text:
Talk:How to use a Motorola DVR/Online help

If I unplug my DVR will I lose saved recordings?

What happens if you make connection changes without unplugging the DVR?

Thanks,

Whitney


text:
Georgia Water/Laws/Federal Aid in Sport Fish Restoration Act of 1950

U.S. Federal Aid in Sport Fish Restoration Act (1950)

General Description
The Act creates a program for management, conservation, and restoration of fishery resources.

Source of Funding
The Sport Fish Restoration program is funded by revenues collected from the manufacturers of fishing rods, reels, creels, lures, flies and artificial baits, who pay an excise tax on these items to the U.S. Treasury.

Fund recipients
Appropriate State agencies are the only entities eligible to receive grant funds. Each State's share is based 60 percent on its licensed anglers (fishermen) and 40 percent on its land and water area. No State may receives more than 5 percent or less than 1 percent of each year's total apportionment. Puerto Rico receives 1 percent, and the Virgin Islands, Guam, American Samoa, Northern Mariana Islands, and the District of Columbia each receive one-third of 1 percent.

Plan structure
The program is a cost-reimbursement program, where the state covers the full amount of an approved project then applies for reimbursement through Federal Aid for up to 75 percent of the project expenses. The state must provide at least 25 percent of the project costs from a non-federal source.

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


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Introduction to Physical Science/Atoms

=Atoms= Atoms are the smallest pieces of matter that still retain elemental form. An atom is rarely alone in space, but is more likely to be grouped with other atoms to form molecules. Molecules are groups of atoms that form either pure elements (all of one type of atom) or compounds (mixtures of different types of atoms within a molecule) Atoms are usually depicted as a transparant globe containing a nucleus and its attendant electrons. The transparant globe is the Atomic Wall.

Components
Atoms contain several component particles.

 * Proton -- a nucleaic particle with Atomic Weight of 1au containing a positive charge
 * Neutron -- a nucleaic particle with Atomic Weight of 1au containing a neutral charge
 * Electron -- a nucleaic particle with Atomic Weight of 0.0009au containing a negative charge

While protons and neutrons are always grouped together in the center at the nucleus, electrons orbit in electron shells within the electron cloud

It contains protons (particles with a mass of one Atomic Unit containing a positive charge) and neutrons (particals with a mass of one atomic unit and a neutral charge). The nucleus is the most massive piece of the atom, containing 99.99% of the atom's mass. The second part of the atom is the electron cloud which is made up of several electron shells.

The picture to the right is of a Helium-2 atom. It contains 2 protons (red circles), 2 neutrons (green circles), and 2 Electrons (yellow circles). In an atom, the number of protons must be equal to the number of neutrons or the atom would collapse.

This atom is regular helium or Helium-2. Helium-2 is the first, most stable isotope of helium. Isotope is noted in an atomin name by the number following the Element which is always equal to the number of neutrons in a single atom of that isotope. Neutrons are the only particles that can be added or removed within an atom without changing the elemental properties. However, changing the isotope of a substance can alter more minor features. Changing the isotope of Uranium cannot make it a gas, but it can, for example make the Uranium more radioactive. When a particle is given more neutrons than the nuclear force can hold within the atom they begin to be released. Depending on the element, this process can take any amount of time from a few miliseconds to millions of years. This time of loss of neutrons is called a half-life and the process of losing particles is called decay. Isotopes that have this decay are known as Unstable Isotopes Unstable Isotopes usually decay untill they reach a point where they become stable again. However, some elements have no stable isotopes, and therefore will continue to decay, losing protons and electrons in the process creating a lighter, more stable element altogether.

title: Introduction to Physical Science/Atoms


text:
AppleScript Programming/Sample Programs/Mail alert

Note: the following will bring your volume low after raising it with the alert.

From anyone (at "Tools->Rules", create a new rule, add criterion such as "Is not junk email", and for an action, choose "Run AppleScript", selecting the script file for the script below):

The code above does work, yet there are a couple of technical improvements that could be made to it.

We don't need to tell Finder to set the volume and to say "You've got mail!". These commands are built into AppleScript, so we could and should do the following instead:

There's another improvement that needs to be made and that is the script shouldn't change the volume from what it was to one. In general code shouldn't have "side-effects" like this. Things should be restored to what they were before the script was called:

Mail can be configured to call different scripts, depending upon different conditions such as who the email is from. If you wanted your Mac to say "You've got mail from Bob!" when receiving and email from Bob, you could define the following script and install it in Mail's scripts folder and define an email rule to call this script when receiving email from Bob.


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AppleScript Programming/Sample Programs/Converter for temperatures

Simple script that converts temperatures from Celsius to Fahrenheit and back.

Edited by Smiler121: Now it doesn't crash when letters and symbols are accidentally entered


text:
User:Ahy1

My wikipedia page.

title: User:Ahy1


text:
Ordinary Differential Equations/Isoclines 1

First Order Differential Equations

Isoclines
An isocline uses another way to eliminate a variable. Instead of calculating y', we set it equal to a constant. Then we solve for y and graph the resulting equation. Frequently you'll see several different constants superimposed onto one graph, so you can see how different values compare.

Isocline is derived from the Greek words for same slope. An isocline is a line which joins neighbouring points with the same gradient, much like a contour line on a map joins all neighbouring points of the same height. What this means is that the isocline represents what happens to a point on the solution curve when the boundary conditions are changed, i.e how the solutions change when C is changed. When we consider many isoclines, it can help us to understand how the solutions "morph" on to each other as C changes.

Example 1: y'=f(x)
When the derivative of the dependent variable is set equal to a function of the independent variable, so

 * $$\frac{dy}{dx}=f(x),$$

then the slope of the solution depends only on x. This means that the slope field of the DE will change only left to right - the slope will not vary from a point to the point directly above or below it. This can be seen in Fig. 1, showing the slope field of

 * $$\frac{dy}{dx}=x$$

and some solutions. As you can see, the different solutions corresponding to different values of C lie directly above and below each other. The isoclines of this DE are given by setting y' equal to a constant:

 * $$\frac{dy}{dx}=k$$

From the original DE, we now have:

 * $$x=k \,$$

Fig. 2 shows a set of isoclines corresponding to a range of k superimposed on Fig 1. We can see that these are vertical lines. This means that the locus of a point on a solution curve will be the corresponding isocline as C varies. Therefore, as C varies, a point on the solution curve will move vertically up and down, and so the entire curve will move up and down. There is, however, no guarantee that all points will move an equal amount for the same change in C.

The isoclines are vertical for all differential equations of the form

 * $$\frac{dy}{dx}=f(x).$$

Example 2: y'=f(y)
A similar property is seen in DEs of the form

 * $$\frac{dy}{dx}=f(y),$$

but the isoclines are horizontal. This is because the gradient of the solution is independent of the value of the x. For example, consider the solutions of

 * $$\frac{dy}{dx}=y,$$

The solutions and the slope field of this DE are shown in Fig. 3. The isoclines are given by:

 * $$\frac{dy}{dx}=k$$

From the original DE, we now have:

 * $$y=k. \,$$

A set of these are superimposed in Fig. 4. One can easily see that all solutions are just left-right translations of other solutions. By changing C, the solutions are moved side to side. However, the amount that they are moved is not linear for a linear change in C, and shown by the increasing spacings of the red curves. This information is not conveyed by the isoclines.

Horizontal isoclines are shared by all DEs of the form

 * $$\frac{dy}{dx}=f(y).$$

Example 3: y'=f(x,y)
The last possible kind of isocline is that belonging to the DE of the form

 * $$\frac{dy}{dx}=f(x,y).$$

There is no catch-all rule for these like there is for the previous two examples, but the isoclines are still easily computed.

Consider the DE

 * $$\frac{dy}{dx}=xy$$

The isoclines are given by the equation

 * $$xy=k, \,$$

Isoclines of various values of k are plotted in Fig. 6. You can see from this that a point of the solution curve will tend vertically towards and horizontally away from the origin (or vice versa, for C changing the other way). This means that the solutions will become increasingly flat-bottomed/topped and wide or narrow and pointed as C changes.

The shape of the isoclines for this kind of DE depends on the original equation.


text:
Human Anatomy/Angiology/Arteries

Arteries are by definition vessels carrying blood from the heart to other organs.

Arteries have three layers - the tunica interna (intima), tunica media, and tunica externa.

title: Human Anatomy/Angiology/Arteries


text:
Human Anatomy/Angiology/Veins

Veins are by definition vessels that bring back to the heart, either from the capillaries within the systemic circuit or from the capillaries in the lungs (pulmonary circuit). Veins consist of three layers; the tunica adventitia (or tunica externa) is the outer layer, the tunica media is the middle layer, and the tunica intima is the inner layer. Large veins such as those in the legs contain bicuspid (two leaflets) valves that prevent the back flow of blood. The valves increase in number the further away from the heart.

title: Human Anatomy/Angiology/Veins


text:
User:Pcu123456789

See my user page on Wikipedia.

title: User:Pcu123456789


text:
Vietnamese/Translationaries

 * Vietnamese English Online-dictionary
 * Vietnamese Dictionaries
 * The Free Vietnamese Dictionary Project

title: Vietnamese/Translationaries


text:
IB Mathematics (HL)/Introduction

Mathematics Higher Level (HL) is a two-year course offered by the International Baccalaureate (IB) and is one of the Group 5 (Mathematics and Computer Science) courses for the IB Diploma Programme. The Standard Level (SL) mathematics courses are Mathematical Studies SL, Mathematics SL, and Further Mathematics SL. The curriculum for Mathematics SL is a subset of the curriculum for Mathematics HL. The curriculum for Further Mathematics SL is composed of all four of the optional topics from Mathematics HL, plus an additional Geometry topic.

In Mathematics HL, a student is required to perform an in-depth study of the Core curriculum topics of algebra, functions and equations, circular functions and trigonometry, matrices, vectors, statistics and probability, and calculus. In addition, there are four optional topics of study ("Options"), one of which must be selected by the school. These four Options are listed below.

 * further statistics and probability
 * sets, relations, and groups
 * series and differential equations
 * discrete mathematics

This Wikibook is intended for use as a study guide to cover these topics.

Students in the course take three External Assessment examinations, appropriately named Paper 1 (P1), Paper 2 (P2), and Paper 3 (P3). P1 and P2 evaluate a student's knowledge of topics from the Core, while P3 evaluates a student's knowledge of the chosen Option. Other details about these exams are outlined below.

 * P1: no calculator allowed, 2 hour time limit, composed of ~10 short response questions (Section A) and ~5 extended response questions (Section B).

 * P2: graphing calculator required, 2 hour time limit, composed of Sections A and B in the same fashion as P1.

 * P3: graphing calculator required, 1 hour time limit, ~5 extended response questions.

Students also complete two portfolio projects to fulfill the Internal Assessment requirements for Mathematics HL. The two portfolio projects can be assigned and completed at any time during the course, though samples from the school must be submitted to the International Baccalaureate for score moderation in March/September of the final year of the course. One project must be a mathematical investigation (requiring a formal conjecture and mathematical proof) and the other involves mathematical modelling.

