Elements Definition and 984 Threads

Suppose we had an infinite series - z = ∑i = 1 to ∞ ( α1(i)x1 + α2(i)x2 + . . . + αm(i)xm ) - rewritten as the cumulative sequence - z(n) = α1(n)x1 + α2(n)x2 + . . . + αm(n)xm - where the xj are linearly independent and normalized (and serve as a finite basis across the sequence). If all...

I posted this elsewhere and was sort of able to figure out a result myself, but 1) I didn't do it right, and 2) No one answered it anyway. I thought I'd give it a shot over here. The problem deals with nested matrices. The gamma matrices can be found here. My question deals with a "vector"...

Hello. I came across a Quadratic Equation that looks like this. 5x2 + 4x + 9 = 0. The '5' in the above equation is called Quadratic Coefficient. The '4' in the above equation is called Linear Coefficient. The '9' in the above equation is called Constant. The 'x' in the above equation is called...

I wonder if it is possible to express a simple principle into a mathematical form. The simple principle says if at time t0 an isolated system is composed of some elements with some properties then at t1 it is composed of other elements with different properties, then in principle it is possible...

I have known: (1) A Hamiltonian, say, H(k), where k is the crystal momentum. (2) An appropriate complete basis set {a_1,a_2,a_3…}. (3) Some symmetric operators {A,B,…} which commute with H(k), i.e. [A,H]=[B,H]=...=0. Of course, by calculation, I can get any matrix element of H(k), i.e...

Homework Statement Now we are going to use the design pattern for collecting objects. We are going to model a hospital nursery filled with newborn babies. A Nursery uses an ArrayList to keep track of Newborn objects. You will write both a Nursery class and a Newborn class. A Newborn has a name...

Homework Statement "Determine the max number of elements in a three-element set that is not reflexive, symmetric, or transitive?" Homework Equations ##a R b⇔(a,b)∈R## The Attempt at a Solution Basically, my professor has stated that there are a total number of seven possible elements in a...

By commutative, we know that ##ab = ba## for all a,b in G. Thus, why do we need to prove separately that ##a^n b^m = b^ma^n##? Isn't it the case that ##a^n## and ##b^m## are in fact elements of the group? So shouldn't the fact that they commute automatically be implied?

The system in which I tried to calculate the Hamiltonian matrix was a particle in a stadium (Billiard stadium). And I used the principle where we take a rectangle around the stadium in which the parts outside the stadium have a very high potential V0. We know the wave function of a rectangular...

Hello, Are there elements that are never found in life forms? Or can some find themselves in life, but perhaps very unlikely?

From my understanding of semiconductors, we are able to create semiconductors by combining different group of elements that fulfill the octet rule to produce covalent bonds and where their electronegativities provide a energy band gap that is between that of a conductor and insulator. Why is the...

Homework Statement Prove that if ##1 \leq d \leq n##, then ##S_n## contains elements of order d. Homework EquationsThe Attempt at a Solution Here is my idea. The order of the identity permutation is 1. Written in cycle notation, the order of (1,2) is 2, the order of (1,2,3) is 3, the order of...

Hello everyone, I am currently trying to understand how we can use feynman diagrams to estimate the matrix element of a process to be used in fermi's golden rule so that we can estimate decay rates. I am trying to learn by going through solved examples, but I am struggling to follow the logic...

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Chapter 5 ... I need some help with Example 5.2.1 in Section 5.2: Rings Generated by Elements ... In the Introduction to Section 5.2.1 (see text above) Lovett writes: " ... ...

I am reading Stephen Lovett's book, "Abstract Algebra: Structures and Applications" and am currently focused on Chapter 5 ... I need some help with Example 5.2.1 in Section 5.2: Rings Generated by Elements ... In the Introduction to Section 5.2.1 (see text above) Lovett writes: " ... ... R[S]...

Homework Statement Show that every matrix A ∈ O(2, R) is of the form R(α) = cos α − sin α sin α cos α (this is the 2d rotation matrix -- I can't make it in matrix format) or JR(α). Interpret the maps x → R(α)x and x → JR(α)x for x ∈ R 2 Homework EquationsThe Attempt at a Solution So I know...

