text:
Prolog/Glossary

This is a glossary of common Prolog terms.

 * Argument
 * Arguments are terms that appear in a compound term. E.g. A1 and a2 are the first and the second argument of the term.

 * Arity
 * The number of arguments that a predicate takes. E.g.  has arity 2. In documentation, the arity of a predicate is written as predicate/arity. E.g..

 * Backtracking
 * If a sub-goal fails, the built-in Prolog search mechanism will go back to the parent-goal. Any variables that were instantiated in the sub-goal will be un-instantiated. Prolog will then search for a new way of satisfying the sub-goal. This process is called backtracking.

 * Clause
 * A single clause of a relation, usually defined as Head :- Body, but see also fact.

Also called structure. It consists of a name followed by N arguments, each of which are terms. N is called the arity of the term.
 * Compound term
 * Fact
 * A clause with no body, that is a head on its own.

 * Functor
 * Combination of name and arity of a compound term. The term  is said to be a term belonging to the functor foo/3 . foo/0 is used to refer to the atom foo.

 * Goal
 * Question stated to the Prolog engine. A goal is either an atom or a compound term. A goal succeeds, in which case the variables in the compound terms have a binding or fails if Prolog fails to prove the goal.

 * Ground Term
 * A Term which has no logic variables in it.

 * Predicate
 * A set of clauses or a relation.

 * Query
 * See goal.

 * Relation
 * Synonym for Predicate.

 * Recursion/Recursive
 * Definition missing

 * Rule
 * See clause.

 * Term
 * Every object in Prolog is a term, that includes variables, compounds, numbers, source code.

 * Unification
 * Prolog process to make two terms equal by assigning variables in one term to values at the corresponding location of the other term. E.g.,

Unlike assignment, which does not exist in Prolog, unification is not directed.
 * Singleton Variable
 * If a variable is named only once in a clause, usually it is replace with _.

title: Prolog/Glossary


text:
User:Perl~enwikibooks/constitution

 * 1) What six purposes of the federal government are set forth in the Preamble to the Constitution?
 * 2) *establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity,
 * 3) Where are alllegislative powers under the Constitution vested?
 * 4) *in a Congress of the United States, which shall consist of a Senate and House of Representatives.
 * 5) What are the qualification of a Representative in Congress?
 * 6) *the Qualifications requisite for Electors of the most numerous Branch of the State Legislature; Age of twenty five Years, and been seven Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State in which he shall be chosen
 * 7) Who decides how many Representatives there are and when is it decided?
 * 8) *determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons. It is decided within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct.
 * 9) What is the term of office for a Representative?
 * 10) * 2 years
 * 11) How are vacancies in the House ot Representatives filled?
 * 12) *the US president (the Executive Authority) issues "Writs of Election" to fill the Vacancies
 * 13) Who chooses the Speaker of the House and íts other officers?
 * 14) *The House of Representatives
 * 15) What house of Congress has the sole power 01 impeachment?
 * 16) *The House of Representatives
 * 17) To how many Senators is each state entitled?
 * 18) *two
 * 19) Who now elects United States Senators?
 * 20) *State has elections for its general population (individuals at least 18) to elect the two senators.
 * 21) What is the term of office for a Senator?
 * 22) *six years
 * 23) What are the qualifications tor a Senator?
 * 24) *Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen
 * 25) Who is the President of the Senate?
 * 26) *vice president of the united states
 * 27) When does the President of the Senate vote?
 * 28) *when the senate is equally divided
 * 29) Who has the sole power to try all impeachments?
 * 30) *Senate. when the president is tried, the Chief justice will preside
 * 31) What punishment does the Constitution provide for a federal officer who has been removed from office by impeachment?
 * 32) *disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: Also, the convicted party is liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.
 * 33) Who determines the time. place, and manner of holding elections for Senators and Representatives?
 * 34) *each State by the Legislature thereof. but the Congress may at any time alter such Regulations, except concerning the places of choosing senators.
 * 35) When does Congress assemble and how frequently?
 * 36) * at least once in every Year.  The Meeting shall be on the first Monday in December (altered by amendment XX)
 * 37) What responsibilities does Section 5 of Article I place on Congress?
 * 38) * Judge of elections, returns, and qualifications of its members. (majority shall constitute a quorum to do business), punish its Members for disorderly Behaviour, keep a Journal of its Proceedings
 * 39) When may the President call a special session of Congress?
 * 40) * The president may call a special session of Congress when Congress has adjourned.
 * 41) What are the "privileges and immunities" of a member of Congress?
 * 42) * Compensation for their Services, privileged from Arrest during their Attendance at the Session of their respective Houses, not be questioned outside the house about a speech or debate.
 * 43) What does the Constitution say about a member of Congress holding another public office?
 * 44) * "no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office"
 * 45) In which house of Congress must revenue bilis originate?
 * 46) * the House of Representatives
 * 47) What four things may the President do with bill passed by Congress?
 * 48) *sign it, veto it, return it with his Objections to the House, ignore it
 * 49) How may Congress "get around" a Presidential veto?
 * 50) *2/3 of the house approve it
 * 51) List all of the powers which the Constitution vests in Congress.
 * 52) *Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States;
 * 53) *To borrow Money on the credit of the United States;
 * 54) *To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;
 * 55) *To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
 * 56) *To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;
 * 57) *To provide for the Punishment of counterfeiting the Securities and current Coin of the United States;
 * 58) *To establish Post Offices and post Roads;
 * 59) *To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
 * 60) *To constitute Tribunals inferior to the supreme Court;
 * 61) *To define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations;
 * 62) *To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;
 * 63) *To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
 * 64) *To provide and maintain a Navy;
 * 65) *To make Rules for the Government and Regulation of the land and naval Forces;
 * 66) *To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
 * 67) *To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
 * 68) *To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, byCession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings;--And
 * 69) *To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
 * 70) What does "general welfare" mean?
 * 71) *Many people disagree over the definition of general welfare. It means what is best for the American people.
 * 72) Who has complete power over money?
 * 73) *congress appropriates funds and has the power to raise taxes, the president is charged with the responsibility of spending the money.
 * 74) What are Congress' war powers?
 * 75) * Section 8: Clauses 11-16 define these powers
 * 76) What is the "implied power" clause of the Constitution?
 * 77) *Congress has the implied power to do what is necessary to carry out its duties. Article 1 says congress has the power “to make all laws which shall be necessary and proper for carrying into execution”
 * 78) What does the Constitution say about slavery?
 * 79) *It doesn't say anything about slavery expressly. They made slaves 3/5ths of a person for representation.
 * 80) What things is Congress prohibited from doing under Section 9 of Article I?
 * 81) * The Migration or Importation of such Persons as any of the States now existing shall think proper to admit, shall not be prohibited by the Congress prior to the Year one thousand eight hundred and eight, but a Tax or duty may be imposed on such Importation, not exceeding ten dollars for each Person.
 * 82) * The Privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of Rebellion or Invasion the public Safety may require it.
 * 83) * No Bill of Attainder or ex post facto Law shall be passed.
 * 84) * No Capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or Enumeration herein before directed to be taken. (See Note 7)
 * 85) * No Tax or Duty shall be laid on Articles exported from any State.
 * 86) * No Preference shall be given by any Regulation of Commerce or Revenue to the Ports of one State over those of another: nor shall Vessels bound to, or from, one State, be obliged to enter, clear, or pay Duties in another.
 * 87) * No Money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of the Receipts and Expenditures of all public Money shall be published from time to time.
 * 88) * No Title of Nobility shall be granted by the United States: And no Person holding any Office of Profit or Trust under them, shall, without the Consent of the Congress, accept of any present, Emolument, Office, or Title, of any kind whatever, from any King, Prince, or foreign State.
 * 89) list the limitation on state governments provided by Section 1 of Article 1.
 * 90) * No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts; pass any Bill of Attainder, ex post facto Law, or Law impairing the Obligation of Contracts, or grant any Title of Nobility
 * 91) * No State shall, without the Consent of the Congress, lay any Imposts or Duties on Imports or Exports, except what may be absolutely necessary for executing it's inspection Laws: and the net Produce of all Duties and Imposts, laid by any State on Imports or Exports, shall be for the Use of the Treasury of the United States; and all such Laws shall be subject to the Revision and Controul of the Congress.
 * 92) * No State shall, without the Consent of Congress, lay any Duty of Tonnage, keep Troops, or Ships of War in time of Peace, enter into any Agreement or Compact with another State, or with a foreign Power, or engage in War, unless actually invaded, or in such imminent Danger as will not admit of delay.
 * 93) What is the basic structure of the electoral college ?
 * 94) * number of electors for each state equal to the number of senators and representatives that the state sends to congress. No congressmen can serve as an elector. Electors vote on seperate ballots for president and vice president (one must not be an inhabitant of the state).
 * 95) if there is no valid electoral college election, who elects the President ?
 * 96) *House of Representatives
 * 97) if there is no valid electoral college election. who elects the Vice-President ?
 * 98) *the Senate
 * 99) Where is the executive power under the Constitution vested?
 * 100) *Article II Section 2
 * 101) What is the term of office of the President?
 * 102) *four years
 * 103) What are the qualification for President?
 * 104) * natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution
 * 105) Who succeeds the President in case of death, resignation or disability?
 * 106) *vice president
 * 107) What are the powers and duties of the President?
 * 108) * The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices, and he shall have Power to grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment.
 * 109) * He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.
 * 110) * The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session.
 * 111) * He shall from time to time give to the Congress Information of the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient; he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper; he shall receive Ambassadors and other public Ministers; he shall take Care that the Laws be faithfully executed, and shall Commission all the Officers of the United States.
 * 112) List the President's war powers.
 * 113) * Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States
 * 114) * Power, by and with the Advice and Consent of the Senate, to make Treaties,
 * 115) How may the President, Vice President and civil officers of the United States be removed from office?
 * 116) * on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.
 * 117) Where does the Constitution vest the "judicial power"?
 * 118) *Article III
 * 119) What is the term of office for federal judges?
 * 120) * as long as they behave
 * 121) How do federal judges get their offices?
 * 122) *Appointment
 * 123) What powers over the federal courts does the Constitution give to Congress?
 * 124) *Power to create the lower courts, power approve or dissaprove the nominations that the president submits for the judges
 * 125) Who creates the courts inferior to the Supreme Court?
 * 126) *Congress
 * 127) What does the Constitution say about tríal by jury?
 * 128) *The Trial of all Crimes, except in Cases of Impeachment, shall be by Jury;
 * 129) What is Treason against the United States?
 * 130) *Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort.
 * 131) How may a person be convicted of treason?
 * 132) *If someone levys war against the US or helps its enemies and two witnesses testify to the same act or the individual confesses.
 * 133) Who declares the punishment for treason?
 * 134) *The Congress shall have Power to declare the Punishment of Treason
 * 135) What does the term "Full Faith and Credit" mean?
 * 136) * Each state has to recognize the validity of the laws and judgments of other states.
 * 137) To what are citizens of each state entitled?
 * 138) *The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.
 * 139) What is extradition and how does it work?
 * 140) * A Person charged in any State with Treason, Felony, or other Crime, who shall flee from Justice, and be found in another State, shall on Demand of the executive Authority of the State from which he fled, be delivered up, to be removed to the State having Jurisdiction of the Crime.
 * 141) How may new states be admitted to the Union?
 * 142) *New States may be admitted by the Congress
 * 143) Who can dispose of property of the United States?
 * 144) *The Congress
 * 145) Who oversees the territories of the United States?
 * 146) * The Congress
 * 147) What is a "Republican Form of Government" and to whom is it guaranteed?
 * 148) *Republic. A commonwealth; the form of government in which the administration of affairs is open to all the citizens.  In another sense, it signifies the state, independently of its form of government.
 * 149) *"every State in this Union"
 * 150) Under what circumstances does the Constitution permit the use of federal troops within a state?
 * 151) * to protect each state against Invasion; on Application of the Legislature; or by the president (when the Legislature cannot be convened) against domestic Violence.
 * 152) How may the Constitution be amended?
 * 153) *on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments
 * 154) *It is made valid to all Intents and Purposes, as Part of the Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof
 * 155) What are the two limitations placed on the "amending process"?
 * 156) *no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article
 * 157) * no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
 * 158) What does the "Supremacy Clause" say?
 * 159) * The laws enacted by congress take precedence over the laws enacted by states.
 * 160) When was the Constitution written and when was it ratified?
 * 161) * The Constitution was adopted by a convention of the States on September 17, 1787. Ratification was completed on June 21, 1788.