A student's overall IB grade for the course is based on that student's performance on all of the External and Internal Assessments, with P1 and P2 being each worth 30% of the overall grade and P3 and the Internal Assessment each being worth 20% of the overall grade.

title: IB Mathematics (HL)/Introduction


text:
Talk:C++ Programming/C++ Mindstorming

future place to discuss the C++ language in realtion to the book contents

see Talk:C++ Programming/Classes/Nice Class, Talk:C%2B%2B_Programming/Code_Style for now...

title: Talk:C++ Programming/C++ Mindstorming


text:
Computer Programming/Physics/Position of an accelerating body function

Source code

The position of an accelerating body can be described by a mathematical function $$\mathbf{s}(t)$$. The generalized function can be attained by using the Taylor series

 * $$\mathbf{s}(t+t_0)=\sum\frac{t^n}{n!}\mathbf{s}^{(n)}(t_0)$$,

where $$\mathbf{s}^{(n)}$$ is the $$nth$$ derivative of $$\mathbf{s}$$:
 * $$\mathbf{s}^{(0)}=\frac{d^0\mathbf{s}}{dt^0}=\mathbf{s}$$
 * $$\mathbf{s}^{(1)}=\frac{d^1\mathbf{s}}{dt^1}=\mathbf{v}$$
 * $$\mathbf{s}^{(2)}=\frac{d^2\mathbf{s}}{dt^2}=\mathbf{a}$$
 * etc.

The accuracy of this function depends on the number of terms used as $$\frac{1}{n!}$$ decreases rapidly. Additionally, the time $$t$$ can be synchronized such that $$t_0=0$$ (Maclaurin series).

Note that for a constant acceleration most of the terms become zero and we're left with

 * $$s(t)=\frac{1}{0!}\mathbf{s}_0+\frac{t}{1!}\mathbf{s}^{(1)}_0+\frac{t^2}{2!}\mathbf{s}^{(2)}_0$$

or

 * $$\mathbf{s}(t)=\mathbf{s}_0+\mathbf{v}_0t+\frac{1}{2}\mathbf{a}t^2$$

C++
template Vector PositionAcceleratingBody(Vector *s0,Number t,size_t Accuracy) {    Vector s(0);     //set to zero if int, float, etc. or invoke the //    "set to zero" constructor for a class Number factor(1);//0!==1 and t^0==1 for(size_t n(0);n<Accuracy;n++) {         if(n)factor*=(t/n);//0!==1 and t^0==1 s+=(factor*s0[n]); //s0 is the array of nth derivatives of s                            //     at t=t0=0 }    return s; }

Justification for Using the Taylor Series
The Taylor series can be derived by systematically selecting which of our variables is a constant and then extrapolating that to the infinite limit.
 * Constant Position
 * $$s(t)=s_0$$
 * or
 * $$s(t)=\frac{t^0}{0!}s^{(0)}(t_0=0)$$

 * Constant Velocity
 * $$v(t)=v_0$$
 * $$s(t)=\int vdt=\int v_0dt$$
 * $$s(t)=v_0t+s_0$$
 * or
 * $$s(t)=\frac{t^0}{0!}s^{(0)}(t_0=0)+\frac{t^1}{1!}s^{(1)}(t_0=0)$$

 * Constant Acceleration
 * $$a(t)=a_0$$
 * $$v(t)=\int adt=\int a_0dt$$
 * $$v(t)=a_0t+v_0$$
 * $$s(t)=\int vdt=\int (a_0t+v_0)dt$$
 * $$s(t)=\frac{1}{2}a_0t^2+v_0t+s_0$$
 * or
 * $$s(t)=\frac{t^0}{0!}s^{(0)}(t_0=0)+\frac{t^1}{1!}s^{(1)}(t_0=0)+\frac{t^2}{2!}s^{(2)}(t_0=0)$$

 * Constant Rate of Change of Acceleration
 * $$a^{(1)}(t)=a^{(1)}_0$$
 * $$a(t)=\int a^{(1)}dt=\int a^{(1)}_0dt$$
 * $$a(t)=a^{(1)}_0t+a_0$$
 * $$v(t)=\int adt=\int (a^{(1)}_0t+a_0)dt$$
 * $$v(t)=\frac{1}{2}a^{(1)}_0t^2+a_0t+v_0$$
 * $$s(t)=\int vdt=\int (\frac{1}{2}a^{(1)}_0t^2+a_0t+v_0)dt$$
 * $$s(t)=\frac{1}{6}a^{(1)}_0t^3+\frac{1}{2}a_0t^2+v_0t+s_0$$
 * or
 * $$s(t)=\frac{t^0}{0!}s^{(0)}(t_0=0)+\frac{t^1}{1!}s^{(1)}(t_0=0)+\frac{t^2}{2!}s^{(2)}(t_0=0)+\frac{t^3}{3!}s^{(3)}(t_0=0)$$

 * etc.


text:
Computer Programming/Physics/Position of an accelerating body function (constant acceleration)

<Source code

The position of an accelerating body is a mathematical function expressed as:

 * $$ \mathbf{s}(t) = \begin{matrix}\frac{1}{2}\end{matrix} \mathbf{a} t^2 + \mathbf{v}_0 t + \mathbf{s}_0 \quad\ $$  if a is constant.

a is acceleration v is initial velocity t is time s is starting position

It is expressed below in various programming languages

=Assembly=

Intel x86 (32-bit)
push edx mul ecx mul ecx shr eax,1 add DWORD PTR [esp],eax mov eax,ebx mul ecx add DWORD PTR [esp],eax pop eax
 * eax = a, ebx = v, ecx = t, edx = s

Intel x86 (32-bit) using the FPU
somewhere in the data section: a dd 0.0 ; m*s^-2 s dd 0.0 ; m v dd 0.0 ; m*s^-1 t dd 0.0 ; s half dd 0.5 ; scalar

code: push 40000000h fld DWORD PTR [esp] fld t fyl2x fld st(0) frndint fsub st(1),st(0) fxch st(1) f2xm1 fld1 fadd fscale fstp st(1) fld a fmul fld half fmul fld v fld t fmul fadd fld s fadd add esp,4 ffree st(0)

=C= inline float PositionofAcceleratingBody(float a, float v, float t, float s) { return .5 * a * t * t + v * t + s; } = C++= template inline Vector PositionofAcceleratingBody(Vector a,Vector v0,Vector s0,Number t) { return (0.5*a*t+v0)*t+s0; }

=Delphi= function PositionofAcceleratingBody(real a, v, t, s): real; begin result := .5 * a * t * t + v * t + s; end;

=PHP= function PositionofAcceleratingBody($a, $v, $t, $s) {    return .5 * $a * $t * $t + $v * $t + $s; }

=Java= public double positionOfAcceleratingBody(double a, double v, double t, double s){ return a * t * t / 2 + v * t + s; }

=Python= def positionOfAcceleratingBody(a, v, t, s): return .5 * a * (t ** 2) + v * t + s


text:
Computer Programming/Physics/Motion of an object through space (piecemeal approximation)

<Source code

The problem with the ../Position of an accelerating body function/ is that although it is theoretically correct, it's not very adaptive in describing the motion of an object through space. To rectify this we attack the calculations piece-meal.

We refer back to the Taylor series form of the position function:

 * $$\mathbf{s}(t+t_0)=\sum\frac{t^n}{n!}\mathbf{s}^{(n)}(t_0)$$.

This can be reduced to the Maclaurin series if we synchronize our clock so that $$t_0$$ is zero:

 * $$\mathbf{s}(t)=\sum\frac{t^n}{n!}\mathbf{s}^{(n)}_0$$.

Herein lies the solution to the problem. The equation, as is, describes the complete path based on the initial constant factors $$\mathbf{s}^{(n)}_0$$. However if we treat this piece-meal, as in we calculate the numerical solution for $$t$$ equal some small incremental time $$\Delta t$$ and re-synchronize $$t_0$$ to $$t_{previous}$$ after each calculation cycle, then we can dynamically build the path of the object through successive calculations using the following incremental form of the function:

 * $$\mathbf{s}(t)=\mathbf{s}(\Delta t+t_{previous})=\sum\frac{\Delta t^n}{n!}\mathbf{s}^{(n)}_{previous}$$.

Notice that we gain accuracy as $$\Delta t\rightarrow 0$$ and if we use more and more terms.

After calculating the initial change in position of the object based on the initial constant factors $$\mathbf{s}^{(n)}_0$$, we need only provide any external accelerations that affect the object, $$\mathbf{s}^{(2)}$$, from which we can calculate the next position $$\mathbf{s}^{(0)}$$ and velocity $$\mathbf{s}^{(1)}$$ of the object as well as the next set of constant factors $$\mathbf{s}^{(n)}$$, of which $$\mathbf{s}^{(0)}$$, $$\mathbf{s}^{(1)}$$ and $$\mathbf{s}^{(2)}$$ are already known.

Velocity is calculated by

 * $$\mathbf{v}(t)=\sum\frac{\Delta t^n}{n!}\mathbf{v}^{(n)}_{previous}$$

or

 * $$\mathbf{s}^{(1)}(t)=\sum\frac{\Delta t^n}{n!}\mathbf{s}^{(n+1)}_{previous}$$.

The other $$\mathbf{s}^{(n)}(t)$$ values can be approximated by

 * $$\mathbf{s}^{(n)}(t)=\frac{\mathbf{s}^{(n-1)}(t)-\mathbf{s}^{(n-1)}_{previous}}{\Delta t}$$ for $$n>2$$,

provided that $$\Delta t$$ is very small.

That is,

 * $$\mathbf{s}^{(n)}(t)=\frac{ds^{(n-1)}}{dt}=\lim_{\Delta t\rightarrow 0}\frac{\Delta s^{(n-1)}}{\Delta t}$$.

