Elements Definition and 984 Threads

Homework Statement Let R be a subring of ℂ such that the group of invertible elements U(R) is finite, show that this group is a cyclic group. (Group operation being multiply). Homework Equations The Attempt at a Solution I have the answer, and I got very close to getting there myself before...

1. Explain briefly an example of open loop system. At the same time, explain how this example works with the functions of the elements in the system. example is pop up toaster The Attempt at a Solution The pop up toaster can be set for the desireddarkness of the toastedbread. The setting of the...

Homework Statement Prove the collection of all finite order elements in an abelian group, G, is a subgroup of G. The Attempt at a Solution Let H={x\inG : x is finite} with a,b \inH. Then a^{n}=e and b^{m}=e for some n,m. And b^{-1}\inH. (Can I just say this?) Hence...

Homework Statement 0.2243 g of compound C give 0.3771 g of carbon dioxide, 0.0643 g of water and 0.2685 g of silver bromide. Determine the empirical formula of the compound. Homework Equations Why the empirical formula only takes C,H and Br into consideration, but singles out Ag? Ans...

I've heard chatter about possible new elements on other planets and even hidden on our own, Could this be possible?

I was just watching a very particular old documentary, when the question hit me. I could probably manage an educated guess, but I don't really know what exactly determines how much of a certain element there is(except H and He, those are obvious).

Homework Statement calculate the voltages and currents for each element in the circuit? the resistances are as follows R1 = 1 KΩ R2 = 2.4 KΩ R3 = 1.2 KΩ R4 = 1 KΩ R5 = 1.2 KΩ. Vs= 6V Homework Equations Is - I1 = 0 I1 - I2 - I3 = 0 I3 - I4 = 0 I2 + I4 - I5 = 0 -Vs +V1 +V2 +V5 = 0...

Author: Michael Comenetz Title: Calculus: The Elements Amazon Link: https://www.amazon.com/dp/9810249047/?tag=pfamazon01-20 Prerequisities: High-School mathematics Level: Undergrad

Author: Euclid Title: Elements Free Resources: http://aleph0.clarku.edu/~djoyce/java/elements/elements.html http://farside.ph.utexas.edu/euclid/Elements.pdf Amazon Link: https://www.amazon.com/dp/1888009195/?tag=pfamazon01-20 (please feel free to give more links to good versions)...

Author: H.M. Schey Title: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus Amazon Link: https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20 Prerequisities: Calculus 1,2,3 Table of Contents: Preface Introduction, Vector Functions, and Electrostatics Introduction...

Hey guys, I'm having trouble with sampling data from a force/torque sensor. I'm using Serial Com to receive the readings from the sensor, which is stored in a character of with 45 individual elements. What I'm trying to do is to pick out pieces of these data and store them separately. I'm...

If you have an operator a represented in some basis l1>, l2> you find its matrix elements by doing Aij = <ilAlj> But more oftenly you are interested in the expectation value of A. So you take: <ψlAlψ>. My teacher tends to call these numbers matrix elements too. But which matrix element...

On one side one can define second-order variables as ranging over all elements of Pk(M) for all natural numbers k (P=power set of M, M is the universe of the model, superscript being iteration). On the other side it is sometimes defined as ranging over all first-order relations and predicates...

I have a question that is a little hard to explain, since i don't know the name of this method, but I'll try my best, if anyone knows the name please do tell me. So let's say we have three numbers, 1 2 3 (in this order) and we have a container for this numbers: C123 and we have some...

The possible values of the diagonal elements of a density matrix are restricted by the condition \mathrm{Tr}~\rho = 1 . Are there any restrictions on the possible values of off-diagonal elements, apart from the obvious \mathrm{Re}~\rho_{nm} = \mathrm{Re}~\rho_{mn}, \mathrm{Im}~\rho_{nm} = -...

Homework Statement I need to evaluate an integral of the form: h(\vec{x}) = \int d^3\vec{x}' \frac{\delta(r' - R)}{|\vec{x}-\vec{x}'|} where r' = |\vec{x}'| = \sqrt{x'^2 + y'^2 + z'^2}. Homework Equations The above, and maybe the fact that \delta(g(x)) = \sum_i \frac{\delta(x -...

