Element Definition and 836 Threads

Hello, This is not a homework problem, nor a textbook question. Please do not remove. Is there a concrete example of the following setup : R is an integrally closed domain, a is an integral element over R, S is the integral closure of R[a] in its fraction field, S is not of the form R{[}b{]} for...

I have this true and false question: " The half life and therefore the decay constant will be the same for every isotope a) True b) False c) only if it is an isotope of the same element " I think this is false, just by intuition.

Hello! (Wave) We consider a Binary search tree and we want to find the element with the next greatest and the next smallest key than the key of a node v. For example, how can we find the next of the node to which q1 points in the in-order traversal? How will we find the next of the node to...

Homework Statement An unknown element has a nucleus with charge 14.00 e and a radius of about 3.60×10-15 m. How much voltage must be used to accelerate a proton (radius 1.20×10-15 m) so that is has sufficient energy to just penetrate the unknown element? Assume that the potential is that for...

Wikipedia says that largest order of any element of Rubik's cube group is 1260 [PLAIN]http://upload.wikimedia.org/math/e/1/c/e1cff178a2562422492a4140a38f93ff.png. http://en.wikipedia.org/wiki/Rubik%27s_Cube_group What about element of smallest order (except the identity element)? I'll...

ds2=guvdxudxv Why is the invariance of ds2 as shown above? Why can't it be something like ds2=guudxudxu or ds2=dxudxu ? Isnt it based on Pythagoras theorem? Why must it have 1 u and 1 v instead of just 2 u or 2 v? Forgive me for such dumb question as I just started.

First assumption: the change of magnetic flux in time outside a conductor is zero. Last semester in circuit analysis we treated circuits with sinusoidal voltage variation as steady state circuits while using the phasor notation. But now that i know electrodynamics i begin to doubt my concepts...

Can somebody explain how you get: <pm|p|pn> = (1/2π)∫e-ipmx/h (-ih∂/∂x) eipnx/h dx ... = ih∂δ(pm - pn)/∂x Conceptually, I am having a problem with how the inner product is formed when a derivative is involved (i.e. the ... steps)

Hello! (Wave) We consider an $\text{ AVL }$ tree $T$. At each node $v$ of the tree the number of nodes of the left subtree of $v$ is stored. I want to write an algorithm that returns the $j^{th}$ smallest element of the tree in time $O(\log m)$ where $m$ is the number of nodes of the tree. How...

This notion perplexes me. Could I please have this explain with an example(s). I am confused are atoms not made up of the same protons and neutrons which are just essentially negatively or positively charged particles which are made of quarks? Which as confusing as that can become. How can one...

we say the surface element of x(u,v),y(u,v),z(u,v) is absolute value of the cross product or i don't understand why this is. i know that the absolute value of the cross product is the area of a parallelogram formed by a,b,a+b, but i get lost after that im guessing something happens where dudv...

The Faraday Tensor is given by: Consider the following outer product with the 4-potential: The Faraday Tensor is related to the 4-potential: F^{mn} = \Box^{m} A^n - \Box^n A^m For example, ## F^{01} = -\frac{1}{c} \frac{\partial A^x}{\partial t} - \frac{1}{c}\frac{\partial...

Hello! (Smile) We have a sequence of numbers $A=(a_1, a_2, \dots, a_n), n \geq 3$, for which, it stands the following: $$\forall i \text{ with } 2 \leq i \leq n-1:$$ either $$ 1. a_{i-1}<a_i \text{ and } a_i>a_{i+1}$$ or $$2. a_{i-1}>a_i \text{ and } a_i<a_{i+1}$$ I have to write an...

A simple answer I got searching the web to as why we can't split atoms of non-radioactive elements is that they are stable.So,why can't we make stable elements unstable(radioactive)? Is this possible at least in theory?

Homework Statement I've solved all but one force. I can't seen to get the force within element D-C. All relevant variables are shown on the pics attached i.e loads, supports, dimensions etc... Homework Equations Sum of forces in x=0, sum of forces in y=0, sum of moments=0 on Here are links...

Hi I'm taking a math course at university that covers introductory group theory. The textbook's definition of the identity element of a group defines it as two sided; that is, they say that a group ##G## must have an element ##e## such that for all ##a \in G##, ##e \cdot a = a = a \cdot e## ...