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

title: User:Perl~enwikibooks/constitution


text:
Radiation Oncology

Radiation Oncology

 * This page is the Cover Page of the book. Please place any actual content on separate subpages of the book.  Be sure to read the instructions for authors. Thanks!
 * Search this Wikibook using Google or use the "Search Box" on the left (doesn't seem as effective as Google).

Volunteer Editors:
 * This is a wiki project - an open source, free access reference book. Anyone is welcome and encouraged to contribute anytime, anything (as long as it relates to Radiation Oncology). Feel free to edit it, update it, correct it, and otherwise increase its teaching potential. We appreciate both small contributions (correcting typos, grammar etc.) as well as contributions to content. If there are subjects missing outright, please feel free to start them. For comments, please use the "discussion" tab on top of each page.
 * Brian Cook, M.D. - (Brim) - Sampson Radiation Oncology, Clinton, NC, USA
 * Tomas Dvorak, M.D. - (Tdvorak) - Orlando Health, Orlando, FL, USA

Full Table of Contents

title: Radiation Oncology


text:
Radiation Oncology/Introduction

Radiation Oncology is a rapidly changing field with new advances being made daily. As a consequence, any textbook becomes out-of-date almost immediately after it is published. Thus, the WikiBook format is ideal for a textbook of radiation oncology, as updates can be made constantly as new information becomes available.

This textbook is meant to be used by residents, medical students, and practicing physicians in radiation oncology.

At the creation of this textbook, the emphasis was placed on keeping the content up-to-date in terms of publishing the results of major trials. It is not meant to be an encyclopedic work. It is impossible to include the results of all trials relating to radiation oncology. Publishing every little detail of each and every trial would bog down this resource and make it difficult to use. Its main purpose is to be a useful reference for those wishing to gain knowledge about clinical radiation oncology.

As it is a WikiWork, its purpose may change.

This book is dedicated to the patients who are the inspiration to those of us involved in this field, as well as to the pioneers in radiation oncology, without whom this textbook could not exist.

If you wish to contribute to this wiki, please see the instructions to authors at the following pages:
 * a working list of standards
 * Talk page.

title: Radiation Oncology/Introduction


text: Template:Radiation Oncology/TOC

title: Template:Radiation Oncology/TOC


text:
Cookbook:Artichoke Dip with Parmesan

| Appetizers | Cuisine of the United States

Artichoke hearts are readily available in cans and jars in many countries, and are increasingly used in the making of snack dips. Many national chain restaurants in the USA have some variety of artichoke dip, which is usually mayonnaise-based. One easy variation on the creamy artichoke dip is jokingly called the Artichoke Heart Attack, owing to the amount of mayonnaise and Parmesan cheese it contains.

As an "equal parts" recipe, this is especially amenable to whipping up at the last minute for a party. Because the recipe consists of a mayonnaise base to which other ingredients are added, it is popular among those who like to add something distinctive.

Ingredients
Equal parts:
 * Artichoke hearts, drained and chopped or squeezed
 * Mayonnaise
 * Parmesan or Romano cheese

Procedure

 * 1) Combine all ingredients to make dip.

Serving

 * At room temperature, it is perfect for the savory dipping of vegetables, potato chips, and all other common party snacks. It becomes even better, however, as a warmed-up dip. Simply place it into a small, shallow, heat-resistant dish and broil it for just a little while, until the top turns slightly tan. It can also work well as a continuously warmed dip in a fondue pot, although it does need to be stirred every once in a while to prevent burning.
 * This dip can also be used as the base for a sandwich. Spread the dip onto a good Italian roll, then broil it. When the dip turns a nice tan color, take it out of the broiler and finish the sandwich with lettuce and tomato.

Notes, tips, and variations

 * There are many who increase the amount of artichokes used, for health-conscious reasons. There are also versions that replace the mayonnaise with soft tofu.

 * Various items that are often added to the base artichoke dip, (to taste):
 * Salt and pepper.
 * Chopped scallions, (green onions)
 * Dill weed
 * Finely-chopped olives, (often with pimento)
 * Chopped tomatoes (an especially common addition)
 * Any number of very finely chopped vegetables (sometimes pre-cooked but raw is fine)
 * Chopped spinach, cooked
 * ½ cup sour cream
 * ½ cup cream cheese
 * Minced garlic
 * Small can chopped green chilis
 * Dijon Mustard (to taste)

title: Cookbook:Artichoke Dip with Parmesan


text:
User talk:Xno~enwikibooks

Ciao Xno, volevo solo informarti che è stato attivato il dominio it.wikibooks.org e sto spostando li i documenti in italiano qui presenti.
 * --Snowdog 09:19, 9 Sep 2004 (UTC)

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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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title: User talk:Xno~enwikibooks


text:
User talk:LouMarini

Ciao Xno, volevo solo informarti che è stato attivato il dominio it.wikibooks.org e sto spostando li i documenti in italiano qui presenti.
 * --Snowdog 09:20, 9 Sep 2004 (UTC)

title: User talk:LouMarini


text:
Pro Engineer/Definitions

A

TOP

Accuracy.

The smallest item that can be recognised by pro/engineer. Usually defined as ratio of the longest diagonal through the model. Typically 0.0012.

Active Model

Title bar has stars on each side of the name. Will accept menu commands from the side menu. Use CTRL+A or the tick icon to make the window active.

Active Window

Window with the blue bar, will accept spinning and rendering commands. Plus some info menu picks. Other commands are restricted for use with the active model.

Alpha

The optional fourth-channel in an RGB image file, typically used for compositing.

Ambient Light

A light that equally affects all portions of all objects in the rendering scene.

Appearance

A set of attributes that determine the appearance of a surface. These attributes include color, reflecting ability, transparency, texture, and so forth.

Area Offset

Offsets a whole or part surface, similar to form. Side walls are added to join the offset area to main surface.