C++
template void Motion(Vector *s,Vector *prev_s,Vector a,Number dt,size_t Accuracy) //s[] is the array of "current derivative of s values" that we are trying to calculate //prev_s[] is the array of "previous derivative of s values" that is used as the constant factors {    size_t n(0); Number factor(1); //Note: the following code for position and velocity can be optimized for speed //     but isn't in order to explicitly show the algorithm for(s[0]=0;n<Accuracy;n++) //Position {         if(n)factor*=(t/n); s[0]+=(factor*prev_s[n]); }

for(s[1]=0,n=0,factor=1;n<(Accuracy-1);n++) //Velocity {         if(n)factor*=(t/n); s[1]+=(factor*prev_s[n+1]); }

s[2]= a; //Acceleration //+PositionDependentAcceleration(s[0])                   //e.g. Newtonian Gravity //+VelocityDependentAcceleration(s[1])                   //e.g. Infinite Electro-magnetic field //+PositionVelocityDependentAcceleration(s[0],s[1]);     //e.g. Finite Electro-magnetic field

for(n=3;n<Accuracy;n++) //Everything else //We're going to assume that dt is so small that s-prev_s is also very small //    i.e. approximates the differential {         s[n]=(s[n-1]-prev_s[n-1])/dt; } }

//Calling the function //...    Vector *s,*prev_s,*temp; //...    //The previous "current s" becomes the current "previous s"     temp=prev_s;     //Speed optimization (instead of copying all of the s array     prev_s=s;        //     into the prev_s array, we just swap the pointers) s=temp; Motion(s,prev_s,a,dt,Accuracy); //...


text:
Ada Programming/Algorithms/Knuth-Morris-Pratt pattern matcher

Pattern_Match_Knuth_Morris_Pratt_Fixed_Test Pattern_Match Max_Pattern_Length  Positive  256 Context Pre_Compute Pattern  String  Context Find_Location Of_Context  Context In_Text     String  Positive Pattern_Error Pattern_Length_T Positive  1Max_Pattern_Length Failure_Function_T  Pattern_Length_T  Positive Slided_Pattern_T String 1  Max_Pattern_Length Context Failure_Function Failure_Function_T M_Pattern        Slided_Pattern_T Pattern_Length   Positive Pattern_Match IFPLID_Context Pattern_MatchContext SRC_Context    Pattern_MatchContext Text_Test1  String  "IMCHG DLH5877 -BEGIN ADDR -IFPLID AT05428113 -SRC FPL -RFL F330" Text_Test2  String  "IMCHG DLH5877 EDDKCLHD -BEGIN ADDR -FAC CFMUTACT AA05428113 FPL -STAR WLD5M -SRC " IFPLID_Pos   Positive IFPLID_Pos_2 Positive  1 SRC_Pos      Positive SRC_Pos_2    Positive Pattern_Match Pre_Compute Pattern  String  Context I J Positive Pattern_Context Context Pattern "" Pattern_Error Pattern_ContextM_Pattern 1Pattern Pattern Pattern_ContextPattern_Length Pattern Pattern_ContextFailure_Function 1 1 I 2 J 1 I Pattern_ContextPattern_Length Pattern I Pattern J            Pattern_ContextFailure_Function I  J  1 I I  1 J J  1 J 1 J Pattern_ContextFailure_Function J  1 Pattern_ContextFailure_Function I 1 I I  1 Pattern_Context Pre_Compute Find_Location Of_Context  Context In_Text     String  Positive Slided_Text_T String 1  In_Text Slided_Text  Slided_Text_T  Slided_Text_T In_Text I J Positive I 1 J 1 I Slided_Text Slided_Text I Of_ContextM_Pattern J             J  Of_ContextPattern_Length I J  1 I I  1 J J  1 J 1 J Of_ContextFailure_Function J  1 I I  1 Pattern_Error Find_Location Pattern_Match Check_Pattern_Found Pattern      String At_Location  Positive In_Text      String Slided_Text_T String 1  Pattern Slided_Pattern  Slided_Text_T  Slided_Text_T Pattern At_Location In_Text At_Location Pattern  1  In_Text Slided_Text_T In_Text At_Location At_Location  Pattern  1  Slided_Pattern Program_Error Check_Pattern_Found IFPLID_Context Pattern_MatchPre_Compute "-IFPLID " SRC_Context    Pattern_MatchPre_Compute "-SRC " Expect_Pattern_Found IFPLID_Pos Pattern_MatchFind_Location Of_Context  IFPLID_Context In_Text    Text_Test1 Pattern_MatchPattern_Error Program_Error Expect_Pattern_Found Check_Pattern_Found Pattern     "-IFPLID " At_Location IFPLID_Pos In_Text     Text_Test1 Expect_Pattern_Not_Found IFPLID_Pos_2 Pattern_MatchFind_Location Of_Context  IFPLID_Context In_Text    Text_Test2 Program_Error Pattern_MatchPattern_Error Expect_Pattern_Not_Found IFPLID_Pos_2 1 Program_Error Expect_Second_Pattern_Found SRC_Pos Pattern_MatchFind_Location Of_Context  SRC_Context In_Text    Text_Test1 Pattern_MatchPattern_Error Program_Error Expect_Second_Pattern_Found Check_Pattern_Found Pattern     "-SRC " At_Location SRC_Pos In_Text     Text_Test1 Expect_Second_Pattern_Found_At_End SRC_Pos_2 Pattern_MatchFind_Location Of_Context  SRC_Context In_Text    Text_Test2 Pattern_MatchPattern_Error Program_Error Expect_Second_Pattern_Found_At_End Check_Pattern_Found Pattern     "-SRC " At_Location SRC_Pos_2 In_Text     Text_Test2 Pattern_Match_Knuth_Morris_Pratt_Fixed_Test

|


text:
IB Mathematics (HL)/Algebra

Arithmetic Sequences and Series
An arithmetic sequence is a sequence that fits the form:

u_n = u_1 + d(n-1) $$ where $$u_n$$ is the $$n^{th}$$ term of the sequence, $$u_1$$ is the first term of the series, and d is called the common difference. The unique characteristic of this sequence is that the next term of the sequence is the previous term added to the common difference. An example of such a sequence is:

1, 2, 3, 4, ... $$ where the common difference is 1 and the first term is 1. The general form for an arithmetic sequence that can be made using the formula above is:

u_1, u_1 + d, u_1 + 2d, u_1 + 3d, ... $$

An arithmetic series is the sum of all the parts of an arithmetic sequence. Using the example above, a series can be written as:

1+2+3+4+... $$ The sum of a finite arithmetic series to the $$n^{th}$$ term "$$u_n$$" is represented in the equation:

S_n=\frac{n}{2} (u_1+u_n)=\frac{n}{2} (2u_1+d(n-1)) $$ The sum can also be written in sigma notation:

\sum_{n=1}^k \left [u_1 + d(n-1) \right ] $$ where $$u_k=u_n$$. All arithmetic series diverge as the number of terms approaches infinity. This is why the sum of any arithmetic series can only be found to a finite number of terms.

Geometric Sequences and Series
A geometric sequence is a sequence that fits the form:

u_n = u_1r^{n-1} $$ where $$u_n$$ is the $$n^{th}$$ term of the sequence, $$u_1$$ is the first term of the series, and r is called the common ratio. In such a sequence, the next term is obtained by multiplying the previous term with the common ratio. An example of a geometric sequence is:
 * $$1, 3, 9, 27...$$

A geometric series is the sum of all the parts of a geometric sequence. For the above example, the geometric sequence is:
 * $$1 + 3 + 9 + 27...$$

The sum of a finite geometric sequence to the $$n^{th}$$ term $$u_n$$ is given by the expression:
 * $$S_n = \frac{u_1(r^n-1)}{r-1} = \frac{u_1(1-r^n)}{1-r}, r \ne 1$$

The sum can also be written using sigma notation:
 * $$\sum_{n=1}^{k}u_1r^{n-1}$$

where $$u_k = u_n$$. Unlike arithmetic series, geometric series do not necessarily diverge. If the common ratio, r, is such that $$\left|r\right|>1$$, then the series diverges. If $$\left|r\right|<1$$, then the series converges, and as n approaches infinity, the value of the $$n^{th}$$ term of the sequence approaches zero.

In the case of a diverging geometric series, the sum can only be calculated for finite values of n. However, in the case of a converging geometric series, the sum of an infinite number of terms is given by the expression: $$S_{\infty} = \frac{a}{1-r}$$ OR $$\lim_{n \to \infty}S_n = \frac{a}{1-r}$$

Compound Interest and Population Growth
Based off the idea of arithmetic series is that of compound interest. Consider a case where $P is invested at a rate of r and compunded n times per year. Time is in years and is denoted t. This will be the progression:

$$P_0 = P\,$$

$$P_1 = P + \begin{matrix} \frac{r}{n} \end{matrix}P = P(1+\begin{matrix} \frac{r}{n} \end{matrix})$$

$$P_2 = P(1+\begin{matrix} \frac{r}{n} \end{matrix}) + (\begin{matrix} \frac{r}{n} \end{matrix})(P(1+\begin{matrix} \frac{r}{n} \end{matrix})) = P(1+\begin{matrix} \frac{r}{n} \end{matrix})^2 $$

$$P_n = P(1+\begin{matrix} \frac{r}{n} \end{matrix})^{nt}$$

The same function holds true for population growth where P is the initial number of people, and r is the rate that the population increases.

Exponents
The algebra section requires an understanding of exponents and manipulating numbers of exponents. An example of an exponential function is $$a^c$$ where a is being raised to the $$c^{th}$$ power. An exponent is evaluated by multiplying the lower number by itself the amount of times as the upper number. For example, $$2^3 = 2 \times 2 \times 2 = 8$$. If the exponent is fractional, this implies a root. For example, $$4^\frac{1}{2}=\sqrt{4} = 2$$. Following are laws of exponents that should be memorized:
 * $$a^ma^n=a^{m+n}$$
 * $$a^m/a^n=a^{m-n}$$
 * $$(ab)^m = a^mb^m$$
 * $$(a^m)^n = a^{mn}$$
 * $$a^{m/n} = \sqrt[n]{a^m}$$

Logarithms
It also requires understanding of logarithms. Logs can be used to sove exponential equations such as $$2^x=8$$ by either logging both sides or applying log rules. The default base number on a log is 10. The log base represents, in exponent form, the number that is being raised to a power. The number that is being logged is the exponent. By relating logs to exponents, we can devise that $$2^x=8$$ is the same as $$\log_{2} 8=x$$. Log rules are as follows:
 * $$\log_{a} a = 1$$
 * $$\log_{b} a^x = x \log_{b} a$$
 * $$\log_{a} b = b^a$$
 * $$\log_{b} a = \frac{\log_{c} a}{\log_{c} b}$$

The same rules apply for $$\ln$$ as it is the same as $$\log_{e}$$

Combinations and Binomial Theorem
This theorem is related to Binomials.

Complex Numbers
Complex numbers are numbers that include the square root of a negative number. The square root of -1 is i.

De Moivre's Theorem
De Moivre's Theorem is the expansion of the polar form of co-ordinates on an argand diagram. The form is expressed below. $$\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right).\,$$ Created by: JTLenzz and Lance Edits made by: lichking21st on 28/03/2013

title: IB Mathematics (HL)/Algebra


text:
User talk:Jiayinte

Beijing Giant translation Company is a professional company, which has devoted itself for the translation industry for about ten years. At present, this translation company has been ranked ahead in the Chinese translation companies for its convenient service to the clients in china and abroad. It has set up the branch companies. in Beijing and shanghai.

title: User talk:Jiayinte


text:
Suomen kieli ulkomaalaisille/Sisältö/Imperatiivi

Imperatiivi tai käskymuoto The imperative mood

The imperative mood is a verb form used when giving commands, orders or exhortations. As you cannot give commands to your self or to people not present, the imperative is usually heard in the second person singular or the second person plural. The singular used if addressing one person, and the plural form if addressing several people. Remember, however, that you will use the third person plural form when addressing one person who you would normal use the formal "te" form pronoun rather than the familial "sinä" form.

Because in English the plural is the same as the verb, whether in singular or plural, the Finnish imperative is not easy to learn in all its forms. The translations use modern vernacular English "you guys" or just "guys", or sometimes "you lot" to indicate that we are addressing more than one person. Always remembering of course that you could also be politely addressing one person!

