OpenLLM-France/wikimedia huggingface dataset:
# Materials Science and Engineering/List of Topics/Origins of Modern Chemistry

The history of chemistry is long and convoluted. It begins with the discovery of fire; then metallurgy which allowed purification of metals and the making of alloys, followed by attempts to explain the nature of matter and its transformations through the protoscience of alchemy. Chemistry begins to emerge when the distinction is made between chemistry and alchemy by Robert Boyle in his work The Sceptical Chymist (1661). Chemistry then becomes a full-fledged science when Antoine Lavoisier develops his laws of Conservation of mass, which demands careful measurements and quantitative observations of chemical phenomena. So, while both alchemy and chemistry are concerned with the nature of matter and its transformations, it is only the chemists who apply the scientific method.The history of chemistry is intertwined with the history of thermodynamics, especially through the work of Willard Gibbs.

## Definitions

In retrospect, the definition of chemistry seems to invariably change per decade, as new discoveries and theories add to the functionality of the science. Shown below are some of the standard definitions used by various noted chemists:
* Alchemy (330) – the study of the composition of waters, movement, growth, embodying and disembodying, drawing the spirits from bodies and bonding the spirits within bodies (Zosimos of Panopolis).
* Chymistry (1661) – the subject of the material principles of mixt bodies (Robert Boyle).
* Chymistry (1663) – a scientific art, by which one learns to dissolve bodies, and draw from them the different substances on their composition, and how to unite them again, and exalt them to an higher perfection (Christopher Glaser).
* Chemistry (1730) – the art of resolving mixt, compound, or aggregate bodies into their principles; and of composing such bodies from those principles (Georg Ernst Stahl).
* Chemistry (1837) – the science concerned with the laws and effects of molecular forces (Jean-Baptiste Dumas).
* Chemistry (1947) – the science of substances: their structure, their properties, and the reactions that change them into other substances (Linus Pauling).
* Chemistry (1998) – the study of matter and the changes it undergoes (Raymond Chang).
# Materials Science and Engineering/List of Topics/Octet Stability by Electron Sharing

The octet rule is a simple chemical rule of thumb that states that atoms tend to combine in such a way that they each have eight electrons in their valence shells, giving them the same electronic configuration as a noble gas. The rule is applicable to the main-group elements, especially carbon, nitrogen, oxygen, and the halogens, but also to metals such as sodium or magnesium. In simple terms, molecules or ions tend to be most stable when the outermost electron shells of their constituent atoms contain eight electrons.

## Overview

In short, an element's valence shell is full and most stable when it contains eight electrons (this stability is the reason that the noble gases are so unreactive). Note that a "full shell" means that there are the eight electrons in the valence shell when the next shell starts filling, even though higher subshells (d, f, etc.) have not been filled. There can be at most eight valence electrons in a ground-state atom because p subshells are always followed by the s subshell of the next shell. This means that once there are 8 valence electrons (when the p subshell is filled), the next additional electron goes into the next shell, which then becomes the valence shell.

## History

In the late 19th century it was known that coordination compounds (formerly called “molecular compounds”) were formed by the combination of atoms or molecules in such a manner that the valencies of the atoms involved apparently became satisfied. In 1893, Alfred Werner showed that the number of atoms or groups associated with a central atom (the “co-ordination number”) is often 4 or 6; other coordination numbers up to a maximum of 8 occur, but less frequently. In 1904 Richard Abegg formulated what is now known as Abegg's rule, which states that the difference between the maximum positive and negative valences of an element is frequently eight. This rule was used later in 1916 when Gilbert N. Lewis formulated the “octet rule” in his cubical atom theory.
# Materials Science and Engineering/List of Topics/Quantum Mechanics

Origins of Quantum Physics
Postulates and Mathematical Formalism of Quantum Mechanics
Mathematical Tools of Quantum Mechanics
The Schrodinger Equation
One-Dimensional Arrangements
Angular Momentum
Three-Dimensional Arrangements
Rotations and Addition of Angular Momentum
Identical Particles
Approximation Methods of Stationary States
Time-Dependent Pertubation Theory
# New Zealand Law/System/R v Shaheed (2002)

