Elements Definition and 984 Threads

1_R=identity in the ring R. /=...not equal Having some issues with this any help will be great: Let R be a ring with identity, such that x_2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R? Thanks

Hello everyone, I'm having some trouble, that I was hoping someone here could assist me with. I do hope that I have started the topic in an appropriate subforum - please redirect me otherwise. Specifically, I'm having a hard time understanding the matrix elements of the density matrix...

Lead AN 82 and gold AN 79 are fairly close to one an other on the Periodic Table - so maybe the alchemists of the middle ages were on to something. In fact it was already done: There are reports that Glenn Seaborg, 1951 Nobel Laureate in Chemistry, succeeded in transmuting a minute quantity of...

say you are multiplying integers from 1 to 1000 and you want to count the number of "unique" elements. How would you do that? Is there a closed form expression for that? counting the unique or non-unique elements is the same since we know the total number of elements and can get the unique or...

As an exercise in cosmology-fiction (I actually got curious about this from an actual cosmology textbook problem), taking into account the stellar nuclear reactions that involve the fusion of hydrogen into helium, what would (roughly) be the proportion (in mass) between Hydrogen and He-4 in a...

Homework Statement Let x and y be irrational numbers such that x-y is also irrational. Let A={x+r|r is in Q} and B={y+r|r is in Q} Prove that the sets A and B have no elements in common. Homework Equations The Attempt at a Solution Since x and y are in A and B, then...

The group in question is U100, the group of units modulo 100, which, correct me if I'm wrong, is equal to {3, 7, 9, 11, 13, 17, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 93, 97, 99}. How many elements are there of...

How are rare Earth elements and minerals extracted from nuclear waste? And I know that some people are saying that there is a low supply of rare Earth elements needed in high tech manufacturing, could that shortage be solved by extracting these rare elements from nuclear waste?

Hi, ive been studying formation of solar system and couldn't find an explanation for why the sun didn't absorb heavy elements from early solar system? why they remained around the sun and formed planets and not get absorbed to the centre? thanks in advance

Homework Statement Find the product of each reaction Homework Equations Butanal (http://www.chemspider.com/Chemical-Structure.256.html?rid=e530204e-5d67-41a8-88e9-fc8e0ffcf41b), reacted first with bromobenzene...

Can a group, G, have repeating elements? And if so does the order of G include these repeated elements? Thanks!

I search for an 'elementary' proof of this, where results about structure of abelian groups are not used. I've tried a standard way of proving this, but hit a wall. I'm mainly interested if my work on a proof can be expanded to a full solution. Homework Statement Let G be an abelian group...

Say we have a matrix P with eigenvalues \lambda_1, \cdots, \lambda_n (possibly some are the same) and P can be diagonalized, then we can always say that the element on the a'th row and b'th column of P^n is equal to P^n(a,b) = \sum_{i = 1}^n \alpha_i \lambda_i^n with \alpha_i independent of n...

Homework Statement http://img267.imageshack.us/img267/8924/screenshot20120118at121.png The Attempt at a SolutionWe have that X = A + B. To show that X is unique, let two such sums be denoted by X1 X2 such that X1 ≠ X2. We write, X1 = A + B X2 = A + B The equations imply, X1 - A - B = 0 X2...

I have a quick question. I've been trying to search for an answer, but I'm probably looking in the wrong places. Is it valid to have negative off-diagonal elements in a density matrix? Thanks!

I'm working with universal enveloping algebras, specifically U(sl(2)). Does anybody know of a nice way of determining what the group like elements are. Of course, one could go a direct route and compare the coproduct Δ(v), v\in U(sl(2)), directly with the desired outcome v\otimesv, but the...

Homework Statement https://photos-1.dropbox.com/pi/xl/rLbkcUie-3Lbcrb5YgTa73zJKs4agFowWz6uGFoBq7s/38240/1324436400/1241536/ the image seems to be broken, so here is a link http://db.tt/fMwm8TrL I recently picked up a future textbook of mine for something to do over the holidays...

Is it possible to extract the diagonal elements of a matrix into a vector?? Is it possible to extract the diagonal elements of a matrix into a vector USING ONLY MATRIX MULTIPLICATION? So no element by element multiplication, and no diag commands. (This will eventually be implemented in...

Homework Statement How many elements of order 4 are in S6? (symmetric group with order 6) Homework Equations The Attempt at a Solution So, the different forms of elements with order 4 in S6 are (abcd)(ef), (abcd) from there I am sunk on how to calculate. I know there are...

Homework Statement Prove that if a,b,c are elements of a field. than a+b = a+c implies b=c Homework Equations a + (-a) = 0 0 + a = a The Attempt at a Solution The solution i found is: a+b = a+c a+b+(-a) = a+c+(-a) 0+b = 0+c b=c what I'm not...

Homework Statement What subgroup is generated by the fixed-point-free permutations? Homework Equations The Attempt at a Solution I know that the elements that have no fixed points are the ones whose cycle type adds up to n (i.e. all the numbers in {1,...,n} have to be used). I don't know what...

I would very much like some help to the following problem. Homework Statement Using mathematical induction, prove that a finite set A of n elements has n(n-1)/2 subsets of two elements. The Attempt at a Solution * Base step n=2: 2(2-1)/2= 1 subset of two elements. * Inductive step: assuming...

HI I don't understand why cadium or other elements have different zeeman effect because of their electron configiration thanks

If a group G is non abelian and a and b in G have orders |a|= n and |b|= m, is there a correlation we can draw between m and n and |ab|?

Q: Given a fraction A/B when does there exist a finite group G and an automorphism f s.t. exactly A/B elements of G are mapped to their own inverses (f(a) = a-1? If so how can we find the group? Does anything change if we allow infinite groups? I have a friend who was preparing for an intro...

