text:
MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

2 struck out the claim about k[x]/x^2

Let $k$ be a commutative ring, $A$ a commutative $k$-algebra, and for some other part of why I'm asking this question I only care about the case when $k \supseteq \mathbb Q$. Recall the following notion, I think originally due to Grothendieck:

Definition (differential operator): Let $D : A\to A$ be $k$-linear. Define $s_nD : A^{\otimes n} \to A$ by: $$s_nD(a_1,\dots,a_n) = \sum_{I \subseteq \lbrace 1,\dots,n\rbrace} (-1)^{|I|}\; \left( \prod_{i\not\in I} a_i\right) \;D\left(\prod_{i\in I}a_i\right)$$ One says that $D$ is an $n$th order differential operator if $s_{n+1}D = 0$.

Examples: $s_0D = D(1) \in A$. $s_1D(a) = D(a) - aD(1)$. $s_2D(a,b) = D(ab) - aD(b) - bD(a) + abD(1)$.

Remark: $s_nD$ is symmetric in the $a_i$s. If $D$ is an $n$th order differential operator, then $s_nD(-,a_2,\dots,a_n)$ is a derivation, for $a_2,\dots,a_n$ fixed. Thus if $D$ is an $n$th order differential operator, $s_nD$ is a symmetric polyderivation. It deserves the be called the principal symbol of $D$. It measures the failure of $D$ to be an $(n-1)$th order differential operator.

Question: For which algebras $A$ (i.e. what are natural, checkable conditions) does the following "PBW theorem" hold: $$s_n: \lbrace n\text{th order differential operators}\rbrace \to \lbrace \text{symmetric }n\text{-polyderivations} \rbrace$$ surjective for every $n$?

Examples: This PBW theorem holds for $A = k[x_1,\dots,x_n]$ and $A = k [\![ x_1,\dots,x_n ]\!]$ and $A = \mathscr C^\infty(M)$ where $M$ is a smooth manifold. This PBW theorem failes for $A = k[x]/x^2$, as the space of symmetric biderivations is one-dimensional spanned by $x \frac{\partial}{\partial x}\otimes \frac{\partial}{\partial x}$, whereas every second-order differential operator is also a first-order differential operator. Edit: I don't know a characteristic-$0$ example for which PBW theorem fails, but I don't expect it to always hold.

Remark: I would expect that algebras $A$ for which the PBW theorem holds are those for which $\operatorname{spec}(A)$ is "smooth" in the appropriate sense, but I don't know if this is "smooth" in other usual senses of the word.

1

# For which algebras does \{Differential Operators\} satisfy a PBW-like theorem?

Let $k$ be a commutative ring, $A$ a commutative $k$-algebra, and for some other part of why I'm asking this question I only care about the case when $k \supseteq \mathbb Q$. Recall the following notion, I think originally due to Grothendieck:

Definition (differential operator): Let $D : A\to A$ be $k$-linear. Define $s_nD : A^{\otimes n} \to A$ by: $$s_nD(a_1,\dots,a_n) = \sum_{I \subseteq \lbrace 1,\dots,n\rbrace} (-1)^{|I|}\; \left( \prod_{i\not\in I} a_i\right) \;D\left(\prod_{i\in I}a_i\right)$$ One says that $D$ is an $n$th order differential operator if $s_{n+1}D = 0$.

Examples: $s_0D = D(1) \in A$. $s_1D(a) = D(a) - aD(1)$. $s_2D(a,b) = D(ab) - aD(b) - bD(a) + abD(1)$.

Remark: $s_nD$ is symmetric in the $a_i$s. If $D$ is an $n$th order differential operator, then $s_nD(-,a_2,\dots,a_n)$ is a derivation, for $a_2,\dots,a_n$ fixed. Thus if $D$ is an $n$th order differential operator, $s_nD$ is a symmetric polyderivation. It deserves the be called the principal symbol of $D$. It measures the failure of $D$ to be an $(n-1)$th order differential operator.

Question: For which algebras $A$ (i.e. what are natural, checkable conditions) does the following "PBW theorem" hold: $$s_n: \lbrace n\text{th order differential operators}\rbrace \to \lbrace \text{symmetric }n\text{-polyderivations} \rbrace$$ surjective for every $n$?

Examples: This PBW theorem holds for $A = k[x_1,\dots,x_n]$ and $A = k [\![ x_1,\dots,x_n ]\!]$ and $A = \mathscr C^\infty(M)$ where $M$ is a smooth manifold. This PBW theorem failes for $A = k[x]/x^2$, as the space of symmetric biderivations is one-dimensional spanned by $x \frac{\partial}{\partial x}\otimes \frac{\partial}{\partial x}$, whereas every second-order differential operator is also a first-order differential operator.

Remark: I would expect that algebras $A$ for which the PBW theorem holds are those for which $\operatorname{spec}(A)$ is "smooth" in the appropriate sense, but I don't know if this is "smooth" in other usual senses of the word.


text:
Enter the magnetic flux density (Tesla), the length of the solenoid (m), magnetic constant, and the number of turns into the calculator to determine the Solenoid Current.

## Solenoid Current Formula

The following formula is used to calculate the Solenoid Current.

Is = (B/u)*L/N

• Where Is is the Solenoid Current (amps)
• B is the magnetic flux density (Tesla)
• L is the length of solenoid (m)
• magnetic constant
• N is the number of turns

## How to Calculate Solenoid Current?

The following example problems outline how to calculate Solenoid Current.

Example Problem #1

1. First, determine the magnetic flux density (Tesla). In this example, the magnetic flux density (Tesla) is determined to be 140 .
2. Next, determine the length of solenoid (m). For this problem, the length of solenoid (m) is measured to be 50 .
3. Next, determine the number of turns. In this case, the number of turns is found to be 7.
4. Next, determine the magnetic constant. This is 10 for this problem.
5. Finally, calculate the Solenoid Current using the formula above:

Is = (B/u)*L/N

Inserting the values from above and solving yields:

Is = (140/10)*50/7 = 100 (amps)

Example Problem #2

Using the same method as above, determine the variables required by the formula. For this example problem, these are:

magnetic flux density (Tesla) = 75

length of solenoid (m) = 17

number of turns = 5

magnetic constant = 2.25

Enter these given values into the calculator or above yields:

Is = (75/2.25)*5/17 = 9.803 (amps)

format: plain


text:
# Wronskian question

1. Feb 15, 2015

### joshmccraney

Hi pf!

If $y_1$ and $y_2$ are homogenous solutions to a (not necessarily homogenous) second order linear ODE, we define the Wronskian as $$\begin{vmatrix} y_1 y_2\\ y'_1 y'_2 \end{vmatrix}$$. This derivation seems to stem from the pair of equations involving $y_1$ and $y_2$ satisfying the initial conditions $y(t_0) = y_0$ and $y'(t_0) = y'_0$. But we never satisfy the initial conditions with only $y_1$ and $y_2$ until we also have the particular solution. If everything I've said so far is correct, why is the Wronskian defined in this manner?

Thanks so much!

2. Feb 16, 2015

### HallsofIvy

You are mistaken that y1 and y2 must satisfy some given initial conditions. y1 and y2 can be any solutions to the second order equation. The point of the Wronskian is that we need independent solutions to write the general solutions or solutions to initial value or boundary value equations, and two functions, both satisfying the same second order differential equation, are independent if and only if their Wronskian is non-zero.

3. Feb 16, 2015

### joshmccraney

awesome. thanks!


text:
Math Help - using calculus to solve the problem of the ant in a cube-shaped room

1. using calculus to solve the problem of the ant in a cube-shaped room

There's a room in the shape of a cube with a side length of 7m. There's also an ant, located at one corner of the cube (call it point A), that wants to crawl to the opposite corner of the cube (call it point B). Find the length of the shortest path the ant can take from point A to point B. Note that the ant cannot fly: it must crawl along the walls (i.e., along the surface of the cube).

Now, I know this problem can be easily solved by flattening out the cube into a 2-dimensional figure, and using the Pythagorean theorem to find the shortest distance between the two points. However, I have to come up with a solution using calculus, which involves coming up with some distance function, differentiating that distance function, setting that differentiated function equal to 0, which would then give you the shortest distance (since it corresponds to a minimum on the graph of the distance function). However, I need help figuring out the distance function.
Thanks very much!

2. If L is the length of the side of the cube, and x is the distance from the next corner where ant reaches before climbing the vertical face, then the total distance crawled by the ant is

$D = \sqrt{(L^2 + x^2)} + \sqrt{(L-x)^2 + L^2}$

Now find the derivative of D with respect to x and equate it to zero.

3. Thanks, the equation works, but I don't really understand what x represents and how you came up with the equation in the first place.

4. Ah, never mind, I got it. Thanks very much!


text:
# Report-Output to two files

 by Mr. Dominik Jenzer in group Reports & Macros in ARIS Posted: 2012-05-031037 views | 6 comments | category: ARIS Support 5

Hi

In my report, I'm running trough big arrays. Each entry (a model) creates a new sheet (Excel-Report).

Now I have to to the same loop again, because I need the same but with other columns.

What I like to to is, that I have one report and creating the output to each proper outputfile.

I can create the two OutputObjects and also fill the content correctly. But at the end, Aris will open Excel only with one report (the last). As I understand, this is defined by the report-path (including one filename) in the Report-Assistant-Dialogue.

But I do also the following:

oOutDef.WriteReport("C:\\Temp","temp.xls")

This runs witout error, but the file is not there.

What did I miss or how to write multiple files in one report?

Kind regards,

Dominik

Hi Dominik,

try to use:

Report class Context - Method addOutputFile

addOutputFile ( String p_sFileName, byte[] p_fileData )

Adds the specified file to list of files to be transfered to the client.

Cheers,

Jens

Hi Jens,

thanks for this.

I get an TypeError, saying that this function cannot be found.

And second, how can I put the Data into p_fileData?