Hey guys, currently I am working on my diploma thesis in the field of beam design for mobile communication. I created a linear array with N elements and computed the corresponding Array Factor with the help of the chebyshev distribution. I assume my Element Factor to have its maximum at 90°...

Hi! (Smile) If we want to look for an element $x$ in a list, we can use a sentinel value. What do we gain, with the use of a sentinel value?

Homework Statement Let ##g \in S_n## and suppose that we know the cycle notation for ##g##. How can one compute its order without repeatedly composing ##g## with itself? Homework EquationsThe Attempt at a Solution [/B] I took the group ##S_4## and tried formulating a conjecture. I composed...

Homework Statement This is part of the online tutorial I'm reading: http://farside.ph.utexas.edu/teaching/em/lectures/node49.html I'm so confused about the notation of Dirac Delta. It's said that 3-dimensional delta function is denoted as \delta^3(x, y, z)=\delta(x)\delta(y)\delta(z) in...

So I saw this a moment ago: How can the second and third terms yield (n+1)+(n-1)=2n and not (n+1)+n=2n+1? PS: I solved the problem by using [a,a(+)]=1. Sorry, this is very simple but I cannot figure out what I did wrong.

If you had to a create a super element to be added to the periodic table, what would it be? I'm talking about it's properties.. give me some good techno babble.

Hi all, I am reading a book on atom interaction with light. It starts with the 2 level system. The book said the diagonal elements of dipole operator is zero, i.e. ##\langle g|x|g\rangle = \langle e|x|e\rangle = 0##. I don't understand why this is true but after searching online and there...

Hi I was wondering say for example you had this simple current divider circuit. I was wondering if R1 for example had zero resistance it would have all current dropped over it. However pertaining to the current divider formula. ##I_i = Is (R_T / R_i)## Thus if R1 = zero the equation is not...

What are some examples where the intersection of two sets is a member of one of the sets? Let A,B,C,D be sets whose elements are sets of integers. A = \{\emptyset, \{1,2\},\{3\} \} B = \{\{4,5,6\},\{7,8\} \} C = \{ \emptyset, \{7,8\} \} D = \{ \{3\}, \{4,5,6\} \} Then A \cap B =...

Hello everyone, I am working with an arbitrary finite group ##G##, and I am trying to prove a certain property about the order of an arbitrary element ##g \in G##. Supposedly, if we are dealing with a such a group, then ##o(g)##, which is the cardinality of the set ##| \langle g \rangle |##, is...

Hello! (Wave) Given the following two lists: what could we do, so that the first list contains both the elements of the first and the second list, sorted? (Thinking) I wrote the following algorithm: pointer *P=L1, *Q=L2,n; while ((P != '\0') && ( Q != '\0')){...

Sorry if I am asking a stupid question. I recently had an argument with my friend which among this two is more dangerous: 3H or 235U(not considering its decay chain products). I was under the impression that 3H has an effective dose about 1000 times smaller than 235U due to its weak...

Hi there. Is there any element, when exposed to saline, will cause the saline to heat up? More to the point, I would like to add something to a jar of saline and heat it up. Is that possible? Thanks, ~J

Homework Statement Determine for what k f(x)=xk is an element of L2 (0,1) vector space k ∈ ℝ Homework EquationsThe Attempt at a Solution \int_{0}^{1} x^{2k} dx = \frac{1-0^{2k+1}}{1+2k} = \sum_{n=0}^{\infty}{(-2k)^{n}} (for k > -½) This sum should converge for \lim_{n \to +\infty}...

Hey! :o $K \leq L, a \in L$ I am looking at the proof that if $a$ is algebraic over $K$, then $K(a)=K[a]$. We show that $K[a]$ is a field, then we have that $K \subseteq K[a] \subseteq K(a) \subseteq L$. Let $0 \neq c \in K[a]$, then $c=f(a), f \in K[x]$. Let $p(x)=Irr(a,K)$. Since...

Hey! (Nerd) If $a,b$ sets, then we symbolize $\{ a,b\}$, the set that has as elements $a$ and $b$ and only these. If $\{ a, b \}$ a set of pair and $a=b$, then we write $\{a,a \}=\{a \}$ and the set $\{ a \}$ is called the singleton, that consists of only one element of $a$. Why can $\{a\}$...