Homework Statement It seems to me that every element of Z_45 has order 1, 3, 5, 9, 15, or 45. It seems impossible to have an element of order 2 by Lagrange's Theorem. Is there another way of looking at this problem?

WTS, is that such set is a subgroup. I need to show closure under group operation and inverse. I can do the inverse which is usually the hardest part, but I'm stuck on the grp op. So let a in K and b in K, both have finite distinct conjugates. Their conjugates are in the group too. WTS...

well, I'm thinking to answer the question in a generalized way. I want to find all the elements of Sn that satisfy the equation xn=e. well, if m|n and xm=e then xn=e, hence, if we raise x (which is of order m and m divides n) to the exponent n we'll have xn=e. so the answer will be this: S={all...

So in describing the elements of M2(Z) that have multiplicative inverses, the answer that I keep coming back to is that the only ones are those with determinants of +/- 1, because the determinant would have to be able to divide all elements. I think I've conifrmed this scouring the web, but...

Consider a matrix A(i,j) What I want to do example: A= [1 2 3; 4 5 6; 7 8 9] I want to to display 1 2 3 4 5 6 7 8 9 I will then save it to a file; I know how to do that. But how do I get MATLAB to display the individual elements sequentially? Thank you. *edit* Nevermind figured it out...

Russell's paradox concerns itself with the set S=\{x|x\notin x\}\;\;\;S\in S ? but it is supposedly solved in ZFC theory. Now, what about the set U=\{y|y\in y\}\;\;\;U\in U ? Is U an element of itself?

Do tuples exist which aren't elements of a cartesian product of sets? Can you just write an ordered list of elements which does not necessarily have to be defined in sets? (or does every tuple need to be defined through sets in order for it to rigourously exist in mathematics?)

This is the quantum part for solving wavefunctions of mulit-electron atoms that need to be approximated by the variation method. Specifically we are supposed to differentiate this equation using the quotient rule : E(c1,c2) = [(c1^2*H11 + 2c1c2H12 + c2^2*H22) / (c1^2*S11 + 2c1c2*S12 +...

Homework Statement For operator H=f(r)γ , where γ=\bigl(\begin{smallmatrix} 0 & I\\ I& 0 \end{smallmatrix}\bigr) , f(r) some even function. Show that matrix element of this operator <\psi_{a}|H|\psi_{b}> is non-vanishing only if ψ_a and ψ_b functions are of the opposite parity...

Hi Guys, I am new here I have been programming for some time in C/C++/etc,but my knowledge in physics/chemistry I am currently improving I wanted to know why is the causes that makes some elements resist and some other elements conduct electricity ?

Hi, Is there any elements or compounds other than cobalt, which raise martensite start temperature during solidification of steel.

Do macro amounts of elements form when atoms of a certain type (e..g. gold) bond together to form a substantial mass? Or do atoms of mixed types bond together and then together take on the properties we ascribe to each element? The reason I ask is that it seems improbable to me that a few...

Hello people, so there is a gr.11 chem question that I've been struggling with... a) Identify three oxidizing agents (other than Fe2+) from the redox table that can also react as reducing agents. b)try to explain this suprising behavior. so, any ideas? i have a redox table in my textbook...

Homework Statement Not sure this is the right place for this but here it goes... I am trying to figure out the derivation of the force elongation relationship of the maxwell elements in parallel in order to derive it for the Kelvin Voigt elements in series. I have attached the material that I...

In layman's language, why have the heavy elements, which were created atom by atom over enormous periods of time, accumulated into large masses into small spaces as we find in the earth, rather than being scattered uniformly? E.g nuggets, and veins of silver and gold.

Homework Statement I have a test coming up and some of the practice questions were things like "Name 6 elements with a maximum oxidation state of +7" or some other number like +8, +6, etc. How do I go about doing this? The Attempt at a Solution There is the obvious trick of counting...

Can anyone think of an example of an infinite group that has elements with a finite order?

Homework Statement "In each of the given cases, decide whether the specified elements of the given vector space V (i) are linearly independent, (ii) span V, and (iii) form a basis. Show all reasoning. V is the space of all infinite sequences (a0, a1, a2, ...) of real numbers v1 =...

Homework Statement Let V = (F2)^3, the set of triples (x; y ; z) of numbers in F2, the field with two elements. V is a vector space over F2. Prove that any subspace of V must have either 1, 2, 4, or 8 elements. Homework Equations F2 = {0,1} The Attempt at a Solution The only...

I'm doing a lecture on electricity for my class and one of the students at the beginning of the semester wanted to know how a curling iron works. So I've never ripped open a curling iron but I assume there's coils of wires within the little 'arm' parts that rely on ohmic heating. However, since...

using only the empty set, pairs, and unions can you form sets with infinitely many elements?

hi every one , i am new in data structure course i need help in this : Struct Person { Char name[20]; int id; float gpa; }; Person student[5]; Compute the addresses of all the elements of array student and show a memory layout for the array if the address of the first...

Hey everyone, I've been going thru a linear alg textbook and there's this one theorem I can't quite follow. It proves that the elements of A(adj A) are |A| if on the diagonal and are 0 if not. Therefore, A(adj A) = |A|I. The first part shows that along the diagonal of this product A(adj...

I'm currently studying grade 11 chemistry... And the periodic table of elements slightly confuses me. I am having trouble understanding which are metalloids, and halogens. In the handout that my teacher gave me, it listed the following as metalloids: B, Si, Ge, As, Sb, Te, Po, and At. It also...

I have to decide whether the following is true or false: If A1\supseteqA2\supseteqA3\supseteq...are all sets containing an infinite number of elements, then the intersection of those sets is infinite as well. I think I found a counterexample but I'm not sure the correct notation. I to...