Elements Definition and 1000 Threads

Hello this is not a homework, just studying for the exam, and : Homework Statement Consider E a linear space with dot product (.,.) and the norm ||x|| = sqrt(x,x) a and b two orthogonals elements of E Find the value of ||a+ b|| et||a- b|| and ||a+ b||-||a- b|| Homework Equations...

Hello all, I am struggling with this relatively simple task. In a university with 88 students, each student can choose to participate in 3 afternoon activities: activity A, activity B and activity C. Each student can choose to participate in some activities, all or none. 33 students...

I'm trying to understand how Hamiltonian matrices are built for optical applications. In the excerpts below, from the book "Optically polarized atoms: understanding light-atom interaction", what I don't understand is: Why are the \mu B parts not diagonal? If the Hamiltonian is \vec{\mu} \cdot...

In a matrix the sum of element of a matrix in a row times it's co factor of that elemt gives the determinant value, but why does the sum of element of a matrix times cofactor of different row is always zero?

In quantum mechanics, observable variables are represented by operators, and thus can be replaced by matrix in a certain basis. If we have H|n>=E(n)|n>, where |n> are eigenfunctions of Hamilton matrix. Here is the problem: what's the physical meaning of <m|P|n>, namely off-diagonal elements of...

Homework Statement b(B) = cls(B) \ Int(B) where b(B) is the boundary, cls is the closure, and int is the interior of set B. This was not hard for me to prove by picking elements and showing that the sets were contained in one another. However, I decided it would be fun to try to derive it by...

Homework Statement Prove that a set with n elements has \frac{n(n-1)(n-2)}{6} subsets containing exactly three elements whenever n is an integer greater than or equal to 3. Our professor wants us to use Induction. Homework Equations P(n) = \frac{n(n-1)(n-2)}{6} n \geq 3 The...

In Heath's commentary on Euclid's Elements he stresses the importance of the application of areas (Book I Proposition 44) with, "The marvellous ingenuity of the solution is indeed worth of the 'godlike men of old'...". The proposition, "To a given straight line to apply, in a given...

Hey everyone Let's say I have two generators, a and b, with the following relations: a^{5}=b^{2}=E bab^{-1}=a^{-1}; Where E is the Identity element. What I've done so far is this - the number of elements of the group is the product of the exponents of both generators, which is 10...

How many elements does each of these sets have where a and b are distinct elements? (with steps please) a) P({a,b{a,b}})b)P({∅,a,{a},{{a}}}) c)P(P(∅)) *i have tried to solve them but i am a little bit confused... Thanks in advance :)

Hi there, I understood that heavy elements could only be formed in stars or supernovae explosions. However I have just read that plutonium can be made by firing deuterons at uranium. Now uranium is a smaller atom than plutonium so what it going on? It seems to me that heavy elements can be...

Hi guys, I'm having problem in HSPICE. I designed a Sample & Hold circuit using MOSFET switches (transmission gate). The problem is that when I activate the MOSFET switches, the capacitor doesn't hold the charge as expected (I did the simulation using ideal components, and the charge holds...

Hi! Is there a way to calculate the classical orbital elements for a satellite or space shuttle around Earth using Matlab? I would like to get started with it since it is something that I've not tried before. so plese help Best regards

Carbon (18%) Hydrogen (10%) Nitrogen (3%) Calcium (1.5%) Phosphorus (1.0%) Potassium (0.35%) Sulfur (0.25%) Sodium (0.15%) Magnesium (0.05%) Copper, Zinc, Selenium, Molybdenum, Fluorine, Chlorine, Iodine, Manganese, Cobalt, Iron (0.70%) Lithium, Strontium, Aluminum, Silicon, Lead...

This is a challenge problem I thought of: Given a real-valued matrix A, develop an algorithm that finds the submatrix with the greatest sum of its element. (If there's a tie, just return an arbitrary submatrix that's tied for the win.) Is there a way other than brute force?

I want to learn do aberrations and compensation actions used as unsharp filter for final image ? I read a Leica paper. There was symmetrical lens Summicron as a subject. I found that at the exit of the lens there were no aberrations without corrected. But when you look inside , some lens...