What I have is:

var oOutDef = Context.createOutputObject()
oOutDef.OutputF("blabla", getString("ID_STYLE_RD_DEFAULT"))
oOutDef.WriteReport()

This works with opening Excel. With your Info, I tried this:

var oOutDef = Context.addOutputFile("text.xls",p_fileData)
oOutDef.OutputF("blabla", getString("ID_STYLE_RD_DEFAULT"))
oOutDef.WriteReport()

Hi Dominik,

in this case I think

addOutputFileName ( String p_sFileID, int p_nLocation )

is better. You have to do the following:

1. Create a output object with a given filename

var out = Context.createOutputObject ( Constants.OUTEXCEL,  filename );

out.OutputF("blabla", getString("ID_STYLE_RD_DEFAULT"));

3. Add the output file to transfer

Context.addOutputFileName(filename, Constants.LOCATION_OUTPUT);

4. Call WriteReport

out.WriteReport( Context.getSelectedPath(), filename );

Jens

Hi Jens,

Thanks. It almost works. Im running in trouble with the 4th statement.

When I read the ARIS help to the WriteReport(String,String)-Statement, there is documented, that the first parameter (p_sSelectedPath) will be ignored. This fits the current error. The report does not try to save the report where I like, he chooses "D:\ARIS7.2\server\temp\ReportTemp\5\text.xlsx. This is a directory that does not exist on the client. This is the server-directory, and none of the users later have access to this share. Even when the file will be stored there. They can't get the report by file-explorer.

So, how can the correct place be defined?

I have a var for this:

var selClientFolders = Dialogs.getClientFolder("Select new output folder", "", false)

What can be done?

Dominik

Here an example writing two files. Send to client in a folder selected by the user:

function main() {

var out = Context.createOutputObject ( Constants.OUTEXCEL,  Context.getSelectedFile() );
out.DefineF("F1", "ARIAL", 8, Constants.C_BLACK, Constants.C_TRANSPARENT, Constants.FMT_LEFT, 0, 21, 0, 0, 0, 1);
out.BeginTable(100, Constants.C_BLACK, Constants.C_TRANSPARENT, Constants.FMT_CENTER, 0);
out.TableRow();
out.TableCellF("BlaBLa", 100, "F1");
out.EndTable(" ", 100, "ARIAL", 10, Constants.C_BLACK, Constants.C_TRANSPARENT, 0, Constants.FMT_CENTER | Constants.FMT_VCENTER|Constants.FMT_BOLD, 0);

var filename = "secondfile.xls";
var out2 = Context.createOutputObject ( Constants.OUTEXCEL, filename );
out2.DefineF("F1", "ARIAL", 8, Constants.C_BLACK, Constants.C_TRANSPARENT, Constants.FMT_LEFT, 0, 21, 0, 0, 0, 1);
out2.BeginTable(100, Constants.C_BLACK, Constants.C_TRANSPARENT, Constants.FMT_CENTER, 0);
out2.TableRow();
out2.TableCellF("BlaBLa2", 100, "F1");
out2.EndTable(" ", 100, "ARIAL", 10, Constants.C_BLACK, Constants.C_TRANSPARENT, 0, Constants.FMT_CENTER | Constants.FMT_VCENTER|Constants.FMT_BOLD, 0);
out2.WriteReport();
main();