Homework Statement I would like to show that if ##p(x) = \sum_{i=1}^m a_i x^i## and ##q(x) = \sum_{j=1}^n b_j x^j##, then ##p(x)q(x) = \sum_{k=0}^{m+n} \left( \sum_{i+j=k} a_i b_j \right) x^k##, where the polynomial ring is assumed to be commutative. Homework EquationsThe Attempt at a Solution...

Hi guys, Here is a wacky question for you: Suppose you have a simple recursive function f(x)=x. Given the fact that a function f(x)=y can be rewritten as a set of ordered pairs (x, y) with x from the domain of f and y from the range of f, it would seem that the function f(x)=x can be written...

Homework Statement Suppose that H is a subgroup of Z under addition and that H contains 2^50 and 3^50. What are the possibilities for H? Homework Equations Relevant concepts are just the definitions for a group and subgroup. https://en.wikipedia.org/wiki/Group_(mathematics)...

Homework Statement First Claim: If ##u \in R## is a unit, then it cannot be nilpotent Second Claim: If ##u \in R## is nilpotent, then it cannot be a unit Homework EquationsThe Attempt at a Solution I realize these are simple problems, but I have no one to verify my work and I want to be...

Source, with more info: http://iupac.org/iupac-announces-the-names-of-the-elements-113-115-117-and-118/ An update of the periodic table from IUPAC is here. (Apparently they are still playing Tetris... :smile:)

Homework Statement I just finished proving that ##\overline{a} \in \mathbb{Z}/n\mathbb{Z}## is nilpotent if and only if every prime divisor of ##n## is a prime divisor ##a##, and this lead me to wonder whether the cyclic subgroup ##\langle \overline{p_1 p_2 ... p_k} \rangle## be consist of all...

Homework Statement Through my exploration/experimentation, I came up with this little conjecture: Let ##F## be a field and ##x## some element in the field. If there exists a natural number ##m## such that ##x^m = 0##, then ##x=0##. In other words, a field contains no nontrivial nilpotent...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Question: Let ~ be the equivalence relation on the set ℤ of integers defined by a~b if a-b is divisible by 5. Let k ∈ Em belong to the equivalence class of m, and l ∈ En belong to the equivalence...

Homework Statement Consider the field K=Z_2[X]/<x^3+x+1>. How many elements does this field have? Then let f(x) = x^3+x+1 and b be a root of f(x) in Z_2[X], Find all other roots of f(x) in K and describe the Galois group Homework EquationsThe Attempt at a Solution So I'm trying to understand...

For a chemistry paper I'm writing, I have to include an example of alpha decay using only elements up to number 35, however, I can't find one that would actually work. Does anyone know of any that could be used?

Hello everyone, My name is Ramon and I just had an idea. Do you think it will be possible in our time to turn elements into other elements? For example rearranging the atoms that make hydrogen or H2O into gold. The reason I was thinking of this is because if we can create a resource we can...

Homework Statement Consider the cone defined by z = √ x 2 + y 2 . By defining new coordinates ρ, φ where x = ρ cos φ, y = ρ sin φ, show that the line element on the cone is ds^2 = 2dρ^2 + ρ^2dφ^2 . Why does this result prove the cone has flat geometry? Homework Equations x=rcosφ y=rsinφ The...

Extracted from 'At the frontiers of Physics, a handbook of QCD, volume 2', '...in the physical Bjorken ##x##-space formulation, an equivalent definition of PDFs can be given in terms of matrix elements of bi-local operators on the lightcone. The distribution of quark 'a' in a parent 'X'...

Homework Statement Consider the motion of charged particles, in one dimension only, in the presence of an electric potential V ( x). Show, by direct substitution, that a function of the form f=f(1/mv^2 + qV) is a solution of the Boltzmann equation under steady-state conditions. Homework...

How could an element and all its atoms die? With nuclear fusion they combine atoms, so are they also making elements?...is it possible to make an element shooting the right number of p+,n, & e- and then contain it/save it for later?

Homework Statement I am asked to offer an example of two commuting elements whose product does not have an order equal to the least common multiple of their individual orders. Homework EquationsThe Attempt at a Solution Consider ##-1## and ##1## in ##\mathbb{Z}##. Then ##1+(-1) = 0## which...