Given A(m,n), eps = Machine Epsilon, fNorm = FrobeniusNorm(A), p >= 1 To filter noise near zero created by floating point error: if (|Aij| < fNorm * eps *p) Aij =0 end if Seem reasonable?

Homework Statement Calculate the power absorbed at t=0,t=0+,and t=200 mS by each of the elements in the circuit of fig 11.25 if us is equal to (a) -10u(-t) V (b) 20 + 5u(-t) V Homework Equations The Attempt at a Solution...

the two energy level atom, whose hamiltonian takes the form \hat{H_A}=E_g|g\rangle\langle g|+E_e|e\rangle\langle e|, where E_g as well as E_e represent the eigenvalues and |g\rangle as well as |e\rangle denote the ground state and excited state. There is an interaction between the atom...

Is there any thing that could, or any way to increase the atomic decay rate of already unstable elements, such as the radio active elements. magnetically or otherwise, even if the thought is only plausible or otherwise theory, I wouldn't mind hearing it. A thought accord to me, what if...

Homework Statement Suppose that a commutative ring R, with a unit, has no zero divisors. Does that necessarily imply that every nonzero element of R is invertible? Homework Equations The Attempt at a Solution We have to show that there exists some b in R such that ab = e. Having...

Is there a list of matrix elements for elementary processes? ##f\bar{f}\to\gamma\to f^\prime\bar{f}^\prime## ##f\bar{f}\to Z^0\to f^\prime\bar{f}^\prime## ##ff^\prime\to W \to \ldots## ##qq^\prime\to \ldots## ##\ldots##

Essentially, I have to show that where {e_1,...,e_n} forms the basis of L, no family of vectors {e'_1 ,..., e'_m} with m>n can serve as the basis of L. The book shows this by saying there exists a 0 vector such that 0 = \sum_{i=1}^{m}x_ie'_i, where not all x_i vanish. I wanted to show it by...

Hi all. I have a question. What is the behaviour of the polarization vector of a pseudoscalar particle under a parity transformation?? Let me explain my problem. I know for sure that the effective matrix element which links a D^* and a \pi can be written as: $$ \langle \pi(p)D^*(q,\lambda)...

When the early Earth melted, the heavy elements were drawn to the center due to gravity. Thus we have a iron core. Why shouldn't the core also have drawn in the heavy elements like uranium? The theory says the heat energy for the melt was due to the radioactive decay Why do we still have a...

Problem: Prove that any element in the intersection of two sets is also in their union. I am reading a proof writing book for dummies & the solution given in text is: http://tinypic.com/r/141hn7/5 http://tinypic.com/r/141hn7/5 First Question: In exam/test, is it OK if I write the...

Hi, I'm new here. Can someone help me with several sets of questions? I know the estimated age of the Milky Way. There is information that there are various types of supernovae in the Milky Way that occur on the average of 2.2 to 2.7 per century. My first set of question: Is this...

I wish to better understand the configuration situation for the outer most valence electrons for the d-block elements, Sc to Zn. I am having a problem understanding how to predict where the two outer most valence electrons must be located for some of the ten d-block elements? For some...

Question on Perfect Magnetic conductor. Are PMC always metal compound like Iron etc. That has high ##\mu##? So most of good magnetic conductor are themselves electric conductor? From articles I read: PEC ##\Rightarrow\;\hat n \times \vec E=0\;\hbox{ and }\;\hat n\times \vec H=\vec J##...

Hello friends, I noticed from Wikipedia the following information: Atomic radii: 4th period(only d-block elements): Sc:160 pm Ti : 140 pm V : 135 pm...

If you keep removing elements from a nonempty set, will you eventually get the null set? Some context below in a problem which I made myself and have been trying to solve: A set S having property P is smallest with respect to property P if S is an improper subset of any set having property P...

2. V=IR, Voltage division, KCL, KVL 3. When I short out the dependent current source by replacing it with an open, can I switch the location of the independent source and the 20 ohm resistor so I can do a voltage division to find the voltage across the 20ohm resistor which is then equal to Vo...

