Operations Definition and 317 Threads

I've been studying the book "Numerical Optimization" by Jorge Nocedal and Stephan J. Wright published by Springer, 1999. I'm puzzled by the use of the Laplacian operator ##\nabla^2## in chapter 10 on nonlinear least squares and in the appendix to define the Hessian matrix. The following is from...

Can I post Operations research problems in Physics Forum? If yes, where, can I post it?

This was a great use of technology last week when a large parking garage collapsed in New York City, and it was too dangerous to send in FireFighters to search for injured and trapped people. FDNY has used Drones for a while now, and has a new Robot Dog that is able to navigate pretty difficult...

TL;DR Summary: My problems comes to a vector expression which needs to be simplified I got an expression pi=εijksk,lul,j Here s and u are two vectors. What will be the vector expression of this vector p with curl s, curl u, and other operations?

A group can be defined by the following three properties. (Source: wikipedia) Is there any example of an operation that fails the associativity test, but meets the other two tests? I'll refer to this hypothetical entity as an almost-group for the purposes of this post lacking any knowledge...

So the chain rule for second derivatives is $$ \frac {d^2 y} {d t^2} = \frac{d}{dx}(\frac {dy} {dx}) \cdot \frac {dx} {dt} \cdot \frac {dx} {dt} + \frac {dy} {dx} \cdot \frac {d^2 x} {d t^2} = \frac{d^2 y}{d x^2} \cdot (\frac {dx} {dt})^2 + \frac {dy} {dx} \cdot \frac {d^2 x} {d t^2}$$ Today I...

This is just basic algebra for the energy-momentum relationship, but the calculations confuse me. May I ask what is wrong with my concept or calculation causing the following problem. Maybe it's because I'm getting older, my ability to think and calculate has declined...

I am really confused by this question as there are multiple possible answers of this question, so I am asking this. There is very minimum role of GFS master in writing and reading operations.. You can either go through these or just tell me what is the correct answer if you are bored to go...

I am really confused by this question as there are multiple possible answers of this question, so I am asking this. There is very minimum role of GFS master in writing and reading operations.. You can either go through these or just tell me what is the correct answer if you are bored to go...

Dear Everybody, I have some trouble with this problem: Finding a sequence of elementary matrix for this matrix A. Let ##A=\begin{bmatrix} 4 & -1 \\ 3& -1\end{bmatrix}##. I first used the ##\frac{1}{4}R1##-> ##R1##. So the ##E_1=\begin{bmatrix} \frac{1}{4} & 0 \\ 0& 1\end{bmatrix}##. So the...

For example: h(x)=f(x)+g(x) If f(x) and g(x) are real numbers and real numbers can be added, subtracted, multiplied and divided (except by 0). why do we insist that the x in f(x) and g(x) be {x: x∈ dom f ∩ dom g}? My thoughts: The equality of two functions requires two criteria: 1) They operate...

Hi PF, I've one question about vector spaces. There is only one way to define the operations of a vector space? For example if V is a vector space there is other way to define their operations like scalar multiplication or the sums of their elements and that the result is also a vector space?

Hey! :giggle: I am looking at the following: a) Create a class QuadraticPolyonym that describes a polynomial of second degree, i.e. of the form $P(x)=ax^2+bx+c, a\neq 0$.The coefficients have to be givenas arguments at the construction ofan instance of the class. Implement a method...

Hi guys, I am losing my mind over this passage... I cannot understand how to get from the first expression with the cross products to the second ##\dot{\textbf{r}}(\textbf{r}\cdot \textbf{r})-\textbf{r}(\textbf{r}\cdot\dot{\textbf{r}})##

I started a degree in MS operations research but now am having second thoughts. I took a class in statistics and optimization using linear algebra. But what I enjoy most is programming in python.I am also teaching myself c++. People say industrial engineer is more about analyzing data while...

Here is how my teacher solved this: I understand what the nabla operator does, ##∇\cdot\vec v## means that I am supposed to calculate ##\sum_{n=1}^3\frac {d\vec v} {dx_n}## where ##x_n## are cylindrical coordinates and ##\vec e_3 = \vec e_z##. I understand why ##∇\cdot\vec v = 0##, I would get...