R v Shaheed (2002)
* D not told entitled to consult lawyer.
* D told (incorrectly) that if he refused to give a blood sample, a court order would be obtained for one.
* The blood sample matched an open rape case (ie not the one for which he had been arrested).
* Court order then obtained.
Held Court of Appeal
* There is a balancing act between a breach of BORA and exclusion of evidence.
* There was a direct connection between the breach and the sample. The evidence would not have been obtained but for the unlawfully obtained sample.
* Sample therefore excluded.
# New Zealand Law/System/Hoani Te Heu Heu Tukino v Aotea District Maori Land Board

Treaty duties can be legally enforced only when they are incorporated into Acts of Parliament
# New Zealand Law/System/Huakina Development Trust v Waikato Valley Authority

* Did a local council have to consider Maori spiritual values when allocating water rights for efﬂuent
* The relevant legislation did not refer to the principles of the Treaty, or spell out relevant considerations
Held:
* Principles of the Treaty and Maori beliefs on purity of water were relevant considerations
* unlikely this outcome would be the same if a list of considerations existed)).
# New Zealand Law/Criminal/Threatening
## Offences
### Threatening to kill or do gbh

Either:
* threatening to kill or do gbh; or
* sending or causing to be received any letter or writing that contains a threat to kill or do gbh knowing the contents thereof.
* Note: The threat need not be communicated to the person threatened, but it must be communicated.

### Threatening to destroy property

Sending or causing to be received any writing (knowing the contents thereof):
    (a) threatening to destroy or damage any property; or
    (b) threatening to destroy or injure any animal,
    except where:
       (i) lawful justification/excuse; or
       (ii) claim of right

### Threatening to cause significant disruption

Without lawful justification or reasonable excuse:
    (a) causing the a significant disruption of:
       (i) the activities of the civilian population of NZ
       (ii) the infrastructure of NZ
       (iii) the civil administation of NZ (including local govt, DHBs, school board trustees); or
       (iv) the commercial activities
    (b) by either:
       (i) threatening to do an act likely:
          (A) result in risk to anyone’s health
          (B) cause major property damage
          (C) cause major property loss
          (D) cause major damage to the national economy; OR
       (ii) communicating information about an act that one believes to be false.
* Note: does not include protests, advocacy, dissent, strikes, lock-outs or other industrial action.

### Threatening dwelling places

With intent to intimidate or annoy any person:
    (a) breaking or damaging, or threatening to break or damage, any dwelling place;
    (b) by the discharge of firearms or otherwise, alarming or attempting to alarm, any person in a dwelling place.

## Cases
### R v Cherri

* Facts
    Woman made repeated threatening calls to police officer while drunk.
* Held
    1. Prosecution must prove that what was said was:
       (a) intended as a threat; and
       (b) intended to influence the mind of the recipient.
    2. Prosecution need not prove:
       (a) intention to carry out threat; or
       (b) capability to carry out threat.
    3. Intoxication is a possible defence, in that defendant did not know what she was doing, but there must be sufficient evidence.

#### Police v Goldie (Note)

* Facts
    A defendant need not intent to carry out a threat.
* Held
    1. The threat must be made intentionally - ie. consciously and voluntarily; and
    2. The defendant must have intended that the threat be taken seriously - ie the defendant must intent to influence the mind of the person to whom it is addressed.
# New Zealand Law/Equity
## Express Trusts

* Re Beckbessinger
* UEB Industries Pension Plan
* Hall v Guardian Trust
* Re Singh
* Fox v Harvey

## Trustees Duties & Powers
### Statutes

* Trustee Act 1956 (1995 reprint)

