Elements Definition and 984 Threads

Hi, Is there a way to find elements in ##GL_2(\mathbb{R})## with an arbitrary order other than by trial and error? Suppose I wanted to find ##A\in GL_2(\mathbb{R}):\; o(A)=165##. Is there no methodical way to find this? Is it possible perhaps I can find a product of matricies, each...

The state, ##| S\rangle##, say, of a system is represented as a vector in a Hilbert space. ##\psi (x, t)## is the representation of the state vector in the position eigenbasis; ##\psi (p, t)## in the momentum eigenbasis et cetera. That is, ##\psi (x, t) = \langle x|S\rangle##; ##\psi (p, t) =...

Homework Statement I have the following code which manipulates with basics of structures. There are function like reading and sorting data from structures. Now, I don't know how to write a function that reads name and surname of an author of a book, and then prints data about books that are...

Hey all. I am currently reading an article and there is a paragraph that I am having a hard time understand. This is what the paragraph says: "Since Ar = Arτ and Ai = -Aiτ, we know that only the lower triangular (including the diagonal) elements of Ar are independent and only the strictly lower...

How do I interpret the following: U={A|A^2=A, A is an element of M22} is not a subspace of M22. I don't quite understand what it's asking in terms of A^2=A. Thanks.

Given x,y elements of a hilbert space H, how do we conclude that x = y? Since there is an inner product, we can say that x = y only if (x,z) = (y,z) for all z in H. But is there a definition of equality which does not depend on the inner product? A hilbert space is a special instance of...

Dear Everyone, I'm searching for some specific elements for infrared (IR) sensor, such as Thermopile, Pyroelectric, Bolometer, MCT(HgCdTe), PbSe, or InSb sensors. Does anyone know how to get these kinds of elements ? ( I need some information about the manufacturers...) The elements are...

I've often wondered, but have never found a solid explanation for, why the chemical elements are found together in nature? Why aren't atoms all in a somewhat homogenous mix? Why are X atoms found with other X atoms? And why are isotopes found together, such as Uranium 235 and the far more...

Homework Statement so for a side task I'm supposed to assign people to groups for an icebreaker in python, can anyone give me links to theories that I could read up on or give me suggestion X number of people at my company signed up for a dinner roulette as a way to meet new people. Everyone...

Looking for research answering the following question: "What is the earliest point in time, in the Universe, that exoplanets comprised of life-sustaining elements such as carbon, water, etc. could have formed?" I've read that the earliest known stars likely formed about 500 million years after...

Hi all, I'm curently meeting the following problem and can't figure it out by myself. Assume we have to vehicles in space, a target and a chaser spacecraft . The target spacecraft defines the RTN frame of reference. Given the position and velocity of the chaser in RTN-coordinates, how can I...

Hello. I'm having trouble understanding what is required in the following problem: Find the relation between the matrix elements of the operators $\widehat{p}$ and $\widehat{x}$ in the base of eigenvectors of the Hamiltonian for one particle, that is, $$\widehat{H} = \frac{1}{2M} \widehat{p}^2...

I have the following theorem : "In a circle the angle at the center is double the angle at the circumference when the angles have the same circumference as base." (Figure is in the link) http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII20.html English isn't my first language, so I...

We have the following statement by Euclid : "I say further that the angle of the semicircle contained by the straight line BA and the circumference CHA is greater than any acute rectilinear angle, and the remaining angle contained by the circumference CHA and the straight line AE is less than...

http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII15.html I have understood the proof in general. It is only a small detail which I'm not sure. Maybe it's because english isn't my first language. Anyway, the part of the proof which says : "Then, since BC is nearer to the center and...

"Then, since on the circumference of each of the circles ABDC and ACK two points A and C have been taken at random, the straight line joining the points falls within each circle, but it fell within the circle ABCD and outside ACK, which is absurd. Therefore a circle does not touch a circle...

Homework Statement Construct $\mathbb{F}_{16}$ as a quotient of $\mathbb{Z}_2[X]$. How many non-zero elements are primitive in this field? Calculate $|GL2_(\mathbb{F}_16)|$. Homework Equations Primitive Theorem The Attempt at a Solution For the first question, I don't know how to construct...