Associative Topology Bus

A method for transferring data between applications whilst retaining associativity.

Axis

See datum axis.

ATB

See Associative Topology Bus

B

TOP

BMP

Bitmap

BMX

Behavioural Modelling Extension

Both Sides

When creating extruded features the feature is created on both sides of the sketch plane.

Boundary Influence

Controls how far the boundary condition propagates across a boundary surface.

Boundary Conditions

Property of surface at edges e.g. tangent/normal to adjacent surfaces or tangent normal to sketch plane

Boundary Surface

A surface defined using two or more curves.

Briefcase

A method in Pro/Intralinkcommonspace to collect objects together.

Brightness

The property of an appearance that determines its intensity after the hue is chosen.

Bump Map

A one-channel texture map that creates the illusion of surface roughness.

Bump Height

The height or depression of the bump map features.

C

TOP

C0 continuity

example

Position continuity only. Curves have a kink at the C0 point and surfaces have a sharp crease along the C0 seam. Abutting curves and surfaces touch one another, but they have no curvature similarities.

C1 continuity

example

Position and tangent continuity. The edges between a ball fillet and its adjacent faces are examples of C1 continuity.

C2 continuity

example

Position, tangent, and curvature continuity. Curves and surfaces are perfectly smooth, and the curvature at the joint between two abutting curves or surfaces is equal. Consequently, the joint is seamless and invisible.

CAD

Computer Aided Design Computer Aided Drafting

CADD

Computer Aided Design And Drafting

CAE

Computer Aided Engineering

CAM

Computer Aided Manufacture

Capped Ends

Creates a surface with ends closed off forming an enclosed volume e.g. a sketch of circle with closed ends will form a cylinder instead of a tube. Requires the sketch to be closed.

CEP

Certified Engineering Provider

CGM

Computer Graphics Metafile

Chamfer

Removes the corner or edge of a solid by a specified amount.

Check In

Process of moving objects from workspace to commonspace.

Check Out

Process of moving objects from commonspace to workspace to view or modify.

Clip

A graphical method for cutting the model through a plane parallel to the view screen at a user definable depth.

Closed Loop

Sketch entities that enclose an area without intersection or overlap

Closed Sketch

The sketched entities form a continuous loop with no gaps or overlapping entities.

Color Blender

A part of the color editor that provides a continuous range of colors. Blend colors between the blender's four color chips.

Color Box

A part of the color editor that allows you to define colors along two axes based on red, green, and blue values of colors.

Color Pallette

A part of the color editor that provides an array of colors.

Color Texture

A three-channel texture map that consists of red, green, and blue values.

Color Wheel

A part of the color editor that allows you to select colors based on hue, saturation, and brightness.

Commonspace

Vault area of Pro/Intralink where pro/engineer models can be stored and shared.

Component

A component is a part or sub-assembly assembled into an assembly

Component Interface

A method by which the preferred assembly references can be denoted at part level.

Control Points

Used in Boundary Surfaces to determine how surfaces are sub-divided.

Coordinate system

See datum coordinate system

Copy Geometry

A feature that can copy geometry references from on model to another. References can be made to all feature types. It should be noted solids cannot be copied but the surface information of a solid can be copied to the target model. See publish geometry.

CPC

Collaborative Product Commerce

Cross-section

See X-section

Create

Accesses the feature creation menu

Curvature

example

Curvature is defined as 1/r. A curvature plot measures the curvature at points on a curve. A line is plotted at that point normal to the curve. The length is proportional to 1/r. The line is scaled up to make it easier to see.

Cut

A feature to remove material from a model.

Curve

See datum curve

D

TOP

Datum Axis

Datum axes are infinitely thin lines that extend indefinitely in both directions. There are usually shown truncated around the parent feature. Axes can be created manually. They are also created automatically when adding hole features, revolved features.

They can be defined in intent manger when defining closed sketches.

Datum Plane

Datum Planes represent infinitely thin flat planes that extend infinitely in two perpendicular directions.

For display purpose a rectangular outline is shown. By default datum planes resize to the size of the model. They can be redefined to a specific size or linked to the size of a feature.

Datum planes can be used in as surfaces in some surface operations.

One side of the datum is coloured yellow and the other side is red.

Datum Curve

Datum curves represent curves (inc. straight) that exist in space as 2D or 3D entities. They can curve in more than one direction at a time.

Datum curves are orange (they appear brown to a lot of users)

Datum Coordinate Systems

Coordinate systems represent an origin in space with an X, Y and Z defined.

The main uses are for offsetting points, creating datum curves from equations and assembling sub assemblies.

Datum Point

A datum point represents a point in space usually defined relative to a coordinate system

Decal

A four-channel texture map that consists of a standard color texture map and a transparency (or alpha) channel. See Alpha.

Declare

Use to link models and layouts.

Delete

Permanently remove a feature or entity from Pro/Engineer. When used on patterns the original feature is deleted.

Del Pattern

Deletes a pattern but leaves the original feature.

Density

Sets the model density. The density is used by mass property calculations.

Depth Cue

Visual setting to dim lines that are furthest away from the view plane.

Designate

Parameters can be designated so the can be 'seen' by PDM systems.

Dihedral Angle

The angle between two adjacent surfaces. Usually the maximum and minimum are returned.

Dim Bound

The ability to regenerate dimensions to upper, lower, mid or nominal tolerance value.

Direction Light

A type of light that creates parallel light rays, which simulates the sun.

Draft

Used to add angled sides to solids and surfaces. Typically used in parts that are cast, molded or forged.

Draft Offset

Similar to area offset but the angle of area's offset can be specified.

E

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EAI

Enterprise Application Integration

Edge

Where two faces meet or the perimeter of a face.

EPS

Encapsulated PostScript

Erase

In the context of Pro/Engineer Erase means suppressed or blanked. Erased features can be resumed or shown to restore them.

ERP

Enterprise Resource Planning

ERM

Enterprise Resource Management

Extend

Grows additional surfaces from existing surface edges

F

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Family Table

A method for creating a 'family' of related parts. This is achieved by varying dimensions, including and excluding features.

Face

Feature

Most operations in Pro/Engineer create features

-Solids

-Surfaces

-Datums

-Cosmetic

-CopyGeom

-UDF's

This includes

Protrusions, tweaks, cuts, holes, trims, axes, surface merges, bends, unbends.

The following are not features

-Parameters

-Colours

-Tolerances

-Layers

All features appear in the model tree if they don't then they are not features

Feature Name

Assigned automatically when the feature is created using the feature type and feature id. The feature name can be modified by the user.

Feature Number

Sequential number assigned to each feature based on the features place in the model's history. A feature's feature number will change when the model's history is modified.

Feature ID

A unique number assigned when a feature is created. This number doesn't change. This number is not reused within a model if a feature is deleted.

Family Table

Use to create families of parts. A part created by family table is called an instance. The table can be used to vary dimensions, suppress/ resume features and substitute components. A containing a family table is called a 'generic' part.

FEA

Finite Element Analysis

Frames

Method by which actions in a Pro/Intralink workspace can be undone.

Free Form

A feature that stretches and pulls existing surfaces.

G

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Gamma

An inherently non-linear reproduction of intensities by a display device (monitor).

Gamma Correction

Correcting image data such that linear changes in image data will produce linear changes in the displayed image.

Generic

A model that contains a family table.

GIF

Graphics Interchange Format

Grid

Grids can be displayed in models, sketcher and details

Graph

A 2D curve or graph that can be used to control features such as variable section sweeps or used to extract a 'y' value based on an x value.

Groups

A collection of features

H

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History

Sequence of features in a model. The sequence of features affects the model geometry. The history is displayed graphically in the model tree. The feature number defines the sequence of the feature.

HPGL

Hewlett Packard graphics Language

Hue

The basic shade, or tint, which defines a color.

I

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IGES

International Graphics Exchange Specification

Insert Mode

Used to add features at an earlier point in the model's history

Instance

A part created by a generic model's family table.

Integrate

Use to merge two different versions of the same model.

Intent Manager

Replaced Sketcher at version 20. Used in the creation of most features. Used to create sketch geometry and add design intent

Interchange

A method swapping models in assembly. Useful when the alternate model is unrelated to the original model.

ISDX

Interactive Surface Design Extension

J

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JPG, JPEG

Joint Photographic Experts Group

K

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L

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Layers

Used to blank/display components, datums, and surfaces. Features cannot be blanked using layers. Layers can also be used as a selection criteria.

Light

Necessary for all renderings, lights have position, color and brightness. Some lights also have direction, spread or concentration. There are four types of lights: ambient, direction, point, and spotlight.

Light Room

A rendering option that determines whether the room is lit by user-defined lights or by a standard ambient lighting.

LM

Licence Management

M

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Mapkey

A method of recording and replaying a series of actions (macro). Excellent way for speeding up common tasks.

Material Side

Sets on which side of open sketch entity material is added.

MDX

Mechanism Design Extension

Mechanica

PTC's FEA and simulation tool

Merge

A feature that joins two surfaces together.

MDO

Mechanism Dynamics Option

Mirror Geom

Mirror whole model

Model Tree

Graphical display of the model's history and structure

MPEG, MPG

Moving Picture Experts Group

N

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Nastran

NASA Structural Analysis System

Note

Notes are added to drawings and models to aid documentation. 3D notes can be linked to features with the option of having a web page link.