### Cases

* Mendelsohn v Centrepoint Community Trust
* Hunter v Hunter
* Greenwood
* Re Aitken Trusts
* Jones v AMP Perpetual
* Stuart v Farmer
* Te Huango
* Re Mulligan
* Re O’Donaghue
* BNZ v NZ Guardian Trust
* Foreman v Kingstone

## Purpose Trusts

* Re Filshie
* Re Budgie

## Maori Land Trusts

* Maori Land Act 1993, Part 12

### Types of Trusts

* putea
* ahu whenua
* whanau
* whenua topu
* kai tiaki

## Charitable Trusts
### Statutes

* Charitable Trusts Act 1957
* Charities Act 2005

### Cases

* NZ Society of Accountants v CIR
* CIR v Medical Council
* Bryant Trust Board v Hamilton CC
* Chch Orchestra Trust v Smitham
* Re Twigger
* Centrepoint Community Growth Trust v CIR
* Re Mason
* Morgan v Wgtn City Corp
* Re Palmerston North Halls Trust Board
* Re Collier
* Alacoque v Roche
* Re Centerpoint Community Growth Trust
* Wilson Home Trusts
* Latimer v CIR

## Resulting Trusts

* Bateman TV v Bateman & Thomas
* General Comms v Development Finance
* Lankshear v ANZ
* Re Beckbessinger
* UEB Industries Pension Plan
* Hall v Guardian Trust

## Equitable Compensation

* Aquaculture v Green Mussel
* Cook v Evatt
* Downview v First City
* NZ Land Development v Porter
* A-G v Equiticorp
* Chirnside v Fay

## Constructive Trusts

* AG for H-K v Reid
* Avondale v Haggie
* DFC NZ v Goddard
* Elders Pastoral v BNZ
* Equiticorp v AG
* Equiticorp v Hawkins
* Fortex v Macintosh
* Gilles v Keogh,
* Lankow v Rose
* Lankshear v ANZ
* Powell v Thompson
* Re Newey (Deceased)

## Tracing

* Claytons Case
* Re Halletts Estate
* Re Ararimu
* Re Registered Securities

## Equitable Estoppel

* Burberry Mortgage v Hindsbank
* Gold Star Insurance v Gamut
* Prudential v Hawkins

## Fiduciaries

* Day v Mead
* Elders Pastoral v BNZ
* Coleman v Myers
* Clark Boyce v Mouat
* AG for H-K v Reid
* Avondale v Haggie
* Contractors Bonding v Snee
* Arklow v McLean

## Unconscionability

* Nichols v Jessup
* O’Connor v Hart
* Contractors Bonding v Snee
* AG for E & W v Reid

## Rule against perpetuities

* Perpetuities Act 1964

## Wills & Administration

* Administration Act 1969
* Simultaneous Deaths Act 195
* Succession Law: A Succession (Adjustment) Act NZ Law Commission Report No 39 (1997)

### Wills: General

* Wills Act 1837
* Re Young
* Re Whyte
* In re Karsten
* Tanner v Public Trusteee
* Re Archibald
* Brown v Pourau

### Mutual Wills

* Fisher v Mansfield
* Re Newey (Deceased)

### Family Protection Act

* Family Protection Act 1955
* Lewis v Cotton
* Re McLean
* Williams v Aucutt
* Re Stewart
* Re Williams

### Law Reform (Testamentary Promises) Act

* Law Reform (Testamentary Promises) Act 1949
* Re Welch
* Rennie v Hamilton

### Property (Relationships) Act

* Property (Relationships) Act
* Re Williams
# New Zealand Law/System/Tavita v Minister of Immigration

Tavita had exhausted appeal rights prior to birth (in NZ) of daughter.
Held, Court of Appeal
* It is no more than arguable that the Minister, in deciding whether to execute a removal order, is obliged to take into account the interests of the child.
* Doubtful whether the Minister or the NZ Immigration Service is entitled to ignore international instruments that NZ is a party to.
# New Zealand Law/Property
## Searching Titles