Homework Statement A compound of ether (0.287 g) and chloroform (0.568 g) evaporates in the temperature 373 K in an empty container with volume 0.0001m3. Find the pressure of each element. I don't know which formula of ether should I use since there are many. However even if I knew the n of...

My understanding is the atomic model has electrons occupying shells and in particular numbers, but what's known about why they arrange themselves into shells and in those particular numbers? The teaching is that electrons have a negative charge and protons have a positive charge - but why do...

First, two definitions: let ## \varrho (M)## be the probability density of macro states ##M ## (which correspond to a subgroup of the phase space) and ## \mathrm{d} \Gamma ## be the volume element of a phase space. In my lecture notes, the derivation for continuity equation of probability...

Homework Statement If I am given ##n(A)## and ##n(B)## for two sets A and B, and also provided with ##n(A\cap B)^2##. We are supposed to find ##n((AXB) \cap (BXA))##. Homework Equations My teacher said that the formula for ##n((AXB) \cap (BXA)) = n(A \cap B)^2##. I am not sure how do you get to...

I have a question about density: would it, in principle, be possible to create something with greater density and hardness than, say, Osmium? Or is that impossible? Is density constrained by the elements of the periodic table, or can something with greater density be created? The finished...

Let $F$ be a field with $q^n$ elements, where $q$ is an odd prime. Write $q^n=2m +1$ with $m \in \mathbb{N}.$ If $r \in F^{\times},$ show that the equation $y^2= r$ has a solution iff $r^m=1.$

Homework Statement I was working through my text on deriving the tensor for Angular momentum of the sums of elements of a rigid body, I follow it all except for one step. Here is a great page which shows the derivation nicely - http://www.kwon3d.com/theory/moi/iten.html I follow clearly to the...

Homework Statement Please see the attached file if my inline insertion does not work. Homework Equations ##det(A)=det(A^T)##[/B]The Attempt at a Solution Since a matrix has a determinant of zero only when it's columns are linearly dependent, we look for a set of points [x1 x2] such that...

we can use avogadro's law and gay lussacs law to find atomicity of gases but what about solid elements

I manufacture heating elements and a customer wired a delta heater in parallel with a wye heater. They claim that this lowers the overall resistance of the delta thus causing this element to draw more amps than what it was designed for. I disagree and do not see how the heater is eternally...

I recently read this kind of question on Quora and found it interesting. Do all of the Earth's materials(and therefore humans) belong the same star of different star? What's more likely? In my opinion, the chances of all of the material belonging to one star are pretty slim because a complex...

Since most planets in the earliest stages of formation are very hot and fluid, why is it that we find on Earth areas where there are substantial deposits of heavier elements - gold, uranium, etc in the crust? Intuition suggests that these relatively rare elements would become widely dispersed...

How many of the [ 92?] naturally occurring elements could be found in hand-full of sand ?. Including those only present at minuscule , but measurable , amounts. http://en.wikipedia.org/wiki/File:PismoBeachSand.JPG

See title. I have a table that I've named B. And I want to create table that is essentially the change in values of B. If I was writing this on paper I would say: Let ##b_i \in B##, for ##0\leq i\leq100##. Then let ##c_i \in C## such that ##c_i= b_{i+1}-b_{i}##. I don't know how to say that in...

I checked out a very nice copy of Euclid's Elements from my university library containing unabridged translations of all 13 books. Nice big book, one proof per page, lots of diagrams. It's been interesting so far to flip through and even work a couple of the proofs myself, but now I want to...

This is from an example in my textbook: "The polynomial x^2+x+1 has no root in Z mod 2, and so is irreducible. Hence the required field is: F = Z_2[x] / <x^2 + x + 1> = {a + bt | a,b are elements of Z_2; t^2+t+1 = 0}. Thus F = {0, 1, t, 1+t} and t^2 = t + 1." I have two questions. My first...

Homework Statement My professor wants us to program on Python, where we have a certain sequence, for example: sequence = ("one", "two", "three", "four") I need to replace one of the sequence elements (example: "one") with another element (example: instead of the word "one", I need to put...