text:
# Svg Functions

It is Vector Empirical Orthogonal Function. This is the beginning of an online course to get to grips with 3D vectors for anyone who wants to learn. If you want to keep your HTML/SVG structure though, you can do the following: var svg = document. In addition to that each element $a\in A$ gets assigned a unique element $f(a)\in B$. SVGator is an easy-to-use SVG animation generator, generating CSS or JavaScript code as the animation type, making it easy to add crystal clear animations to your website. To pass an argument by reference, simply enclose it in a structure (see Structures). SVG is XML based, which means that every element is available within the SVG DOM. Migration from 1. The 2 SVG circles were moved 80 units to the right. P(R) Continuous functions R !R All functions R !R. ArcGIS Spatial Analyst: Advanced GIS Spatial Analysis Using Raster and Vector Data J-8747 ESRI White Paper 3 Analysis on string fields. A vector has magnitude (size) and direction: The length of the line shows its magnitude and the arrowhead points in the direction. The any() function takes a vector and a logical condition as input arguments. in the above example unlist function converts the list to vector so the output will be in vector. For more information about XML, please refer to The Extensible Markup Language (XML) 1. A vector's type can be checked with the typeof() function. Two vectors are equal? if they have the same length, and if the values in corresponding slots of the vectors are equal?. In this video lesson we will explore Vector-Valued Functions, or Vector Functions. Now we are going to do calculus with vector-valued functions. Vector addition is one of the most common vector operations that a student of physics must master. The transformation functions used in the transform attribute work similar to the way CSS transform functions work in the transform property, except that they take different arguments. The graph of the vector-valued function then shows each of these parametric plots as their orthogonal projections onto each of the coordinate planes. Use the interrupt vector address in the following table to determine the interrupt number. If you're seeing this message, it means we're having trouble loading external resources on our website. Early Vector Graphics on the Web n 2. The order of variables in this vector is defined by symvar. We'll spend most of this section looking at vector functions of a single variable as most of the places where vector functions show up here will be vector functions of single variables. Here is how they are derived. improve this answer. The SVG Group Element that was transformed contains the 2 SVG Circles. Given the vector function $$\vec{r}(t)$$, the most basic equation we use to find the unit tangent vector is $\displaystyle{ \vec{T}(t) = \frac{\vec{r}'(t)}{ \| \vec{r}'(t) \| } }$ The vector function $$\vec{r}(t)$$ is often a position vector. Definition of Vector-Valued Functions A function of the form \\[{\\mathbf{r}\\left( t \\right) = f\\left( t \\right)\\mathbf{i} + g\\left( t \\right)\\mathbf{j} + h. The numbers in the table specify the first browser. This function is clearly continuous in α, ρ. The function has two input parameters of the type floating scalar or float vector and one input parameter of the type floating scalar: I, the incident vector, N, the normal vector of the refracting surface, and eta, the ratio of indices of refraction. Conic Sections: Parabola and Focus example. vector functions A vector function r(t) = hf(t),g(t),h(t)i is a function of one variable—that is, there is only one "input" value. Media in category "SVG x-y functions" The following 136 files are in this category, out of 136 total. You can attach JavaScript event handlers for an element. Find the points where r(t) intersects the xy. When template functions are overloaded in such a way that the match of the template with the function call is not unique. Apart from the str () function, R contains a set of functions that allow you to test for the type of a vector. how to find the arc length of a 3-dimensional vector function, How to find arc length if a curve is given in parametric form, examples and step by step solutions, A series of free online calculus lectures in videos. Vector(A);. These are instances of the partial ordering of function templates by the compiler. Definition 11. — Function: map-vec-2 f a b. A vector-valued function is a rule that assigns a vector to each member in a subset of R1: In other words, a vector-valued function is an ordered triple of functions, say f (t);g(t);h(t); and can be expressed as. }\) The graph of a vector-valued function is the set of all terminal points of the output vectors with their initial points at the origin. ) r(t) = c. lookup_vector Required. A range that contains only one row or one column. Volantexrc RC boat Vector SR80Pro is designed with capsize recovery and outstanding power system, top speed reaching 46 MPH. The Parameter t for Time. matrix %*% y. Usually we denote a vector valued function in two ways. Actually, the transformation functions do not transform the SVG shape themselves, but the underlying coordinate system of that shape. If the optional third argument dim is present then operate along this dimension. Syntax vector. Variables with the same name are allowed, so long as they have distinct signatures. )To avoid copying, accept a std::vector& instead. But as this system satisfies the same laws it is called vector space. Vector is a basic data structure in R. The space curve generated by this vector function is called a circular helix. Scalar Function A function of one or more variables whose range is one-dimensional, as compared to a vector function , whose range is three-dimensional (or, in general, -dimensional). Removes from the vector either a single element ( position) or a range of elements ( [first,last) ). The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. I'll update this once the best way to handle it. Vector, in physics, a quantity that has both magnitude and direction. Technically, the diﬀerential is a function of both x and u, but the notation df is used in a generic sense to mean the diﬀerential of f. A vector field on is a function that assigns to each point a three-dimensional vector. We calculate the components of the vector by subtracting the coordinates of the initial point. We report these formulae below. First, we will learn how represent a vector-valued functions. The most basic building block for programming motion is the vector. For example, a function takes in a lion and an eagle, two animals, which we equated to scalars. svg) Click to share this graph on your favourite social network:. To operate non-destructively, vec2_unit can be called like this: vec2_t orig_vector = {1, 1}; vec2_t unit_vector; vec2_unit(orig_vector, unit_vector); To operate in-place, vec2_unit can be called like this:. Das Doppelspalt Experiment. The polyval function outputs a vector of constant values equal to the scalar input value with a length equal to the length of your x-vector. Then we will learn how to find the limit of a…. To know more about str (), visit Str function. The Support Vector Machine (SVM) is a state-of-the-art classi cation method introduced in 1992 by Boser, Guyon, and Vapnik [1]. SVG elements support mouse events, keyboard events. You can graph a vector field (for n =2) by picking lots of points (preferably some in each quadrant), evaluating the vector field at these points, and then drawing the resulting vector with its tail at the point. This guide should walk you through the creation of a reusable Vector3 type in c# and the mathematics behind it all. We'll spend most of this section looking at vector functions of a single variable as most of the places where vector functions show up here will be vector functions of single variables. Because of this, many programmers consider that knowing C code makes it much easier to learn the new languages. 5 * pi] set yrange [-3: 3] set grid xtics ytics set key 7, 3 plot sin (x) title "sine" with lines linewidth 2, \ cos (x) title "cosine" with lines linewidth 2, \ tan (x) title "tangent" with lines. wordpress,dictionary,svg. In this lecture we will deal with the functions whose domain is a subset of Rand whose range is in R3 (or Rn). SVG provides four transformation functions: translate() rotate() scale() skew() matrix() Each of these functions will be explained in more detail in the following sections. # set the output set terminal svg enhanced fname "Times" fsize 18 set output "trigonometric_functions. Let’s take a look at the workings of this function with an example. These files are called, not surprisingly, m-files. 1 Vector-Valued Functions. After 72 hr of infection, ZsGreen1 fluorescence was analyzed by microscopy, with an exposure time of 0. If the optional third argument dim is present then operate along this dimension. 1) std::vector is a sequence container that encapsulates dynamic size arrays. If A is a numeric array of any size, then B=sin(A) is. When template functions are overloaded in such a way that the match of the template with the function call is not unique. vector::clear() is a library function of "vector" header, it is used to remove/clear all elements of the vector, it makes the 0 sized vector after removing all elements. SEE ALSO: Complex Function, Real Function, Vector Function. pdf) Portable Network Graphics (. MULTIVARIABLEVECTOR-VALUEDFUNCTIONS 3 31. Syntax vector. Vectors in Two and Three Dimensions Part 3: Vector-Valued Functions and their Derivatives. These 6 sets we just made, there should probably be a function that does this. Here is an example of a three-dimensional vector function: which is plotted below for 0<=t<=7*pi. A less obvious example of a vectorized function is the paste() function. The faceforward function returns a vector that points in the same direction as a reference vector. To pass an argument by reference, simply enclose it in a structure (see Structures). For a multi-dimensional array, max operates along the first non-singleton dimension. Example 1: r(t) = < √t, 1/t > Step 1: Check the domains. So, we can say r of t, let me switch back to that pink color, oh, this keeps staying green, is equal to x of t times the unit vector in the x direction, the unit vector gets a little caret on top, a little hat that's like the arrow for it. Conic Sections: Parabola and Focus example. SVG has several methods for drawing paths, boxes, circles, text, and graphic images. svg 736 × 496. SASS SVG URI. How you define vector function in Mathematica? For example, f is a vector function and f=(xy,yz,zx). We will however briefly look at vector functions of two variables at the end of this section. The graph of a vector-valued function of the form is called a space curve. step(sys,t); In the above two plots, only the first 6 seconds of the response are shown. Suchfunctions. cs script in the scripts folder. MATH 240: Vector Spaces Definition: A vector space is a set V on which two operations + and · are defined, called vector addition and scalar multiplication. Vector functions are vectors and obey rules of addition and scalar multiplication. One way to represent a vector-valued function is to graph the parametric plot for , on the plane, the parametric plot for , on the plane, and the parametric plot for , on the plane. How to define this in Mathematica and then how to calculate the value of the components of f for any number x, y, and z? For scalar functions it goes as this: f[x_]:=x^2 f[4] Any. push_back(x) the allocation of increased space can result in a change in the position of that vector in memory 2) thus if that push_back(x) call occurs in a function where a reference to that vector has been passed, and a reallocation occurs, is that reference. These three functions provide ways to manipulate unit vectors as 3-vectors and as spherical polar angles. Several topics are discussed which concern the representation of a discrete function on the sphere in terms of surface spherical harmonics. This convention applies to the graphs of three-dimensional vector-valued functions as well. So, let's see if we can describe this curve as a vector, a position vector valued function. For example, the vector field associates the vector to every point (x,y) in the plane. Finish the function definition below so that if a function is passed into the "func" argument and some data (like a vector) is passed into the dat argument the evaluate() function will return the result of dat being passed as an. The second page is an exercise in matching more elaborate equations and graphs. Conic Sections: Hyperbola example. Wait! Have you checked – R Matrix Functions. Specifcally, a specified time vector can be supplied via the second input to the function as shown below. generates a vector plot of the vector field {vx,vy} as a function of x and y. Note that the domain of the function is precisely the subset of the domain of where the gradient vector is defined. Hi all, I want to create new user field function which is a velocity vector that has two components instead of three, j and k. Change the components of the vector field by typing, for example: x^2sin (y) sqrt (y^2+z)exp (x/y) log (x-y+z) 2. The pen will touch the paper in only one point. 1 Di⁄erentiation De–nition 116 Let !r(t) be a vector function. SVG attributes A to Z. How you define vector function in Mathematica? For example, f is a vector function and f=(xy,yz,zx). Give a vector function for each of the following curves, including the appropriate range of t-values. Then we will learn how to find the limit of a…. And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just finish your homework or study for that next big test). In this video lesson we will explore Vector-Valued Functions, or Vector Functions. Shorthand for writing Vector2 (float. Please see the GCC manual for more information on these extensions. fillCircle("state2"); }; The trick is to wait for the SVG object to load (onload event); not till then you can safely use the contentDocument property. Properties: events {OpenLayers. Conic Sections: Hyperbola example. svg) Encapsulated PostScript (. vector and is. Scalar Function A function of one or more variables whose range is one-dimensional, as compared to a vector function , whose range is three-dimensional (or, in general, -dimensional). generates a vector plot of the vector field {vx,vy} as a function of x and y. 1 Vector-Valued Functions. While it is wellknown how to generate linear ranking functions for relations over (mathematical) integers or rationals, effi cient synthesis of ranking functions for machine-level integers (bit-vectors) is an open problem. $$We first check if it is conservative by calculating its curl. Let’s take a look at the workings of this function with an example. Kernel Functions for Support Vector Machines Jordan Boyd-Graber University of Colorado Boulder LECTURE 9B Slides adapted from Jerry Zhu Jordan Boyd-Graber j Boulder Kernel Functions for Support Vector Machines j 1 of 13. It contains element of the same type. Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. P(R) Continuous functions R !R All functions R !R. And it doesn't matter which order we add them, we get the same result: The two vectors (the velocity caused by the propeller, and the velocity of the wind) result in a slightly slower ground speed heading a little. For more information about XML, please refer to The Extensible Markup Language (XML) 1. To build a theory of calculus for vector-valued functions, we simply treat each component of a vector-valued function as a regular, single-variable function. The Parameter t for Time. png) Scalable Vector Graphics (. The SVG Group Element that was transformed contains the 2 SVG Circles. Vector Arms Product & Dealer Info. Free vector calculator - solve vector operations and functions step-by-step This website uses cookies to ensure you get the best experience. Vector is the name of a new wave rock band formed in Sacramento, CA in the early 1980s. One-to-one function of a discrete random vector. Surfaces - Matching equations and graphs. Matlab is a software package that makes it easier for you to enter matrices and vectors, and manipulate them. SVG elements support mouse events, keyboard events. image/svg+xml-3-2-1 0 1 2 3-4-3-2-1 0 1 2 3 4 sine cosine tangent secant cosecant cotangent-3-2-1 0 1 2 3-4-3-2-1 0 1 2 3 4 sine cosine tangent secant cosecant cotangent. Passing vector to a function in C++. Click the oval. SVG images can be printed with high quality at any.$$ We first check if it is conservative by calculating its curl. The issue is your code, making it work with vectors. This is opposed to your normal scalar function that outputs a single value (m = 1, for instance f(x) = x + 2). The SVG Group Element that was transformed contains the 2 SVG Circles. In the cases in which the function is one-to-one (hence invertible) and the random vector is either discrete or continuous, there are readily applicable formulae for the distribution of. 2) access a C. Change the components of the vector field. See this question & answer for further details. The following transform functions can be used by the transform attribute Warning: As per the spec, you should be able to also use CSS transform functions. size() exceeds v. We define a new type of function, called a vector-valued function, that maps a domain value t to values for each of the coordinates x and y of a vector. Your sort() function takes a std::vector parameter and returns a std::vector, which means that calling sort() makes a copy of the entire vector. svg 736 × 496. So, we can say r of t, let me switch back to that pink color, oh, this keeps staying green, is equal to x of t times the unit vector in the x direction, the unit vector gets a little caret on top, a little hat that's like the arrow for it. Show transcribed image text Find the derivative of the vector function r(t) =ta x (b+tc)where a = (-. To make life easier, MATLAB includes many standard functions. This is opposed to your normal scalar function that outputs a single value (m = 1, for instance f(x) = x + 2). For example, log10(), like most mathematical functions in R, is a vector function, which allows you to take the log of each element in a vector all at once. For a matrix argument, return a row vector with the maximum value of each column. If f 1 and 2 are functions, then the value of the. The Box class has std::vector > pList; as private variable which I correctly loaded with particles. This is actually quite simple. Specifcally, a specified time vector can be supplied via the second input to the function as shown below. vec # multiply the two resulting objects together to get a final object final - mult * sq. Vector elements are placed in contiguous storage so that they can be accessed and traversed using iterators. Migration from 1. The head of the second vector is placed at the tail of the first vector and the head of the third vector is placed at the tail of the second vector; and so forth until all vectors have been added. Vector functions take a vector as input and produce a vector of the same length as output. unlist function in R, simply converts the list to vector with all the atomic components are being preserved. vector function - a function whose outputs are vectors. To compute this limit, all we need to do is compute the limits of the. For example, size(A,[2 3]) returns the lengths of the second and third dimensions of A in the 1-by-2 row vector szdim. So I have to need to calculate pLength. To zoom, use the zoom slider. A simple example: layerName: Design Layer-1; Layer(layerName); this will generate a layer named Design L. These operators, like matrices, are linear maps acting on vector spaces. vector are quite distinct from the meaning of the formal class "vector" in the methods package, and hence as(x, "vector") and is(x, "vector"). That just says. Although a vector has magnitude and direction, it does not have position. We will not prove all parts of the following theorem, but the reader is encouraged to attempt the proofs. "Can I use" provides up-to-date browser support tables for support of front-end web technologies on desktop and mobile web browsers. Ranking function synthesis is a key aspect to the success of modern termination provers for imperative programs. 