Do it !
The form is simply the inflecton stem of the first person form less the -n (i.e. the first person singular stem)

Lukea to read > Minä luen > lue-n  >  Lue! Read!

Syödä to eat > Minä syön > syö-n  >  syö!  Eat!

Antaa to give > Minä annan > anna-n >  Anna! Give!

Mennä to go > Minä menen > mene-n > mene! Go!

Further examples

Olla hyvä to be good > Minä olen hyvää > ole-n >  ole hyvä!  ''be good!

Depending on the situation, the little phrase ole hyvä be good can mean please or you're welcome

You are at a friend's house and her mother invites you to try some cake.

 * Äiti: Ota kakkua!
 * Sinä: Kiitos.
 * Äiti: Ole hyvä!

 * Mum: Take some cake!
 * You: Thanks.
 * Mum: Your welcome!

Suomea Ole Hyvä!  Finnish Please!  (The title of well known book on Finnish for Foreigners)

Osta se heti! buy it now!

Tulepa tänne! come here!

 * the optional -pa suffix in this example softens the harshness of the command and makes it more polite

Don't do it !
The negative imperative when talking to one person is the same as the positive imperative except that its preceeded by the word Älä don't!

Älä syö nyt! Don't eat now!

Älä mene sinne! Don't go there!

Älä osta tätä! Don't buy this one!

Älä osta tuota! Don't buy that one!

Further examples

Älä häiritse minua! ''Don't disturb me! ''

Älä kiroile!  Don't swear!

TALKING TO 2 OR MORE PEOPLE (2nd person plural)
... Or to one person who you are not on first name terms with

Do it guys !
This is formed from stem of first infinitive plus -kaa or -kää

This stem is not the same as we used in the previous section. The first infinitive is the dictionary form less the 1st infinitive marker. The first infinitive marker for Type 1 verbs is the final -a or -ä, for Type 2 verbs the final -da or -dä, and for Type 3 verbs the final -na, -nä, -la, -lä, -ra, -rä, -ta, or -tä. Verb types 4, 5 and 6 also preserve the t in the stem, so follow type 1 verbs by just dropping the final -a or -ä.

Auttaa >  Autta-a  >  Auttakaa äitiä! Help mummy guys!

Syödä >  Syö-dä  >  Syökää ruokanne! Eat your food guys!

Mennä >  Men-nä  >  Menkää ulos! Go outside guys!

Olla hyvä >  Ol-la hyvä  > Olkaa hyvää! Be good guys!

Pestä >  Pes-tä  >  Pes'''kää hampaat! Wash teeth guys!

(Note: in Finnish you wash your teeth rather than brush them). Its not normal to add "your" to this phrase as most people actually wash their own teeth and not habitually other peoples!)

Palata >  Palat-a  >  Palatkaa ennen klo. 10 Get back before 10 you guys.

Häiritä > Häirit-ä  > Häiritkää äitiäsi, ei minua   Disturb your Mom, guys, not me!

''Lisää esimerkkejä

Ope sanoi kaikille "Kirjoittakaa kolme esimerkkia ennen ensi tuntia!"

 * Teach(er) said to everyone "Write the examples before the next lesson!

Äiti huusi meille "Lähettäkää minulle postikortti!"

 * Mum shouted to us "Send me a postcard, you lot!"

Don't do it guys !
This is formed by the word Älkää don't followed by the verb's 1st infinitive stem (see previous section) followed by the suffix -ko or -kö

Auttaa > autta-a >  Älkää auttako  Don't help, you guys!

Panna > pan-na >  Älkää panko omaa viinaa Do not brew your own spirits, guys!

''Lisä esimerkkejä:

Älkää kysykö minulta! Don't ask me, guys !

Älkää menkö sinne! Don't go there, guys !

Älkää uskoko sanaakaan, siitä mitä hän sanoo! Don't believe a single word he says, guys!


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Wikijunior:Languages/Kannada

What writing system(s) does this language use?
The Kannada script is thought to be an abugida of the Brahmic family, primarily to write the Kannada language, one of the South Indian languages in India. It is also used for Konkani, Tulu and Kodava languages. Like the scripts used to write other South Asian languages, the Kannada script is very different from the letters you are reading now. An example of a sign with words in Kannada script and in English is to the left.

How many people speak this language?
Approximately sixty million people speak Kannada mainly in the state of Karnataka in South India. People in other Indian states and mainly in western countries form a small percentage of Kannada speaking population.

Where is this language spoken?
Kannada is spoken in the Karnataka state of India. Kannada is also the official language of the state and is considered as one of the eighteen official languages of India.

What is the history of this language?
Kannada is one of the oldest languages of India after Sanskrit. It has a verbal history of over 2,300 years and Kannada words could be identified in Emperor Ashoka's edicts. Kannada had become administrative language in 4th century. Kannada became a literary language in the 6th century though evidence exists of older texts which have not been found till now. The oldest inscriptions of Kannada language can be found in the "Halmidi Shaasana" of the fourth century. The oldest literary epic in Kannada "Kavirajamarga" which follows the Sanskrit tradition of Poetics. Pampa is the best known of the earliest poets whose "Adipurana" and "Vikramaarjunavijayam" form the brightest jewels in the Kannada literary history.

Who are some famous authors or poets in this language?
"Kavirajamarga" - a treatise on poetics and language was the first literary work. Though there has been much debate over the author, academics all over common term the author as "kavirajamargakaara". Pampa, Ranna and Ponna formed the "Ratnatraya" meaning the "Jewel trinity" of early Kannada literature. The Vachana saahithya then formed the biggest milestone in Kannada literature with Bhakti traditionists like Basavanna, Akkamahadevi, Allamaprabhu, Jedara Dasimayya etc. This also laid the cornerstone for the Veerashaiva movement in Karnataka ending in a huge social upheaval and a wateshed in the demographics of the region. Some of the Shaivaite poets of recognition have been Harihara and Raghavanka. Kumaravyaasa and Lakshmeesha wrote Mahabhaaratha's that complied with the ethos of the Kannada language and culture. The Dasa saahithya propounded by Purandara Dasa, Kanakadasa and other monks of the Dwaita tradition also formed a watershed in Kannada literature.

A long slump in any significant contribution to literature was broken by the Navodaya literature in the turn of the century by greats like B.M.Srikantaiah, T.S.Venkanaiah, D.V.Gundappa, Kuvempu, D.R.Bendre, Pu.Ti.Narasimhachar. Great works like "RamayanaDarshanam" and "MankutimmanaKagga" reclaimed the Kannada ethos and upheld the uniqueness of the Kannada psyche. Following on the heals of Navodaya, the Navya tradition rebelled against the traditionalists and formed a new path. The proponents of this path were Gopalakrishna Adiga, V.K.Gokak, U.R.Ananthamurthy etc. Further, Dalit and Bandaya saahithya enriched the varied range of Kannada litearture with authors like Devanuru Mahadeva and Siddalingaiah.

Other notable laureates of the century were Shivaram Karanth, Shreeranga, Niranjana, A.Na.Krishnarao, P.Lankesh, Girish Karnad.

Kannada literature's richness has been emphasized by the fact that till recently it had the unique distinction of having received seven Jnanapeetha awards.

What are some basic words in this language that I can learn?
amma, ammaji, maatey - mother

appa, appaaji, pitaa, ayya - father

thatha - grandfather

ajji - grandmother anna, annayya - elder brother

tamma, tammayya - younger brother

akka, akkayya - elder sister

tangi, tangamma - younger sister

bhaava - elder brother in law

bhaavmaida, maiduna, maida - younger brother in law

maava - father in law

atte - mother in law

doddamma - elder aunt

chikkamma - younger aunt

doddappa - elder uncle

chikkappa - younger uncle..

naanu, naan, en, naa, eer - I

naavu, em, naam - We

neev, eev, - you(plural)

neen, nee - you(singular)

oota - lunch, dinner.

tindi - eatable, tiffin.

hogu, pogu - go

baa, baru - come

baruve, baruththeeni - coming

hoguve, hoguththeeni - going

anna - boiled rice

akki - raw rice

jola - jowar

raagi - ragi

hittu - flour, mixed flour.

saaru, huli - thick spicy soup.

rasa, tili saaru - dilute spicy soup.

mudde - a special dish of karnataka made using rice, ragi, jowar, or wheat ..etc.

rotti (like roti)- a special pan-cake dish of karnataka made using rice, ragi, jowar, or wheat ..etc.

title: Wikijunior:Languages/Kannada


text:
User:Hermitage17

My contribution

 * Catalogue of Galaxy Clusters

title: User:Hermitage17


text:
Cookbook:Lemon Impossible Pie

 * Desserts

The impossible pie is so-called because it has no crust but separates into layers while baking. It has a unique taste that is very nice.

Ingredients

 * 4 eggs
 * ½ cup lemon juice
 * 1⅔ cup milk
 * 1 cup plain flour
 * ½ cup white granulated sugar
 * 1 cup shredded coconut (optional)

Procedure

 * 1) Preheat oven to 190°C (375°F).
 * 1) Whisk all ingredients until thoroughly mixed. The optimal method is to whisk the wet ingredients first and slowly add the dry ingredients while whisking slowly.
 * 2) Pour into greased baking dish.
 * 3) Bake until an inserted skewer comes out clean. It should take at least 45 minutes.
 * 4) Serve hot or cold with ice cream.

Notes, tips, and variations

 * Use orange juice instead of lemon.

title: Cookbook:Lemon Impossible Pie


text:
Georgia Water/Laws/Contributors

The structure of this guide and the initial summaries were created by two students at the University of Georgia School of Law, Christian Perrin ('06) and Wilson Barmeyer ('06). The work was done under the direction of Professor Kathy Hatcher (School of Ecology) and Professor Laurie Fowler (School of Ecology and School of Law).

title: Georgia Water/Laws/Contributors


text:
Japanese/Lessons/Telling time

Expressing time uses "時" (じ, e. hour) and "分" (ふん, e. minute). Note that the reading of "ふん" depends on the sound before it. See the time vocabulary page for a list of the possible readings.

Conversationally, the Japanese use 12-hour time. When it's not clear from context, "午前" (ごぜん) and "午後" (ごご) are used for before and after noon, respectively.

To ask for the time, use:

Then, if HH is the hour and MM are the minutes (you see HH:MM at the clock), a possible answer cloud be:

For example:

When "何" means "what", it's pronunciation is either "なに" or "なん", depending on what sound follows it.

When used to represent the hour of the day, the numbers, "four", "seven", and "nine" are pronounced differently from normal.
 * ４時 (よじ)
 * ７時 (しちじ)
 * ９時 (くじ)

There are two ways of pronouncing "１０分"; "じっぷん" and "じゅっぷん". The former is taught as "correct" in school, but the latter is more common.

