Yet, the open character is lost because one needs to log in using the Toledo Blackboard (a digital learning platform) in order to get access.

Open access licenses
Open access (OA) refers to unrestricted online access to (mainly) peer-reviewed scholarly journal articles. While in scholarly publishing it is common to keep an article's content intact and to associate it with a fixed author, open access (publishing) mostly offers access to the material and defines a set of use (or re-use) rights, included in Creative Commons Licenses. These Licenses replace the model of all rights reserved of copyright with the more flexible model of some rights reserved. In other words, through a Creative Commons License creators communicate which rights they reserve and which rights they waive for the benefit of recipients or other creators (in order to make the material open content). Different models for financing OA journals exist. Some charge publication fees (paid by authors or by their funding agencies or employers) and some do not. Some of the no-fee journals have institutional subsidies, where others do not.

An example of open access (publishing) is Open CourseWare (OCW). This is a collection of high quality course materials in a virtual learning environment created by universities (Berkeley, MIT, Yale, Notre Dame, Michigan, TU_Delft, Stanford, …) and shared freely with the world via the internet. In addition to that, there are several open access journals. We mentioned earlier that the problem with this type of journals is that their impact factor, based on the number of citations to articles published during the two to five preceding years, is initially very low. However, there are some well-known examples of open access journals, which are mainly to be found in the medical sciences, such as: BioMed Central (BMC), MedKnow Publications, [ http://publicaccess.nih.gov/  National Institute of Health Public Access (NIH)] and  Public Library of science (PloS). Many open access academic publication platforms (with participation of K.U.Leuven academics) can be found within a wide variety of scientific fields: the field of Software Engineering for Robotics, the BioMedical and Scientific field, chemistry, Molecular Imaging, etc.

Open standards
Open standards are certain specifications of technologies that are publicly available. They are meant to facilitate interoperability and data exchange among different products or services and are intended for widespread adoption. Some examples of open standards are: Open Document Format (ODF) used by Open Office, Portable Network Graphics (PNG) images, Portable Document Format (PDF/X) designed by Adobe Systems.

Although current policies actually discourage knowledge sharing, and in fact encourage knowledge privatisation, our short overview of initiatives and methods should clarify that it is possible to ‘open up’ knowledge production and distribution within universities. Perhaps it is important to start validating and supporting these initiatives and methods – as part of the public role of the university, and in order to make real their mission statements.

Open source software projects
Multiple project in OPTEC: K.U.Leuven Center of Excellence: Optimization in Engineering
 * Acado Toolkit - A Toolkit for Automatic Control and Dynamic Optimization (open-source), Boris Houska and Hans Joachim Ferreau (for C++ and Matlab).
 * qpOASES- Parametric Quadratic Programming for MPC (open-source), Hans Joachim Ferreau.
 * lssvmlab- a Least Squares Support Vector Machines toolbox.
 * timeopt - Time Optimal Robot Trajectory Planning (open-source), Diederik Verscheure.
 * glas- Generic Linear Algebra Software (open-source), Karl Meerbergen.
 * rdp- Robust Dynamic Programming (open-source), Moritz Diehl and Jakob Björnberg.
 * liftopt- Nonlinear Optimization (open-source), Jan Albersmeyer.
 * orocos- Smarter control in robotics & automation! (open-source), Herman Bruyninckx and Peter Soetens.
 * SCPCVX - an interface for Sequential Convex Programming Methods (SCP) using the CVX package in Matlab.

The Bioinformatics Research Group
 * Toucan-2 is a workbench for regulatory sequence analysis on metazoan genomes : comparative genomics, detection of significant transcription factor binding sites, and     detection of cis-regulatory modules (combinations of binding sites) in sets of coexpressed/coregulated genes.

The VISICS, a part of the Centre for Processing Speech and Images (PSI) within the K.U.Leuven
 * ARC 3D Webservice is a Family of Web Tools for Remote 3D Reconstruction.