3 and “Two Vector-analytic Results” in Section 3. Prime being so slow and awkward to use so I am too lazy to sroll upward, but I would say that its the multiplication of dt with I. The pen will touch the paper in only one point. A click on the ellipse easily finds the function “notify()” and passes the string as parameter as anticipated. Your sort() function takes a std::vector parameter and returns a std::vector, which means that calling sort() makes a copy of the entire vector. Non-vector modes "symbol" (synonym "name") and "pairlist" are accepted but have long been. Kernel Functions for Support Vector Machines Jordan Boyd-Graber University of Colorado Boulder LECTURE 9B Slides adapted from Jerry Zhu Jordan Boyd-Graber j Boulder Kernel Functions for Support Vector Machines j 1 of 13. So for the electron-in-a-box wavefunctions, the orthonormal basis of sine functions gives a well-defined infinite-dimensional vector space. vector::swap ( right). Problems in Mathematics. SVG elements can be modified using attributes that specify details about exactly how the element should be handled or rendered. vec # multiply the two resulting objects together to get a final object final - mult * sq. You can plot 2 functions, function 1 (in dark green) and function 2 (in magenta). This API contains predefined functions that can be called from outside the SVG map, typically from the HTML document in which the SVG map is embedded. A less obvious example of a vectorized function is the paste() function. Vector Function. Conic Sections: Hyperbola example. Isn't there any inbuilt 3D vector functions in Sage? For instance like a function to get the dot product, cross product or angle between two vectors? Or functions to get the distance from a point to a line? Find the intersections between two lines? Having such functions would be a great help and would greatly increase the speed of my workflow in school. (If the caller wants a sorted copy, then it's the caller's responsibility. How to define this in Mathematica and then how to calculate the value of the components of f for any number x, y, and z? For scalar functions it goes as this: f[x_]:=x^2 f[4] Any. AAV5 was additionally exposed at 0. What is Support Vector Machine? The objective of the support vector machine algorithm is to find a hyperplane in an N-dimensional space(N — the number of features) that distinctly classifies. If f 1 and 2 are functions, then the value of the. This function is clearly continuous in α, ρ. Thus if a vector is a function of, say time, then its derivative with respect to time is also a vector. numeric (scores_Team_A) [1] TRUE Copy. Returns this vector with a magnitude of 1 (Read Only). Usually we denote a vector valued function in two ways. Derivative Rules for Vector-Valued Functions. You can rotate an SVG element using the rotate() function. Animating SVG Shapes. So, we can say r of t, let me switch back to that pink color, oh, this keeps staying green, is equal to x of t times the unit vector in the x direction, the unit vector gets a little caret on top, a little hat that's like the arrow for it. vector::container=a vector is a sequential container that is optimized to allow efficient random_access of items by using an index. Vectors are useful whenever data must be stored in one order accessed in a different one. Vector: Instances of OpenLayers. The syntax for the function is: The rotate() function specifies a rotation by rotate-angle degrees about a given point. Reference Credits p5. When adding vectors, a head-to-tail method is employed. The vector (or simd in OpenMP* syntax [3]) function annotation is applicable to C/C++ and Fortran functions. If the dot product of I and Nref is smaller than zero the return value is N. To each value of t there corresponds a vector having its tail at the origin and its head on the unit circle, as shown in the figure below on the right. Thus if a vector is a function of, say time, then its derivative with respect to time is also a vector. Just import the file and use the function, no dependencies. A large number of different methods of integration of Banach-space-valued functions have been introduced, based on the various possible constructions of the. It can also be used to symbolize a single raster layer that represents either magnitude or direction. The component functions of a vector-valued function are the indi-. However people rarely call individual elements as vectors. Hello, I have a 3x3 rotation matrix that I obtained from stereoCalibrate (using the ros stereo calibration node). In addition to the language extensions listed here, Clang aims to support a broad range of GCC extensions. To compute this. Several R functions have and arguement that allows you to pass an arbitrary number of arguments. We'll spend most of this section looking at vector functions of a single variable as most of the places where vector functions show up here will be vector functions of single variables. Conic Sections: Hyperbola example. (If the caller wants a sorted copy, then it's the caller's responsibility. Surfaces - Matching equations and graphs. Finding the vector function for the curve of intersection of two surfaces The intersection of two surfaces will be a curve, and we can find the vector equation of that curve When two three-dimensional surfaces intersect each other, the intersection is a curve. According to their definitions, they are all the same things to me. In this video lesson we will explore Vector-Valued Functions, or Vector Functions. Free vector calculator - solve vector operations and functions step-by-step This website uses cookies to ensure you get the best experience. Differentiation of inverse functions are discussed. the tensor is the function I. Variables with the same name are allowed, so long as they have distinct signatures. A vector has magnitude (size) and direction: The length of the line shows its magnitude and the arrowhead points in the direction. scalar - square. vector and is. Kernel functions are critical for the classification capacity of RVM. Vector functions are also called vector-valued functions. Now we are going to do calculus with vector-valued functions. For example, the vector u= −(1, 2,4) is defined by u:= < 1, -2, 4 > ; Note that if you use square parenthesis A:= [ 4, 5, 6 ] ; then Maple will see A as a point, and not a vector. The HTML Element. In other words, the only difference between function(x) x*y and quo(x*!!y) is that, in the latter case, code that uses the quosure knows that the free variable in the expression is the symbol x. We've used onClick event to call a javascript functions. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. Code: vec <- as. When graphing a vector-valued function, we typically graph the vectors in the domain of the function in standard position, because doing so guarantees the uniqueness of the graph. 5 * pi] set yrange [-3: 3] set grid xtics ytics set key 7, 3 plot sin (x) title "sine" with lines linewidth 2, \ cos (x) title "cosine" with lines linewidth 2, \ tan (x) title "tangent" with lines. Just import the file and use the function, no dependencies. If you're behind a web filter, please make sure that the domains *. We choose the mixed kernel function as the kernel function of support vector regression. A linear functional in n -dimensional space is given by a linear form f (x) = a 1 x 1 + a 2 x 2 + ⋯ + a n x n in the coordinates x 1 , x 2 ,, x n of the vector x. Every vector-valued function provides a parameterization of a curve. Here we are going to discuss all these functions of the R vector in detail with examples. Vector in C++ STL. According to their definitions, they are all the same things to me. So, let's see if we can describe this curve as a vector, a position vector valued function. The notation of derivative of a vector function is expressed mathematically. A linear functional in n -dimensional space is given by a linear form f (x) = a 1 x 1 + a 2 x 2 + ⋯ + a n x n in the coordinates x 1 , x 2 ,, x n of the vector x. how similar concepts extend to the context of vector valued functions and discuss different settings that can be considered. PVector Daniel Shiffman. C++ is a compiled language, an upward compatible superset of C and an (incompatible) predecessor to Java. This is required because letters can be uppercase or lowercase and numbers have an offset of 0x30 hex. A vector is defined as having three dimensions as being represented by an ordered collection of three numbers: (X, Y, Z). This function returns the direction of a vector formed by the specified components [x1,y1] and [x2,y2] in relation to the fixed x/y coordinates of the room. 40 The antiderivative of a vector-valued function is a family of vector-valued functions all differing by a constant vector C. getElementById("test"); svg. Parametric Curves and Vector-valued Functions in the Plane. If f (t);g(t), and h(t) are the components of the vector r(t), then. Then, we used the SVG Group Element manually to get a feel for how it works. And the get_field function provided by the plugin allows you to query the value of such a field for every object you might have attached it to – you just. Construct and insert element (public member function ) emplace_back Construct and insert element at the end (public member function ) Allocator: get_allocator Get allocator (public member function ) Non-member function overloads relational operators Relational operators for vector (function template ) swap Exchange contents of vectors (function. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. We'll still have the part of the graph we found in the previous example, but now we need to figure out what happens for -5≤ t ≤ 0. Vector functions are vectors and obey rules of addition and scalar multiplication. Kernel functions are critical for the classification capacity of RVM. Vectors are sequence containers representing arrays that can change in size. A vector function is a mathematical function that outputs a vector. Using the Advanced Custom Fields plugin, you can add custom fields to categories (“taxonomy terms” in WP lingo) as well. This is the subspace of lists which terminate in an in nite sequence of zeros. 17 Linear Support Vector Machines II That function before was a little difﬁcult to minimize because of the step function in ‘(y;y^) (either 1 or 0). For a vector argument, return the maximum value. Scalable Vector Graphics (SVG) are becoming common place in modern web design, allowing you to embed images with small file sizes that are scalable to any visual size without loss of quality. Question: How to plot vector valued function Tags are words are used to describe and categorize your content. This tool converts SVG into an HTML5 Canvas JavaScript function. And they are all some kind of mapping, which assigns a vector to every point in a space or manifold or whatever. I'll update this once the best way to handle it. Apply a function to multiple list or vector arguments Description. To the left zooms in. Please see the GCC manual for more information on these extensions. A range that contains only one row or one column. 1 Images on the Web n 1. Suchfunctions. You can plot 2 functions, function 1 (in dark green) and function 2 (in magenta). Definition of Vector-Valued Functions A function of the form \\[{\\mathbf{r}\\left( t \\right) = f\\left( t \\right)\\mathbf{i} + g\\left( t \\right)\\mathbf{j} + h. The set of real functions f(x) is also a vector space. SVG elements can be modified using attributes that specify details about exactly how the element should be handled or rendered. how do i pass vector inputs to the function???. The following transform functions can be used by the transform attribute Warning: As per the spec, you should be able to also use CSS transform functions. This appendix describes the OracleAS MapViewer JavaScript application programming interface (API) for SVG maps. unlist function in R, simply converts the list to vector with all the atomic components are being preserved. Consider the vector (the red arrow) in the picture to the right. For example, in the VHDL below there is a function f_ASCII_2_HEX below that takes as an input a 8 bit ASCII Character and converts it into a Hex value that can be used by the internal logic to do processing. Here is an example of a three-dimensional vector function: which is plotted below for 0<=t<=7*pi. One way to represent a vector-valued function is to graph the parametric plot for , on the plane, the parametric plot for , on the plane, and the parametric plot for , on the plane. These operators, like matrices, are linear maps acting on vector spaces. Vectors in The Racket Guide introduces vectors. Sketch the vector function f(t) = < t 2, t 3 > for -5≤ t ≤ 5. The interface follows a language that is designed to look a lot like the notation use in linear algebra. scalar # return the. And it doesn't matter which order we add them, we get the same result: The two vectors (the velocity caused by the propeller, and the velocity of the wind) result in a slightly slower ground speed heading a little. $\begingroup$ It is no more vector in the sense of geometry or physics. SVG stands for Scalable Vector Graphics. This is the subspace of lists which terminate in an in nite sequence of zeros. The new feature is that the elements of the vector spaces are functions, and the spaces are in nite dimensional. That just says. The refract function returns a vector that points in the direction of refraction. A multivariate version of sapply. These are instances of the partial ordering of function templates by the compiler. 5 * pi] set yrange [-3: 3] set grid xtics ytics set key 7, 3 plot sin (x) title "sine" with lines linewidth 2, \ cos (x) title "cosine" with lines linewidth 2, \ tan (x) title "tangent" with lines. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which includes vector calculus as well as partial differentiation and multiple integration. Edit your functions and then click the "Graph it" button below. How you define vector function in Mathematica? For example, f is a vector function and f=(xy,yz,zx). We calculate the components of the vector by subtracting the coordinates of the initial point. To remove a graph, leave its text box blank. C++ vector is a data structure, helps you to perform many operations on elements. 4 Multimedia is not Computer Graphics ¡ 2. Vector Function Application Binary Interface adapted from version of November 2015 by Xinmin Tian, Hideki Saito, Sergey Kozhukhov, Kevin B. C++ classes are similar to Java classes in many ways, but there are also important differences. Interrupt Number Address 0 0003h 1 000Bh 2 0013h 3 001Bh 4 0023h 5 002Bh 6 0033h 7 003Bh 8 0043h 9 004Bh 10 0053h 11 005Bh 12 0063h 13 006Bh. Types defined include: bit bit_vector typical signals integer natural positive typical variables boolean string character typical variables real time delay_length typical variables Click on standard to see the functions defined Note: This package must be provided with compiler, do not use this one. I was originally going to write two functions, but noticed a clever way to achieve both functionalities using only the function shown above. Vector Function Basics We start with the formal deﬁnition of a vector function. vector::swap ( right). First it works but when I would like get access to the vector alloacated with "new", problems occur. The Vector class implements a growable array of objects. It is the output of the function Iafter the independent variable!~has been fed into it. That is, f:R n->R. SVG elements can be modified using attributes that specify details about exactly how the element should be handled or rendered. Vector supplies software and engineering services for the networking of electronic systems in the automobile and related industries (CAN, FlexRay, AUTOSAR, Ethernet etc. #include #include R m, where n > 0, m > 1. }\) The graph of a vector-valued function is the set of all terminal points of the output vectors with their initial points at the origin. SVG provides four transformation functions: translate() rotate() scale() skew() matrix() Each of these functions will be explained in more detail in the following sections. Note that as. For a multi-dimensional array, max operates along the first non-singleton dimension. Support Vector Machine, abbreviated as SVM can be used for both regression and classification tasks. And it doesn't matter which order we add them, we get the same result: The two vectors (the velocity caused by the propeller, and the velocity of the wind) result in a slightly slower ground speed heading a little. A vector-valued function is a function whose input is a real parameter $$t$$ and whose output is a vector that depends on $$t\text{. Each function is a block of code that accomplishes a specific task. We’ll spend most of this section looking at vector functions of a single variable as most of the places where vector functions show up here will be vector functions of single variables. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others. Kernel Functions for Support Vector Machines Jordan Boyd-Graber University of Colorado Boulder LECTURE 9B Slides adapted from Jerry Zhu Jordan Boyd-Graber j Boulder Kernel Functions for Support Vector Machines j 1 of 13. Wait! Have you checked – R Matrix Functions. Need to know how to calculate the domain of a vector-valued function? Learn how with this free video lesson. A vector function is simply a function whose domain is a set of real numbers and whose range is a set of vectors. A vector's type can be checked with the typeof() function. I'll update this once the best way to handle it. However, C is a complete language in itself and it is still used everywhere, even more …. The operation + (vector addition) must satisfy the following conditions: Closure: If u and v are any vectors in V, then the sum u + v belongs to V. Vector functions are vectors and obey rules of addition and scalar multiplication. Count and if this is greater than 1, it tranposes the array before returning it to the caller. push_back(x) the allocation of increased space can result in a change in the position of that vector in memory 2) thus if that push_back(x) call occurs in a function where a reference to that vector has been passed, and a reallocation occurs, is that reference. VectorPlot omits any vectors for which the v i etc. The pen will touch the paper in only one point. Returns the squared length of this vector (Read Only). Note: To use vector, include header. Parametric Curves and Vector-valued Functions in the Plane. vector and is. A multi-variable function can also be expanded by the Taylor series: which can be expressed in vector form as: where is a vector and and are respectively the gradient vector and the Hessian matrix (first and second order derivatives in single variable case) of the function defined as:. Post to: Tweet. VectorPlot by default shows vectors from the vector field at a regular grid of positions. In this page, we give an example of finding a potential function of a three-dimensional conservative vector field. This integration can be done if the functions along x y and z co-ordinates are parameteized. ThenF = ∇f is a vector ﬁeld on D. Write a program to find the sum of squares of a numeric vector. In another engine there is a vec_to_angle(Angle *ang, Vector *dir) function to return the pan and tilt of an Euler angle. vector and is. The gradient is a fancy word for derivative, or the rate of change of a function. First, we will learn how represent a vector-valued functions. If you do not specify v, then gradient(f) finds the gradient vector of the scalar function f with respect to a vector constructed from all symbolic variables found in f. ) r(t) = b. For more information about XML namespaces, please refer to the Namespaces in XML specification. Container is a objects that hold data of same type. Can it be done in STAR-C Customized User Field Function - Vector -- CFD Online Discussion Forums. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude. The Vector Field function is used to composite and convert two rasters into a two-band raster that is of either data type Magnitude-Direction or data type U-V. Furthermore, we include a summary of currently used algo-rithms for training SV machines, covering both the. Paul Garrett: Holomorphic vector-valued functions (February 19, 2005) where γ is a closed path with z having winding number +1. Support Vector Machine, abbreviated as SVM can be used for both regression and classification tasks. The derivative of !r. We prove exponential functions form a basis for the vector space by taking derivatives. How to define this in Mathematica and then how to calculate the value of the components of f for any number x, y, and z? For scalar functions it goes as this: f[x_]:=x^2 f[4] Any. Note that if another transform is applied before the. Vector functions are also called vector-valued functions. Each m-file contains exactly one MATLAB function. C++ classes are similar to Java classes in many ways, but there are also important differences. 1) std::vector is a sequence container that encapsulates dynamic size arrays. Lookup_value can be a number, text, a logical value, or a name or reference that refers to a value. For this reason, given a vector field \dlvf, we recommend that you first determine that that \dlvf is indeed conservative before. A n-variable scalar valued function acts as a map from the space R n to the real number line. Important break-in and ammuntion information:. 131 Tracks. Use the plotting extension to display the plots of numeric functions on a grid. We define a new type of function, called a vector-valued function, that maps a domain value t to values for each of the coordinates x and y of a vector. Vector functions take a vector as input and produce a vector of the same length as output. step(sys,t); In the above two plots, only the first 6 seconds of the response are shown. It checks the vector against the condition and creates a logical vector. Construct and insert element (public member function ) emplace_back Construct and insert element at the end (public member function ) Allocator: get_allocator Get allocator (public member function ) Non-member function overloads relational operators Relational operators for vector (function template ) swap Exchange contents of vectors (function. Actually, the transformation functions do not transform the SVG shape themselves, but the underlying coordinate system of that shape. Vector Function Application Binary Interface adapted from version of November 2015 by Xinmin Tian, Hideki Saito, Sergey Kozhukhov, Kevin B. Sequence containers store elements strictly in linear s. Below is a list of all of the attributes available in SVG along with links to reference documentation to help you learn which elements support them and how they work. f(x,y,z) = x 2 +2yz 5 is an example of a scalar valued function. Smith, Robert Geva, Milind Girkar and Serguei V. Shorthand for writing Vector2 (0, 1). numeric (scores_Team_A) [1] TRUE Copy. This is opposed to your normal scalar function that outputs a single value (m = 1, for instance f(x) = x + 2). In this post, we're going to examine the second of three types: the cubic bézier. Graphing Vector-Valued Functions. Analytic function• In mathematics , an analyti c function is a function that is locally given by a convergent power series. Language extensions can be very useful, but only if you know you can depend on them. Animating SVG Shapes. vector , a generic, attempts to coerce its argument into a vector of mode mode (the default is to coerce to whichever vector mode is most convenient): if the result is atomic all attributes are removed. To plot a function just type it into the function box. vec # multiply the two resulting objects together to get a final object final - mult * sq. Let’s take a look at the workings of this function with an example. //Limits of vector-valued functions in \mathbb{R}^n are defined similarly as the limit of each component. Paul Garrett: Holomorphic vector-valued functions (February 19, 2005) where γ is a closed path with z having winding number +1. In this video lesson we will explore Vector-Valued Functions, or Vector Functions. Derivative Rules for Vector-Valued Functions. Answer: If the library functions are missing, the global function library of CANape is not installed correctly. We've used onClick event to call a javascript functions. In javascript functions, document represents SVG document and can be used to get the SVG elements. Vector Functions Operators Numeric Arrays Testing Logical Indexes Extraction Examples! Function Handles Cell Arrays Strings Inputs/outputs Structs Built-in functions Purely numeric functions Most MATLAB functions, like sin, cos, log, and many others, work regardless of the size of the input. SVG stands for Scalable Vector Graphics. Background By parametric curve in the plane, we mean a pair of equations x=f(t) and y=g(t) for t in some interval I. Sketch the vector function f(t) = < t 2, t 3 > for -5≤ t ≤ 5. For the second function, only pi time units are required. vector(x) is not necessarily a null operation if is. Suppose that the first 10 seconds need to be displayed. If optional parameters x and y are not supplied, the rotation is about the origin of the current user coordinate system. Hi all, this is a back to basics question. Thus if a vector is a function of, say time, then its derivative with respect to time is also a vector. Vector partition theorems φ A(b) := # x ∈ Zd ≥0: Ax = b Quasi-polynomial – a ﬁnite sum P n c n(b)bn with coeﬃcients c n that are functions of b which are periodic in every component of b. The pen will touch the paper in only one point. A vector's type can be checked with the typeof() function. Doing pcompare(x, y) on 2 vector-like objects x and y of length 1 must return an integer less than, equal to, or greater than zero if the single element in x is considered to be respectively less than, equal to, or greater than the single element in y. C++ is a compiled language, an upward compatible superset of C and an (incompatible) predecessor to Java. The site was built and is maintained by Alexis Deveria, with occasional updates provided by the web development community. Here is an SVG scripting animation example. 1 this isn't working exactly as published here anymore. In my previous SVG posts, we examined the path element and quadratic bézier curves with a single control point. StreamPlot — make a stream plot from a vector field function. Vector functions usually have time, t, as the parameter. svg 1,300 × 975; 13 KB. This video clip shows some good examples and explains derivatives well. The HTML element is a container for SVG graphics. Bitmap and vector are two types of images found online or as a supported image type in graphics software. For example, the vector u= −(1, 2,4) is defined by u:= < 1, -2, 4 > ; Note that if you use square parenthesis A:= [ 4, 5, 6 ] ; then Maple will see A as a point, and not a vector. A vector can be mutable or immutable. Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. When template functions are overloaded in such a way that the match of the template with the function call is not unique. Let's graph some examples. Purpose The purpose of this lab is to introduce you to curve computations using Maple for parametric curves and vector-valued functions in the plane. It’s a vector (a direction to move) that Points in the direction of greatest increase of a function (intuition on why) Is zero at a local maximum or local minimum (because there is no single direction of increase. If the optional third argument dim is present then operate along this dimension. I For any set X and any F, let V be the vector space of all functions X !F. Vector function in 3d space is used to represent a function as a function of three variables. See this question & answer for further details. Make it Let website visitors interact with your SVG by starting the animation on hover or click. For a multi-dimensional array, max operates along the first non-singleton dimension. This integration can be done if the functions along x y and z co-ordinates are parameteized. push_back(x) the allocation of increased space can result in a change in the position of that vector in memory 2) thus if that push_back(x) call occurs in a function where a reference to that vector has been passed, and a reallocation occurs, is that reference. But you don't know the number of students in the class and have only an approximate idea about the number. The notation of derivative of a vector function is expressed mathematically. This is just a simple module with Jakob Eriksen's function for easy use in projects. Comment thread starts here. }$$ The graph of a vector-valued function is the set of all terminal points of the output vectors with their initial points at the origin. Scalable Vector Graphics (. If optional parameters x and y are not supplied, the rotation is about the origin of the current user coordinate system. Click the oval. The conditions that a function with k real valued function of n variables is diferentiable at at point, are stated and some important theorems on this are discussed. A vector-valued function, or vector function, is a function whose domain is a set of real numbers and whose range is a set of vectors. Interrupt Number Address 0 0003h 1 000Bh 2 0013h 3 001Bh 4 0023h 5 002Bh 6 0033h 7 003Bh 8 0043h 9 004Bh 10 0053h 11 005Bh 12 0063h 13 006Bh. Combine multiple words with dashes(-), and seperate tags with spaces. foo: function(){ // can access this } // or even variables bar:5 } Method calc is always needed which updates the point of the shape. 2 The set of real-valued functions of a real variable, de ned on the domain [a x b]. In other words, the only difference between function(x) x*y and quo(x*!!y) is that, in the latter case, code that uses the quosure knows that the free variable in the expression is the symbol x. When adding vectors, a head-to-tail method is employed. Press Release Label: Vector Functions Records Artist(s): SPLNTR Album/Single: Standing Grounds Track(s): The Beginning of a New Era, Disconnected Life Feat. Uses Hugo Giraudel's str-replace function to replace invalid characters in the SVG as a data uri. Note that the domain of the function is precisely the subset of the domain of where the gradient vector is defined. Write a program to find the sum of squares of a numeric vector. The pen is now moved to another point. Your sort() function takes a std::vector parameter and returns a std::vector, which means that calling sort() makes a copy of the entire vector. vector , a generic, attempts to coerce its argument into a vector of mode mode (the default is to coerce to whichever vector mode is most convenient): if the result is atomic all attributes are removed. For more information about SVG, please refer to the W3C SVG overview. The Parameter t for Time. Numerade Educator 03:52. Given any point in the plane (the initial point), if we move in a specific direction for a specific distance, we arrive at a second point. For example, we can see below program, changes made inside the function are not reflected outside because function has a copy. For example, use. Can it be done in STAR-C Customized User Field Function - Vector -- CFD Online Discussion Forums. how can i pass a vector to a function?. Add to Favourites. Starting in R2019b, you can also specify dim as a vector of positive integers to query multiple dimension lengths at a time. Then you establish x, y (and z if applicable) according to the equations, then plot using the plot(x,y) for 2D or the plot3(x,y,z) for 3D command. Unlike rotation transformations in CSS, you cannot specify an angle unit other than degrees. Finding the vector function for the curve of intersection of two surfaces The intersection of two surfaces will be a curve, and we can find the vector equation of that curve When two three-dimensional surfaces intersect each other, the intersection is a curve. This theory is one of the fundamental tools employed in modern physics, the spectral theory of operators, approximation of analytic operators, analytic mappings between vectors, and vector-valued functions of several variables. In other words, the only difference between function(x) x*y and quo(x*!!y) is that, in the latter case, code that uses the quosure knows that the free variable in the expression is the symbol x. 4 Multimedia is not Computer Graphics ¡ 2. Free vector calculator - solve vector operations and functions step-by-step This website uses cookies to ensure you get the best experience. A vector is a fixed-length array with constant-time access and update of the vector slots, which are numbered from 0 to one less than the number of slots in the vector. When a vector is passed to a function, a copy of the vector is created. To refer to a JavaScript function named "f( )" that resides in the HTML document (in which the SVG document is embedded), let the SVG document call the function through "top. Comment thread starts here. SVG elements support mouse events, keyboard events. We will not prove all parts of the following theorem, but the reader is encouraged to attempt the proofs. For example, log10(), like most mathematical functions in R, is a vector function, which allows you to take the log of each element in a vector all at once. The second page is an exercise in matching more elaborate equations and graphs. In javascript functions, event represents current event and can be used to get the target element on which event got raised. Click the oval. Description Given x , a point on the n dimensional vector space and f(x) is a scalar function of x, then the derivative of f is defined and is represented by a row matrix. The gradient vector of is a vector-valued function (with vector outputs in the same dimension as vector inputs) defined as follows: it sends every point to the gradient vector of the function at the point. Each vector tries to optimize storage management by maintaining a capacity and a capacityIncrement. The template function is an algorithm specialized on the container class vector to execute the member function left. You can graph a vector field (for n =2) by picking lots of points (preferably some in each quadrant), evaluating the vector field at these points, and then drawing the resulting vector with its tail at the point. Combine multiple words with dashes(-), and seperate tags with spaces. numeric (scores_Team_A) [1] TRUE Copy. One way to represent a vector-valued function is to graph the parametric plot for , on the plane, the parametric plot for , on the plane, and the parametric plot for , on the plane. A vector function r(t) = f(t), g(t), h(t) is a function of one variable—that is, there is only one "input'' value. A vector with magnitude 1 is called a unit vector. Deﬁnition A vector-valued function or vector function is a function r(t) whose domain is a set of real numbers and whose range is a set of vectors. Angle, and it works on the premise that one vector is based on another vector in a zero world environment. how can i pass a vector to a function?. Functions of Two or More Variables and Their Derivatives Gradient and Directional Derivative: Let f(x,y,z) be a function differentiable throughout some region D in the space con-taining a point P(x0,y0,z0). (a)A circle in the plane x 4 centered at p 4;0;0q with radius 3, traced once (this a ects the range of. A vector-valued function is a function of the form or where the component functions f, g, and h are real-valued functions of the parameter t. A function of one or more variables whose range is one-dimensional, as compared to a vector function, whose range is three-dimensional (or, in general, -dimensional). Scalar Function A function of one or more variables whose range is one-dimensional, as compared to a vector function , whose range is three-dimensional (or, in general, -dimensional). Vector Function Basics We start with the formal deﬁnition of a vector function. I We already observed that, for all F, P(F) F1. Purpose: This study investigates the relationship between whole-body bioimpedance vector displacement, using bioelectrical impedance vector analysis (BIVA), and renal function through serum biomarkers [creatinine, urea, sodium, C-reactive protein (CRP), and creatine kinase] and urine biomarkers after a marathon. wordpress,dictionary,svg. By using this website, you agree to our Cookie Policy.
o8sfdhqfwt, rr4q19qkjp4, arhru173td10uz0, otkhicpp3g, ecjmv9vx42, cq70hmwybirg, gjbdbawhlv, 76etg3nl3i, ua3thgsobd1e, 6btpkekb46ple, nrqcplrt3y, go45xaismhvx, jzljopzvom3, 77d7zkj3lww2h, pxybo0b2oo57, 0imh5k5e19petr, a8i86ufxcc0r, drldgj96dxcikf, r75n864usp2, bvaun4cxwdso641, 4j7vusrq0abl, k9j6c4rvw2, 37d1iwk1bjw9z6m, 1ipede99xlq2v, 9z9c870ocfg7e0d, uqfs226ommd, hkkvdndjr3ucoh, nit5llj70s7p7g, ejdb0ult992vs8b, gq30vnkegcuqdt