The pronunciation of "7時" (しちじ) and "1時" (いちじ)  is similar, so it is unofficial but in Japan school education, "7 o'clock" may be pronounced as "Na-Na-Zi" to distinguish pronunciation as necessary.
 * "7時" (しちじ), "1時" (いちじ)

However, a few exceptional organizations such as the Japanese military, dislike the confusion caused by the similar -pronunciation, so the military formally pronounce 7 of 7 o'clock as “Na-Na” contrary to the Japanese custom pronunciation of time.

The pronunciation of "分" is "ふん" when it stands alone, but changes to "ぷん" in certain cases.

title: Japanese/Lessons/Telling time


text:
Talk:French/Lessons/Revolutionary France

Untitled
Okay, I can see why my edit was reverted, but maybe we should actually say that in the lesson itself: "For simplicity, only those past participles which are similar to the passé simple form of the verb are listed."

Also, two of them, which I didn't bother to check at the time, are actually incorrect: connaître should be connu (instead of connus) and lire should be lu (instead of lut) according to the textbook I'm using for my current French class.

Also, how similiar do the past participles have to be to the passé simple form to count? For instance, conduit (for conduire) isn't listed, if I recall correctly. Is there some kind of standardized list?BooksihAcolyte 15:24, 15 May 2006 (UTC)


text:
Ordinary Differential Equations/Higher Order

Differential equations of the second order and higher are generally much more difficult than first-order DEs to solve, and require new methods to solve them. First we will look at how we have to treat higher-order DEs differently, then we will move on to actually solving them.

2: Homogeneous Second-Order Equations

 * Explanation
 * Examples
 * Problems
 * Answers

3: Non-Homogeneous Second-Order Equations

 * Explanation
 * Examples
 * Problems
 * Answers


text:
User:BookishAcolyte

I have successfully gotten my username changed from BooksihAcolyte to BookishAcolyte!

You can find me under the same name on the English and French Wikipedias. A lot of my work there has been translations, as well as edits for spelling and grammar, wikifying, etc. I've had an account here on wikibooks for a couple of years, but I am just barely getting active here, so I'm effectively quite new and don't entirely know the ropes yet. I'm more familiar with wikipedia's standards, but those have changed since the time when I was most active.

I'm a Feminist Studies major. Please help me improve Feminism. As of April 2009, it's a rather incomplete book.

I can read quite well in French, but I have many errors in my writing. I could maybe puzzle my way through an article in Japanese given full furigana (pronunciation notations) or a good dictionary, and I can get the general gist of most articles in Spanish.

title: User:BookishAcolyte


text:
Cookbook talk:Lemon Impossible Pie

Shouldn't we just call this a custard if there's no pastry? Kellen T 15:52, 15 May 2006 (UTC)

 * Hm... I don't know. My friend always calls it this name. I have actually never seen it. Maybe we will make it soon and I will find out. :) pfctdayelise 23:02, 16 May 2006 (UTC)

title: Cookbook talk:Lemon Impossible Pie


text:
User talk:William Peterson

A belated welcome:

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. Kellen T 16:09, 15 May 2006 (UTC)
 * Please also check out the Cookbook policy page and the Cookbook talk pages.

title: User talk:William Peterson


text:
User talk:Chaerani

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. Kellen T 16:12, 15 May 2006 (UTC)
 * Please also check out the Cookbook policy page and the Cookbook talk pages.

title: User talk:Chaerani


text:
User:Jacnoc

Will add more later.

Jacnoc (Desk)

title: User:Jacnoc


text:
Statics/Vector Math

Adding Vectors
Let's say you have a box on the ground, and the box is being pulled in two directions with a certain force. You can predict the motion of the box by finding the net force acting on the box. If each force vector (where the magnitude is the tension in the rope, and the direction is the direction that the rope is "pointing") can be measured, you can add these vectors to get the net force. There are two methods for adding vectors:

Parallelogram Method
This is a graphical method for adding vectors. First, a little terminology: This method is most easily executed using graph paper. Establish a rectangular coordinate system, and draw the first vector to scale with the tail at the origin. Then, draw the second vector (again, to scale) with its tail coincident with the head of the first vector. Then, the properties of the sum vector are as follows:
 * The tail of a vector is where it originates.
 * The head of a vector is where it goes. The head is the end with the arrowhead.
 * The length of the sum vector is the distance measured from the origin to the head of the second vector.
 * The direction of the sum vector is the angle.

Example
In the image at the right, the vectors (10, 53°07'48") and (10, 36°52'12") are being added graphically. The result is (19.80, 45°00'00"). (How did I measure out those angles so precisely?  I did that on purpose.)

The native vector format for the parallelogram method is the 'polar form'.

Computational Method
When you use the computational method, you must resolve each vector into its x- and y-components. Then, simply add the respective components.

Converting Polar Vectors to Rectangular Vectors
If a vector is given by (r, θ), where r is the length and θ is the direction,
 * x = r cos θ
 * y = r sin θ

Converting Rectangular Vectors to Polar Vectors
If a vector is given by $$\left \langle x, y \right \rangle$$, Remember that the arctan function only returns values in the range [-π/2, π/2]; therefore, if your vector is in the second or third quadrant, you will have to add π to whatever angle is returned from the arctan function.
 * $$r=\sqrt{x^{2}+y^{2}}$$
 * $$\theta=\arctan \frac{y}{x}$$

Example
Again referring to the image at the right, notice that the first vector can be expressed as $$\left \langle 6,8 \right \rangle$$, and the second is equivalent to $$\left \langle 8,6 \right \rangle$$. (Verify this.) Then, you simply add the components: $$\left \langle 6,8 \right \rangle + \left \langle 8,6 \right \rangle = \left \langle 6+8,8+6 \right \rangle=\left \langle 14,14 \right \rangle$$ You should verify that $$\left \langle 14, 14 \right \rangle$$ is equal to (19.80, 45°00'00").

Multiplying Vectors
There are two ways to multiply vectors. I will not get into specific applications here; you will see many of those as you progress through the book.

The Dot Product
The dot product of two vectors results in a scalar. The dot product is the sum of the product of the components. For example: < 1, 2 > ∙ < 3 , 4 > ---    |   +-> 2 x 4 = 8 +-> 1 x 3 = 3 --                       11 A useful relation between vectors, their lengths, and the angle between them is given by the definition of the dot product:

$$\vec a \cdot \vec b = ab \cos \theta$$
 * $$\vec a$$ and $$ \vec b$$ are the vectors.
 * $$a$$ and $$b$$ are the vectors' magnitude.
 * $$\theta$$ is the angle between the vectors.

The Cross Product
The cross product of two vectors results in another vector. The cross product is only applicable to 3-space vectors. Remember the three unit vectors: Now if you have two vectors $$\vec a = \left \langle x_1, y_1, z_1 \right \rangle$$ and $$\vec b = \left \langle x_2, y_2, z_2 \right \rangle$$, the cross product is given by solving a determinant as follows:
 * $$\hat i$$ is the unit vector along the x-axis
 * $$\hat j$$ is the unit vector along the y-axis
 * $$\hat k$$ is the unit vector along the z-axis

$$\vec a \times \vec b = \begin{vmatrix} \hat i & \hat j & \hat k \\ x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \end{vmatrix} = \begin{vmatrix} y_1 & z_1 \\ y_2 & z_2 \end{vmatrix}\hat i + \begin{vmatrix} z_1 & x_1 \\ z_2 & x_2 \end{vmatrix} \hat j + \begin{vmatrix} x_1 & y_1 \\ x_2 & y_2 \end{vmatrix} \hat k$$

For more information on how to solve a determinant, consult the external links below.

The cross product of two vectors, the lengths of those vectors, and the short angle between the vectors is given by the following relation: $$\vec a \times \vec b = ab \sin \theta$$

The Right-Hand Rule
Geometrically, the cross product gives a vector that is perpendicular to the two arguments. Notice the reference to a vector, not the vector. This is because there are infinitely many vectors that are normal to two non-zero vectors. The direction of the cross product can be determined using the right-hand rule: Extend the fingers of your right hand, lay your straightened hand along the first vector, pointing your finger tips in the same direction as the vector. Curl your fingers through the short angle from the first vector to the second vector. Your thumb will point in the direction of the product vector.

Dot Products

 * A unit vector dotted into itself gives one.
 * A unit vector dotted into a different unit vector gives zero.

Cross Products
Order the unit vectors in this order: $$\hat i, \hat j, \hat k$$. Start at the first vector, move to the second vector, and keep going to the cross-product. If you moved immediately to the right first, the answer is positive. If you moved to the left first, the answer is negative. For example:
 * $$\hat i \times \hat j = \hat k$$
 * $$\hat j \times \hat i = -\hat k$$

Vector Rules
Given vectors $$\vec a, \vec b, \vec c,$$ and scalar r:
 * $$\vec a \cdot \vec b = \vec b \cdot \vec a$$
 * $$r(\vec a \cdot \vec b) = (r \vec a) \cdot \vec b = \vec a \cdot (r\vec b)$$
 * $$\vec a \times \vec b = -\vec b \times \vec a$$
 * $$r(\vec a \times \vec b) = (r \vec a) \times \vec b = \vec a \times (r\vec b)$$
 * $$(\vec a \times \vec b) \cdot \vec c = \vec a \cdot (\vec b \times \vec c)$$

title: Statics/Vector Math


text:
User:Aaronsama/Templates

This page is a showcase and link center to the templates I've designed.

Ruby
Template:Ruby Template:Rubywikt Template:Ruby-2 Template:Rubywikt-2 Template:Wikt

Navigation
Template:Jalesson-3 Template:Jalesson-4 Template:Jalesson-5 Template:Jalesson-6 Template:Jalesson-7 Template:janav

Page Headers
Template:Japagehead Template:Japagehead2 Template:Japagehead3

Columns

 * 1) Two columns
 * 2) *Template:col-2t
 * 3) *Template:col-2m
 * 4) *Template:col-end
 * 5) Three columns
 * 6) *Template:col-3t
 * 7) *Template:col-3m
 * 8) *Template:col-end
 * 9) Four columns
 * 10) *Template:col-4t
 * 11) *Template:col-4m
 * 12) *Template:col-end

Tags
Template:Need soundbite

title: User:Aaronsama/Templates


text:
Ruby Programming/Writing methods

Method definition
A method definition is started with the  keyword and ended with the   keyword. Some programmers find the method definition notation in Ruby very similar to the one of Python.

To define a method that takes a parameter, you can put the name of the variable in parantheses after the method name. When the method is invoked, the code in the method will be run with a local variable with the name of the specified parameter.

If you need multiple parameters you can separate them with a comma.

Invoking methods
You can invoke methods with or without parentheses although it can be considered bad style if you omit them, so the safe way is to always write them in the beginning until you know when it's safe to leave them away.

If you want to invoke a method with parameters you need to put the parameter(s) between the brackets (or if you omit them, between the invisible brackets) and separate them with commas if there are more than one.

You can also use the value of a variable as a parameter.

Default values
Often, a method may have parameters of which many, if not all, could have clever defaults. Having to specify all of the parameters every time you invoke the method can be an inconvenience. Because of this, it's possible to define default values. This can be actually quite easily; simply assign the parameter a value in the definition. You can combine parameters with and without default values.

