OpenLLM-France/wikimedia huggingface dataset:
# Pro Engineer/Surface FAQ

What is the difference between a surface model and a solid model?
* A surface can be open e.g. it does not completely enclose a volume
* A surface has no thickness
* A solid is a special type of surface model. The CAD system knows where the inside is. Therefore, the CAD system will know whether a given point in space is inside or outside of the solid.
* Solids can be created from closed surfaces
* Thin solid can be produced from most surfaces
Is there a need for surfaces?
There are lots of geometry shapes that cannot be produced any other way. Surfaces are a cleaner way to produce certain types of feature.
Are surfaces difficult to master?
Not really. Once you understand the terminology the are no more difficult that than solid features, in fact extrude, revolve, blend and sweep are created in exactly the same way as their solid counterparts.
What are the Magenta and Yellow lines in Pro/ENGINEER 2001 and earlier?
In wireframe and hidden line views, surfaces are displayed with tangential edges as magenta (double-sided surfaces). Surface edges, cuts, are displayed as yellow (single-sided surfaces).
How do I stop surfaces cluttering the screen?
If you use automatic layers then blank the surface layer. If you use manual layers create a layer, add the surfaces to the layers using the Feature, All of Type option, then blank that layer.
# Pro Engineer/Surface Tips

Symmetrical Models When creating symmetrical surface models only model half and transform, mirror it. Use insert mode to add features before the mirror feature.
Merging Merge surfaces at the end of the model where possible, the model will be more robust.
Avoid 2 and 3 sided boundary surfaces Avoid using 2 and 3 sided boundary surfaces. Use 4 boundaries to get the best quality surfaces in pro/engineer otherwise downstream features such as solids and offsets may not work correctly. see Surfaces:Avoiding 3 sided boundaries
Do not use boundary surfaces to create flat surfaces Using boundary surfaces to create flat surfaces will not result in perfectly flat surfaces.
Tips for creating datum curves for use with boundary surfaces Avoid 2 projection curves as it is almost impossible to control the tangency conditions at the curve ends. If 2 projections are used try to line up intersections of the sub curves, otherwise the resulting curves will have lots of segments.
Avoid curve intersecting surfaces for the same reason.
Try to use curve, thru points because you can control the tangency of the curve. It is also possible to tweak the curve and pull it into the right shape. Or use a curve from ISDX as a single feature.
When creating curves for the 'same dir' of a boundary surface try to create it with a similar number of segments. This can be achieved by using divide in sketcher.
Build the datum curves with the same tangency conditions as required in the boundary surfaces.
When creating splines (and ISDX curves) use the minimum number of points, this reduces the risks of introducing ripples into the curve. (unless of course you want ripples!)
Use colours Set surfaces to a shiny black as this shows up the shape of reflected highlights. The outline of highlights should be smooth if not the surface is probably not smooth.
# Pro Engineer/Pro Intralink Tips

Configuration
Remove search paths and search.pro from pro/engineer configuration files (both local and global config files)
Remove PRO_FORMAT_DIR from the config.pro. Check out formats from commonspace.
File Manipulation
Never try to manipulate files at the operating system level.
Only use Pro/engineer linked to Intralink to open and modify Intralink controlled files.
Clean temporary files from start up directory
Check In and Check Out
Check in the latest version of an object when someone else needs it.
Check files in regularly. This will store a design history and the file will be backed up.
Administrators should set access to the root directory as read only to force users to set a destination directory.
Only check in the files you intended to change - review the checkin form and remove any that should not have been modified.
Family Tables
Check out the generic and all instances before the modification of family table driven parts.
Verify family tables before checking in to Intralink.
Workspace
Create a new workspace for each new task. When finished delete the workspace. This will reduce disk usage and minimise 'check in' conflicts.
Check the status of an object before working on it. This will avoid check in conflicts and having to use Integrate.
Frames
Turn on frames. This will enable you to undo mistakes easily.
Pro/Engineer
Use Intralink to rename objects it is safer than Pro/Engineer as Pro/Engineer will only update objects that are in session. Intralink will update all objects it knows about.
Viewing Objects Without Opening Pro/Engineer
Highlight the object (drawing, part or assembly) click Object, Information a preview of the object is shown in a small window. Click the upward arrow to show the image full size. 3D objects in the small image and large window can be rotated by holding down the middle mouse button and moving the mouse. Holding down the ctrl + MMB zooms the object and shift + MMB pans the object.
# Pro Engineer/Repeat Region Relation Example: Replacing characters in parameters