* Bradley v AG [1978]

## Caveats

* Sims v Lowe
* Harrison v NZI Bank ltd
* Holt v Anchorage Mgt
* Landco Albany v Fu Hao Construction

## Indefeasibility of Registered Title

* Frazer v Walker
* Davies v Laughton
* Duncan v McDonald
* Faulkner v Tauranga DC
* Bunt v Hallinan
* Sutton v O’Kane
* Congregational Christian Church v Broadlands
* Efstratiou v Glantschnig

## Powers of Corrections - ss 80 and 81 LTA

80 Errors in register may be corrected
    (1) The Registrar may, upon such evidence as appears to him sufficient, subject to any regulations under this Act, correct errors and supply omissions in certificates of title or in the register, or in any entry therein, and may call in any outstanding instrument of title for that purpose.
    (2) The Registrar may cancel or correct any computer register and, if appropriate, create a new computer register in order to correct any error or supply any omission in any computer register.
81 Surrender of instrument obtained through fraud, etc
    (1) Where it appears to the satisfaction of the Registrar that any certificate of title or other instrument has been issued in error, or contains any misdescription of land or of boundaries, or that any entry or endorsement has been made in error, or that any grant, certificate, instrument, entry, or endorsement has been fraudulently or wrongfully obtained, or is fraudulently or wrongfully retained, he may require the person to whom that grant, certificate, or instrument has been so issued, or by whom it is retained, to deliver up the same for the purpose of being cancelled or corrected, as the case may require.
    (2) If the Registrar is satisfied as to any matter referred to in this section and there is a computer register involved, the Registrar may cancel or correct any computer register and, if appropriate, create a new computer register.
    (3) The Registrar must not take action under subsection (2) without first giving notice to any person appearing to be affected and giving a reasonable period for any response.

## Mortgages and Leases

* Downsview Nominees v First City Corp
* Neva Hldgs v Wilson
* Italia Holdings v Lonsdale
* Fatac Ltd v Commissioner for Inland Revenue
* Cash Handling v Augustus Terrace
* Nordern v Blueport

## Easements

* Jansen v Mansor

## Encroachment

* Kingfish Lodge v Archer

## Co-ownership

* Re Foley
* Fleming v Hargreaves
* McMahon v McMahon

## Joint Family Homes Act 1964

* The Future of the Joint Family Homes Act, New Zealand Law Commission Report 77 (2001)

## Flats, Home Units and Offices

* Disher v Farnworth

## Residential Tenancies Act 1986

* Residential Tenancies Act 1986 (2003 Reprint)

## Maori Land

* Te Runanganui o Te Kia Whenua v AG
* AG v Ngati Apa
# New Zealand Law/System/Baigents Case

Simpson v AG [1994] 3 NZLR 667 [aka Baigent’s Case]
* The plaintiffs alleged that police officers had persisted in bad faith with the search of the late Mrs Baigent's house when they knew that her property had been mistakenly named in a search warrant issued for a drug dealers' house.
* The plaintiffs sued on the grounds the police breached section 21 of the Bill of Rights Act, the right to be secure against unreasonable search and arrest.
Held, Court of Appeal
* The fact that the Bill of Rights did not include a specific remedies section did not mean Parliament did not intend to compensate for breaches of the Act;
* The Bill of Rights had to be interpreted in light of New Zealand's obligations under the Intl Covenant on Civil and Political Rights;
* The Courts can award remedies for breaches of the Bill of Rights;
* The liability of breaches of the Act fell on the Crown.
# MATLAB/Engineering thermodynamics/Trouble with MATLAB code

There seems to be a bug in Xsteam when T_hs is called in a certain regime. I believe this occurs in the saturated regime near h = 1500 kJ/kg between s = 3.17 and 3.18 kJ/kg
# MATLAB/Divergent series investigations