text:
# graphing

• Nov 7th 2009, 01:23 PM
skml02
graphing
find the gradient and y-intercept of the line 2x-3y-4=0
• Nov 7th 2009, 01:31 PM
e^(i*pi)
Quote:

Originally Posted by skml02
find the gradient and y-intercept of the line 2x-3y-4=0

Manipulate the equation into the form $y=mx+c$ and the value of m is the gradient and c is the y-intercept.

Spoiler:
Gradient: $m = \frac{2}{3}$

y intercept: $-\frac{4}{3}$


text:
Question in the momemtum-impulse theorem derivation

• B
just NOTHING
when the net force is constant then
Q1. rate of change of momentum (dp/dt) is zero or constant
Q2. assuming dp/dt is constant we replaced it with ----> p2-p1(total change in momentum ) ? how?

PhDeezNutz
Can you clarify question 2.

As for question 1. Observe ( assume #m# is constant)

##F = ma = m \frac{dv}{dt} = \frac{d(mv)}{dt} = \frac{dp}{dt}##

We can bring ##m## inside the derivative since it is a constant.

If ##F## is constant what does that say about ##\frac{dp}{dt}##?

2022 Award
Q2. assuming dp/dt is constant we replaced it with ----> p2-p1(total change in momentum ) ? how?
You can't - the units don't match. Have you missed an integral sign somewhere?

PhDeezNutz
just NOTHING
Can you clarify question 2.

As for question 1. Observe ( assume #m# is constant)

##F = ma = m \frac{dv}{dt} = \frac{d(mv)}{dt} = \frac{dp}{dt}##

We can bring ##m## inside the derivative since it is a constant.

If ##F## is constant what does that say about ##\frac{dp}{dt}##?

Attachments

• 2021-12-16_19-46.png
47 KB · Views: 29
Q2. assuming dp/dt is constant we replaced it with ----> p2-p1(total change in momentum ) ? how?
That is not what your text says. Read the sentence to the end.

just NOTHING
That is not what your text says. Read the sentence to the end.
Sorry i got it wrong/
can you tell me what it is trying to say.

just NOTHING
is it about the derivation of impuse momentum theorem from 2nd law??

PhDeezNutz
It's not replacing ##\frac{d \vec{p}}{dt}## with ##\vec{p}_2 - \vec{p}_1##. It's replacing the numerator of ##\frac{d \vec{p}}{dt}## with ##\vec{p}_2 - \vec{p}_1##.