Simplified for readability, base on from http://communities.ptc.com/message/240198#240198 (external link), which follows this.
from http://communities.ptc.com/message/240198#240198 (external link)
# Pro Engineer/Getting the best from support

When contacting PTC's support people, it is important to bear in mind a number of suggestions in order to help them help you.
# Programming Fundamentals/Array Examples Python
## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
# Programming Fundamentals/Arrays
## Overview

This chapter introduces arrays, which may be referred to as lists in some programming languages. Arrays are used for data structures and are able to store an arrangement of elements. Various versions of arrays will be introduced for use in different scenarios. All arrays will be the same data type and capable of working with functions and other variables, as we will learn throughout the chapter.

## Chapter Outline

* Arrays and Lists
* Index Notation
* Displaying Array Members
* Arrays and Functions
* Math Statistics with Arrays
* Searching Arrays
* Sorting Arrays
* Parallel Arrays
* Multidimensional Arrays
* Dynamic Arrays
* Code Examples
** C++
** C#
** Java
** JavaScript
** Python
** Swift
* Practice: Arrays

## Learning Objectives

* Understand key terms and definitions.
* Identify static and dynamic arrays and the code structures necessary to process each type.
* Identify single-dimension arrays and multi-dimensional arrays and the code structures necessary to process each type.
* Given example pseudocode, flowcharts, and source code, create a program that uses arrays or lists to solve a given problem.
# Programming Fundamentals/Arrays and Functions
## Overview

In modular programming, specific task functions are often created and used/reused for array processing. Array processing functions are usually passed with the array and any data necessary to process the array for the given task.
It should be noted that arrays are passed by reference in most current programming languages. Array processing functions must take care not to alter the array unless intended.

## Discussion

Arrays are an important complex data type. We continue to concentrate on simple one dimension arrays, also called a list. Most programmers develop a series of user-defined specific task functions that can be used with an array for normal processing. These functions are either passed with the array along with the number of elements within the array, or just the array itself if the programming language has functions to determine current array size. Some functions also accept additional parameters necessary for that particular function’s task.
This module covers displaying array members by calling an array function dedicated to that task.

### Output
## Key Terms
### array function

    A user-defined specific task function designed to process an array.

## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
* Wikiversity: Computer Programming
# Programming Fundamentals/Array Examples Swift
## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
* Wikiversity: Computer Programming
# Programming Fundamentals/Array Examples CSharp
## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
# Programming Fundamentals/Assignment
## Overview

An assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable.

## Discussion

The assignment operator allows us to change the value of a modifiable data object (for beginning programmers this typically means a variable). It is associated with the concept of moving a value into the storage location (again usually a variable). Within most programming languages the symbol used for assignment is the equal symbol. But bite your tongue, when you see the = symbol you need to start thinking: assignment. The assignment operator has two operands. The one to the left of the operator is usually an identifier name for a variable. The one to the right of the operator is a value.
Simple Assignment
The value 21 is moved to the memory location for the variable named: age. Another way to say it: age is assigned the value 21.
Assignment with an Expression
The item to the right of the assignment operator is an expression. The expression will be evaluated and the answer is 14. The value 14 would be assigned to the variable named: total_cousins.
Assignment with Identifier Names in the Expression
The expression to the right of the assignment operator contains some identifier names. The program would fetch the values stored in those variables; add them together and get a value of 44; then assign the 44 to the total_students variable.

## Key Terms
### assignment

    An operator that changes the value of a modifiable data object.

## Multimedia

* Flowgorithm: Declare Assign and Output A Value https://www.youtube.com/watch?v=HNCqFvzo9uo

## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
* ↑ Wikipedia: Assignment (computer science)
# Programming Fundamentals/Array Examples C++
## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
# Programming Fundamentals/Array Examples Java
## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
# Programming Fundamentals/Array Examples JavaScript
## References

* cnx.org: Programming Fundamentals – A Modular Structured Approach using C++
# Portfolio theory and mathematical models

* Risk and portfolio analysis
** Value at risk
* The optimum portfolio
** Tobin's theorem
* The market portfokio
** Systematic risk and unsystematic risk
* The capital asset pricing model(CAPM)
** The mathematical deriviation of the CAPM
** The relationship between the CAPM and SML
* Capital budgeting and Capital structure
** The estimation of project betas
** Capital gearing
** Modigliani-Miller theorem
** Arbitrage Pricing Theory
** Sharpe ratio
* Matrices
* Orthogonal Projection
* Random variables
* Regression
* Portfolio modeling
* Mean-variance analysis
* Capital market theory
# Portuguese/Conditional tense irregular verbs