Open content projects
Faculty or Arts, Katholieke Universiteit Leuven
 * MultiCampus Open Educational Resources: the case of OER-HE

Department of mechanical engineering: Wikipages designed within a course embedded control systems
 * Embedded control design systems

Suggestions for improvement

 * 1) KPI adaptation

 * 1) Active support of 'open' initiatives

 * 1) Creation of an 'open' course content platform


license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

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User:Pibeagles

I am here to look around. I only make slight adjustments when I edit, like spelling errors and stuff. I was just curious as to what kinds of things that account holders can do that everybody else can't.

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User:Cosmos~enwikiversity

Looking forward to contributing.

title: User:Cosmos~enwikiversity


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User talk:Cosmos~enwikiversity

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Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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text:
Digital Logic 1

Course objectives
This course presents the student with an introduction to boolean logic. While the information is presented with digital circuits in mind, the first section of the course talks about the overall concept of logic, boolean operations, and how to combine them in a way that is agnostic of the medium. As a result, this course will also help students looking to pursue software programming or even discrete mathematics.

The course as a whole has been planned to allow students who complete this course to gain a mastery in the analysis and design of both combinational and sequential logic circuits.

=Prerequisites= This course assumes student has fundamental knowledge of basic circuit analysis (Ohm's Law, Node Voltage, Mesh Current, Norton, Thevenin, and Superposition).

While a student could learn the material just by reading the course's explanations and completing the included activities, the material in this course is best learned by performing experiments by prototyping the logic on a breadboard using logic chips or laying out the logic in a program such as Logisim.

The following chips should be sufficient for completing all of the activities in the course.

= Topics = Basics Combinational Logic Sequential Logic = See also =
 * Number Systems and Conversions
 * Logic Gates and Symbols
 * Truth Tables and Boolean Algebra
 * Minimization and Implementation with Karnaugh Maps
 * Adders, Subtractors, Multipliers, and Comparators
 * Multiplexers, Encoders, and Decoders
 * Flip Flops
 * Latches
 * Digital Logic 2 (HDL and FPGAs)

=References and Contributors=

Textbook used: Fundamentals of Digital Logic by Brown and Vranesic Copyright 2003, McGraw Hill Higher-Ed

Contributor: User:Man4857 Vincent Nhieu, Student California State Polytechnic University, Pomona

title: Digital Logic 1


text:
User:Egm6321.f10.team3.Sudheesh/Homeworks/Homework7

= Problem 1 - Plot Legendre functions=

Given
Legendre polynomials (functions /first homogeneous solutions)

 * $$\begin{align}

& {{P}_{0}}(x)=1 \\ & {{P}_{1}}(x)=x \\ & {{P}_{2}}(x)=\frac{1}{2}(3{{x}^{2}}-1) \\ & {{P}_{3}}(x)=\frac{1}{2}(5{{x}^{3}}-3x) \\ & {{P}_{4}}(x)=\frac{1}{8}(35{{x}^{4}}-30{{x}^{2}}+3) \\ \end{align}$$

Legendre functions (second homogeneous solutions)

 * $$\begin{align}

& {{Q}_{0}}(x)=\frac{1}{2}\log \left( \frac{1+x}{1-x} \right) \\ & {{Q}_{1}}(x)=\frac{1}{2}x\log \left( \frac{1+x}{1-x} \right)-1 \\ & {{Q}_{2}}(x)=\frac{1}{4}(3{{x}^{2}}-1)\log \left( \frac{1+x}{1-x} \right)-\frac{3}{2}x \\ & {{Q}_{3}}(x)=\frac{1}{4}(5{{x}^{3}}-3x)\log \left( \frac{1+x}{1-x} \right)-\frac{5}{2}{{x}^{2}}+\frac{2}{3} \\ & {{Q}_{4}}(x)=\frac{1}{16}(35{{x}^{4}}-30{{x}^{2}}+3)\log \left( \frac{1+x}{1-x} \right)-\frac{35}{8}{{x}^{3}}+\frac{55}{24}x \end{align}$$