O

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Object

An object can be a Feature, Component, Note or an other item that appear in the model tree

Offset Edge

Used in Intent Manager to construct sketch entities from existing geometry.

One Side

When creating extruded features the feature is created on one side of the sketch plane. The direction can be changed with redefine and selecting Direction.

Open Ends

Creates a surface feature without ends, e.g. a tube

Open Sketch

A sketch where the two ends do not meet, or there is a gap in the sketch. Open sketches also occur when the sketch entities form a closed loop, but there are additional sketch entities coincident with the closed loop.

Open Loop

P

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Palette

A collection of rendering objects that are displayed together in an editor. There are palettes for appearances and lights.

Part

Solid model representing a component

PDM

Product Data Management Parametric Data Manager (PTC)

Photorender

A rendering utility that creates photorealistic images of a scene.

PIV

Product Item Version - this represents the combination of the object name version and revision.

Pixel

A single dot of an image, displayed by the combination of three primary colors: red, green, and blue.

Plane

See datum plane

PLM

Product Lifecycle Management

PLM

Product Line Manager (PTC)

Point

See Datum point

Point Light

A type of light where the illumination radiates from the center of the bulb.

Program

Program is used to create intelligent parts that change based on user input.

Protrusion

Generic terms for any solid feature.

Pro/Intralink

Data manager for Pro/Engineer

PS

Postscript

Publish Geometry

Group geometry you want other users to reference

Program

Facility to modify the model design with the option to add conditional statements to control the model design.

Q

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Quilt

A group of surfaces joined together.

R

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Reference Control

Limits what references can be made.

Reference Dimension

Reference Dimensions can be added in models and drawings. They are driven dimensions and cannot be used to modify the model.

Reference Entity

Reference entities in Intent Manager are created by :-

Specify Refs, Entities picked to create dimensions Entities pick during Use Edge and Offset Edge.

Redefine

Used to change a features definition. Sketch planes, the section sketch, depth etc.

Reflection

The degree to which a model reflects its surroundings.

Regenerate

Incorporates changes made to the model since the last regeneration

Relations

Facility to drive dimension values by equation. Dimensions values can be related to other dimensions, parameters or graph features.

Render

To create a shaded image in order to give the model a more realistic appearance

Reorder

Moves a feature before or after other features in the model's history.

Reroute

Changes the references used to construct a feature. Or used to swap and old feature for a new feature.

Resume

Restores / unsuppresses suppressed features

RGB

The red, green, and blue values of a color.

RHO

See tutorial

Round

A feature that creates a fillet along an edge or between two surfaces.

RUG

Regional User Group

S

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Saturation

The purity of the hue in a color. An "unsaturated" color is gray.

Self Shadows

A rendering option that causes shadows from a model to be cast onto itself.

Skeleton

Model used to define geometry that is shared between parts in an assembly. Often used to to create mechanism frameworks, define global datums.

Shell

A feature that removes a specified surface and hollows the solid to a specified wall thickness.

Simplified Rep

A subset of the main model with components blanked or substituted with simple alternatives. Part simplified reps can be used to cut models into sub sections.

The principal use is to speed up rendering, and to make easier to work on complex models.

Solid

A volume fully enclosed by surfaces where the any point in space can be analysed to know whether it is inside or outside the enclosed area.

Spline

A curve that passes through a number of points. Can be defined in sketcher on a 2D plane or in 3D through a series of points or vertices.

Spot Angle

The diameter of a spotlight's circle of light.

Spot Light

A type of light whose light rays are confined within a cone.

Spot Focus

The sharpness of a spotlight's beam.

STEP

Standard For The Exchange Of Product Model Data

Specify Refs

Used to specify which entities you want intent manager to use for dimensions and constraints.

STL

Stereo Lithography

Style

Feature created by ISDX

Surface

A face bounded by at least three edges

Suppress

Same as Delete except feature can be restored (resume (d)) at a later date

Sweep

Geometry formed by a profile dragged (swept) along a trajectory

Swept Blend

Geometry formed by different profiles positioned on a trajectory

T

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TAN

Technical Application Note

Texture

An image that is used to determine the color or appearance of a surface. See Appearance.

TIFF

Tagged Image File Format

TPI

Technical Point of Interest

Trail

The trail or trail file records all actions made during a session. It is possible to replay trail files to rebuild models lost due to crashes or as a presentation method.

Trajectories

Used to create sweeps, variable section sweeps, and swept blends. Trajectories can be defined by sketching or selecting existing geometry.

Transform

Translate or move a surface with the option to create a copy. (can be used on datum curves)

Transparency

The degree to which you can see through a surface.

Trim

Type of cut specifically for surfaces.

Tweak

A feature that transforms an existing feature.

U

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Units

Units of measure for length mass and force. Custom units can be defined. Models can be converted from one type of unit to another.

UPR

Universal Product Representation

Use Edge

Used in Intent Manager to construct sketch entities from existing geometry.

User Defined Feature UDF

UDF's allow collections or features to be used. UDF's are a special type of group.

V

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Var Sec Swp

See Variable Section Sweep

Vertex (vertices)

Ends of edges, curves typically found where a number of edges join. Also found where sub-entities of a ketch join.

Variable Section Sweep

A sweep where the section changes in size. Requires at least two trajectories.

W

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WMF

Windows Metafile

Workspace

Models are checked out from commonspace to workspace for modification. The workspace is a database and folder area located in the users network directory.

X

TOP

X-section

(Cross-Section) A slice through either a solid or quilt.

Y

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Yellow Side

One side of datum, system will assume the yellow side to be positive first. The positive side

Z

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Product Acronyms

AAX

Advanced Assembly Extension

APX

Assembly Performance Extension

ARX

Advanced Rendering Extension

ASX

Advanced Surfacing Extension

BMX

Behavioural Modelling Extension

CDRS

Conceptual Design & Rendering Software

DAO

Design Animation Option

DDO

(Import) Data Doctor Option

EMO

Expert Machinist Option

IDX

Industrial Design Extension

ISDX

Interactive Surface Design Extension

MDO

Mechanical Dynamics Option

MDX

Mechanical Design Extension

MSO

Machine Simulation Option

NOO

NC Optimisation Option

RSD

Routed System Designer

title: Pro Engineer/Definitions


text:
Pro Engineer/Detail FAQ

FAQ - Detail
How do I display PCD centrelines for radial pattern holes? In detail mode - Advanced, Setup, Modify Val. Find the entry RADIAL_PATTERN_AXIS_CIRCLE and set the value to YES File, Exit and repaint the screen to see changes. Note: This only works for pattern of holes defined using the radial type holes, where the dimension type is set to diameter when created not radius.

How do I change the size of datum points? In detail mode - Advanced, Setup, Modify Val. Find the entry DATUM_POINT_SIZE and set the value (value is in inches) e.g. 3 is 3 inches not 3 mm File, Exit and repaint the screen to see changes.

How do I change the shape of datum points? In detail mode - Advanced, Setup, Modify Val. Find the entry DATUM_POINT_SIZE and set the value to one of the following CROSS, DOT, CIRCLE, TRIANGLE, or SQUARE. File, Exit and repaint the screen to see changes.

How do you blank items on layers in assemblies/parts in the drawing? Assuming the assemblies use default layers or the features to blank are on layers. Create a layer in the drawing with exactly the same name. When it is blanked it will effectively blank all features on the chosen layers in all components in the assembly.

How do include symbols in notes? Create the note as normal at the location where the note is required type &sym(name) where name is the name of the symbol. You will need retrieve the symbol so it is part of the drawing before this will work.

How do I create a PLUS-PLUS tolerance? Use Modify, Value pick the negative tolerance and add a minus sign in front of the value e.g 0.2 becomes -0.2 hit enter and Pro/Engineer will now show a plus-plus tolerance. This is because Pro/Engineer stores the integer as a positive value and applies a negative value to it, making the tolerance value negative creates a positive (two negatives = a positive).

What are the curly brackets that appear when editing notes? A typical note will appear as below when editing

{0: First line of note}

{1: Second line of note}

The brackets and number control the text formatting. If you delete the number or the colon then the text line will return to default text formatting values.

title: Pro Engineer/Detail FAQ


text:
User talk:Patrick fleckney

HI My name is Patrick Fleckney and I am a science correspondant for a national newspeprr and astronomy & space magazine. I welcome feed about any of the contributions I have made to WIKIBOOKS.

Current Contributions:

1. The Sun

2. The planet Mercury

title: User talk:Patrick fleckney


text:
General Relativity/Einstein's equation

<General Relativity

 * Main article: Einstein's field equation

The Einstein field equation or Einstein equation is a dynamical equation which describes how matter and energy change the geometry of spacetime, this curved geometry being interpreted as the gravitational field of the matter source. The motion of objects (with a mass much smaller than the matter source) in this gravitational field is described very accurately by the geodesic equation.