Homework Statement Suppose R is a partial order on a set A. Then every finite, nonempty set B \subseteq A has an R-minimal element. Homework Equations Partial orders are characterized by: Reflexivity: xRx Transitivity: xRy \wedge yRz \rightarrow xRz Antisimmetry...

Is there a "vector" version of The Elements? I have noticed that many theorems in classical geometry can be proven using vectors. Thus, I am naturally inclined to believe that pretty much every theorem in the Elements can be proven using vectors (using the vector space axioms and the vector...

Let $G$ be a group of order $56$ having at least $7$ elements of order $7$. 1) Prove that $G$ has only one Sylow $2$-subgroup $P$. 2) All elements of $P$ have order $2$. The first part is easy since it follows that the number of Sylow $7$-subgroups is $8$. I got stuck on part 2. From part 1 we...

Let $G$ be a finite group of order $4n+2$ for some integer $n$. Let $g_1, g_2 \in G$ be such that $o(g_1)\equiv o(g_2) \equiv 1 \, (\mbox{mod} 2)$. Show that $o(g_1g_2)$ is also odd. I found a solution to this recently but I think that solution uses a very indirect approach. Not saying that that...

Folks, Trying to get some appreciation for what is going on in the attached schematic of 1)Euler bernoulli and 2) Timoshenko beam elements. For the first one, ie the top picture, how was ##u- z \frac{dw}{dx}## arrived at? thanks

I would like to know on how to determine the elements based on received frequency from Space? Such as water H2O Does anyone have any suggestions on where to find the reference materials? Thanks in advance for any suggestions

1) Show that (R,*,+) is a ring, where (x*y)=x+y+2 and (x+y)=2xy+4x+4y+6. Find the set of unit elements for the second operation. I understand that the Ring Axioms is 1. (R,+) is an albein group. 2. Multiplication is associative and 3. Multiplication distributes. I just don't understand how to...

If I have (for simplicity) a vector ( A, B) where A and B are matrices how does the transpose of this look, is it ( AT, BT) or (AT BT)

Homework Statement Compute 21 elements of the Riemann curvature tensor in for dimensions. (All other elements should be able to produce through symmetries) Homework Equations R_{abcd}=R_{cdab} R_{abcd}=-R_{abdc} R_{abcd}=-R_{bacd} The Attempt at a Solution I don't see how 21...

Hello, why the same quantity of different elements behave in the same way (take about 22,4 L) when they are gas and they don't when they are liquid ?

Homework Statement One liter of nitrogen combines with 3 L of hydrogen to form 2 L of ammonia. If the molecules of nitrogen and hydrogen have two atoms each, how many atoms of hydrogen and nitrogen are in one molecule of ammonia? Homework Equations Chemical equations The...

Find all the abelian groups of order $2100.$ For each group, give an example of an element of order $210.$ $2100 = 2^2 \cdot 3 \cdot 5^2 \cdot 7,$ then $G_1 = \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb Z_3 \times \mathbb{Z}_5 \times \mathbb{Z}_5 \times \mathbb{Z}_7 \cong \mathbb Z_{10}...

Homework Statement Let A be a set with 8 elements and B be a set such that A U B has 12 elements. What is the number of elements in P(B\A) U P(∅)? Homework Equations The Attempt at a Solution I have no idea what it means to ask what are the number of elements in a probability.. Is it the...

Is there a specific reason for how compounds are named? Like NaCl for instance, what's the criteria to have NaCl rather than ClNa?

Hi, suppose I want to look up the crystal structure of a pure element (for example, the structure of pure Tellurium), is there an online database or reference to easily find this information? Thanks.

Folks, I am having difficulty understanding how this global matrix is assembled with the naming convention used as shown in attached. The numbers in the corners such as 1(1,2) etc in figure 4.6.3 (b) denote the global and element numbers respectively. Can anyone shed light on how this...

I know that in the process of fusion in Stars, the hydrogen fuses into helium and so on until Iron is formed. The fusion stops after the formation of Iron and the graviatational force wins to take over the star evolution. Then how do we account for the elements which are havier than Iron?

Folks, The element equations for a uniform bar element with constant EA according to the attachment is given as ##\displaystyle \frac{E_a A_e}{h_e}\begin{bmatrix} 1 &0 &-1 &0 \\0 &0 &0 &0 \\-1 &0 &1 &0 \\ 0 &0 &0 &0 \end{bmatrix}\begin{Bmatrix} u^e_1\\v^e_1 \\u^e_2...