Find

 * (1) Plot $$\displaystyle \left\{ {{P}_{0}}(x),{{P}_{1}}(x),{{P}_{2}}(x),{{P}_{3}}(x) \right\}$$ and observe $$\displaystyle {{P}_{n}}(x)$$ as $$\displaystyle x\to \pm 1$$

 * (2) Plot $$\displaystyle\left\{ {{Q}_{0}}(x),{{Q}_{1}}(x),{{Q}_{2}}(x),{{Q}_{3}}(x) \right\}$$ and observe $$\displaystyle {{Q}_{n}}(x)$$ as $$\displaystyle x\to \pm 1$$

 * (3) Plot $$\displaystyle \left\{ {{P}_{0}}(x),{{Q}_{0}}(x) \right\}$$, $$\displaystyle \left\{ {{P}_{1}}(x),{{Q}_{1}}(x) \right\}$$, $$\displaystyle \left\{ {{P}_{2}}(x),{{Q}_{2}}(x) \right\}$$, $$\displaystyle \left\{ {{P}_{3}}(x),{{Q}_{3}}(x) \right\}$$, $$\displaystyle \left\{ {{P}_{4}}(x),{{Q}_{4}}(x) \right\}$$

 * (4) Observe even-ness and odd-ness of $$\displaystyle \left\{ {{P}_{i}}(x),{{Q}_{i}}(x) \right\}$$, $$\displaystyle i=0,1,2,3,4$$ and guess

 * $$\displaystyle \int\limits_{-1}^{+1}{{{P}_{i}}(x){{Q}_{i}}(x)dx=}?$$

(1) Plot $$\displaystyle \left\{ {{P}_{0}}(x),{{P}_{1}}(x),{{P}_{2}}(x),{{P}_{3}}(x) \right\}$$

 * [[Image:Sudheesh HW7 1 fig1.jpg|center|650px]]

 * As $$\displaystyle x\to \pm 1$$, $$\displaystyle {{P}_{n}}(x)\to \pm 1$$. When n is even (0,2..), $$\displaystyle {{P}_{n}}(\pm 1)=1$$ and when n is odd (1,3,...), $$\displaystyle {{P}_{n}}(\pm 1)=\pm 1$$. It can also be seen that $$\displaystyle {{P}_{n}}(x)$$ have steepest slope as $$\displaystyle x\to \pm 1$$.

(2) Plot $$\displaystyle\left\{ {{Q}_{0}}(x),{{Q}_{1}}(x),{{Q}_{2}}(x),{{Q}_{3}}(x) \right\}$$

 * [[Image:Sudheesh HW7 1 fig2.jpg|center|650px]]

 * As $$\displaystyle x\to \pm 1$$, $$\displaystyle {{Q}_{n}}(x)$$ also have steepest slope like $$\displaystyle {{P}_{n}}(x)$$.

(3a) Plot $$\displaystyle \left\{ {{P}_{0}}(x),{{Q}_{0}}(x) \right\}$$

 * [[Image:Sudheesh HW7 1 fig3.jpg|center|650px]]

(3b) Plot $$\displaystyle \left\{ {{P}_{1}}(x),{{Q}_{1}}(x) \right\}$$

 * [[Image:Sudheesh HW7 1 fig4.jpg|center|650px]]

(3c) Plot $$\displaystyle \left\{ {{P}_{2}}(x),{{Q}_{2}}(x) \right\}$$

 * [[Image:Sudheesh HW7 1 fig5.jpg|center|650px]]

(3d) Plot $$\displaystyle \left\{ {{P}_{3}}(x),{{Q}_{3}}(x) \right\}$$

 * [[Image:Sudheesh HW7 1 fig6.jpg|center|650px]]