We say about an element that this element is solid, liquid and gaseous in nature...(like we say oxygen and nitrogen are gaseous)...My question is that how can we say that an ELEMENT is solid, liquid or gaseous...From what I understand, elements are kind of ''represented'' by their atoms...So how...

Lets say I have a matrix A=rand(31,51). How can I extract its elements from its center (say row = 15, column = 26) in circular manner. I want to have a matrix that displays only those elements of 'A' which are inside a circle with its center at A(15,26). Radius of circle can be any number say 5...

Any suggestions on how I should approach question C1? Every time I think I have a solution I find that I have made the implicit assumption either that F is abelian or that the roots of w are in the center of F. I don't think either assumption is valid. If I let K be the root field of the poly...

So I want to read Euler's : Elements of Algebra. However, I see many editions on Amazon. What is the best version of this book?

Hi, I am using a vector to store vales in the Jtable. I am storing 3 rows in the table. I have written a clean button handler to remove values from the table. Its code is: rowOne.removeAllElements(); rowTwo.removeAllElements(); rowThree.removeAllElements()...

Homework Statement Homework Equations V=IR The Attempt at a Solution Hello. I am working on this problem and I just wanted someone to check it out if I did it correctly. I was kinda confused about some of the nodes and why we even needed to find voltages at those points because in a lot...

Hey, didn't know where to turn and thought this might be a good start. I've been designing a world for the last six years based of the four Greek elements; earth, air, water, fire and H'teal. (Transfer and absorption of biological energy, life and death combined) The main three bad and good...

with at most k swaps. (In other words, like the largest number formed by swapping k digits.) Example. A=[4,2,3,5,1], k = 1 ---> [5,2,3,4,1] I'm wondering why my algorithm is failing the test cases which I'm unable to see. using System; using System.Collections.Generic; using System.IO...

Any ideas on how to begin Many thanks :)

What do you think? RU2563511 MICROBIOLOGICAL METHOD OF TRANSMUTATION OF CHEMICAL ELEMENTS AND CONVERSION OF ISOTOPES OF CHEMICAL ELEMENTS Viktor Kurashov, Tamara Sakhno SUBSTANCE: radioactive raw materials containing radioactive chemical elements or their isotopes, are treated with an aqueous...

Hello. It's given the following type (sorry for the mix italian-english): struct El{ int info; struct El* next; }; typedef struct El ElementoLista; typedef ElementoLista* ListaDiInteri; And I have to remove all elements of value n; I did this: void remLista(ListaDiInteri *l, int n)...

I have tried looking for papers on the composition of earth, but none of them seem to list the abundance of compounds. They just list the elements. So, what are the abundances of the most common compounds, by mass and/or percent of Earth?

Hi, I am using NetBeans 8.1. I want to add elements in a list Box on a Button press. My code would read text from textField & then insert into list box: private void button1ActionPerformed(java.awt.event.ActionEvent evt) { // TODO add your...

Homework Statement The elements lead, silicon, germanium, tin and carbon all lie in the same group of the periodic table. Which of the following is true? A) Like carbon, all the elements are non-metalsB) Carbon is closer in properties to silicon than tin is to leadC) Tin is closer in...

Suppose the color of some elements is red and blue but after the reaction between them a new compound formed with yellow color .so on what factor does the the color of compound depend? I think it may depend depend upon the number of electron transferred and the remaining one...

I was reading the wikipedia article on Lithium and noticed that it says: Trace amounts of lithium are present in all organisms. The element serves no apparent vital biological function, since animals and plants survive in good health without it, though non-vital functions have not been ruled...

This is a basic question about the behavior of $a^k$ for $a\in\mathbb{Z}/n\mathbb{Z}$ and $k=1,2,\dots$. I know that Fermat's little theorem says $a^{p-1}=1$ in $\mathbb{Z}/p\mathbb{Z}$ for prime $p$; thus, the sequence $1,a,a^2,a^3,\dots$ is periodic with period at most $p-1$. More generally...

Consider the following extract taken from page 60 of Matthew Schwartz's 'Introduction to Quantum Field Theory':We usually calculate ##S##-matrix elements perturbatively. In a free theory, where there are no interactions, the ##S##-matrix is simply the identity matrix ##\mathbb{1}##. We can...