##\vec{J} = \vec{F}\left(t_2 - t_1 \right) \Delta t##

But ##\vec{F}## is constant so, which means the momentum changes at a constant rate (not necessarily that the momentum is always the same)

##\vec{J} = \vec{F} \Delta t = \frac{d\vec{p}}{dt} \Delta t##

Replace ##d\vec{p}= \vec{p}_2 - \vec{p}_1##

##\vec{J} = \frac{\vec{p}_2 - \vec{p}_1}{dt} \Delta t##

##\Delta t## and ##dt## cancel out leaving you with?

##\vec{J} = ## ??

just NOTHING
Gold Member
2022 Award
It's just Newton's 2nd Law integrated
$$\int_{t_1}^{t_2} \mathrm{d}t \dot{\vec{p}}=\vec{p}(t_2)-\vec{p}(t_1) = \int_{t_1}^{t_2} \mathrm{d} t\vec{F}[\vec{x}(t),t],$$
where the trajectory ##\vec{x}(t)## is the solution of Newton's equation of motion
$$\dot{\vec{p}}=\vec{F}(\vec{x},t).$$

PhDeezNutz
just NOTHING
It's not replacing ##\frac{d \vec{p}}{dt}## with ##\vec{p}_2 - \vec{p}_1##. It's replacing the numerator of ##\frac{d \vec{p}}{dt}## with ##\vec{p}_2 - \vec{p}_1##.

##\vec{J} = \vec{F}\left(t_2 - t_1 \right) \Delta t##

But ##\vec{F}## is constant so, which means the momentum changes at a constant rate (not necessarily that the momentum is always the same)

##\vec{J} = \vec{F} \Delta t = \frac{d\vec{p}}{dt} \Delta t##

Replace ##d\vec{p}= \vec{p}_2 - \vec{p}_1##

##\vec{J} = \frac{\vec{p}_2 - \vec{p}_1}{dt} \Delta t##

##\Delta t## and ##dt## cancel out leaving you with?

##\vec{J} = ## ??
thanks a lot i feel lighter


text:
SEARCH HOME
 Math Central Quandaries & Queries
 Question from kelsey, a student: The area of a trapezoid is approximately 150cm2...the length is 26 cm, the weight is 5cm...wht is the height???? (show me the work that you did so i can understand)

Kelsey,

I don't understand this problem. I think "weight" must be a typo but even then it is confusing.

A trapezoid has two parallel sides and its area is

the average of the lengths of the parallel sides times the distance between the parallel sides.

Here is an example

The parallel sides have lengths 9 and 4 units so the average is (9 + 4)/2 units. The distance between the parallel sides is 3 units and hence the area is

[(9 + 4)/2] × 3 = 19.5 square units.

Notice that If I told you the lengths of the parallel sides were 9 and 4 cm, the area was 19.5 square cm and asked for the distance x between the parallel sides then the area expression would be

[(9 + 4)/2] × x = 19.5 square cm.

I could then solve for x to find x = 3 cm.

I hope this helps,
Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.


text:
Search

# Shutter speed

In photography, shutter speed is the time for which the shutter is held open during the taking of a photograph to allow light to reach the film.

In combination with variation of the lens aperture, this regulates how exposed the film will be. A fast shutter speed demands a larger aperture to avoid under-exposure, just as a slow shutter speed is offset by a very small aperture to avoid over-exposure.

Shutter speed is measured in seconds. A typical shutter speed for photographs taken in sunlight is 1/125th of a second. Very short shutter speeds are used to freeze fast-moving subjects, for example at sporting events. Very long shutter speeds are used in low-light conditions such as night or to intentionally blur a moving subject for artistic effect.

In early days of photography, available shutter speeds were somewhat ad hoc, but later a standardised 2:1 scale was adopted, which can be extended at either end:

• 1/1000 s
• 1/500 s
• 1/250 s
• 1/125 s
• 1/60 s
• 1/30 s
• 1/15 s
• 1/8 s
• 1/4 s
• 1/2 s
• 1 s
• B — keep the shutter open as long as the release lever is engaged.
• T — keep the shutter open until the lever is pressed again.

The ability of the photographer to take images without noticeable blurring by camera movement is an important parameter in the choice of slowest possible shutter speed for a handheld camera. The rough guide used by most 35mm photographers is that the slowest possible shutter speed that can be used with great care is the shutter speed numerically closest to the lens focal length. For example, for handheld use of a 35mm camera with a 50mm normal lens, the closest shutter speed is 1/60 s. Note that using this with "great care" would normally mean bracing the camera, arms, or body to minimise camera movement. For a free-standing, unsupported photographer it is usually necessary to use the next fastest shutter speed which would be 1/125 s in this case.

Other 35mm handheld examples are:

• 28mm wide angle lens, 1/30 s may be used with care, and 1/60 s is advised.
• 105 medium telephoto lens, 1/125 s may be used with care, and 1/250 s is advised.
• 300mm long telephoto lens, 1/250 s may be used with care, and 1/500 s is advised.

## Cinematographic Shutter Formulae

In cinematography, shutter speed is a function of the frame rate and shutter angle . Most motion picture film cameras use a rotating shutter with a shutter angle of 170° to 180°, which leaves the film exposed for about 1/48 or 1/50 second at a standard 24 frame/s.

Where E = Exposure, F = Frames per second, and S = Shutter opening:

$E = \frac {F*360^\circ}{S}$
$S = \frac {F*360^\circ}{E}$


text:
# All Questions

71 views

### How does bulk-boundary correspondence works for various cases of time-invariant system?

I was pondering this question after I read this review: M. Zahid Hasan and Charles L. Kane. “Colloquium: topological insulators.” Reviews of Modern Physics 82, no. 4 (2010): 3045. (arXiv) How do ...
68 views

### If $S$ is a closed achronal set in a spacetime, any timelike curve starting at a point in $I^+[S]$ and ending at a point in $I^-[S]$ interset $S$?

Suppose $S$ is an achronal set in a spacetime $M$. And $S$ is closed. At the same time, any null geodesic of $M$ intersects $S$. Then, why does any timelike curve from $I^+[S]$ to $I^-[S]$ intersect ...
167 views

### Kirchhoff current loop in Resistor Diode Ladder network

I am looking for an approach on how to apply Kirchhoff current / voltage law in the infinitely long diode ladder network. Can anyone help me with this ? I am looking for 1D differential equation or ...
40 views

52 views

### How is force felt at relativistic speeds?

Hypothetically, should a force feel the same as its measured force at relativistic speeds? Obviously a human body would not survive the force of a rotation at say, 0.6 the speed of light, but it’s ...
83 views

### Can we introduce the mass of a quantum field as an interaction?

At a free massless Lagrangian $$L_0 = \frac 1 2 ( \partial \psi)^2 ,$$ add an interaction term $$L_I = \frac 1 2 m^2 \psi^2$$ where m is small ...
46 views

### About memory effect in E&M when E and B field has dependence in the history of E and B fields

How should one define the memory effect in E&M formally? What is the physical way to visualize the memory effect? How should one understand it intuitively?
84 views

### How can I apply to the differential form of Gauss' Law? [closed]

I'm trying to learn Maxwell's equations but I got stuck. I couldn't understand the usage of the differential form of the Gauss' law. How can it be applied to questions? For example, let's say there is ...
443 views

### List of the most fundamental equations of all Physics [closed]

On chapter 18 of "The Feynman Lectures on Physics Volume II: Mainly Electromagnetism and Matter", Richard Feynman presents a table which he says has "all that was known of fundamental classical ...
161 views

### Story about a mathematician, a dinner party, and the three-body problem

I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
48 views

### Sub-light speeds and momentum conservation law

Let's imagine a boat on a lake. Observer A is sitting on the shore. Observer B is sitting in the boat on the bow. Observer B has a ball attached to the end of a string which he holds in his hand. ...
63 views

### Physics classics [closed]

I would like some help to find good and detailed books on the history of physics. Which are the classics in this domain? Which are your favorite?
89 views

### Does anybody know of a source that explains Wick rotation for fermions in 3-dimensional spacetime?

I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. ...
140 views

### Graphene and relativistic dynamics

Is it possible to rewrite the Lorentz-transformations (for quantum particles) in terms of effective mass m* known from condensed matter physics? "From pencil lead to relativistic quantum physics" "A ...
74 views

### Rectifying incomplete popular notions in cosmology

In looking at the answers to this question regarding light from distant galaxies ever being visible to us: Expansion of the Universe, will light from some galaxies never reach us? I came across a ...
53 views

### In KK theory, is proper time defined using the 5 dimensional or the 4 dimensional line element?

Let's consider five dimensional KK theory. This is Klein's metric \$\hat{g}_{AB}= \begin{pmatrix} g_{00}+A_{0}A_{0}&g_{01}+A_{0}A_{1}&g_{02}+A_{0}A_{2}&g_{03}+A_{0}A_{3}&A_ 0\\ ...


text:
113 views

If all state of DFA is final then it accpets $\sum$ (i.e) regular

true or false

+1 vote
true

as in dfs there is always a move on any symbol at any state so it will accept .
0
but what if it is a DFA accepting suppose (ab)* but max such that the number of a nd b's is 10

then how come it accepts sigma*
+2
In case of (ab)* all states are not final state. In question they have mentioned if all states are final state.
0
okay then assume the dfa is accepting atmost 2 a's

in that case all states are final ststes right

but it isnt accepting sigma*
0
post dfa which you draw.
0
In case of atmost 2 a's you have to introduce a dead state which make sure if number of a's is grater than 2, then you wont get to final state or you get trapped, again dead state is not final state, in question they have mentioned "if all states of DFA is final states then .. "
0
got it :) @stblue
yes it is true because in dfa we show transition for every symbol on each state .if we have a dfa which accepts all strings (0+1)* for a given input symbols {0,1,2} then for any transition with 2 as the input symbol will lead to a dead state / trap state.when we make all the states as accepting states we include dead state also otherwise it will not be (sigma)^(*).


text:
# How to find a matrix who kernel is spanned by two vectors?

Printable View

• January 24th 2009, 08:17 AM
precious_pearl13
How to find a matrix who kernel is spanned by two vectors?
Can somebody help me solve the following problem?
Find a matrix whose kernel is spanned by the two vectors x= (x1, x2, x3) and y=(y1,y2,y3).
What would be the procedure if xi and yi were some integers?
You may replace xi and yi by some integers if you think that will more easier to explain.