Hi. I'm trying to understand a statement from the book Field Quantization on the evaluation of the S-matrix elements for a certain initial and final state in QED. The author states, if one is evalutating a matrix element on the form \langle k_1' \lambda_1', \ldots, \bar p_1' \bar s_1'...

Hi! I'm trying to learn the Feynman rules trough Wick's theorem right now and I'm focusing on QED. Here the first order term of the S-operator can be written as -ie\int d^4x :\bar \psi(x) \gamma^\mu \psi(x) A^\mu(x): but the author of the book I'm reading (Greiner Reinhart) claims that all...

Our math Teacher asked us to find how many equivalence relations are there in a set of 4 elements, the set given is A={a,b,c,d} I found the solution to this problem there are 15 different ways to find an equivalence relation, but solving the problem, i looked in Internet that the number of...

Problem: -The Union of set A, set B and set C has 104 elements. -The Union of Set A and B has 51 elements -The Union of Set A and C has 84 elements -The Union of Set B and C has 97 elements -The Intersection of Set A and the Union of Set B and C has 17 elements. -Set C has twice as many...

Is there a technical term in group theory for (what I would call) partially specified elements of a group? I mean "partially specified" in the following sense: An elements of a group acts as permuation on the set of elements of the group. So a group element can be considered to be a function...

A friend wrote this in an exchange we had about iron and its role in the process of fusion. I question the last sentence. Is it right, and what is the "coating"? The creation of the element iron via fusion "is the final peal of a star's natural life" (if the star is massive enough to even get...

Homework Statement The question asks me to determine whether the statement is true or false, the statement being .∅∈{0} Homework Equations The Attempt at a Solution I said that the statement was true, but apparently it is false. Wouldn't a set such as {1,{1}} be made up of the...

Homework Statement Suppose \Omega = \mathbb{R}. Let A_n = [0,\frac{1}{n}]. Let \mathcal{A}=\{A_n:n\in\mathbb{N}\}. Is \{0\} an element of \mathcal{F}=\sigma(\mathcal{A})?Homework Equations The Attempt at a Solution Clearly \lim_{n\rightarrow\infty} A_n = \{0\}. Not sure how to show that it...

Hi all, I would like to know if its possible and consistent to compose the global system matrix with different FEM elements such as frame, plane, shell solid etc... Theoritically all of them will have the same DOF per node just only comprising the local matrix will differ. And as long as we...

In the following circuit, a) identify all combinations of 2 or more circuit elements that are connected in series and b) Identify pairs of circuit elements that are connected in parallel. http://imgur.com/keorO a) Seems easy enough, the 4 and 6 ohm resistors are in series, and so are the 5...

Homework Statement List the elements of the subgroups <3> and <7> in U(20). Homework Equations The Attempt at a Solution U(20)= {1, 3, 7, 9, 11, 13, 17, 19} = <3> = <7>. So basically I have that the common elements of, <3> and <7> and U(20), under + modulo 20, are all...

Hello there! First of all, I couldn't find this topic around here but I could be blind, so if the answer is posted somewhere else, just leave me the link as a response, thank you! :blushing: I am trying to figure out few things about where the heaviest elements come from. I know that Iron...

Homework Statement In the process of trying to prove something else I found it would be helpful if rn\inI, where I is an ideal, n\inN, and r\inR and R is a ring, then r is in I. Homework Equations I is an ideal if a\inI and b\inI then a+b\inI, a\inI and r\inR then ar\inI, and I is not the empty...

Homework Statement If Z2={[0],[1]} with addition and multiplication modulo 2. How many elements does GL(2,Z2)={2 by 2 matrices with determinant 1 and entries from Z2} have? The Attempt at a Solution A\inGL(2,Z2) then det(A)=[1]={...,-3,-1,1,3,5,...} Suppose A=|a b:c d| then...

Homework Statement Ok so this satellite is orbiting the earth. The position vector is r = -0.707i + 0.707j + 0k and velocity vector is v = 0i + 0.5j + 0k. To find Vo (the angle between vector n and e), my book said the formula to use is arccos{(e dot r)/(|e||r|)}. However, I got 98 degree by...

I thought all heavy elements came from supernovae, but a recent article by John Baez corrected my ignorance. There is a nice photo too at http://math.ucr.edu/home/baez/diary/index.html#now