Mathematical form of Einstein's field equation
Einstein's field equation (EFE) is usually written in the form:

 * $$R_{\mu\nu} - {1 \over 2} {R g_{\mu\nu}} + \Lambda g_{\mu\nu} = 8 \pi {G \over c^4} T_{\mu\nu}$$

Where

 * $$R_{\mu\nu}$$ is the Ricci curvature tensor
 * $$R$$ is the Ricci scalar (the tensor contraction of the Ricci tensor)
 * $$g_{\mu\nu}$$ is a (symmetric 4 x 4) metric tensor
 * $$\Lambda$$ is the Cosmological constant
 * $$\pi$$ is pi=3.1415..., the ratio between a circle's circumference and diameter
 * $$G$$ is the Gravitational constant
 * $$c$$ is the speed of light in free space
 * $$T_{\mu\nu}$$ is the energy-momentum stress tensor of matter

The EFE equation is a tensor equation relating a set of symmetric 4 x 4 tensors. It is written here in terms of components. Each tensor has 10 independent components. Given the freedom of choice of the four spacetime coordinates, the independent equations reduce to 6 in number.

The EFE is understood to be an equation for the metric tensor $$g_{\mu\nu}$$ (given a specified distribution of matter and energy in the form of a stress-energy tensor). Despite the simple appearance of the equation it is, in fact, quite complicated. This is because both the Ricci tensor and Ricci scalar depend on the metric in a complicated nonlinear manner.

One can write the EFE in a more compact form by defining the Einstein tensor
 * $$G_{\mu\nu} = R_{\mu\nu} + (\Lambda - {1 \over 2}R) g_{\mu\nu}$$

which is a symmetric second-rank tensor that is a function of the metric. Working in geometrized units where G = c = 1, the EFE can then be written as

 * $$G_{\mu\nu} = 8\pi T_{\mu\nu}\,$$

The expression on the left represents the curvature of spacetime as determined by the metric and the expression on the right represents the matter/energy content of spacetime. The EFE can then be interpreted as a set of equations dictating how the curvature of spacetime is related to the matter/energy content of the universe.

These equations, together with the geodesic equation, form the core of the mathematical formulation of General Relativity.

Conservation of energy and momentum
An important consequence of the EFE is the local conservation of energy and momentum; this result arises by using the differential Bianchi identity to obtain

 * $$\nabla_b G^{\mu\nu}=G^{\mu\nu}{}_{;b}=0$$

which, by using the EFE, results in

 * $$\nabla_b T^{\mu\nu}= T^{\mu\nu}{}_{;b}=0$$

which expresses the local conservation law referred to above.

Nonlinearity of the field equations
The EFE are a set of 10 coupled elliptic-hyperbolic nonlinear partial differential equations for the metric components. This nonlinear feature of the dynamical equations distinguishes general relativity from other physical theories.

For example, Maxwell's equations of electromagnetism are linear in the electric and magnetic fields (i.e. the sum of two solutions is also a solution).

Another example is Schrodinger's equation of quantum mechanics where the equation is linear in the wavefunction.

The correspondence principle
Einstein's equation reduces to Newton's law of gravity by using both the weak-field approximation and the slow-motion approximation. In fact, the gravitational constant $$G$$ appearing in the EFE's is determined by making these two approximations.

The cosmological constant
The cosmological constant term $$\Lambda g_{\mu\nu}$$ was originally introduced by Einstein to allow for a static universe (i.e., one that is not expanding or contracting). This effort was unsuccessful for two reasons: the static universe described by this theory was unstable, and observations of distant galaxies by Hubble a decade later confirmed that our universe is in fact not static but expanding. So $$\Lambda$$ was abandoned (set to 0), with Einstein calling it the "biggest blunder he ever made".

Despite Einstein's misguided motivation for introducting the cosmological constant term, there is nothing wrong (i.e. inconsistent) with the presence of such a term in the equations. Indeed, quite recently, improved astronomical techniques have found that a non-zero value of $$\Lambda$$ is needed to explain some observations.

Einstein thought of the cosmological constant as an independent parameter, but its term in the field equation can also be moved algebraically to the other side, written as part of the stress-energy tensor:
 * $$T_{\mu\nu}^{\mathrm{(vac)}} = -\frac{\Lambda}{8\pi}g_{\mu\nu}$$

The constant
 * $$\rho_{\mathrm{vac}} = \frac{\Lambda}{8\pi}$$

is called the vacuum energy. The existence of a cosmological constant is equivalent to the existence of a non-zero vacuum energy. The terms are now used interchangeably in general relativity.

Solutions of the field equations
The solutions of the Einstein field equations are metrics of spacetime. The solutions are hence often called 'metrics'. These metrics describe the structure of the spacetime including the inertial motion of objects in the spacetime. As the field equations are non-linear, they cannot always be completely solved (i.e. without making approximations). For example, there is no known complete solution for a spacetime with two massive bodies in it (which is a theoretical model of a binary star system, for example). However, approximations are usually made in these cases. These are commonly referred to as post Newtonian approximations. Even so, there are numerous cases where the field equations have been solved completely, and those are called exact solutions.

The study of exact solutions of Einstein's field equations is one of the activities of cosmology. It leads to the prediction of black holes and to different models of evolution of the universe.

Vacuum field equations
If the energy-momentum tensor $$T_{\mu\nu}$$ is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations, which can be written as:

 * $$R_{ab} = 0\,$$

The solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution.

The above vacuum equation assumes that the cosmological constant is zero. If it is taken to be nonzero then the vacuum equation becomes:
 * $$R_{\mu\nu} = \Lambda g_{\mu\nu}\,$$

Mathematicians usually refer to manifolds with a vanishing Ricci tensor as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds.

title: General Relativity/Einstein's equation


text:
General Astronomy/Kepler's Laws

Johannes Kepler was a mathematician who attempted to derive a set of fundamental principles which would explain the motions of the planets. He believed in the heliocentric view of the solar system proposed by Copernicus, and he also possessed a rich set of observations of the planets made by Tycho Brahe.

After twenty years of painstaking attempts and various discarded ideas based on geometry, he finally arrived at a mathematical model of orbital motions based on the ellipse. Kepler summarized his findings in the form of three laws of planetary motion, frequently referred to as Kepler's First, Second and Third Laws, respectively:

 * Kepler's First Law, also known as The Law of Ellipses — The orbits of the planets are ellipses, with the sun at one focus.
 * Kepler's Second Law, or The Law of Equal Areas in Equal Time — The line between a planet and the sun sweeps out equal areas in the plane of the planet's orbit over equal times.
 * Kepler's Third Law, or The Law of Harmony — The time required for a planet to orbit the sun, called its period, is proportional to half the long axis of the ellipse raised to the 3/2 power. The constant of proportionality is the same for all the planets. It is often called the Law of Harmony because it shows a harmonic relation between distances and periods.

At that time he developed these laws, there was not yet a developed theory of gravity capable of explaining why the planets moved as they were observed to. Later, Isaac Newton, using his universal inverse-square law theory of gravity, was able to show how Kepler's Laws fit into a scientific theory of celestial mechanics.

Elliptical orbits
An ellipse is a shape formed by taking a diagonal slice through a cone. It is essentially the shape of a circle viewed at an angle.

An ellipse can be drawn by taking a piece of paper, two push-pins, a loop of string, and a pencil. The two pins are pushed through the paper into a suitable surface, providing the two foci for the ellipse. They should be closer together than the loop is long. The loop of string is placed around the base of these pins, leaving some slack. The pencil is now placed so that the pins and the loop form a triangle with a slight tension on the string.

Now try to draw a shape by moving the pencil about the pins while keeping the string taunt. The result should be an ellipse. The shape of the ellipse can be varied either by moving the pins closer together or further apart. This shape, according to Kepler, defines the path that a planet takes when it orbits the Sun.

Kepler's Second Law says in brief that an object speeds up as it gets closer to the Sun and slows down as it moves further away. Where the distance from the Sun to the orbital path is longer, only a smaller arc needs to be traversed to sweep out an area that requires a wider arc near the Sun.

As the planet moves closer to the Sun along its orbit the gravitational force works to increase the velocity. In contrast, as the planet is moving further away, the gravity of the Sun gradually decelerates the body and it is slowed down.

A line that divides an ellipse in half and passes through the widest part of the ellipse is called the major axis. A line perpendicular to this axis and dividing the ellipse in half is called the minor axis. Half the length of the major axis is called the semi-major axis, and is represented by $$a$$. The period required for a planet to complete one full orbit is represented by $$P$$. The relationship between the period P and the length of the semimajor axis $$a$$ is known as Kepler's Third Law, and can be represented as follows:

where the symbol ∝ means "proportional to", and implies that there is a direct mathematical relationship between the period squared and the length of the semi-major axis cubed.

The Second and Third Laws provide a basis for calculating the period of any planet orbiting the Sun, as well as determining where the planet will be located along the orbital path.

Eccentricity and Orbital Paths
The ratio of the distance of a focus from the center of an ellipse to the semi-major axis is called the eccentricity of the orbit. When the two foci of the ellipse are on top of each other, the eccentricity is exactly 0.0 and the shape is a circle. As the eccentricity increases, the orbiting planet moves much further away than at the closest approach. The orbital eccentricities for planets in our Solar system vary from as much as 0.21 for Mercury down to 0.0068 for Venus.