(3e) Plot $$\displaystyle \left\{ {{P}_{4}}(x),{{Q}_{4}}(x) \right\}$$

 * [[Image:Sudheesh HW7 1 fig7.jpg|center|650px]]

 * When $$\displaystyle n$$ is 'even' (0,2,4), $$\displaystyle {{P}_{n}}(x)$$ is 'even' and $$\displaystyle {{Q}_{n}}(x)$$ is 'odd'

 * When $$\displaystyle n$$ is 'odd' (1,3), $$\displaystyle {{P}_{n}}(x)$$ is 'odd' and $$\displaystyle {{Q}_{n}}(x)$$ is 'even'

 * As a result, in each $$\displaystyle \left\{ {{P}_{n}}(x),{{Q}_{n}}(x) \right\}$$ combination, one is odd and the other is even.

 * So Guess:

 * $$\displaystyle \int\limits_{-1}^{+1}{{{P}_{i}}(x){{Q}_{i}}(x)dx=}0$$

Contributing members
= Problem 5 - Relations Between Inverse Hyperbolic Tangent Function And Legendre Functions $$\displaystyle {{Q}_{0}}(x),{{Q}_{1}}(x)$$=

Given

 * Legendre functions:

 * {| style="width:100%" border="0" align="left"

 * $${{Q}_{0}}(x)=\frac{1}{2}\log \left( \frac{1+x}{1-x} \right)$$
 * $$\displaystyle (Eq. 5.1)$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{Q}_{1}}(x)=\frac{x}{2}\log \left( \frac{1+x}{1-x} \right)-1$$
 * $$\displaystyle (Eq. 5.2)$$
 * }
 * }
 * }

Find

 * Show that:

 * {| style="width:100%" border="0" align="left"

 * $$\displaystyle{{Q}_{0}}(x)={{\tanh }^{-1}}(x)$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $$\displaystyle{{Q}_{1}}(x)=x\cdot {{\tanh }^{-1}}(x)-1$$
 * }
 * }
 * }

Solution

 * We know that:

 * {| style="width:100%" border="0" align="left"

 * $$\tanh (\alpha )=\frac{{{e}^{\alpha }}-{{e}^{-\alpha }}}{{{e}^{\alpha }}+{{e}^{-\alpha }}}$$
 * $$\displaystyle (Eq. 5.3)$$
 * }
 * }
 * }

 * Substitute $$\displaystyle \alpha =\frac{1}{2}\log \left( \frac{1+x}{1-x} \right)$$ in $$\displaystyle Eq. 5.3$$ implies:

 * {| style="width:100%" border="0" align="left"

 * $$\tanh \left( \frac{1}{2}\log \left( \frac{1+x}{1-x} \right) \right)=\tanh \left( \log \sqrt{\frac{1+x}{1-x}} \right)=\frac{{{e}^{\log \sqrt{\frac{1+x}{1-x}}}}-{{e}^{-\log \sqrt{\frac{1+x}{1-x}}}}}{{{e}^{\log \sqrt{\frac{1+x}{1-x}}}}-{{e}^{-\log \sqrt{\frac{1+x}{1-x}}}}}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $$=\frac{{{e}^{\log \sqrt{\frac{1+x}{1-x}}}}-{{e}^{\log \sqrt{\frac{1-x}{1+x}}}}}{{{e}^{\log \sqrt{\frac{1+x}{1-x}}}}-{{e}^{\log \sqrt{\frac{1-x}{1+x}}}}}=\frac{\sqrt{\frac{1+x}{1-x}}-\sqrt{\frac{1-x}{1+x}}}{\sqrt{\frac{1+x}{1-x}}+\sqrt{\frac{1-x}{1+x}}}=\frac{(1+x)-(1-x)}{(1+x)+(1-x)}=\frac{2x}{2}$$
 * }
 * }
 * }