Homework Statement I want to find the orders of the elements in Z_8/(Z_4 \times Z_4), (Z_4 \times Z_2)/(Z_2 \times Z_2), and D_8/(Z_2 \times Z_2). Homework Equations The Attempt at a Solution The elements of Z_2 \times Z_2 are (0,0), (1,0), (0,1), (1,1), and the elements of Z_8 are of course...

Let A be the set of n \times n matrices. Then the identity element of this set under matrix multiplication is the identity matrix and it is unique. The proof follows from the monoidal properties of multiplication of square matrices. But if the matrix is not square, the left and right...

I wanted to mention that this solenoid has many winds over many layers. The thickness of the windings is 2.4 inches coming off of the engineering schematics, and has many many many turns, which is unknown. It has a 6T field at the zeroth point on-axis. I'm doing research with a professor and...

I usually do not ask for this kind of stuff, but this time I really have no way to verify if this is correct(and it has to be). So here it goes: On a subcritical nuclear reactor with 100 fuel elements we read the signal of 10e-9 A. When we add 10 more fuel elements, signal jumps to 10e-8 A. How...

Hello all, I am re-teaching myself calculus (I don't remember anything from Calculus in college, and I only took calc I in college) I am using the book stated in the title. I got up to page 65...so far so good. Until it started asking me to compute definite integrals. Nowhere so far...

Hello, I have a feeling that the solution to this question is going to be incredibly obvious, so my apologies if this turns out to be really dumb. How do I solve the following eigenvalue problem: \begin{bmatrix} \partial_x^2 + \mu + u(x) & u(x)^2 \\ \bar{u(x)}^2 & \partial_x^2 + \mu +...

What elements? How a light beam became a light? Thanks in advanced.

The theory says that if you have x objects containing a repeats of one element and b repeats of another, Np(without repetition)=x!/(a!b!). If you have x objects and repetitions are allowed, Np(with repetition)=xx, correct? Combining these, if we have x objects containing a repeats of one...

The three circuit elements are capacitors, resistors, and inductors, which act in the following manner: Capacitor: V = (1/C) q Resistor: V = R dq/dt Inductor: V = L d2q/dt2 Is it possible to build a passive device that acts like: V = (const.) d3q/dt3 Google search has come up with...

Here is the question: Here is a link to the question: Abstract Linear Algebra? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement A word has n letters, in which one of those letters is present a times and another is present b times (all other letters are present only once). a.) How many combinations of x letters are there from this word? b.) How many arrangements of x letters are there from this word...

I just want to check if there is anything wrong with my understanding... Let's say we have a group of order 42 that contains Z_6. Since the group of units of Z_6 has order (3-1)(2-1), it means that we have 2 elements of order 6 in G, right? In other words, for any cyclic subgroup of order n...

Hello. I'm just beginning my course in algebra. I've been reading Milne, Group Theory ( http://www.jmilne.org/math/CourseNotes/GT310.pdf page 29). I've found there a very nice proof of the fact that given two elements in a finite group, we cannot really say very much about their product's...

I have 17 elements, and I want to put them in 3 sets. This makes 2 sets with 6 elements, and 1 set with 5 elements. Now I want to find an algorithm to partition n elements in k sets. Can anyone give me an algorithm, or a math expression for me to implement in a algorithm? Thanks

Howdy, If I have the following configuration of nodes: 2---4--6 | \ | /| | \ | / | | \| / | | \/ | 1---3--5 What should the dimensions of my FEM stiffness be? Thanks

Homework Statement Let ##R## be a PID and let ##\pi\in{R}## be an irreducible element. If ##B\in{R}## and ##\pi\not{|}B##, prove ##\pi## and ##B## are relatively prime. Homework Equations ##\pi## being irreducible means for any ##a,b\in{R}## such that ##ab=\pi##, one of #a# and #b# must be a...

Since I was first introduced to chemistry, it's been because "it has two more than eight, and it wants eight to be "happy" so it loses two electrons and gains a positive two charge." It's good enough for me to write on tests, but 'happy' isn't exactly a scientifically accurate term. And why...

Hi there I've been struggling to convert the following two vectors into orbital elements, the vectors are as follows: R = 0i - 7950j + 0k km V = 5i + 0j + 5k km/sec I would like someone to help with the calculations of the following COEs: - semimajor axis (a) - eccentricity vector...