Elements Definition and 984 Threads

If a question asks me to prove something about the elements of a set, say {0,1,a,b}, then is it assumed that all elements are distinct? Because I am attempting a proof, but the only way to prove the proposition is if all elements are distinct. However, it doesn't say in the original question...

We did a chemistry experiment were we burned different metal chlorides on the bunsen to observe the different flame colors produced. Anyhow I'm writing up the report but there's one thing I'm not sure about. I can't make any mistakes because I made the mistake of displaying way too much...

I'm looking to show that: Order (ab(a^-1)) = Order b So far... Let x be order of ab(a^-1), so we have: e = (ab(a^-1)^x) = (a^x)(b^x)(a^(x-1)) = (a^x)(b^x)((a^-1)^x) so by associativity we have... = (a^x)((a^-1)^x)(b^x) = (((a)(a^-1))^x)(b^x) = (e^x)(b^x) = b^x Hence...

Homework Statement I need to find a group with twelve elements that is noncommutative. Homework Equations The Attempt at a Solution I was considering a group G of the integers (-5,-4,-3,-2-,-1,0,1,2,3,4,5) with respect to subtraction. Subtraction is associative/noncommutative...

Homework Statement I am an amateur researching elementary particles; on tabulating atoms the elements, atoms of the highlighted elements in the diagram below formed one group (of two possible groups); I should like to know if there is anything unique to the highlighted elements...

Homework Statement Let G be a group and let g be an element G such that |g| = mn, where gcd(m, n) = 1. Show that there are unique elements a, b in G such that g = ab = ba and |a| = m and |b| = n. The attempt at a solution Since gcd(m, n) = 1, there are integers s and t such that ms + nt =...

I'm having a difficult time figuring out how to find length and area elements for Gauss's, Ampere's, and Biot-Savart Laws! Can someone please help explain! This applies to symmetrical, non-symmetrical, and infinite objects! I'm not asking what is the area of a sphere but, say with an infinite...

I am trying to debug a SUPG FEM code for flow problems (based on Brooks Hughes 1982) and have a question about the Lumped Mass Matrix. My understanding of the Lumped Mass Matrix is that for any given element the mass of that element is simply distributed evenly over the number of nodes. In...

Homework Statement (From an exercise-section in a chapter on Lagrange's theorem:) Let G be a finite abelian group and let m be the least common multiple of the order of its elements. Prove that G contains an element of order m. The Attempt at a Solution We have x^m = e for all x in G. By...

Given a group, it seems everything (all properties) about the group can be determined by how elements multiply with each other. Correct? For example, everything about the group could be read off from the multiplication table.

Hi, I am looking for a certain operation that makes a 1 tensor from a 2 tensor by filtering out only the diagonal elements. For instance, (f1g1 f1g2 f1g3) (f2g1 f2g2 f2g3) (f3g1 f3g2 f3g3) becomes (f1g1) (f2g2) (f3g3) after a certain...

Abelian group w/ 1000 elements? My guess is... Z mod 100 under addition. I am new to algebra though...any thoughts? Also, what about multiplication?

Got a question about fissionable (as opposed to fissile) elements. I vaguely remember the minimum A number for (theoretically) fissionable elements is somewhere in the vicinity of 153 to 156. But I don't recall the exact figure, neither google nor ask.com have been of help and I'd like...

Lets say i have some number 'N' of numbers - in a particular order. I then remove some fraction 'F' of those numbers. I want to know the probability of there being (some number) 'Y' consecutive initial-numbers remaining. Any ideas? Would it just be F^Y ?

I'm quite confused what order of elements consists of. I understand that the order of an element g in a group G is the smallest positive integer n such that g^n = e. And I also understand that to find the order of a group element g, you compute the sequence of products g, g^2, g^3,… until you...

Potassium reacts with Chlorine to produce the ionic solid potassium chloride (KCl). Which elements would you predict would react with Iodine in a similar type of reaction? I know that K has a +1 charge and Cl has a -1 charge. Iodine has a -1 charge and all the elements in column 1A have a...

How can I assign polarities for electric elements , say resistors.. You can explain on this circuit

Why there are much more metallic elements in the world than the non-metalllic one? We can see on the periodic table most of the elements are metallic but why? is there any relevance to the electronic configuration? I can't find any helpful web-site to solve this problem.Please give me some...

Homework Statement I desperately need help, cause I cannot find anything about hermite cubic elements and I need to make fortran program who solves this equation with hermite cubic elements: please explain to me how to solve this equation need answer fast for semestral signature...

Where could I find the spectra of most elements on line? I would expecially the He 2 spectrum, the Be and the B ones. Where could I find it?

I'm trying to figure out how to prove the following... If a, b \in G where G is a group, then the order of bab^{-1} equals the order of a. I'm rather stumped because the group is not necessarily abelian and it seems like it would have to be in order to directly show that you can rearrange...

Does anyone knows some good finite elements routines in 2D?

is there a better way to chart elements? surely chemicals characteristics don't behave by atomic number

I was looking at the values for the Van der Waals radius on various elements in wikipedia and noticed that Molybdenum does not have one. I searched a bit and found this site http://www.webelements.com/periodicity/van_der_waals_radius/ which lists the elements that have a Van der Waals...

A general question. A unit element is one that has it's multiplicative inverse in the ring. An element p is prime if whenever p=ab then either a or b is a unit element. Can a prime be a unit element? The answer is, i think, no but thus far I've been unable to find a contradiction.

what elements are used to prevent losing neutrons and what are the ways of preventing losing of neutrons in nuclear power plant and atomic bomb?