Shown below are the 15 terms of the series for ε equal to 0, .001, and .01, respectively. The series converges to -1/12 in the limit that ε>0 vanishes.
This code runs on both MATLAB and Octave. It sums,
    $S(N,\epsilon )=\sum _{n=1}^{N}nz^{n}$ where, $z=e^{-\epsilon +i\epsilon }\approx 1\ \mathrm {if} \ \epsilon <<1$.
The numerical simulation suggests that for real $\epsilon$:
    $\lim _{\epsilon \to 0}\sum _{n=1}^{\infty }ne^{-\epsilon n}\cos(\epsilon n)=-{\frac {1}{12}}$
Warning: This result does not hold if $\epsilon$ is a complex number that goes to zero, unless the real and imaginary parts are constrained to be equal in magnitude. This would be a significant simulation if the series converges to -1/12 for all ratios of real to imaginary parts of ε. Nevertheless, it is curious that a real to imaginary ratio of one yields the well known value, 1/12≈.083333

#### Questions

* Verify that $\int _{0}^{\infty }xe^{-\epsilon x}\cos(\epsilon x)dx=0$ if ε > 0
* Why is this interesting?
* Can Octave do symbolic integration?

#### Output of MATLAB code

The code that follows gave this output:
# MATLAB/Engineering thermodynamics

This page is devoted to XSteam.m, which is a MATLAB code available available on the internet.

### MATLAB code to generate steam tables

* The code that follows was written by Magnus Holmgren, who generously released it under conditions that permit it to be posted here. The following link should be used to retrieve the code because it contains valuable instructions on using it:
    http://www.mathworks.com/matlabcentral/fileexchange/9817-x-steam--thermodynamic-properties-of-water-and-steam
This website also has a US units version, as well as detailed instructions on how to call the function. Once you have this code in a MATLAB folder with the title XSteam.m you can call it from the command window with a variety of arguments. The following two examples are taken from the pdf file that accompanies the download:
XSteam('h_pt',1,20) Returns the enthalpy of water at 1 bar and 20 C.
XSteam('TSat_p',1) Returns the saturation temperature of water at 1 bar.

#### Backup copy of XSteam.m
### MATLAB code that uses Xsteam to generate steam tables and graphs

This version of the code uses an Excel spreadsheet that must be placed in the same folder as the executable code. The spreadsheet is called parameters, and the first row contains the pressures. The columns contain the corresponding temperatures. Do not include the saturation temperature -- that is automatically included. The and the MATLAB code is called TableGraphMaker.m.

#### Copy of parameters

click to view or hide :
| 25 | 50 | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 |
| 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 |
| 250 | 250 | 250 | 250 | 250 | 250 | 250 | 250 | 250 | 300 | 300 |
| 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 300 | 350 | 350 |
| 350 | 350 | 350 | 350 | 350 | 350 | 350 | 350 | 350 | 400 | 400 |
| 400 | 400 | 400 | 375 | 375 | 370 | 375 | 375 | 380 | 425 | 425 |
| 450 | 450 | 450 | 400 | 390 | 380 | 400 | 400 | 400 | 450 | 450 |
| 500 | 500 | 500 | 425 | 400 | 390 | 415 | 415 | 425 | 500 | 500 |
| | | | 450 | 425 | 400 | 425 | 425 | 450 | | |
| | | | 500 | 450 | 425 | 450 | 450 | 500 | | |
| | | | | 500 | 450 | 500 | 500 | | | |
| | | | | | 500 | | | | | |

#### Copy of TableGraphMaker.m
## Footnotes and references

* ↑ XSteam available at http://www.mathworks.com/matlabcentral/fileexchange/9817-x-steam--thermodynamic-properties-of-water-and-steam
* ↑ aka "student"
# MATLAB/Getting started

This resource "shadows" an excellent introduction by the people who maintain Matlab.
You can access appropriate chapters of this introduction by clicking the link that begins each section. (These tutorials are also available from your main MatLab GUI window.