Returning values
You often want a method to return a value. You can do so by using the return statement.

However, because Ruby developers are lazy, they developed a feature that always returns the last evaluated statement (sometimes it's a bit tricky to know which one this is). Knowing this, you can turn the above example into the following:

Note that a return statement finishes the execution of a method. Combined with the fact that you can return without a value this is often useful to stop a method from further execution if certain conditions are met.

title: Ruby Programming/Writing methods


text:
A-level English/Wise Children/Feminism

Quotes

 * "A father is a hypothesis but a mother is a fact"
 * "I wonder why they call it father Thames"
 * "I'm not ready to be a father"
 * "No man ever is"
 * "We boast the only castrato grandfather clock in London" - notice the emasculation of the grandfather clock, 'castrato'=castrated, shows lack of need for a paternal/dominating male figure in the Chance household.
 * "Grandma had never known, not until she picked us up on that very first day, what men were for"

Representation of women
In 'Wise Children', as in much of Carter's work - notably 'Nights at the Circus' - Carter punctuates the myth of male superiority and female goodness. The women in the book are none of them saints and the most saintlike of them, Lady Atlanta, is revealed to have had an affair with Peregrine, her brother-in-law, resulting in him possibly being the father of the 'darling buds of May', Saskia and Imogen. The men in the book are also seen to be flawed and their grasp onto power, or, in Melchior's case, legitimate and high theatre, fails, as seen in the disastrous 'A Midsummer Night's Dream' and the innocuous comment made to him on the Tube: 'I say, didn't you used to be Mechior Hazard?'. The Chance twins 'irreverantly high-kick their way through Shakespeare' (The Guardian, 21 December 2005)and the legend of the femme-fatale is disintegrated with the exuberant, larger than life character Daisy Duck.

An excellent example of Carter almost giving a feminist edge to an existing situation comes in the final chapter during Tiffany's confrontation with Tristram. The scene is immediately reminiscant of not only the reconciliation of Claudio and Hero in Much Ado About Nothing but also the final scene in A Winter's Tale. However, instead of the male (who has been in the wrong) being accepted by the female character, Tiffany rejects the humbled Tristram. This is arguably more realistic.

title: A-level English/Wise Children/Feminism


text:
BLL German

Welcome to the Bite-sized Language Lessons for German!

German is a useful language to know for several reasons. There are many native German speakers, around 120 million people, most of whom live in central Europe and German culture has long contributed to the world heritage in a wide range of subjects such as music, philosophy, literature and science.

Though English is certainly the world's lingua franca, German influence does not only stem from its past. Over 60 million Americans, 2.7 million Canadians, 12 million Brazilians and several millions in Eastern Europe and the rest of the world have German ancestors and some of them still form German-speaking communities within their respective countries.

German grammar suffers, unfortunately, from the popular myth that the language is hard to learn, the grammar is complex and the pronunciation difficult. Seeing how you're reading these words you've not been inundated completely by these claims so heed this; while intricate, German grammar is fairly regular and, with practice, becomes second nature, and the intricacies allow for a great deal of nuance in expression. Pronunciation varies, of course, greatly with the wide geographical spread of its speakers; from Tirolian trilling of ones "r"-s to the softer flow of the northern lowlands, so take your pick.

The levels
This course is divided into six levels following the Common European Framework of Reference for Languages, ranging from A1 ("Breakthrough", the first level a beginner can achieve) to C2 ("Mastery", near-native fluency). Hence, the first level of this course will lead the student from zero to A1 proficiency, the second level of this course will lead him from A1 to A2, and so on. A brief description of what students should be able to do at each level of proficiency can be found at this Association of Language Testers in Europe and it shall serve as a guideline for the course.

A : Basic User
 * A1 - Breakthrough (start here if you're an absolute beginner)
 * A2 - Waystage

B : Independent User
 * B1 - Threshold
 * B2 - Vantage

C : Proficient User
 * C1 - Effective Operational Proficiency
 * C2 - Mastery

Additional vocabulary lists that are referred to within the course

 * Language names
 * Professions
 * Study subjects

More information about this course:

 * For students: How to study
 * The idea behind it: Bite-sized Language Lessons
 * Information for contributors

title: BLL German


text:
Java Programming/Interfaces

An interface is an abstraction of class with no implementation details. For example,  is a standard interface in Java. You cannot instantiate an interface. An interface is not a class but it is written the same way. The first difference is that you do not use the keyword but the  keyword to define it. Then, there are fields and methods you cannot define here: An interface represents a contract:
 * A field is always a constant: it is always public, static and final, even if you do not mention it.
 * A method must be public and abstract, but it is not required to write the and  keywords.
 * Constructors are forbidden.

You can see that the  method is abstract (unimplemented). To use an interface, you have to define a class that implements it, using the keyword:

A class can implement several interfaces, separated by a comma. Java interfaces behave much like the concept of the Objective-C protocol. It is recommended to name an interface, to mean the type of action this interface would enable on a class. However, it is not recommended to start the name of an interface by  as in C++. It is useless. Your IDE will help you instead.

Interest
If you have objects from different classes that do not have a common superclass, you can't call the same method in those classes, even if the two classes implement a method with the same signature.

The solution is to write an interface that defines the method that should be implemented in the two classes as the  in the Code listing 4.14 and then both classes can implement the interface as in the Code listing 4.15.

You can also implement this using a common super class but a class can only inherit from one super class whereas it can implement several interfaces.

Java does not support full orthogonal multiple inheritance (i.e. Java does not allow you to create a subclass from two classes). Multiple inheritance in C++ has complicated rules to disambiguate fields and methods inherited from multiple superclasses and types that are inherited multiple times. By separating interface from implementation, interfaces offer much of the benefit of multiple inheritance with less complexity and ambiguity. The price of no multiple inheritance is some code redundancy; since interfaces only define the signature of a class but cannot contain any implementation, every class inheriting an interface must provide the implementation of the defined methods, unlike in pure multiple inheritance, where the implementation is also inherited. The major benefit of that is that all Java objects can have a common ancestor (a class called ).

When overriding methods defined in interfaces there are several rules to be followed:
 * Checked exceptions should not be declared on implementation methods other than the ones declared by the interface method or subclasses of those declared by the interface method.
 * The signature of the interface method and the same return type or subtype should be maintained when implementing the methods.
 * All the methods of the interface need to be defined in the class, unless the class that implements the interface is abstract.

Extending interfaces
An interface can extend several interfaces, similar to the way that a class can extend another class, using the keyword:

This way, a class implementing the  interface has to implement the , the   and the   methods:

Doing so, a  object can be casted into ,   and.

Question 4.2: Consider the following interfaces.

List all the methods that an implementing class of  should implement.

Question 4.3: Consider the following classes and the following code.

Change the implementation of the code in order to be able to uncomment the commented line without compile error.

You have to create an interface that defines the method  and makes   and   implement it:

Now your code has to cast the objects to the  type and then you can uncomment the code.

Programmation Java/Interfaces

title: Java Programming/Interfaces


text:
Talk:Hungarian/Lesson 2

swap proposal
I think its boring to learn numbers before you can say basic sentences. And there should be more practices with simple statements and questions. --Sourcerror 09:33, 26 April 2007 (UTC)

 * As a teacher I would like to disagree with you. This method is well adapted to Hungarian: you get used to reading and pronouncing words before you step into basic morphology. Moreover, you always have to learn numerals, the earlier the better! Some may find it boring... In fact, you should consider it a funny game :)

--R Camus 11:58, 25 July 2007 (UTC)

Decimals
How do decimals work in Hungarian? How would you say 5,1 (I have heard that "," is used as the decimal separator)? How about a long series of decimals, like 6,54321? I appreciate any help anyone can offer. TomTheHand 20:50, 15 May 2006 (UTC)

 * The shorter decimals are treated as vulgar fractions.
 * 5,1 -> "öt egész egy tized" literaly: five "whole" (-> integer) and one tenths ("1/10")
 * In theory, the same applies to longer rational numbers (so 15,14 = tizenöt egész tizennégy század / lit. fifteen whole and fourteen hundredths ("14/100"); 500,123 = ötszáz egész százhuszonhárom ezred) but if the decimal is very long like 9,087654321 (or an irrational number) one would simply say "kilenc egész nulla-nyolc-hét-hat-öt-négy-három-kettő-egy")
 * --194.152.154.2 01:24, 4 June 2006 (UTC)

 * Thank you! Would "öt egész egy" be understood, or would someone think it's very odd to leave off the tized/tenths?  I'm trying to write a program that will translate numbers into other languages and I'm trying to keep things simple, but I don't want to do anything so simple it sounds dumb. TomTheHand 14:47, 6 June 2006 (UTC)

 * It would be understood, but you probably won't hear something like this in formal speeches.
 * I don't know if this program is intended to "say" or "display" the numbers, but if the latter, you might want to know that the Hungarian orthogr. rules for numbers are quite complicated, even for a native speaker. Eg. the numbers are written without a hyphen if they are lower than 2000 (1763 = ezerhétszázhatvanhárom), or if they are higher, but lower than 10^6 & divisible by 10^3 (53 000 = ötvenháromezer), but with a hyphen if these requirements are not satisfied* (2734 = kétezer-hétszázharmincnégy). This is just an example, there are other odd rules, too. (These can be found @ A Guide to Hungarian Orthography by the Hungarian Academy of Sciences (Wikisource), unfortunately only in Hungarian.)
 * * It would still be written without a hyphen, if x > 10^6, but x mod 10^6 == 0. --194.152.154.2 19:29, 6 June 2006 (UTC)

 * Goodness. Well, the program is actually intended to "say" the numbers, so hopefully I'll manage to avoid hyphenation issues.  What I'll do is use tized, század, and ezred for up to three decimal places, and simply read out the digits for larger decimals, as you suggested.  Thank you! TomTheHand 20:09, 6 June 2006 (UTC)

 * Leaving out "tized", "század", "ezred", etc. from the end of the number is completely normal. Only in very formal speech or professional speech (maths, statistics, etc.) do they use these termini, best, a native 88.66.41.90 (talk) 22:53, 14 March 2008 (UTC)

'Hány' is rarely countable
While it is true that mennyi is used with countable objects too, hány is not used with uncountable things. Like 'Hány víz van nálad?' would sound quite strange (I guess 'How many water do you have?' is problematic in English the same way, but I'm not a native English speaker). Someone correct me if I'm wrong. Hungarian is my mother tounge, but I haven't really thought about that countable/non countable thing until now.