Is possible some elements (like Cadmium or Bohr) absorb neutrons, without any nuclear reaction in their atomic nucleus? If the answer is YES, then why there isn't any nuclear reaction?

Hello everyone. I'm trying to figure out a trick to finding the degree of (81)^1/5+29(9)^1/5+17(3)^1/5-16 over Q. I know that the degree of this number, call it a, is equal to the degree of the field extension [Q{a}:Q], and also the degree of the minimal polynomial which has this as a...

Homework Statement Let G be an abelian group. Show that the set of all elements of G of order 2 forms a subgroup of G. Find all elements of order 2 in Z6. The Attempt at a Solution The elements of Z6 are 1,4,5. I'm not sure how to find the set of all elements of order 2. Can someone help...

1. Problem Evaluate \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} z^{2} e^{-A \sqrt{x^{2}+y^{2}+z^{2}}} dxdydz 2. Useful Formulae none 3. Attempt at Solution Well, this is part of a much larger problem. I am trying to compute the dipole moment matrix elements...

Homework Statement we shall describe a simple model for a linear molecule, say, CO2. the states |L>, |C>,|R> are the eigenstates of D operator (corresponds to dipole moment) D|L>=-d|L> , D|C>=0 , D|R>= +d|R>. When the electron is localized exactly on the carbon atom, its energy is E1...

[Sorry about the long post] I'm doing an essay where I am exploring whether or not elements were, for the most part, formed under conditions of thermodynamic equilibrium. We know that some element clearly aren't (such as Potassium 40 and uranium which decay radioactivly). I've scoured the web...

If a set contains elements that are *themselves* sets, then would it be correct to say that one of those elements is a subset of the set? E.g. Q = { {a}, {b}, {c} } I know that { {a} } is a subset of Q (because it contains ONE of the elements) But is {a} a subset of Q? I don't...

I know its a rather simple question but if you think about it, it requires much knowledge of d orbital. Is there an easy way a HS student can determine charges of elements using only a periodic table and no prior knowledge of orbitals? My old chem teacher said you could take the element and...

There is much abuzz about the prediction of stable superheavy elements that might exist. Now what I wonder is, did they ever consider that if these particles can exist, why have we not detected them yet. Id have to say if a supernova cannot produce them, we have no hope at all.

This is actually about nanoparticles for better batteries: http://www.technologyreview.com/Energy/20524/?a=f But my point is that nanoparticle fabrication is becoming a known, industrially mass-produceable manufacturing technique. So why can't nuclear fuel elements be made nano-sized...

[SOLVED] how many elements are in two power sets Homework Statement a.How many elements are in the power set {1,2,3,4}? b.How many elements are in the power set {1,2,3,4,5}? Homework Equations The Attempt at a Solution a. {empty set, {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}...

i'm a bit confused about the currents in the expression for a matrix element for an interaction... e.g. you could have a current like (adjoint spinor)x(spinor) which is scalar, this makes sense to me. or you could have a current like (adjoint spinor)x(gamma matrix)x(spinor) which is vector...

I have a question: it is generally stated that 100 micrometers is the acceptable limit on the thickness of the oxidation layer on Zircaloy4 fuel rods. But I'm at loss as what is the reason for this limit ? Is it structural integrity ? Thermal resistance ? Mechanical tolerance ?

Homework Statement How many subsets of a set with 100 elements have more than one element? The thing throwing me off here is the zero-set, and whether it counts as an element or that. Can someone start me off?

What is the proper way for me to write symbols for elements such as Chlorine?

So this sentence kind of confuses me: "On the other hand, if \alpha is a root of x^3 - x + 1, then \beta = \alpha^2 is a root of x^3 - 2x^2 + x - 1. The two fields Q(\alpha) and Q(\beta) are actually equal though if we were presented only with one of the two polynomials, it might take us some...

I hope some one can help with this. 2 different but identical rated elements are used for exactly the same purpose, the only difference between the 2 is, one has the element bent into three outer coils and three inner coils, the other has four outer coils and four inner coils, the one with...

Homework Statement If N is a normal subgroup of a group G and every element of N and G/N has finite order, prove that every element of G has finite order. Homework Equations Um, a finite group element is given such that g^k = e (identity) for some integer k. We also know that the...

Can someone list all the elements in each matrix of SO(3)? As opposed to the general definition of A^tA=1 with det(A)=1. In other words give the general form of all matrices in SO(3). This is usually done with SU(2) but haven't seen it with SO(3).

What r the superheavy elements? what do they do?any advantage or disadvantage?(please be specific) thnx!

Hi I am writing a program in Matlab and I want to search a string within a cell to identify where certain characters start and end. However, once I identify the start and end points I want to extract all the characters within that range. So for example let's say that I have a 25 row by 1...

Homework Statement Draw out the electron configuration of [Fe(H2O)6]3+ The Attempt at a Solution I did the work, but i am not sure if its correct: Is the following electron configuration correct for this complex? [Fe(H2O)6]3+: [Ar] 4s [ i L ] 3d [ i L l i L l i L l...

A group G has exactly 8 elements of order 3 (Unanswered as of 1/31) How many subgroups of order 3 does G have? So we have 8 elements, its prime decomposition is 8=2^3. The number of different ways to get factors is how many subgroups, at least that is what I interpret from my notes...so...

Let A be a set of n distinct elements. There is a one to one correspondence between binary relations on the set A and subsets R<= A x A a. Computer the number of binary realtions on A b. A binary relation R is said to be symmetric if for every (a,b) in R, (b,a) is also in R. Compute the...