### Desktop basics

Desktop Basics shows you the default layout before you open an m-file. (The codes you write are called m-files). It also give very basic information on how to use MATLAB as a calculator, e.g., 2+3=5.
* If you ever accidentally change your desktop layout, select Home>>Layout>>Default
* Each window can be maximized using the triangular icon near each window's title. Once maximized, it can be restored to Default using the square/rectangles icon situated next to the triangular icon.
* If you can't find the Editor window verify that you have opened something for editing!
* Use the up down arrows ( ↑ and ↓ ) to recall previous commands that you have typed.

### Matrices and arrays

Matrices and Arrays shows you how to create arrays, (including arrays of zeros). Important array operations to know about are concatenation (i.e. adding rows or columns), transpose, inverse, and element-wise operations.
* Element-wise operations are preceded by a dot .(e.g. [1 3].*[2,4]=[1*2,3*4]=[2,12]}, while omission of the 'dot' ([1 3]*[2,4]) returns an error.

### Array indexing

Array indexing Helps you sort out the rows and columns of arrays. It introduces just two of many uses of the colon
* 1:2:9 creates [1,3,5,7,9].

### Workspace variables

Workspace Variables introduces you to the Workspace Variables window in the lower left corner of your GUI.
* You can also get this information by typing whos.
* Save and restore your workspace variables with save filename.mat and load filename.mat

### Character string

Character Strings
* teaches you about 'Hello world', as well as ['Hello',' ','world']
* use the functions num2string and int2string to convert numbers and integers into strings.

### Calling functions

Calling Functions introduces you to functions using max, dis, and clc as examples.
* Note the flexibility: clc takes no arguments while max can take one or more arguments and can return either a single value or a double value (in the form of a 1x2 array, e.g., [a,b] = max([4 6 1])

### 2D and 3D plots

2D and 3D Plots will tell you most of what you need to know about plotting.
* See MATLAB/Cookbook/symbolicIntegration for plotting functions defined symbolically.

### Programming and scripts

Programming and Scripts will get you started in running m-files. There are two types: functions and scripts.

### Help and documentation

Help and Documentation If you know the name of your function, type help functionname for quick help and help functionname for a link to pages explaining the function.

## Links and footnotes

* ↑ Open MATLAB and look for the statement: New to MATLAB? Watch this Video, see Examples, or read Getting Started . If you do not see this line, use Help>>Matlab>>Getting Started
# MATLAB/Cookbook/plot3D

This makes a color contour plot:
# Natural numbers/Not 3/2^n larger than n^2/Exercise

Show that (with $n=3$ being the only exception) the relation
    $2^{n}\geq n^{2}\,$
holds.
# Natural logarithm/Taylor polynomial to degree 4/1/Power series approach/Exercise

Determine the Taylor polynomial up to fourth order of the natural logarithm at point $1$ with the power series approach described in remark from the power series of the exponential function.
# Natural numbers/Adding up/Induction/Intersection points/Motivation/Example

We would like to find an easy formula for the sum of the first $n$ natural numbers, which equals the maximal number of intersection points of a configuration of $n+1$ lines. We claim that
    $\sum _{k=1}^{n}k={\frac {n(n+1)}{2}}\,$
holds. For small numbers $n$, this is easy to check just by computing the left-hand and the right-hand side. To prove the identity in general, we try to understand what happens on the left and on the right, if we increase $n$ to $n+1$, like we have added in example another line to a line configuration. On the left-hand side, we just have the additional summand $n+1$. On the right-hand side, we go from ${\frac {n(n+1)}{2}}$ to ${\frac {(n+1)(n+1+1)}{2}}$. If we can show that the difference between these fractions is $n+1$, then the right-hand side behaves like the left-hand side. Then we can conclude: the identity holds for small $n$, say for $n=1$. By comparing the differences, it also holds for the next $n$, so it holds for $n=2$, then again for the next $n$ and so on. Since this argument always works, and since one arrives at every natural number by taking the successor again and again, the formula holds for every natural number.