I am going to start doing this degree MS Operations research https://www.isye.gatech.edu/academics/masters/ms-operations-research/curriculum. But I am wondering if you can actually get a job with a degree in operations research, I been doing research and people say operations research is more...

Given: x\in A\cap B\leftrightarrow x\in A\wedge x\in B x\in A\cup B\leftrightarrow x\in A\vee x\in B x\in A-B\leftrightarrow x\in A\wedge x\notin B A=B\leftrightarrow(\forall x(x\in A\leftrightarrow x\in B)) Then prove using only the above and the laws of logic that: ™ (A\cup B)-(A\cap...

1) If we have two functions C(y, r) and I(y, r) can we write: ∂C/∂I×∂I/∂r=∂C/∂r ? Can we also write ∂I/∂C=1/(∂C/∂I) ?

$\left[ \begin{array}{rrrr|r} 1& -5& 4& 0&0\\ 0& 1& 0& 1&0\\ 0& 0& 3& 0&0\\ 0& 0& 0& 2&0 \end{array}\right] $ OK my first move on this is $r_3/3$ and $r_4/2$. $\left[ \begin{array}{rrrr|r} 1& -5& 4& 0&0\\ 0& 1& 0& 1&0\\ 0& 0& 1& 0&0\\ 0& 0& 0& 1&0 \end{array}\right]$ $r_2-r_4=r_2\quad$ doesn't...

I'm trying to understand the precise reason we claim that a value being conserved means that the system in question is invariant under the corresponding symmetry transformation. Take parity for example. If the parity operator satisfies the commutation relation ##[P, H] = 0## for a given...

Part a: Gate H X Y Z S T R_x R_y Theta pi pi pi pi pi/2 pi/4 pi/2 pi/2 n_alpha (1/sqrt(2))*(1,0,1) (1,0,0) (0,1,0) (0,0,1) (0,0,1) (0,0,1) (1,0,0) (0,1,0) Using the info from the table and equation 1, I find: U_H=(i/sqrt(2))*[1,1;1,-1] U_X=i*[0,1;1,0] U_Y=i*[0,-i;i,0] U_Z=i*[1,0;0,-1]...

I am trying to investigate my doubts that reversible operations can model (or at least mimic) information copy process. For simple model I take two numbers ##A \neq B##. Now I can't copy value of A into B without erasing (irreversibly) value of B. However I can use transformation that replaces...

Dear all, I have two small questions regarding operations on sets. (1) Prove that \[A\subseteq B\subseteq C\] if and only if \[A\cup B=B\cap C\]. (2) What can you say about sets A and B if \[A\B = B\] ? In the case of (1), I have used a Venn diagram and I understand why it is true, but...

I have a question on tensor-product states that I'd like to ask, thanks in advance! 1. The basis vector of a two-particle state can be written as ##|\mu_i \rangle |\nu_j \rangle## for orthonormal vectors ##|\mu_i \rangle, |\nu_j \rangle## spanning their single-particle Hilbert spaces. The inner...

How do we deal with missing solutions when we have to solve equations with non-reversible operations? You can always check the solutions to see if solutions are extraneous or not, but how do we know weather or not there are missing solutions to the problem?

Hi, Could you please help me with the queries below? Please have a look on this attachment. Question 1: It says, "Because the processor cannot know when an interrupt will occur, it automatically saves on the register stack status information about the program that is executing at the time...

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Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...

why x2 . y2 = (x-y) (x+y) and xy . y2 cannot be (x-y) (y+y)

Homework Statement Prove or disprove: if A⊆B∪C, then A⊆B or A⊆C. Homework EquationsThe Attempt at a Solution I am unsure of how to go about proving this. I know that A is a subset of B union C then A is a subset of B or A is a subset of C and I understand what a subset is and what a union is...

Homework Statement Hi, the problem states to draw a Venn Diagram for A\cap(B-C) Homework Equations (B - C) means include all elements in the set B that are not in C. Definition from my book: Let A and B be sets. The difference of A and B, denoted by A - B, is the set containing those...

Determine which of the folllowing operations are Associative, Identity, or Inverse $\textit{Additive on $\mathbb{Z}$}$ $\textit{Subtraction on $\mathbb{N}$}$ $\textit{Division on $\mathbb{R}$}$ $\textit{Division on $\mathbb{Z}/\{0\}$}$ $\textit{Composition on $D_4$}$ $\textit{Composition on the...