 * That is,

 * {| style="width:100%" border="0" align="left"

 * $$\tanh \left( \frac{1}{2}\log \left( \frac{1+x}{1-x} \right) \right)=x$$
 * }
 * }
 * }

 * Therefore,

 * {| style="width:100%" border="0" align="left"

$${{\tanh }^{-1}}(x)=\frac{1}{2}\log \left( \frac{1+x}{1-x} \right)={{Q}_{0}}(x)$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 5.4)$$
 * }
 * }

 * Now substitute $$\displaystyle Eq. 5.4$$ in $$\displaystyle (Eq. 5.2)$$ yields

 * {| style="width:100%" border="0" align="left"

$${{Q}_{1}}(x)=x\cdot {{\tanh }^{-1}}(x)-1$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 5.5)$$
 * }
 * }

.

 Author solved this problem without referring to the $$\displaystyle F\phi 9$$

Contributing Members
= Problem 9 - Generate Legendre Polynomials Using Second Reccurence Relation=

Given
Second reccurence relation of Legendre polynomials:

 * {| style="width:100%" border="0" align="left"

 * $$\left( n+1 \right){{P}_{n+1}}-\left( 2n+1 \right)x{{P}_{n}}+n{{P}_{n-1}}=0$$
 * $$\displaystyle (Eq. 9.1)$$
 * }
 * }
 * }

Legendre polynomials for n=0,1:

 * {| style="width:100%" border="0" align="left"

 * $$\displaystyle {{P}_{0}}(x)=1$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $$\displaystyle {{P}_{1}}(x)=x$$
 * }
 * }
 * }

Find
Generate $$\displaystyle \left\{ {{P}_{2}},{{P}_{3}},{{P}_{4}},{{P}_{5}},{{P}_{6}} \right\}$$ using second reccurence relation starting from $$\displaystyle {{P}_{0}}$$ and $$\displaystyle {{P}_{1}}$$ and compare with [[media:2010_11_09_15_00_14.djvu|Eq.4-6 in page-2 Mtg-36]]

Solution

 * $$\displaystyle Eq. 9.1$$ can be written as:

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{n+1}}=\frac{\left( 2n+1 \right)x{{P}_{n}}-n{{P}_{n-1}}}{\left( n+1 \right)}$$
 * $$\displaystyle (Eq. 9.2)$$
 * }
 * }
 * }

Generate $$\displaystyle {{P}_{2}}$$

 * Substitute $$\displaystyle n=1$$ in $$\displaystyle Eq. 9.2$$ implies:

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{2}}=\frac{\left( 2\times 1+1 \right)x{{P}_{1}}-1\times {{P}_{0}}}{\left( 1+1 \right)}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{2}}=\frac{3x\cdot x-1\times 1}{2}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$${{P}_{2}}=\frac{1}{2}\left( 3{{x}^{2}}-1 \right)$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 9.3)$$
 * }
 * }

Generate $$\displaystyle {{P}_{3}}$$

 * Plugg in $$\displaystyle n=2$$ in $$\displaystyle Eq. 9.2$$ implies:

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{3}}=\frac{\left( 2\times 2+1 \right)x{{P}_{2}}-2{{P}_{1}}}{\left( 2+1 \right)}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{3}}=\frac{5x\cdot \frac{1}{2}\left( 3{{x}^{2}}-1 \right)-2x}{3}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$${{P}_{3}}=\frac{1}{2}\left( 5{{x}^{3}}-3x \right)$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 9.4)$$
 * }
 * }

Generate $$\displaystyle {{P}_{4}}$$

 * Put $$\displaystyle n=3$$ in $$\displaystyle Eq. 9.2$$ implies:

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{4}}=\frac{\left( 2\times 3+1 \right)x{{P}_{3}}-3{{P}_{2}}}{\left( 3+1 \right)}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{4}}=\frac{7x\cdot \frac{1}{2}\left( 5{{x}^{3}}-3x \right)-3\times \frac{1}{2}\left( 3{{x}^{2}}-1 \right)}{4}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{4}}=\frac{35{{x}^{4}}-21{{x}^{2}}-9{{x}^{2}}+3}{8}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$${{P}_{4}}=\frac{1}{8}\left( 35{{x}^{4}}-30{{x}^{2}}+3 \right)$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 9.5)$$
 * }
 * }

Generate $$\displaystyle {{P}_{5}}$$

 * Put $$\displaystyle n=4$$ in $$\displaystyle Eq. 9.2$$ implies:

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{5}}=\frac{\left( 2\times 4+1 \right)x{{P}_{4}}-4{{P}_{3}}}{\left( 4+1 \right)}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{5}}=\frac{9x\cdot \frac{1}{8}\left( 35{{x}^{4}}-30{{x}^{2}}+3 \right)-4\times \frac{1}{2}\left( 5{{x}^{3}}-3x \right)}{5}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{5}}=\frac{63{{x}^{5}}}{8}-\frac{54{{x}^{3}}}{8}+\frac{27x}{8\times 5}-2{{x}^{3}}+\frac{6x}{5}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$${{P}_{5}}=\frac{1}{8}\left( 63{{x}^{5}}-70{{x}^{3}}+15x \right)$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 9.6)$$
 * }
 * }

Generate $$\displaystyle {{P}_{6}}$$

 * substitute $$\displaystyle n=5$$ in $$\displaystyle Eq. 9.2$$ yields:

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{6}}=\frac{\left( 2\times 5+1 \right)x{{P}_{5}}-5{{P}_{4}}}{\left( 5+1 \right)}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{6}}=\frac{11x\cdot \frac{1}{8}\left( 63{{x}^{5}}-70{{x}^{3}}+15x \right)-5\times \frac{1}{8}\left( 35{{x}^{4}}-30{{x}^{2}}+3 \right)}{6}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

 * $${{P}_{6}}=\frac{231{{x}^{6}}}{16}-\frac{770{{x}^{4}}}{48}+\frac{55{{x}^{2}}}{16}-\frac{175{{x}^{4}}}{48}+\frac{50{{x}^{2}}}{16}-\frac{5}{16}$$
 * }
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$${{P}_{6}}=\frac{1}{16}\left( 231{{x}^{6}}-315{{x}^{4}}+105{{x}^{2}}-5 \right)$$
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * style="width:2%; padding:1px; border:2px solid #FF0000" |
 * $$\displaystyle (Eq. 9.7)$$
 * }
 * }

$$\displaystyle Eq. 9.3 - Eq. 9.5$$ are same as the[[media:2010_11_09_15_00_14.djvu|Eqs.4-6 in page-2 Mtg-36]] respectively.


text:
Graded m-theory

The universe... lately I have been treating the universe as contained in a black body radiator of layered boundary. At the limit of our universe on all sides it is possible that the boundary at infinity could be treated as a black body radiator with varied specific heat which means that there could be temperature profile that would be present which is non-uniform. The internal properties could contain multi-universe on particular layers. Like the sun has different layers so does our inverted universe at its boundary. Meaning there is a limit that exists at infinity of our universe which is consistent with a black body radiator of graded specific heat. This should account for a non uniform heat profile that that could expand on one plane wile compress on another.