There are three verbs that are irregular in the conditional mood: trazer, dizer and fazer. Here are their conjugations below.
TRAZER - To Bring
| I would bring | Eu trar | ia |
| You (s,inf) would bring | Tu trar | ias |
| He would bring (also ela, você) | Ele trar | ia |
| We would bring | Nós trar | íamos |
| You (p) would bring | Vós trar | íeis |
| They would bring (also elas, vocês) | Eles trar | iam |
DIZER - To Say
| I would say | Eu dir | ia |
| You (s,inf) would say | Tu dir | ias |
| He would say (also ela, você) | Ele dir | ia |
| We would say | Nós dir | íamos |
| You (p) would say | Vós dir | íeis |
| They would say (also elas, vocês) | Eles dir | iam |
FAZER - To Do
| I would do | Eu far | ia |
| You (s,inf) would do | Tu far | ias |
| He would do (also ela, você) | Ele far | ia |
| We would do | Nós far | íamos |
| You (p) would do | Vós far | íeis |
| They would do (also elas, vocês) | Eles far | iam |
# Portuguese/Contents
## Portuguese Wikibook

Welcome to the Portuguese language Wikibook. Here you can learn the different parts to the Portuguese language through our grammar references and our course. Why not start with the feature word? Previous knowledge on a closely-related languages (Romance languages—occasionally called the Latin languages or, less often, the Romanic or Neo-Latin languages) like Catalan, French, Italian and Spanish might make studying Portuguese much easier.
There are several differences among the three main dialects of Portuguese: as it is spoken in Portugal (European Portuguese), as it is spoken in Brazil (Brazilian Portuguese), and as it is spoken in Africa (African Portuguese). While their written forms are very similar, there are some differences in the spoken language (both in phonology and syntax) that are specific to each of them. Galician, which is a language spoken in Galicia, is not a Portuguese dialect, as sometimes it is stated, but Galician and Portuguese can be seen as two dialects of the same language - Galician-Portuguese).
Brazilian and African Portuguese show a great influence in their vocabulary from aboriginal languages and Bantu languages which are not present in European Portuguese. Their phonology is more similar to older European Portuguese variants. Brazilian Portuguese also has several unique Americanisms.

## Courses for Portuguese spoken in Portugal

A guide to Portuguese pronunciation

## Courses for Portuguese spoken in Brazil

See also an alternative course in Brazilian Portuguese.
Planning
Level One - Beginners Ten lessons for the absolute beginner.
A guide to Portuguese pronunciation

## Appendix A - Vocabulary

| Palavra em Destaque jantar - to eat (dinner) (verb) | Nouns Rooms of the House Parts of the Body Days, Months, Seasons | Adjectives & Adverbs Common adjectives Common adverbs Numbers Colours | Verbs | Slang Slang (Portugal) Slang (Brazil) Common phrases |
* What time is it?

## Appendix B - Grammar

| Articles Definite and Indefinite Articles Practise Definite and Indefinite Articles Common Prepositions and Contractions | Verbs Variation of the Portuguese Verbs Regular verbs (explanation) Irregular verbs(explanation) 'To be' in Portuguese: 'ser' and 'estar' |
| Pronouns Personal Pronouns of Subject Personal Pronouns of Object Possessive Pronouns and Adjectives How To Say "You" in Portuguese | Regular Verbs Present tense Conditional tense Future tense Imperfect tense Preterite tense Pluperfect tense Present Subjunctive tense Imperfect Subjunctive tense Personal infinitive |
| Miscellaneous Conjunctions Interjections | Irregular Verbs Present tense Conditional tense Future tense Imperfect tense Preterite tense Present Subjunctive tense |

## See also

* Online resources
* Learn Portuguese in German - Lernen Sie Portugiesisch auf Deutsch
* Learn Portuguese in French - Apprendre le portugais en français
* Learn Portuguese in Portuguese - Aprender português em português
# Portfolio theory and mathematical models/Tobin's theorem

Tobin's theorem is one of the modern portfolio theories, which was developed from Markowitz theory adding the concept of risk free assets. This is also known as Separation theorem.