The scientific name for the point of closest approach is the periapsis, while the most distance separation is the apoapsis. In the case of planets orbiting the Sun, these are called the perihelion and aphelion, respectively. (The -helion suffix comes from the Greek name for the Sun deity, Helios. This word is also the source of the name for the element Helium.)

Perhaps the most counter-intuitive aspect of the Third Law is that for any two identical bodies orbiting the Sun with the same semi-major axis, the orbital period is the same. This is true even if one is orbiting in a perfect circle and the other has an orbit that is highly elliptical (has a relatively high eccentricity). The elliptical shape will fit entirely within the circle except at two points (the ends of the major axis, at which the two curves will be tangent), so it is actually a shorter orbital path. However the aphelion of the ellipse will be located further from the Sun, so the planet will spend more time traversing the distant section of the orbit. The shorter orbit and the slower traverse of the aphelion compensate for each other, resulting in an identical period with the circular orbit.

Some Examples Using Kepler's Third Law
Originally, Kepler's Third Law was used to describe the motions of the planets around the Sun. As it turns out, it also works very well with regards to other two-body orbital systems like the orbits of moons around Jupiter, or the orbits of binary stars about the center of mass of their system. In all of these cases the period of the orbit squared is proportional to the length of the semi-major axis cubed, with the differences between the orbital systems reflected in the constant of proportionality.

In this section we will consider the special case of the planets going around the Sun. If we choose to measure the length of the semi-major axis of an orbit in astronomical units (abbreviated AU, where 1 AU is the distance from the Earth to the Sun) and we measure the orbital period in years (abbreviated as $$y$$), then we can express Kepler's Third Law as

where $$P$$ is measured in years and $$a$$ is measured in astronomical units. What follows are a few example of how to use this equation.

Mars' Orbital Period
Repeated measurements of Mars' orbit have determined that the semi-major axis of its orbit has a length of 1.52 AU. How long does it take for Mars to orbit the Sun once?

Solution: In this question, we are being asked for the orbital period $$P$$ of Mars. We know from reading the question that the length of the semi-major axis $$a$$ is 1.52 AU. Solving Kepler's Third Law for the period gives us

 * $$P=\left(\frac{y}{\sqrt{AU^3}}\right)\sqrt{a^3}=\left(\frac{y}{\sqrt{AU^3}}\right)\sqrt{(1.52AU)^3}=1.87y$$

which tells us that it takes 1.87 years for Mars to go around the Sun once.

An Unknown Asteroid's Orbital Semi-Major Axis
An amateur astronomer spends several months tracking an asteroid and is able to determine that it takes approximately 3/4 of a year for it to orbit once around the Sun. What is the semi-major axis of this asteroid's orbit?

Solution: Reading the question tells us that the orbital period of the asteroid is 3/4 of a year, or 0.75 $$y$$. We are expected to find the length of the semi-major axis $$a$$, so we need to solve Kepler's Third Law for that. Doing so gives us

 * $$a=\left(\frac{AU}{\sqrt[3]{y^2}}\right)\sqrt[3]{P^2}=\left(\frac{AU}{\sqrt[3]{y^2}}\right)\sqrt[3]{(0.75 y)^2}=0.83AU$$

which means that is has a semi-major axis somewhere between that of Venus' orbit and Earth's orbit.

title: General Astronomy/Kepler's Laws


text:
General Astronomy/Daily Motions

Every day, the Earth turns once on its axis. At the Earth's equator, we move around the center of the Earth with speeds near a thousand kilometers per hour because of this rotation. We feel nothing, but we can see the effect of Earth's rotation. An observer on Earth sees everything in the sky appear to rotate around Earth at the rate of once per day. This motion is not apparent to an observer who steps outside for a moment, since it is so slow. For the motion to become apparent, an observer must watch the sky for a period of hours. During the day, the motion manifests itself in the movement of the Sun, which proceeds from the East in the morning towards the west in the evening. At night, the constellations move, seeming to circle about the pole.

Because the daily motion of the stars is driven by the same mechanism that drives the motion of the Sun, the stars move in almost exactly the same way that the Sun moves. Indeed, everything in the sky moves in almost exactly the same way over the course of a day. The motion of the Sun and the planets only differ at all because the planets have their own motion around the Sun along their orbits, and is noticeable from Earth.

As the Earth spins, it appears to us that the celestial sphere is spinning. It spins about the Earth's pole, so that the celestial poles appear stationary and the stars and planets seem to move in circles around the poles. Stars move at 15° an hour.

The schematic illustrates the daily motion of the celestial sphere resulting from the spin of the Earth. The Sun, Moon, planets and stars make circles around the Earth. Since the observer is tilted with respect to Earth's rotation axis, the daily motion also appears tilted. As a result, celestial objects appear to rise and set at an angle.

Looking at the diagram, we see that stars should rise roughly in the East and come up at an angle. In the Northern Hemisphere, the stars move to the south as they rise, while stars move northward in the Southern Hemisphere as they rise. To an observer standing at the equator, the axis of rotation is horizontal, and stars rise in the East perpendicular to the horizon.

Since the stars seem to rotate around the celestial pole, some of the stars very near the pole never rise or set. Certainly, Polaris never sets — it remains fixed. Only an observer very close to the equator will see any of the stars in the Little Dipper rise or set. The stars close enough to the pole never seen to rise or set are called circumpolar stars. These stars always remain above an observer's horizon. Different stars are circumpolar to different observers.

Imagine standing at the North Pole. You would see Polaris overhead with all the other stars spinning around it. In reality, you are the one who is spinning. From the North Pole, all of the motion of the stars is horizontal. Stars at the horizon skim along the horizon, never rising or setting. The stars higher in the sky also move horizontally, never moving up or down. From the poles, all visible stars are circumpolar.

At the Earth's equator, the situation is different. The celestial poles appear at the horizon on the north and south points. As stars move around the poles, they all rise and set, no matter how close to the pole they are. From here, there are no circumpolar stars. As you move from the equator to the pole, you will see gradually more and more stars become circumpolar, until on finally reaching the pole you find that all stars are circumpolar.

For centuries, the day has been the most fundamental unit of time in the calendar. Measuring the passage of days is as easy as counting sunrises or sunsets. The earliest clocks, the predecessors to the sundial, worked by tracking the daily motion of the Sun across the sky.

A sundial uses the position of the Sun to give the time. (The gnomon of a sundial can be used to find north: the shortest shadow cast by the sun (at noon) points north.) Of course, not all clocks work by measuring the Sun, although all work by measuring some reliably periodic and regular process. A wristwatch, for example, measures the oscillations of a quartz crystal. Atomic clocks use the natural period of oscillation of cesium atoms to measure time. Other systems of time are tied to the motion of the Earth, but there are a variety of ways to measure time in this way. The time measured by any particular method is not guaranteed to agree with the time measured by another, so it is sometimes necessary to convert between different "kinds" of time.

The time measured by sundials is called local solar time. The local solar time progresses according to the Sun's motion around the Earth. Since the Earth's speed in its orbit around the Sun changes slightly over the course of a year, this motion is not completely uniform. Sometimes, when the Earth is moving faster in its orbit, the solar day is shorter. Early timekeepers never noticed this slight difference, but the appearance of accurate mechanical clocks made it possible to measure the small changes in the length of the day.

To deal with this problem, astronomers invented mean solar time. The mean solar time averaged the length of the day so that each day was of the same length. This standard is up to fifteen minutes off from the true solar time, but is much more convenient for clocks that are accurate enough to see the difference. Over the course of a year, the local solar time drifts, but the two always agree after a full year has passed.

For much of history, every town in the world kept a slightly different "correct time" from every other town. Under local solar time, noon occurs at the moment the Sun passes through the observer's meridian. Two observers in different locations will observe local noon to occur at different times. This is why local solar time is called "local." This difference wasn't a problem when transportation and communication were slow, but the advance of trains and telegraphs made even a small difference between nearby towns important. To deal with this, the time zones were developed. The standard time was defined to be the time at a nearby line of longitude. For most locations, the time zone was offset by an round number of hours from the time measured at Earth's prime meridian.

For historical reasons, the prime meridian is based on the line of longitude through the observatory in Greenwich, England. That time zone is known as Greenwich Mean Time, and is often used as a standard for when one wishes to compare times without taking local time zones into account. For this reason (since it is used universally) it is also called Universal Time. This is the most commonly used form of solar time, and the most commonly used measure of time in general.

It's very natural to use the Sun as a standard of time, since the cycles of day and night are so important to life on Earth. For this reason, most people think of a day as the time it takes the Sun to move through the sky once. The apparent motion of the Sun in the sky is similar to the motion of everything else, but not exactly the same. The daily motion is driven almost entirely by the rotation of the Earth, but the Sun's motion differs from the stars' motion. This happens because the Earth is moving around the Sun. The Earth moves a little in its orbit while a it rotates and day passes. Because the Earth's position has changed, a full rotation doesn't quite bring the Sun all the way around the sky. This means that the Earth makes a little more than a full rotation over the course of a solar day.

A sidereal day is the amount of time it takes for the stars to go once around the sky, equal to 23 hours and 56 minutes. The word sidereal means "relating to the stars." The difference in length between the solar and sidereal day causes the rising and setting times of stars to change throughout the year. If the star Rigel, for example, rises at noon today, it will rise at 11:56 tomorrow. In six months, it will rise at midnight. Because the difference between solar days is tied to the orbit of the Earth, there is exactly one more sidereal day in a year than there are solar days.