“ http://en.wikipedia.org/wiki/Electromagnetic_radiation electromagnetic radiation can be well-defined as for matter. Thermal radiation in a cavity has energy density (see Planck's Law) of Differentiating the above with respect to temperature, http://en.wikipedia.org/wiki/Temperature Macroscopically, temperature is related to the amount of internal energy and enthalpy of a system: the higher the temperature of a system, the higher its internal energy and enthalpy. For a system in thermal equilibrium at a constant volume, temperature is thermodynamically defined in terms of its energy (E) and entropy (S) as: Temperature is an intensive property of a system, meaning that it does not depend on the system size, the amount or type of material in the system, the same as for the pressure and density. By contrast, mass, volume, and entropy are extensive properties, and depend on the amount of material in the system” (Extracted from Wikipedia) U/V=(8π^5 〖k^4 (∂E)〗^3)/(15〖(hc ∂S)〗^3 ) Therefore the energy per unit volume of the universe at its boundary is U/V. This means the universe contains a non uniform specific heat everywhere the energy per unit volume should be distributed with some fractal non-uniform space-time scale-size functionality. This of course should be consistent with thermal dynamics and in particular statistical mechanics and quantum mechanics.

This means ∂E/∂S is a function of V thus ∂U/∂V ≈ (∂E(V)/∂S)^3. We live in a universe of non uniform specific heat is the result.

Dennis William Melton

title: Graded m-theory


text:
Template:=

=

title: Template:=


text:
User talk:Man4857

 Hello Man4857, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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Sorry for the differentiation from the norm. I'll use the scheme to sign my contributions. Man4857 04:25, 3 December 2010 (UTC)

Hello
Hi there Glad to see more participants in this school. I plan to do some edits this summer, will appreciate your input every now and then. Thuvack | talk
 * Will be happy to provide input as needed. --Man4857 17:17, 5 December 2010 (UTC)

title: User talk:Man4857


text:
User talk:Nathanoregan5

 Hello Nathanoregan5, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 04:14, 3 December 2010 (UTC)

title: User talk:Nathanoregan5


text:
User talk:Angelar

 Hello Angelar, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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title: User talk:Angelar


text:
User talk:Thallwood

 Hello Thallwood, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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title: User talk:Thallwood


text:
User talk:Melissamazurkewicz

 Hello Melissamazurkewicz, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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title: User talk:Melissamazurkewicz


text:
User talk:Skiffboy~enwikiversity

 Hello Skiffboy, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Skiffboy. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Skiffboy~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:43, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:22, 19 April 2015 (UTC)

title: User talk:Skiffboy~enwikiversity


text:
Learning civility

Feel free to read and discuss.

Civility in life

 * 1) Are you an asshole? - Take the ARSE, an asshole self-rating exam
 * 2) Bad is stronger than good: Why good bosses eliminate the negative first (Bob Sutton, Sep 12, 2010)
 * 3) Responding to hostile emails from high conflict personalities (Psychology Today, Dec 2, 2010)

Civility on the internet

 * 1) Someone is wrong on the internet (xkcd, Duty Calls)
 * 2) Is Internet Civility an Oxymoron? (The Wall Street Journal)

Civility in wiki

 * 1) Civility
 * 2) Wikipedia:Civility
 * 3) Category:User essays on civility
 * Wikiversity studies: Learning from conflict and incivility
 * 1) Etiquette - Etiquette
 * 2) Respect people
 * 3) Wikiversity Course on Virtues: Civility

Quotes

 * 1) "Civility costs nothing and buys everything." Lady Mary Wortley Montagu, 1689–1766
 * 2) "Judge man’s civility not by his compassion for his friends, but by his compassion for his enemies." - The Da Vinci Code, 2003
 * 3) "Civility: freedom from barbarity, kindness, politeness" (Samuel Johnston)

title: Learning civility


text:
User talk:Kebabaria

 Hello Kebabaria, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Mu301Bot 08:17, 3 December 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 08:17, 3 December 2010 (UTC)

title: User talk:Kebabaria


text:
Ideas in Geometry/Mapping the Globe

The globe is a sphere of outstanding proportions, however these days we can see each and every portion of it up close and personal.

This is done by the use of a technique known as:

title: Ideas in Geometry/Mapping the Globe


text:
Talk:Motivation and emotion/Textbook/Motivation/Spiritual

-- Jtneill - Talk - c 12:39, 13 December 2010 (UTC)