Homework Statement Let S={p+qα+rα2 : p, q, r \in \mathbb{Q}}, where α=\sqrt[3]{2}. Then S is a subfield of \mathbb{C}. Prove that each nonzero element of S has a multiplicative inverse in S. The Attempt at a Solution Let p, q, r\in\mathbb{Q} such that not all of p, q, r are zero. If...

Do {1,2,3} and {1,2} differ in, or by exactly one element? Or do those two things mean the same thing. Also, what about {1,2,3} and {1,2,4}.

Hi! (Nerd) Show that,given a set of numbers $S$,we can count the second smallest element of $S$ with $n+ \lceil \lg n \rceil-2$ comparisons at the worst case. Hint: Find the smallest element,considering a tournament tree for its finding. I don't really know how to use the hint.. (Sweating)...

I was reading the finite element method in engineering by Rao and in the first example he ends up with a matrix that is singular. The matrix is the following: \begin{pmatrix} 2 &-2 & 0\\ -2 & 3&-1\\ 0&-1& 1 \end{pmatrix} Which is a symmetric matrix as far as I can remember...

Homework Statement Let S be the subset of group G that contains identity element 1 such that left co sets aS with a in G, partition G .Probe that S is a subgroup of G. Homework Equations {hS : h belongs to G } is a partition of G. The Attempt at a Solution For h in S if I show that hS is S...

Hi, I'm hoping to clear up a few uncertainties in my mind about proving that the identity element and inverses of elements in a group are unique. Suppose we have a group \left(G, \ast\right). From the group axioms, we know that at least one element b exists in G, such that a \ast b = b \ast...

Good day! I am a beginner in Finite Element Analysis and Structural Mechanics. I have problem in understanding the insight of potential energy approach to derive spring element equations. I have already search for similar post and I found this, and agree with the example raise...

Recently I have been researching the topic and I have not found any completely clear answer. To restate my question (as I asked in the title), is there any element that would not absorb neutrons and if not which element has the lowest neutron absorption rate? Thank you.

Homework Statement Prove A \times (B \cap C) = (A \times B) \cap (A \times C) The Attempt at a Solution Let x \in A and y \in B \cap C \rightarrow y \in B \wedge y \in C now \exists (x,y) \in A \times (B \cap C) so (x,y) \in A \times B \wedge (x,y) \in A \times C thus...

Hi guys, :smile: I am a mechanical engineer, and want to learn finite element analysis. I want to know what is the best book to start with. Assume I have no prior knowledge of the subject. :redface: Thanks, Sety.

Homework Statement Hi every one, I am really confused on how to calculate the inverse of this Levi Civita symbole's element \epsilon^{tabc}, I tried to used this equation...

Dear all, I am writing my finite element code for linear elasticity analysis with linear tetrahedral elements. I am not new to the finite element method and my code already works well with element types of triangles, quadrangles in 2D and hexahedrons in 3D but I don't get the correct result...

I have heard of various metals and other materials turning from solid to liquid or plasma when temperature and pressure goes up. Is there a metal or other material that goes otherwise , like turns from liquid to solid when temperature and pressure is increased? Is there a material that can...

This one has me puzzled... using a variable power pack to heat an element - the powerpack is way overrated for the element (120A @ 12V secondary of transformer) so decided to build a smaller version. To get the element to about the right heat (glowing red) i set the large PP to about 25A and...

http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI14.html Hi, I was reading proposition 14 of Euclid's elements and there is only one thing which I find weird : why do we need postulate 4 to conclude that " the sum of the angles CBA and ABE equals the sum of the angles CBA and ABD."...

I am going through section 14 in chapter 3 in Mary Boas' "Mathematical Methods for the Physical Sciences 3rd ed" Example 1 is clear, but this line is confusing in example 3 (I don't understand why it shows that these are not an element of the set). I have pasted example 1 for reference...

I've got a 300 liter water heater that has an electrical element (14 kW). The issue is that the element is positioned in the top third of the heater. I fear the water will become segregated so that only water in the top third will be heated, and the lower section will remain cold. The target...

hi every body Consider we have a null hypersurface. how we can calculate volume element on it?