A sidereal month is the period of the moon in relation to the stars; approximately 27 (1/3) days (13 degrees a day). Ancient peoples used this period to track time, as evidenced by the Big Horn Medicine Wheel in Sheridan, Wyoming.

Sidereal time is widely used in astronomy because it can be used to tell which stars will be up. At a given sidereal time, the stars in the sky will always be the same. Accurately finding the position of stars is easier than finding the position of the Sun, so measurements of the solar time are usually based indirectly on the sidereal time. Modern techniques measure time from atomic clocks, which are then tied to the motion of the Earth by measurement of the sidereal time.

A synodic month is one new moon to the next; approximately 29.5 days. This is about two days longer than the sidereal month. The reason for this is that while the Moon is orbiting the Earth, the Earth is orbiting the Sun. Therefore, the Moon has to travel more than 360 degrees to return to its original position above the same meridian on the Earth.

For anyone living on the coast, tides play an important role in everyday life. Despite this, the cause of the tides was a mystery for centuries, before gravity was well understood. People have always suspected that tides are related to the moon, since high tides always occur when the Moon is highest in the sky and again when the Moon is lowest below the horizon. This turns out to be correct.

Tides occur because the gravitational pull from the Moon is greater on the side of the Earth facing the Moon than on the side facing away. As a result, the gravitational pull "stretches" the Earth. The tidal pull from the Moon gives the Earth an oblong shape. The pull affects the ocean more strongly than the ground, because the ocean is liquid and less resistant to movement.

The stretching effect from the tides creates two places on Earth where the tides are high, with one high tide on the side of the Earth facing the Moon and the other on the side opposite the Moon. As the Earth rotates, the locations under the positions of high tides also move. If the moon didn't orbit around the Earth, high tide would occur exactly twice a day, every 12 hours. The orbit of the moon changes the position of the high tides over the course of the month, which lengthens the time between high tides to about 12½ hours.

The Sun also has a tidal influence on the Earth, although this is a much smaller effect than the Moon's tidal influence. Because of the difference in the gravitational pull from the Sun on opposite sides of the Earth is much smaller, the Sun's tendency to make the Earth bulge is much less. Still, the contribution to tides from the Sun is noticeable. When the Sun, Moon and Earth are aligned, the Sun adds to the Moon's tidal pull, making the tides greater. This is called the spring tide. (The spring tide has no connection with the season of spring.) When the Moon is at a right angle with the Sun, the Sun's tidal pull interferes with the Moon's, making the tides weaker. This configuration is called the neap tide.

title: General Astronomy/Daily Motions


text:
Java Programming/Java Overview

The new features and upgrades included into Java changed the face of programming environment and gave a new definition to Object Oriented Programming (OOP in short). But unlike its predecessors, Java needed to be bundled with standard functionality and be independent of the host platform.

The primary goals in the creation of the Java language: The Java language introduces some new features that didn't exist in other languages like C and C++.
 * It is simple.
 * It is object-oriented.
 * It is independent of the host platform.
 * It contains language facilities and libraries for networking.
 * It is designed to execute code from remote sources securely.

Object orientation
Object orientation ("OO") refers to a method of programming and language technique. The main idea of OO is to design software around the "things" (i.e. objects) it manipulates, rather than the actions it performs.

As the hardware of the computer advanced, it brought about the need to create better software techniques to be able to create ever increasing complex applications. The intent is to make large software projects easier to manage, thus improving quality and reducing the number of failed projects. Object oriented solution is the latest software technique.

 * Assembly languages : Software techniques started with the assembly languages, that were close to machine instruction and were easy to convert into executable code. Each hardware had its own assembly language. Assembly language contains low level instructions like move data from memory to hardware registers, do arithmetic operations, and move data back to memory. Programmers had to know the detailed architecture of the computer in order to write programs.

 * Procedural languages : After the assembly languages, high level languages were developed. Here the language compiler is used to convert the high level program to machine instructions, freeing the programmers from the burden of knowing the computer hardware architecture. To promote the re-use of code and to minimize the use of GOTO instructions, "procedural" techniques were introduced. This simplified the creation and maintenance of software control flow, but left out the organization of data. It became a nightmare to debug and maintain programs having many global variables (i.e. variables that contain data that can be modified anywhere in the application).

 * Object oriented languages : In OO languages, data is taken seriously with information hiding. Data that is specific to an object can only be accessed by procedures in that object. As a result, objects contain data as well as control flow and a program becomes a series of interactions between objects.

Platform dependence
In C or C++ programming, you start to write source code:

... you compile it to a machine code file:

... and then you execute it:

In this situation, the machine code file and its execution are specific to the platform (Windows, Linux, macOS, ...) it was compiled for, that is to say to the targeted platform:

... because the compiled file is a machine code file designed to work on a specific platform and hardware. It would have produced different results/output for another platform. So if you want your program to run on several platforms, you have to compile your program several times:

It poses greater vulnerability risks. Note here that when a certain code is compiled into an executable format, the executable cannot be changed dynamically. It would need to be recompiled from the changed code for the changes to be reflected in the finished executable. Modularity (dividing code into modules) is not present in Java's predecessors. If instead of a single executable, the output application was in the form of modules, one could easily change a single module and review changes in the application. In C/C++ on the other hand, a slight change in code required the whole application to be recompiled.

The idea of Java is to compile the source code into an intermediate language that will be interpreted.

The intermediate language is the byte code. The interpreter is the Java Virtual Machine (JVM). The byte code file is universal and the JVM is platform specific:

So a JVM should be coded for each platform. And that's the case. So you just have to generate a unique byte code file (a  file).

The first implementations of the language used an interpreted virtual machine to achieve portability, and many implementations still do. These implementations produce programs that run more slowly than the fully-compiled programs created by the typical C++ compiler, so the language suffered a reputation for producing slow programs. Since Java 1.2, Java VM produces programs that run much faster, using multiple techniques.

The first of these is to simply compile directly into native code like a more traditional compiler, skipping bytecode entirely. This achieves great performance, but at the expense of portability. This is not really used any more.

Another technique, the just-in-time (JIT) compiler, compiles the Java bytecode into native code at the time the program is run, and keep the compiled code to be used again and again. More sophisticated VMs even use dynamic recompilation, in which the VM can analyze the behavior of the running program and selectively recompile and optimize critical parts of the program. Both of these techniques allow the program to take advantage of the speed of native code without losing portability.

Portability is a technically difficult goal to achieve, and Java's success at that goal is a matter of some controversy. Although it is indeed possible to write programs for the Java platform that behave consistently across many host platforms, the large number of available platforms with small errors or inconsistencies led some to parody Sun's "Write once, run anywhere" slogan as "Write once, debug everywhere".

Standardization
C++ was built atop the C language and as a result divergent ways of doing the same thing manifested around the language. For instance, creating an object could be done in three different ways in C++. Furthermore, C++ did not come with a standard library bundled with its compilers. Instead, it relied on resources created by other programmers; code which rarely fit together.

In Java, standardized libraries are provided to allow access to features of the host machines (such as graphics and networking) in unified ways. The Java language also includes support for multi-threaded programs—a necessity for many networking applications.

Platform independent Java is, however, very successful with server side applications, such as web services, servlets, or Enterprise JavaBeans.

Java also made progress on the client side: first it had Abstract Window Toolkit (AWT), then Swing, and the most recent client side library is the Standard Widget Toolkit (SWT). It is interesting to see how they tried to handle the two opposing consuming forces. Those are :

 * Efficient, fast code; port to most popular hardware (write once, test anywhere) : Use the underlying native subroutine to create a GUI component. This approach was taken by AWT, and SWT.

 * Portability to any hardware where JVM ported (write once, run anywhere) : To achieve this to the latter, the Java toolkit should not rely on the underlying native user interface. Swing took this approach.

It is interesting to see how the approach was switched back and forth. AWT → Swing → SWT.

Secure execution
With the high-level of control built into the language to manipulate hardware, a C/C++ programmer could access almost any resource, either hardware or software on the system. This was intended to be one of the languages' strong points, but this very flexibility led to confusion and complex programming practices.

Error handling
The old way of error handling was to let each function return an error code then let the caller check what was returned. The problem with this method was that if the return code was full of error-checking codes, this got in the way of the original one that was doing the actual work, which in turn did not make it very readable.

In the new way of error handling, functions/methods do not return error codes. Instead, when there is an error, an exception is thrown. The exceptions can be handled by the keyword at the end of a  block. This way, the code that is calling the function does not need to be mangled with error checking codes, thus making the code more readable. This new way of error handling is called Exception handling.

Exception handling was also added to C++. However, there are two differences between Java and C++ Exception handling:
 * In Java, the exception that is thrown is a Java object like any other object in Java. It only has to implement  interface.
 * In Java, the compiler checks whether an exception may be caught or not. The compiler gives an error if there is no catch block for a thrown exception.

The optional exception handling in the Java predecessors leads the developers not to care about the error handling. As a consequence, unexpected errors often occur. Java forces the developers to handle exceptions. The programmer must handle exception or declare that the user must handle it. Someone must handle it.