 * On the other hand, when the nouns are countable, you can use both "hány" and "mennyi". E.g. "Hány hal van a kosárban?" vs. "Mennyi hal van a kosárban." Although stilistically I feel, that "Mennyi" is "nicer" than "Hány" 88.66.41.90 (talk) 22:55, 14 March 2008 (UTC)

Sound bites
The sound bites on this page cause my Firefox to crash. Mozilla/5.0 (Windows; U; Windows NT 6.0; en-US; rv:1.9.0.6) Gecko/2009011913 Firefox/3.0.6 —The preceding unsigned comment was added by 74.210.15.9 (talk • contribs) 01:29, 16 February 2009 (UTC)

title: Talk:Hungarian/Lesson 2


text:
User:Dudtz~enwikibooks

http://en.wikipedia.org/wiki/User:Dudtz

title: User:Dudtz~enwikibooks


text:
User:Nemo The Pyro

Under Construction

title: User:Nemo The Pyro


text:
User talk:Bobshush

help
hey do you need help in the psych department?--Nemo The Pyro 01:30, 16 May 2006 (UTC)

title: User talk:Bobshush


text:
Bodybuilding and Weight Training

The purpose of this book is to help you safely engage in bodybuilding (sometimes referred to as "weight lifting," or simply "lifting").

The first part of the book will focus primarily on the basics: creating a weight lifting schedule, designing your diet (which professionals describe as one of the most important parts of bodybuilding), and finding a gym.

Later in the book, you will be instructed in the techniques of the most common bodybuilding exercises, including bench-presses, squats, and dumbbell curls. This section can be considered a reference section, but it is important to thoroughly read through each exercise's guide before attempting the exercise.

Finally, the third section is a reference section which you will find important when constructing your diet.

Contents

 * 1) Getting Started
 * 2) /Introduction/
 * 3) /Finding a Gym/
 * 4) /Creating a Schedule/
 * 5) /Foundations/
 * 6) /The Muscular System/
 * 7) /The Skeletal System/
 * 8) /The Nervous System/
 * 9) /Nutrition/
 * 10) /Constructing a Diet/
 * 11) /Sample Diets/
 * 12) /Recipes/
 * 13) Exercise Guides
 * 14) /Overview/
 * 15) Upper Body
 * 16) Pectorals/Chest
 * 17) /Bench Presses/
 * 18) /Dumbbell Flys/
 * 19) parallel bar dips
 * 20) Arms
 * 21) /Dumbbell Curls/
 * 22) /Tricep Dips/
 * 23) Back
 * 24) /Deadlift/
 * 25) Abdominals
 * 26) Lower Body
 * 27) /Static Lunges/
 * 28) /Squats/
 * 29) Other/Both Upper and Lower Body
 * 30) /Clean and Jerk/
 * 31) /Bodyweight Training/
 * 32) Part Three: Diets and Nutrition
 * 33) /Sample Diets/
 * 34) /Recipes/

Contributors

 * Josh1billion
 * Kevin Lakhani
 * witerhawk

title: Bodybuilding and Weight Training


text:
Bodybuilding and Weight Training/Introduction

Bodybuilding can be a fun and engaging sport. It can also be dangerous if not taken seriously, however, injury is rare and should not be a reason to stay away.

There are a few important questions to ask yourself before you start:

1. Where will you work out, and when? At least three days per week are recommended (not consecutively, though, because your muscles need time to rest and grow in between workout days). Your workout might average somewhere around half an hour to an hour for an average workout.

2. Can you manage to eat several meals high in protein every day? Almost all bodybuilders recommend a high-protein diet. This is important, because protein is the "building block" of muscle. How much protein should you be willing to consume? A common range is 1.0 to 1.5 grams of protein per day for each pound of your body weight (for example: if you weigh 160 pounds, you should try to consume 160 to 240 grams of protein every day for the best results). Be aware that protein supplements are available, such as whey protein powder, but it is generally advocated that at least half of your daily protein intake consists of "real" foods as opposed to protein supplements. Also, many bodybuilders believe it's best to eat around six smaller meals in your day instead of three large meals if you're able.

3. What are your goals? Is your goal to become generally stronger? Perhaps your goal is to transform your body? Depending on your goals, you may need to adjust your workout accordingly. For example, if you're looking to not only gain muscle but also lose fat, you may want to use your resting days as cardio-workout days where you can do cardio exercises such as running and swimming.


text:
User:Josh1billion~enwikibooks

You can find my Wikipedia user account here: Josh1billion

title: User:Josh1billion~enwikibooks


text:
User:Tachyon01~enwikibooks

About Me
I am a student of mathematics at the University of California, Santa Cruz, with my research interests in complex geometry, analysis, and mathematical physics. I work at an observatory, where I am involved in tracking and discovering supernovas. I reside in Santa Cruz, California. I also occasionaly teach math at Monterey Peninsula College, (ironically, located in Monterey, California,) where I teach algebra and calculus. I am also a huge San Jose Sharks fan.

title: User:Tachyon01~enwikibooks


text:
User talk:Tachyon01~enwikibooks

How to use my talk page

Please leave a message. I'll try to reply as soon as I can as it warrants. If I don't right away, I'm probably busy and will get to it shortly. Please sign any messages. Any attacks will be deleted swiftly.

 * Post a new message

 Current discussion

Click on "Post a new message" above to leave your comments

 * Questions, comments, suggestions, blah..., leave them here. Be sure to sign all comments.  Tachyon01

Your account will be renamed
Hello,

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

Unfortunately, your account clashes with another account also called Tachyon01. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Tachyon01~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:49, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:34, 19 April 2015 (UTC)

title: User talk:Tachyon01~enwikibooks


text:
Talk:Chinese/Lesson 5/Exercises

Hi, i;m going to make the program. I'm chinese and have taught the chinese language for about 10 years now.

title: Talk:Chinese/Lesson 5/Exercises


text:
Pharmacology/Cephalosporins

Cephalosporins are known as beta-lactam antibiotics because their chemical structure consist of a beta-lactam ring adjoined to a thiazolidine ring. They are usually classified in four major groups based on their spectrum of activity.

First generation→ Cefazolin, cefadroxil, cephalexin, cephapirin, cephradine The first generation are most active against gram(+) bacteria ( susceptible strains of S. aureus, S. epidermidis, Streptococcus pyogenes, S.agalactiae and S. pneumoniae) and a few gram(-) microbes (E. coli, Klebsiella, shigella and Proteus mirabilia)

Second generation→ Cefaclor, cefmetazole, cefonicid, cefotan, cefoxitin, cefuroxime, cefpodoxime, cefprozil

title: Pharmacology/Cephalosporins


text:
Complex Analysis/Complex Functions/Analytic Functions

From our look at complex derivatives, we now examine the analytic functions, the Cauchy-Riemann Equations, and Harmonic Functions.

''Note: Holomorphic functions are sometimes referred to as analytic functions. This equivalence will be shown later, though the terms may be used interchangeably until then.''
 * 2.4.1 Holomorphic functions

Definition: A complex valued function $$f(z)$$ is holomorphic on an open set $$G$$ if it has a derivative at every point in $$G$$.

Here, holomorphicity is defined over an open set, however, differentiability could only at one point. If f(z) is holomorphic over the entire complex plane, we say that f is entire. As an example, all polynomial functions of z are entire. (proof)

The definition of holomorphic suggests a relationship between both the real and imaginary parts of the said function. Suppose $$f(z)=u(x,y)+v(x,y)i$$ is differentiable at $$z_0=x_0+y_0i$$. Then the limit
 * 2.4.2 The Cauchy-Riemann Equations
 * $$\lim_{\Delta z\to0}\frac{f(z_0+\Delta z)-f(z_0)}{\Delta z}$$

can be determined by letting $$\Delta z_0(=\Delta x_0+\Delta y_0i)$$ approach zero from any direction in $$\Complex$$.

If it approaches horizontally, we have $$f'(z_0)=\frac{\partial u}{\partial x}(x_0,y_0)+i\frac{\partial v}{\partial x}(x_0,y_0)$$. Similarly, if it approaches vertically, we have $$f'(z_0)=\frac{\partial v}{\partial y}(x_0,y_0)-i\frac{\partial u}{\partial y}(x_0,y_0)$$. By equating the real and imaginary parts of these two equations, we arrive at:
 * $$\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y},\frac{\partial v}{\partial x}=-\frac{\partial u}{\partial y}$$

These are known as the Cauchy-Riemann Equations, and leads us to an important theorem.

Theorem: Let a function $$f(z)=u(x,y)+v(x,y)i$$ be defined on an open set $$G$$ containing a point, $$z_0$$. If the first partials of $$u,v$$ exist in $$G$$ and are continuous at $$z_0$$ and satisfy the Cauchy-Riemann equations, then f is differentiable at $$z_0$$. Furthermore, if the above conditions are satisfied, $$f$$ is analytic in $$G$$. (proof).

Now we move to Harmonic functions. Recall the Laplace equation, $$\nabla^2(\phi):=\frac{\partial^2(\phi)}{\partial x^2}+\frac{\partial^2(\phi)}{\partial y^2}=0$$
 * 2.4.3 Harmonic Functions

Definition: A real valued function $$\phi(x,y)$$ is harmonic in a domain $$D$$ if all of its second partials are continuous in $$D$$ and if at each point in $$D$$, $$\phi$$ is analytic in a domain $$D$$ , then both $$u(x,y),v(x,y)$$ are harmonic in $$D$$. (proof)

Next


text:
Complex Analysis/Elementary Functions

In this chapter, we examine the behavior of elementary functions and introduce exponential, logarithmic, and trigonometric functions.

Chapter 3: Elementary Functions

 * 1) /Polynomial Functions/
 * 2) Exponential and Trigonometric Functions
 * 3) /Logarithmic Functions/
 * 4) Inverse Trigonometric Functions

title: Complex Analysis/Elementary Functions


text:
User:IrfanAli

Hi ! I am Irfan.

title: User:IrfanAli


text:
Talk:Physics Study Guide/Physics constants

How can gravitational field strength be expressed so precisely, when there is a major variation (in the 2nd significant figure IIRC) from the North Pole to the equator, due to both the different distances to the centre of the Earth, and the larger centripetal force experienced at the Equator?

Should the list not say: g (at London, UK) or something similar?


text:
BLL German/Contributing

Thank you for volunteering to contribute something to this Wikibook!

In order to ensure that your contribution will be helpful to the students and much appreciated by other contributors, please read the following notes carefully. They will also serve as suggestions for those who would like to contribute but don't know what and as a TO-DO list for contributors.

After each task you will find who could complete this task / contribute in this way.

Contributing a lesson (advanced student or native speaker)

 * If you are at at least intermediate level in German, you can write a lesson based on an available outline, e. g. the one for level A1 lesson 5. Please use level A1 lesson 1 as a guide to the appearance and structure of the lesson.
 * If you would like to contribute a lesson for which no outline exists yet, please make sure you understand the basic idea behind the course first. Then think about which level the lesson belongs to (consult the page describing what students will be able to do after completing each level). Afterwards, see whether the lesson you propose can follow right after the last existing lesson for that level, that is, whether it won't require more than 10-15 new words or more knowledge of grammar than would normally be taught in one lesson. If it fits, go ahead and add the lesson (note that for level A1 lessons 1-4 plus the one on pronunciation are already available at an external website and need only be converted). If it is too advanced for now, please add it to the page BLL German/For future use instead, so that it can be adapted and inserted once the time is right.