## Tobin's (separation) theorem

where
    $r_{f}$: the interest rate of risk-free assets
The investors who don't take risks at all would invest all own money to the risk-free asset, and the investors who will take risks as much as possible would not have risk-free asset at all. The majority investors who like middle risk and riddle return would have both risk-free assets and tangency portfolio.
In case we make a portfolio with both risk-free assets and risk assets, if all investors act risk-aversively like this, we would certainly choose the combination of risk-free assets and tangency portfolio, which is the conclusion that Torbin reached.
If we suppose a indifference curve (of a investor), which is tangent to the line which comes from $r_{f}$, the following is defined( the indifference curve is salient to the line):
Risk free assets : the whole Risk assets = line segment between the tangency point of the indifferent curve and the tangency portfolio : line segment between the tangency point of the indifferent curve and the $r_{f}$

## What is "separated"?

1. The optimum allocation ratio within the risk assets
and
2. The optimum allocation ratio between the risk-free assets and the whole risk assets
are separated.
# Portuguese/Contents/BPL1

Bem vindo! Welcome to this Brazilian Portuguese Language Course. This is a collaborative effort by many contributors. Please feel free to edit these pages to improve as you see fit.
* Lesson 1: genders, personal pronouns, adjectives and nouns, verb 'estar', progressive tense, dialogue.
* Lesson 2: verb 'ser', possessive pronouns, days of the week and months, common greetings, goodbyes and thanks, introduction to verbs and dialogue.
* Lesson 3: verb 'ir', compound future, present indicative of regular verbs, past perfect and imperfect, dialogue.
* Lesson 4: verb 'ter', past imperfect indicative of regular verbs, irregular verbs, oblique and straight pronouns, cardinal numbers, dialogue.
* Lesson 5: verb 'haver', past perfect indicative of regular verbs, irregular verbs, hours and minutes, dialogue.
* Lesson 6: verb 'pôr', future of regular verbs, irregular verbs, ordinal numbers, dialogue.
* Lesson 7: verb 'fazer', participle, adress pronouns, conditional of regular verbs, imperative of regular verbs, dialogue.
* Lesson 8: weather, compound past, compound past perfect, dialogue.

## See also

* Portuguese verb conjugation (at Wikipedia)
* Portuguese orthography (at Wikipedia)
* Portuguese phonology (at Wikipedia)
# Portuguese/Conjunctions

Conjunctions are words that join phrases together. The most common in Portuguese are:
e - and
Os colegas bebem café frio e chá quente
The colleagues drink cold coffee and hot tea.
mas - but
Este copo está vazio, mas o outro copo está cheio.
This glass is empty, but the other glass is full.
porque - because
Eu tento interessar-me por política porque tenho que ir votar para o mês que vem. I am trying to get interested (lit. interest myself) in politics because I have to go to vote next month.
enquanto - while
Ele cantou enquanto os seus pais ouviam.
He sang while his parents listened.
logo - therefore, so
Estou cansado, logo não vou me levantar.
I am tired, therefore I won't get up.
# Puzzles/Analytical puzzles

* Surprising Limit
* Clock Talk
# Puzzles/Analytical Puzzles/Clock Talk/Solution

Answers: 1: The hands pass 22 times in a 24-hour period.
Imagine we start at 00:01 and end at 24:01, the minute hand will cross the hour hand exacly 22 times. The first time a little after 01:05, second time - a little after 02:10, then after 03:15, 04:20, 05:25, 06:30, 07:35, 08:40, 09:45, the tenth time after 10:50 - almost at 10:55 and the 11th time after 11:55 in fact at 12:00. The whole sequence repeats for the next 12 hours.
2: Starting from 00:01, after 4 passes it will be a little after 04:20. More precisely 04:21:49.
After "H" hours and "M" minutes (where H<12 and M<60):
1. The hour hand has moved just a fraction of the first turn (in one 24-hour period it will make two 12-hour turns),
2. The minute hand has made "H" complete turns and will be in its way to complete the next turn,
3. To cross, the two hands ought to be at the same place:
4. Therefore, before noon (remember, H<12) the two hands cross at:
5. After noon you can use the formula M = 11(H-12)/60 (H in a 24 hour format can be greater that 12) or assume that the cycle repeats itself (just interchange AM/PM).
Conclusion: they cross 22 times a day.
About the 4th pass, this is a little ambiguous. It depends whether you consider the first pass at 00:00:00 AM (H=0, M=0) or the last one at 12:00:00 AM (H=23, M=60).
# Puzzles/Analytical Puzzles/Surprising Limit/Hint

Puzzles|Analytical puzzles | Surprising Limit|Hint
Show that
$\lim _{n\rightarrow \infty }n\sin(2\pi n!e)=2\pi .$
(calculable in head!)