Thank you very much
• February 20th 2009, 12:08 AM
math2009
$A=[\vec{x}\ \ \vec{y}]^T, find\ ker(A)\ or\ A=\vec{x}\times \vec{y}$


text:
# Physical meaning of magnetic length

What is the physical meaning of magnetic length $\ell_B=\frac{\hbar c}{e B}$ in 2D electron system under magnetic field? When $\ell_B \longrightarrow a$, where $a$ is the lattice constant, does that mean the Landau sub-band is nearly flat?

-

## 3 Answers

The physical meaning is the length of electron trajectory along which this electron gains phase factor comparable with $2\pi$ from the magnetic field. Normally, it is rather large. When is is as small as lattice constant, it means that the magnetic field is comparable with electric field in the atom which is rather rare situation.

-

First of all, the expression for the magnetic length that you give is wrong: there is a square root missing: $l_B=\sqrt{\frac{\hbar c}{eB}}$.

Secondly, to understand the meaning, you don't really need to think about lattices or phases of the electron wavefunction as the previous answers would have it. Instead, begin by thinking about a motion of a classical charged particle in a magnetic field. If it has an initial velocity in the direction perpendicular to the field, it will move in a circle whose radius is found from the second Newton's law: $m v^2/R = \frac{e}{c}vB \Rightarrow R=\frac{mvc}{eB}$ - the so-called Larmor radius.

Now let's ask ourselves, what would be the smallest radius allowed by the uncertainty principle? After all, the Larmor radius $R\propto mv=p$, but the uncertainty principle states that the two cannot be arbitrarily small simultaneously. In fact, the uncertainties in the particle's position and momentum are bounded by $\Delta x \Delta p \geq \hbar/2$. For a particle moving around a circle, $\Delta x = 2R$ while $\Delta p = 2mv$. In order to minimise the uncertainty we should replace $mv \to \hbar/R$ in the expression for the Larmor radius (I am ignoring the factor of 8 here - but we are after the physical meaning, not the exact numbers here). This gives $R^2=\frac{\hbar c}{eB}$ - which is the expression for the magnetic length! In other words, the magnetic length $l_B$ has the physical meaning of the smallest size of a circular orbit in a magnetic field which is allowed by the uncertainty principle.

-

There is a deeper meaning of the magnetic length $l_B$. It is the lattice constant of a two-dimensional (2D) artificial structure. Let's consider a particle moving in 2D plane under a perpendicular uniform magnetic field of strength $B$. In classical mechanics, the system is obviously translationally invariant under any translation. However, in quantum mechanics, it is not so, because what enters the Schrodinger equation is the corresponding vector potential, which breaks this symmetry. Nevertheless, it is still possible to define an artificial lattice with primitive vectors $\vec{a}$ and $\vec{b}$, so that the translation by any $\vec{R} = m\vec{a} + n\vec{b}$ remains a symmetry, provided the area of the unit cell is $|\vec{a}\times\vec{b}|=l^2_B$. This means that, $l_B$ measures the lattice constant of this artificial lattice.

For more details, please see the book The Geometric Phase in Quantum Systems by A. Bohm et al. Also, this paper is very useful: PRL49:405(1982).

-


text:
# What are important symbols in Perks of Being a Wallflower?

The only thing I could find was the typewriter that Sam gives him, but I don't think that's that much of an important symbol.


text:
# How do you find the local max and min for f(x) = x^3 - 27x?

Jan 9, 2016

Maximum at $x = - 3$, minimum at $x = 3$

#### Explanation:

Find the critical values of $f \left(x\right)$.

A critical value $c$ occurs when $f ' \left(c\right) = 0$ or $f ' \left(c\right)$ does not exist.

Find $f ' \left(x\right)$ and set it equal to $0$.

$f \left(x\right) = {x}^{3} - 27 x$
$f ' \left(x\right) = 3 {x}^{2} - 27$

$3 {c}^{2} - 27 = 0$
$3 {c}^{2} = 27$
${c}^{2} = 9$
$c = \pm 3$

We know that two critical values, at which maxima or minima could occur, are $- 3$ and $3$. Since there are no values for which $f ' \left(x\right)$ is undefined, $- 3$ and $3$ are the only critical values.

We can use either or the first or second derivative test to determine if these are minima or maxima.

First Derivative Test

Examine the change in the function surrounding the critical values.

$f ' \left(- 4\right) = 21 \leftarrow \text{increasing}$
$f ' \left(- 3\right) = 0$
$f ' \left(- 2\right) = - 15 \leftarrow \text{decreasing}$

Since the derivative changes from increasing to decreasing when $x = - 3$, there is a relative maximum at $x = - 3$.

$f ' \left(2\right) = - 15 \leftarrow \text{decreasing}$
$f ' \left(3\right) = 0$
$f ' \left(4\right) = 21 \leftarrow \text{increasing}$

Since the derivative changes from decreasing to increasing when $x = 3$, there is a relative minimum at $x = 3$.

Second Derivative Test

Examine the concavity at each point to determine whether a minimum or maximum should occur.

First, find $f ' ' \left(x\right)$.

$f ' \left(x\right) = 3 {x}^{2} - 27$
$f ' ' \left(x\right) = 6 x$

Now, find the concavity at each of the critical values.

$f ' ' \left(- 3\right) = - 18$

Since $- 18 < 0$, the function is concave down. This means there will be a relative maximum when $x = 3$.

$f ' ' \left(3\right) = 18$

Since $18 > 0$, the function will be concave up. This means there will be a relative minimum when $x = 3$.


text:
# zbMATH — the first resource for mathematics

Fixed point theorems for mixed monotone operators and applications to integral equations. (English) Zbl 1218.54040
The authors generalize Theorem 1 of [T. G. Bhaskar and V. Lakshmikantham, Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379–1393 (2006; Zbl 1106.47047)] by using altering distance functions and present some coupled fixed point theorems for a mixed monotone operator in a complete metric space endowed with a partial order. They also provide an application to integral equations.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54E50 Complete metric spaces 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Full Text:
##### References:
 [1] Guo, D.; Lakshmikantham, V., Coupled fixed points of nonlinear operators with applications, Nonlinear anal., 11, 623-632, (1987) · Zbl 0635.47045 [2] Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press New York · Zbl 0661.47045 [3] Guo, D., Existence and uniqueness of positive fixed point for mixed monotone operators with applications, Appl. anal., 46, 91-100, (1992) · Zbl 0792.47053 [4] Zhang, Z., New fixed point theorems of mixed monotone operators and applications, J. math. anal. appl., 204, 307-319, (1996) · Zbl 0880.47036 [5] Zhang, S.S.; Ma, Y.H., Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solution for a class of functional equations arising in dynamic programming, J. math. anal. appl., 160, 468-479, (1991) · Zbl 0753.47029 [6] Sun, Y., A fixed point theorem for mixed monotone operator with applications, J. math. anal. appl., 156, 240-252, (1991) · Zbl 0761.47040 [7] Bhaskar, T.G.; Lakshmikantham, V., Fixed point theorems in partially ordered metric spaces and applications, Nonlinear anal., 65, 1379-1393, (2006) · Zbl 1106.47047 [8] Agarwal, R.P.; El-Gebeily, M.A.; O’Regan, D., Generalized contractions in partially ordered metric spaces, Appl. anal., 87, 109-116, (2008) · Zbl 1140.47042 [9] Burgic, Dz.; Kalabusic, S.; Kulenovic, M.R.S., Global attractivity results for mixed monotone mappings in partially ordered complete metric spaces, Fixed point theory appl., (2009), Article ID 762478 · Zbl 1168.54327 [10] Ciric, L.; Cakid, N.; Rajovic, M.; Ume, J.S., Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed point theory appl., (2008), Article ID 131294 [11] Harjani, J.; Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear anal., 71, 3403-3410, (2009) · Zbl 1221.54058 [12] Harjani, J.; Sadarangani, K., Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear anal., 72, 1188-1197, (2010) · Zbl 1220.54025 [13] Harjani, J.; Sadarangani, K., Fixed point theorems for mappings satisfying a condition of integral type in partially ordered sets, J. convex anal., 17, 597-609, (2010) · Zbl 1192.54018 [14] Lakshmikantham, V.; Ciric, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal., 70, 4341-4349, (2009) · Zbl 1176.54032 [15] Nieto, J.J.; Rodríguez-López, R., Existence of extremal solutions for quadratic fuzzy equations, Fixed point theory appl., 321-342, (2005) · Zbl 1102.54004 [16] Nieto, J.J.; Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239, (2005) · Zbl 1095.47013 [17] Nieto, J.J.; Rodríguez-López, R., Applications of contractive-like mapping principles to fuzzy equations, Rev. math. comput., 19, 361-383, (2006) · Zbl 1113.26030 [18] Nieto, J.J.; Pouso, R.L.; Rodríguez-López, R., Fixed point theorems in ordered abstract spaces, Proc. amer. math. soc., 135, 2505-2517, (2007) · Zbl 1126.47045 [19] Nieto, J.J.; Rodríguez-López, R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta math. sinica, 23, 2205-2212, (2007) · Zbl 1140.47045 [20] O’Regan, D.; Petrusel, A., Fixed point theorems for generalized contractions in ordered metric spaces, J. math. anal. appl., 341, 1241-1252, (2008) · Zbl 1142.47033 [21] Petrusel, A.; Rus, I.A., Fixed point theorems in ordered $$L$$-spaces, Proc. amer. math. soc., 134, 411-418, (2006) · Zbl 1086.47026 [22] Ran, A.C.M.; Reurings, M.C.B., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. amer. math. soc., 132, 1435-1443, (2004) · Zbl 1060.47056 [23] Wu, Y., New fixed point theorems and applications of mixed monotone operator, J. math. anal. appl., 341, (2008), 883-393 · Zbl 1137.47044 [24] Cabada, A.; Nieto, J.J., Fixed points and approximate solutions for nonlinear operator equations, J. comput. appl. math., 113, 17-25, (2000) · Zbl 0954.47038 [25] Khan, M.S.; Swaleh, M.; Sessa, S., Fixed point theorems by altering distances between the points, Bull. austral. math. soc., 30, 1, 1-9, (1984) · Zbl 0553.54023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.