To my understanding, a matrix is just a way of representing a system of equations in an organized format. So for example, if we have some system of equations, we can get them into standard form, and translate them into what's known as an augmented matrix. This is similar to using synthetic...

My lecture notes and recommended textbook Hillier and Liberman are not enough for me. My methodology and formulation of problems still seems like too much guess-work. Can anyone recommend any good resources, lecture notes or textbooks, for stochastic DP? Many thanks

Homework Statement Hi I am looking at this question attached part c). 2. Homework Equations The Attempt at a SolutionI can by my notes which tell me that if I reach a column with a negative reduced cost and also all of that column is negative, then to stop, as z is unbounded, to conclude...

Is there a notion of “coherent” operations on Jacobian matrices? By this I mean, an operation on a Jacobian matrix A that yields a new matrix A' that is itself a Jacobian matrix of some (other) system of functions. You can ascertain whether A' is coherent by integrating its partials of one...

Hey! :o Let A be a regular ($n\times n$)-Matrix, for which the Gauss algorithm is possible. If we choose as the right side $b$ the unit vectors $$e^{(1)}=(1, 0, \ldots , 0)^T, \ldots , e^{(n)}=(0, \ldots , 0, 1 )^T$$ and calculate the corresponding solutions $x^{(1)}, \ldots , x^{(n)}$ then...

Homework Statement [/B]Homework Equations Division by two means moving the bits right by 1 unit. 2's complement = 1's complement + 1 The Attempt at a Solution For Question: 6 Number is 11010110 This is 2's complement. So to find original number we subtract by 1 and get: 11010101 Now we do 1's...

Hi, I have derived a matrix from a system of ODE, and the matrix looked pretty bad at first. Then recently, I tried the Gauss elimination, followed by the exponential application on the matrix (e^[A]) and after another Gauss elimination, it turned "down" to the Identity matrix. This is awfully...

Hello! (Wave) It is stated in my notes that the calculation of $a^{n-1} \pmod{n}$ by fast exponentiation takes $O(\log{n})$ arithmetic operations and $O((\log{n})^3)$ bit operations.By using fast exponentiation, in order to calculate $a^{n-1} \pmod{n}$ we write $n-1$ as $n-1=n_0+2 n_1+ \dots+...

For example, Richard Feynman used his own symbols for trigonometric functions and their inverses. I write logarithms differently. I make a symbol which is like a radical, but instead of a √-shape at the end, it is the Greek letter lambda (λ). Under the radical shape is the argument, and below...

fresh_42 submitted a new PF Insights post How to Tell Operations, Operators, Functionals and Representations Apart Continue reading the Original PF Insights Post.

Hey all, I'm currently working on my CS degree with a mathematics minor. After this Fall, I will only have one more course to take to finish my minor. I'm debating between Linear Algebra and Deterministic Operations Research. I do have other options, but these seem to be most applicable to CS...

For finding the inverse of a matrix A, we convert the expression A = I A (where I is identity matrix), such that we get I = B A ( here B is inverse of matrix A) by employing elementary row or column operations. But why do these operations work? Why does changing elements of a complete row by...

I'm a high school junior trying to figure out what I may want to major in. I know that a lot of students change their majors, but I think I should at least have some idea, as it's relevant for deciding where to apply. One of my top choices is Cal Poly SLO, which requires applicants to declare...

Hey all, Posting once again. I'm only in my second class on programming ever (with no prior experience to classes). I'm learning about move/copy operations. My textbook says that the move operations is "obviously more efficient than the copy" operation, but it doesn't explain why. Is it more...

To what extent is the PEMDAS order of operations convention, and to what extent is this convention significant? For example, how would math change if we stipulated that ##1+2*3 = 3*3 = 9##? Would it be the same or would it be completely different?

It's strange to me that multiplication and division are considered fundamental operations. It makes sense for me that addition is a fundamental operation but multiplication is just like a function or algorithm that takes several numbers and apply additions. This is true even for multiplication...

Hey all, I majored in Physics with a solid GPA as an undergrad and then I joined the Navy as an officer and spent all of my time in Special Operations with significant combat leadership experience. During my time in I also earned a masters in Physics from the Naval Postgraduate School where I...