Contributing a text (native speaker)
If you have an idea for a useful and natural-sounding German text that could be used in one of the lessons, please add it to BLL German/For future use. If you know of a way to make an existing lesson text longer without exceeding the vocabulary / grammar limit, feel free to edit the lesson right away. Longer lesson texts are more helpful to learners in that they provide more models to follow.

Contributing vocabulary (anybody)
Additional vocabulary for the main part of a lesson is only welcome if it allows for a significant increase of the text length and still stays within the limit of 10-15 new words per lesson. However, there is no limit to the lists of optional vocabulary, because students will choose which words to learn from those. Feel free to add any useful words that fit the topic there. If the topic for which you have new words hasn't been introduced yet, add the list to BLL German/For future use or the vocabulary section on the main page.

Contributing grammar (student or native speaker or linguist)
Part of the idea of the Bite-sized language lessons is to introduce grammar in tiny steps, so that the student can decide for himself when to progress to the next item. Hence, please don't add to the grammar section of an existing lesson unless you think you can explain something better. If you know a good explanation of a topic of grammar that has not yet been covered, please add it to BLL German/For future use so that it will be included in the lesson where that aspect of grammar is covered.

Contributing exercises (student or native speaker)
Exercises are very important because they allow the student to see whether he really understood the expressions and grammar introduced in a lesson. Also, there is no such thing as too many exercises - challenged students will be grateful for every exercise they can find and talented students will just skip the rest of the exercises once they are sure they understand what was taught. Hence, feel free to add any amount of exercises to any lesson, so long as they correspond to what was taught and don't require additional knowledge. If you have written an exercise for something that wasn't taught yet, put it in BLL German/For future use and it will be included in a future lesson.

Contributing cultural information (anybody)
Every lesson should not just teach the language but also give the student some knowledge of the culture / customs / history / politics / everyday life / etc. of German-speaking countries. Go ahead and add some, just make sure it doesn't cover more space than the list of vocabulary or the grammar section. If there is more to say, link to a more detailed article e. g. on Wikipedia. As with the other contributions, if you believe that something would fit better in a future lesson, put it in BLL German/For future use.

Contributing recordings (native speaker only)
Recording are immensely important for the students because in internet courses they generally receive much less auditive input than in a regular classroom. However, they need models for their pronunciation. Recordings made by native speakers are the only way to give them that. Feel free to record any and every part of a lesson in German. The lesson text and the vocabulary are priorities, but e. g. listening comprehension / dictation exercises and anything else you can think of are very welcome, too.

Contributing your experience as a fellow student (student only)
As a student of German you have a particularly valuable thing to contribute: your experience. How did you manage to learn a particular word or its gender? How did you manage to learn a part of grammar? How would you explain it? What general tips can you give learners? This is a part of learning where native speakers are of no help at all, because they never had to study their language. Your input is very welcome, just add it at the appropriate place within the lesson or put it in BLL German/For future use.

Misc contributing (anybody)
The course also needs people to improve the formatting, convert the external lessons to Wiki format, check for spelling mistakes etc. in both English and German or create a nice cover image, logo or small image to be used inside the lesson.

title: BLL German/Contributing


text:
Bartending/Cocktails/Cocksucking Cowboy

A Cocksucking Cowboy is a layered shooter made from two parts cold butterscotch schnapps with one part of Baileys Irish Cream. The drink is also known as a Buttery Nipple, though the Buttery Nipple is often thought to be composed of 1/2 Butterscotch and 1/2 Irish Cream. Note that Baileys does not have to be used, but any type of Irish Cream may be.

As of 2004, it is an extremely popular shooting drink in Australian pubs and clubs and may be purchased premade in segmented shotglasses sealed with foil, and "kits" with bottles of each liqueur are also sold, both under the name "CS Cowboy".

title: Bartending/Cocktails/Cocksucking Cowboy


text:
Talk:Windows Programming/Windows System Architecture

This article is, of course, completely wrong. Once we have made enough fun of it, I'll delete this horror --KJK::Hyperion 09:35, 16 May 2006 (UTC)

 * With all due respect, most of the information in this artical is taken directly from books, including Petzold's "Programming Windows". I don't doubt that a few errors have crept in here or there, but to say it's completely wrong or to call it a "horror" is inappropriate, and inaccurate. --Whiteknight (talk) (projects) 13:06, 16 May 2006 (UTC)

 * No, seriously, this whole book is shitty and misleading. How about this page? It portrays ntdll.dll in kernel mode. It mentions a component called wingdi.dll that doesn't even exist. It talks about features at vastly different layers all at once without any sense of structure (like lumping together msvcrt.dll with the other DLLs, and ws2_32.dll which is completely irrelevant at this point). Petzold is an inappropriate source, too: Petzold is an expert in the user interface and graphics subsystem, but for a real overview of the system architecture? try Russinovich, Solomon, Pietrek. Seriously, we only allow it to exist because it totally cracks us up --KJK::Hyperion 01:43, 1 June 2006 (UTC)

 * First off, I am inclined to respect information published by Petzold, and I have no reason not to take at face value information that he presents about windows, especially since that information is duplicated in a number of other, respectable sources. For instance, the diagram depicting ntdll.dll operating in kernel mode was adapted from Eldad Eilam' "Reversing: Secrets of Reverse Engineering." Other details about the system internals are taken from Johnathan Hart's "Windows System Programming". ws2_32.dll is mentioned here as a matter of interest primarily: it's inclusion demonstrates the modular nature of windows, and shows are certain families of functions are contained in specific libraries. The overall purpose of this book is to talk about programming windows in an overview, not to discuss the minute details of the system architecture. Therefore, we are presenting modules from various levels of operation simultaneously to show that a programmer needs to interact with multiple different modules from across the system to create an effective program. This is not to say that some of the DLL files are misnamed, but that's a simple error that is easily fixable. Rather then complain about the material, you should jump in and help contribute. If this book is "shitty" and "misleading", it's because knowledgable wikibookians arent contributing to it. --Whiteknight (talk) (projects) 13:10, 1 June 2006 (UTC)


text: User talk:202.54.70.141

title: User talk:202.54.70.141


text:
User talk:Swiftfox

Welcome
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Good luck! --Derbeth talk 11:43, 16 May 2006 (UTC)

title: User talk:Swiftfox


text:
WebObjects/EOF/Modeling/EOModeler on Windows

Sigurður Anton Ólafsson
If anyone is having a problem with EOModeler on Windows XP, here’s a solution:

I had a problem with EOModeler, it simply wouldn’t start. It’s a part of WebObjects 5.2.4, that is WebObjects 5.2 that had been updated to 5.2.4 The bug came in during the update.

The solution is this:
 * 1) after the original installation of WebObjects 5.2, verify that EOModeler works.
 * 2) You can also check if you see the following processes running in task manager: nmserver.exe, machd.exe, pbs.exe –these are all necessary for EOModeler to run.
 * 3) Right Click My Computer and select Manage
 * 4) Select Services
 * 5) In the Services Menu, make all Apple Services manual and turn them off.
 * 6) Go on with the WebObjects Update to 5.2.4
 * 7) Turn the Apple Services back on and make them automatic.
 * 8) Restart computer.
 * 9) EOModeler should now work.

Oracle JDBC
http://docs.info.apple.com/article.html?artnum=75145


text:
WebObjects/Web Applications/Development/J2EE Integration

Thomas Pelaia
I wouldn't consider myself a WAR expert, but I do deploy my WebObjects application using JBoss and it works very well.

Have you tried a "Hello World" type example application? If you can get a simple application running under JBoss then you should be okay with a more complicated one. I suggest starting with "Hello World" and then adding a simple EOF and that should cover everything.

There were a few tricky configurations in the initial setup. To be clear, I am using XCode, but it probably doesn't matter. Here are a few things to check.

Check you jboss-web.xml file. You definitely need to configure this file properly if you are using EOF. The application will never get started properly without this file configured correctly.

Make sure your deployment license gets built into the WAR file for deployment by setting the SERVLET_DEPLOY_LICENSE item.

Make sure the servlet project settings are correct:
 * SERVLET_SINGLE_DIR_DEPLOY = NO
 * SERVLET_TRUE_WAR = YES
 * SERVLET_WEBAPPS_DIR = /Library/JBoss/3.2/deploy

Also, I explicitly defined a package for all of my classes. This prevents JBoss from complaining upon startup, however, JBoss still ran the application just fine anyway.


text:
WebObjects/EOF/Using EOF/The EOF Commandments

Some things to avoid when working with EOF. Some of these things are contraindicated in Apple documentation, others are not. But all are things that experience shows EOF does not expect, and can lead to all sorts of trouble, including mysterious exceptions, and EOF getting confused about what changes must be saved to the database.

public void addAppointment(String time, String reason) { super.willChange; NSMutableDictionary mutableAppointments = appointments.mutableClone; mutableAppointments.setObjectForKey(reason, time); setAppointments(mutableAppointments.immutableClone); }
 * 1) Don't set EO properties in the EO constructor -- use awakeFromInsertion(...) or awakeFromFetch(...) instead.
 * 2) Don't do anything to an EO before inserting it into an editing context. Always insert EOs into ECs immediately. See rule #1.
 * 3) Don't modify any EO properties in validateFor...(...) methods. Doing this in validateValueForKey(...) is ok as ChuckHill noted in the list.
 * 4) If over-riding awakeFromInsertion(...), remember to call ther superclass implementation. Same with awakeFromFetch(...).
 * 5) Don't change the behavior of methods that EOF uses.  For example, do not override to-many relationships to return a sorted list of the related objects.  Make another method to do this.
 * 6) Don't use EOF in model class static initializers. Doing so forces EOF into operational mode before the frameworks are initialized. Use lazy loading of the entity instead.
 * 7) Don't use mutable classes (e.g. NSMutableArray, NSMutableDictionary, any other class that can change internal state after creation) as attributes.  If you want this effect, use immutable classes and provide cover methods to replace the immutable instance with an updated instance.  You and EOF will be much, much, much happier.  e.g.


text:
WebObjects/EOF/Using EOF/EOF Best Practices

Overview
First, do no harm -- Read and obey The EOF Commandments before reading this.

Creating EOEnterpriseObjects
Rather than use

MyEO eo = new MyEO; ec.insertObject(eo);

Prefer this form:

MyEO eo = (MyEO) EOUtilities.createAndInsertInstance(ec, "MyEO");

This has two main advantages. One, it prevents the use of an EO which has not been inserted into an EOEditingContext (see The EOF Commandments). Two, it supports the case where two or more entities in the EOModel(s) are implemented by the same Java class.

A reasonable question to ask here is, If this is good: MyNewPage nextPage = (MyNewPage)pageWithName(MyNewPage.class.getName);

then why not this?

MyEO eo = (MyEO) EOUtilities.createAndInsertInstance(ec, MyEO.class.getName);

The key here is that the to second parameter to createAndInsertInstance? is the EOEntity name from the model, not the class name. For component creation it is the class name. The thing is that the entity name and the class name are often not the same. The class names will include package name, but the entity names will not. Also, I've run across cases where multiple entities in the model are implemented by the same class. Gary Teter makes good use of this in the WireHose frameworks.