I am confused as to why thallium is toxic, while the other members of group 13 are safe? (Quotes are from Wikipedia) Boron - "Elemental boron [is] non-toxic to humans and animals" Aluminum - "... [has] extremely low acute toxicity..." Gallium - "...metallic gallium is not considered toxic..."...

Suppose you want the 1-particle matrix elements of an operator in QFT, e.g. \langle p' |\phi^4(x)|p\rangle It seems you would calculate this perturbatively by first Fourier transforming the x-variable to q, assuming an incoming particle with momentum p, an outgoing particle with momentum p'...

Hello! (Wave) Consider two sets $D=\{ d_1, d_2, \dots, d_n\}$ and $E=\{ e_1, e_2, \dots, e_m \}$ and consider an other variable $K \geq 0$. Show that we can answer in time $O((n+m) \lg (n+m))$ the following question: Is there is a pair of numbers $a,b$ where $a \in D, b \in E$ such that $|a-b|...

Hello! :o Which are the elements of $\mathbb{F}_{2^2}$ ?? (Wondering) There are $4$ elements, right?? For each element $a$ in $\mathbb{F}_{2^2}$ it stands that $a^2=a \Rightarrow a^2 \in \mathbb{F}_{2^2}$, right??

I'd like to understand more about how/why carbon-based life comes about. All things are atomically based, why is it that carbon atoms/elements are able to sustain life better than any other element? Thank you

For group 15 elements the order of basicity given is NH3 > PH3 > AsH3 > SbH3 > BiH3 And order of reducing strength is BiH3 > sbH3 > AsH3 > PH3 > NH3 Why are they in opposite order? Reducing nature means tendency to donate electrons. Basicity means strength of bases and hence as basicity...

Hi! (Smile) A heap is a complete binary tree $T$. That means that a node of the tree has at most two children and for each nonempty subtree $t$ of $T$ it holds that the key of $t$ is greater than all the keys of the left subtree of $t$ and smaller than all the keys of the right subtree of $t$...

Why is it that one atom such as hydrogen has one proton while others have many. What is the mechanism driving this force which causes some atoms to be marked for one protons and others for many? And once they are say marked as hydrogen they can be nothing else, correct? Since hydrogen is the...

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...

Hello! (Wave) I want to describe an algorithm that given an unsorted array $B$ that stores $m$ integers, and any integer number $y$, determines if there are two elements of the array of which the quotient is equal to $y$. The time complexity of the algorithm should be $O(m \log m)$. We have to...

I am reading D.G. Northcott's book: Lessons on Rings and Modules and Multiplicities. I am currently studying Chapter 2: Prime Ideals and Primary Submodules. I need help with an aspect of the proof Proposition 3 in Chapter 2 concerning the demonstration that all the maximal elements of...

Homework Statement I wanted to ask why the symbols of capacitor , resistor and inductor is such which they have..?? Why are we denoting capacitor by 2 parallel plates why not 2 zig-zag plates..and same for inductor??Homework EquationsThe Attempt at a Solution As much I got , resistor has such...

Hey! :o Let $p$ an odd prime and $F=F_{p^n}$ the finite field with $p^n$ elements. 1. Show that the set $F^2=\{a^2, a \in F\}$ has $\frac{p^n+1}{2}$ elements. Conclude that , if $t \in F$ the set $t-F^2=\{t-a^2, a \in F\}$ has $\frac{p^n+1}{2}$ elements. 2. For $t \in F$ show taht the set...

Hello! (Wave) I want to describe an algorithm with time complexity $O(m)$ that, given a set $M$ with $m$ numbers and a positive integer $p \leq m$, returns the $p$ closest numbers to the median element of the set $M$. How could we do this? (Thinking)

Hi, I'm trying to understand the process of finding the elements of a given group, such as SE(2). What I do understand is limited to finding elements of very simple symmetry groups, such as those corresponding to rotations/reflections of shapes. My overall knowledge of groups is also pretty...

My interest leans more towards space opera than hard science fiction, but I'm aware that I can't completely ignore the universe as we know it. A question that has intrigued me lately is: "Are there really new elements and materials to be found in the galaxy, or are we going to find the same...