## Hint

* Use the series expansion of e:
$e=1+{\frac {1}{2}}+{\frac {1}{3!}}+{\frac {1}{4!}}+...$
* $sin$ is a periodic function with periodicity $2\pi$.
Solution
# Puzzles/Analogies

The word analogy itself coming from Greek words;ana- "upon, according to" and logos -"word","speech"
Hence, it is a type of linguistic skills of grouping the words into their own groups.
The analogy puzzles are used to identify the relationship between a pair of words.
The format of analogies (in puzzles) are usually as followed: 1. [A] is to [B] as [C] is to [D] 2. [A]:[B] :: [C]:[D]
Usually, only the first pair of words are provided [A] and [B] (at times [C] are also provided) and the subject must correlate [C] relationship to [D]
For example: (1) carrot:vegetable :: banana: _____________
As we can see, in the first pair of words, the word carrot are grouped into vegetable category, hence the word bananas in a way should be categorized into fruits category
(2) angry is to happy as fast is to ____________
The word angry are opposite to word happy, the second pair of word, the word opposite of fast is slow

## Bibliography

* http://www.puzz.com/1001/analogies.htm
* https://www.superteacherworksheets.com/analogies.html
* http://media.bethelsd.org/website/resources/static/thinkingSkillsGuide/skills/solv_analogies.htm
# Puzzles/Analytical Puzzles/Clock Talk
## Problem

Imagine we have a standard analog wall clock. How many times in a 24 hour period will the minute hand cross the hour hand?
What time is it when the minute hand has passed over the hour hand exactly 4 times? This second part is meaningless - it all depends when you start from. I imagine that the puzzle setter was assuming a start from 12:00, but that is ambiguous, it would be better to select one of 11:59 or 12:01 to start from!
Show Hint
Show Solution
# Puzzles/Action sequences/Three Bottles

Puzzles | Action sequences | Three Bottles
Suppose you have a full bottle containing twenty-four ounces of liquid. You also have three empty bottles: one of five ounces, one of eleven ounces, and one of thirteen ounces. How could you divide the twenty-four ounces of liquid into three equal parts, so that you have three bottles containing eight ounces of liquid each?
Solution
# Puzzles/Analytical Puzzles/Surprising Limit

Puzzles| Analytical puzzles|Surprising Limit
Show that
$\lim _{n\rightarrow \infty }n\sin(2\pi n!e)=2\pi .$
(calculable in head!)
Hint | Solution
# Puzzles/Analytical Puzzles/Surprising Limit/Solution

Puzzles|Analytical puzzles|Surprising Limit|Solution
$2\pi n!e=2\pi n!+{\frac {2\pi n!}{2}}+{\frac {2\pi n!}{3!}}+{\frac {2\pi n!}{4!}}+...$
Since sine is a periodic function, adding or subtracting multiples of $2\pi$ can not change the result, thus the first few terms on the right hand side can be dropped (those first few where ${\frac {n!}{z!}}$ is a whole number thus n is greater or equal to z), and one is left with
$\lim _{n\rightarrow \infty }n\sin(2\pi n!e)=\lim _{n\rightarrow \infty }n\sin({\frac {2\pi }{n+1}}+{\frac {2\pi }{(n+1)(n+2)}}+...).$
Since $\sin(x)\approx x+...$ for small $x$ (Taylor expansion of sine), the limit is
$\lim _{n\rightarrow \infty }n\sin({\frac {2\pi }{n+1}})=\lim _{n\rightarrow \infty }n{\frac {2\pi }{n+1}}=2\pi$.
# Puzzles/Action sequences/Three Bottles/Solution

Puzzles | Action sequences | Three Bottles | Solution
| Move | 24 oz | 13 oz | 11 oz | 5 oz |
| Start | 24 | 0 | 0 | 0 |
| 24 oz to 13 oz | 11 | 13 | 0 | 0 |
| 13 oz to 5 oz | 11 | 8 | 0 | 5 |
| 13 oz to 11 oz | 11 | 0 | 8 | 5 |
| 5 oz to 13 oz | 11 | 5 | 8 | 0 |
| 24 oz to 13 oz | 3 | 13 | 8 | 0 |
| 13 oz to 5 oz | 3 | 8 | 8 | 5 |
| 5 oz to 24 oz | 8 | 8 | 8 | 0 |
# Puzzles/Analytical Puzzles/Clock Talk/Hint

Think about the first time the minute hand crosses the hour hand. Suppose the clock started just after midnight, would the first cross be at exactly 1:05?