Networking capabilities
However powerful, the predecessors of Java lacked a standard feature to network with other computers, and usually relied on the platforms' intricate networking capabilities. With almost all network protocols being standardized, the creators of Java technology wanted this to be a flagship feature of the language while keeping true to the spirit of earlier advances made towards standardizing Remote Procedure Call. Another feature that the Java team focused on was its integration in the World Wide Web and the Internet.

The Java platform was one of the first systems to provide wide support for the execution of code from remote sources. The Java language was designed with network computing in mind.

An applet could run within a user's browser, executing code downloaded from a remote HTTP server. The remote code runs in a highly restricted "sandbox", which protects the user from misbehaving or malicious code; publishers could apply for a certificate that they could use to digitally sign applets as "safe", giving them permission to break out of the sandbox and access the local file system and network, presumably under user control.

Dynamic class loading
In conventional languages like C and C++, all code had to be compiled and linked to one executable program, before execution. In Java, classes are compiled as needed. If a class is not needed during an execution phase, that class is not even compiled into byte code.

This feature comes in handy especially in network programming when we do not know, beforehand, what code will be executed. A running program could load classes from the file system or from a remote server.

Also this feature makes it theoretically possible for a Java program to alter its own code during execution, in order to do some self-learning behavior. It would be more realistic to imagine, however, that a Java program would generate Java code before execution, and then, that code would be executed. With some feedback mechanism, the generated code could improve over time.

Automatic memory garbage collection
In conventional languages like C and C++, the programmer has to make sure that all memory that was allocated is freed. Memory leaks became a regular nuisance in instances where the programmers had to manually allocate the system's memory resources.

Memory resources or buffers have specific modes of operation for optimal performance. Once a buffer is filled with data, it needs to be cleaned up after there is no further use for its content. If a programmer forgets to clean it in their code, the memory is easily overloaded. Programming in C/C++ languages became tedious and unsafe because of these very quirks, and programs built in these languages were prone to memory leakages and sudden system crashes — sometimes even harming the hardware itself. Freeing memory is particularly important in servers, since it has to run without stopping for days. If a piece of memory is not freed after use and the server just keeps allocating memory, that memory leak can take down the server.

In Java, freeing up memory is taken out of the programmers hands; the Java Virtual Machine keeps track of all used memory. When memory is not used any more it is automatically freed up. A separate task is running in the background by the JVM, freeing up unreferenced, unused memory. That task is called Garbage Collection.

The Garbage Collector is always running. This automatic memory garbage collection feature makes it easy to write robust server side programs in Java. The only thing the programmer has to watch for is the speed of object creation. If the application is creating objects faster than the Garbage Collector can free them, it can cause memory problems. Depending on how the JVM is configured, the application either can run out of memory by throwing the, or can halt to give time for the Garbage Collector to do its job.

Applet
The Java creators created the concept of the applet. A Java program can be run in a client browser program. Java was released in 1995; the time when the Internet was becoming more available and familiar to the general public. The promise of Java was in the client browser-side in that code would be downloaded and executed as a Java applet in the client browser program.

 * See also Java Programming/Applets.

Forbidden bad practices
Over the years, some features in C/C++ programming became abused by the programmers. Although the language allows it, it was known as bad practices. So the creators of Java have excluded them from the language:
 * Operator overloading
 * Multiple inheritance
 * Friend classes (access another object's private members)
 * Restrictions of explicit type casting (related to memory management)

Evaluation
In most people's opinions, Java technology delivers reasonably well on all these goals. The language is not, however, without drawbacks. Java tends to be more high-level than similar languages (such as C++), which means that the Java language lacks features such as hardware-specific data types, low-level pointers to arbitrary memory addresses, or programming methods like operator overloading. Although these features are frequently abused or misused by programmers, they are also powerful tools. However, Java technology includes Java Native Interface (JNI), a way to call native code from Java language code. With JNI, it is still possible to use some of these features.

Some programmers also complain about Java's lack of multiple inheritance, a powerful feature of several other object-oriented languages, such as C++. The Java language separates inheritance of type and implementation, allowing inheritance of multiple type definitions through interfaces, but only single inheritance of type implementation via class hierarchies. This allows most of the benefits of multiple inheritance while avoiding many of its dangers. In addition, through the use of concrete classes, abstract classes, as well as interfaces, a Java language programmer has the option of choosing full, partial, or zero implementation for the object type they define, thus ensuring maximum flexibility in application design.

There are some who believe that for certain projects, object orientation makes work harder instead of easier. This particular complaint is not unique to the Java language but applies to other object-oriented languages as well.

Java Programozás/A nyelv jellemzői

title: Java Programming/Java Overview


text:
User talk:68.95.236.24

You know you can make an account, right? See Special:Userlogin Dysprosia 22:25, 9 Sep 2004 (UTC)

title: User talk:68.95.236.24


text:
Scouting

The Guide to Scouting aims to be a complete resource detailing what is needed to maintain an active presence in all the activities that Scouting organizations offer around the world.

Scoutcraft

 * /Knots/

United States of America

 * Rank advancement requirements in the Boy Scouts of America
 * Earning Merit Badges in the Boy Scouts of America
 * Selecting, Planning, and Executing Your Eagle Service Project

title: Scouting


text:
Cryptography/Diffie-Hellman

Diffie-Hellman, named for creators Whitfield Diffie and Martin Hellman, was the first (publicly known, at least) public key algorithm and was published in 1976. Its security relies on the discrete logarithm problem, which is still thought to be difficult.

Diffie-Hellman is generally used to generate a unique key by two (or more) parties with which they may then encrypt and exchange another key. This is similar to the use of the ../RSA/ algorithm within PGP.

Alice and Bob select a large prime number n, which will be the modulus. They then select another number c that is primitive mod n, which will be the base. These two numbers may be broadcast far and wide. At this point Bob and Alice both select large, random integers (a and b, respectively) in secret, and exchange the result of the exponentiation:

Alice performs $$A=c^a mod\ n$$ and sends A to Bob in the clear.

Bob then performs $$B=c^b mod\ n$$ and sends B to Alice in the clear.

At which point Alice knows a and B, so she computes:

$$K_2=B^a\ mod\ n$$

while Bob, knowing A and b, computes:

$$K_1=A^b\ mod\ n$$

and,

$$K_1\ =\ K_2$$

This is simply based on the commutative property of multiple exponents

$$(x^y)^z\ =\ (x^z)^y$$.

An eavesdropper can get A and B, but cannot easily calculate the key.

title: Cryptography/Diffie-Hellman


text:
Organic Chemistry/Introduction to reactions/Transition states

Introduction to Reactions

Transition State
Many reactions occur in a single step when two reactant molecules collide with sufficient energy in the proper spatial orientation to create a product. Many other reactions, however, do not occur in a single step, and such reactions are said to have transition states. Multistep reactions have products that result from a series or chain of reactions, and these reactions are the kind that actually do pass through a transition state.

Intermediate Molecules
Multi-step reactions have an intermediate molecule that forms as a sort-of halfway point between the reactant and the product. This intermediate molecule cannot be isolated in solution, because it is typically of much higher energy than either the reactants or the products. However it does have a finite lifetime before it reacts.

At a basic level of organic chemistry the intermediate molecule is often merely predicted or assumed, but many are also known to exist due to experimental observations in the laboratory. Racemization of molecular configuration without another, more plausible explanation is one type of proof that certain reactions pass through a transition state.

"EXAMPLE: In a 1st order nucleophilic substitution (SN1 reaction) the chirality of a carbon is 'flipped' from S to R configuration (or vice versa) 50% of the time, leading to a racemic product (assuming it is chiral). This is because the chiral carbon becomes achiral in the carbocation intermediate, due to the sp2 carbon center that is flat and thus subject to nucleophilic attack from either the top or the bottom. If there were no intermediate, simple retention or inversion would be expected 100% of the time.  This type of racemization during an SN1 reaction may be seen as evidence of a carbocation intermediate."

Energy Diagrams and Transition States
Observing energy diagrams of reactions, you may notice that instead of a single peak energy, the energy peaks, drops a little, peaks once again and then returns to a lower energy state for the product. The "saddle" (minimum) between the two peaks represents a reaction intermediate - a place where the reaction temporarily "rests" between energy peaks. The energy peaks (maxima) are defined as 'transition states' with no finite existence.


text:
User:Jorgemartin~enwikibooks

DISTRIBUCION DE LINUX PARA PYMES

 * RESUMEN

title: User:Jorgemartin~enwikibooks


text:
Pro Engineer/Create Features

Models in Pro/Engineer are constructed from a series of features. The features are represented in a model tree that can be displayed on screen. The basic workflow changed between Pro/Engineer version 2001 and the Pro/Engineer Wildfire releases. The procedures here are written for Pro/Engineer Wildfire releases, as generically as possible. Where there is a difference between Wildfire releases, Wildfire 2.0 has been used.

Feature Creation

 * 1) Typical feature creation processes

Solid features

 * 1) Extrude
 * 2) Revolve
 * 3) Hole
 * 4) Chamfer
 * 5) Round (Fillet)

Datum features

 * 1) Datum planes
 * 2) Datum curves
 * 3) Datum points
 * 4) Datum coordinate systems

title: Pro Engineer/Create Features