Properties Definition and 1000 Threads

Homework Statement Consider hermitian matrices M1, M2, M3, M4 that obey the property Mi Mj + Mj Mi = 2δij I where I is the identity matrix and i,j=1,2,3,4 a) Show that the eigenvalues of Mi=+/- 1 (Hint: Go to the eigenbasis of Mi and use the equation for i=j) b) By considering the relation Mi...

Sorry, my question was simply too long and complex to fit into the title. Basically my question is this. In the middle ages Iron was treated by repeatedly hearting it up and hammering it on the anvil. As far as I understand this, this would create a more dense material. So I asked myself...

Homework Statement The generators of the ##SO(n)## group are pure imaginary antisymmetric ##n \times n## matrices. Therefore, the dimension of the ##SO(n)## group is ##\frac{n(n-1)}{2}##. Therefore, the basis for the so(n) Lie algebra is given by the ##\frac{n(n-1)}{2}## basis vectors as...

Hello, I can not find the way to solve the following equation: sum of k^2 f(k) from k=1 to n. In Particular, k^2 * (1/k)

Homework Statement Am I doing this right? The question is... (ab) + (a' + b') = 1 Homework Equations (a) Commutative a · b = b · a a + b = b + a (b) Associative (a · b) · c = a · (b · c)...

I don't understand the requirements for a red-black tree. Using this photo: https://upload.wikimedia.org/wikipedia/commons/6/66/Red-black_tree_example.svg One of the 5 required properties is that all leaves are black. A leaf is a node without a child, so that would only be 11 and 15 two links...

QUESTION: In general: when a flow is considered steady does that mean all properties of the flow are steady? Or: can a flow have steady and unsteady properties?

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help...

Just checking (while trying to prove the Schwarz inequality for $<f|H|g>$, I know $ <f|g>=<g|f>^* $ please confirm/correct : If $ \psi=f+\lambda g, \:then\: \psi^*=f^*+\lambda^* g^* $ Is $ <f^*|g>=<g^*|f>^* $ and $ <f^*|H|g>=<g^*|H|f>^* $ (H hermitian)? Is $ <f^*|H|g><g^*|H|f> = -...

Hi Can anyone point to me a reference where orthogonal properties of confluent hypergeometric functions are discussed? Navaneeth

This maybe a general science question but I'll put it here. When we say that an element has so-and-so properties, how do we know those are the only properties it has. For example:- We say an element has properties like electron affinity, electro-negativity etc. How do we know these are the only...

I don't know why this is possible To use delta function properties( sifting property) integral range have to (-inf ,inf) or at least variable s should be included in [t_0,t_0+T] but there is no conditions at all (i.e. t_0 < s < t_0+T) am I wrong?

In my book following points have been given 1-due to conservative nature of electric field ,the electrostatic field lines will not form any closed loop.I want to ask how forming a loop makes if non conservative? 2-Field lines have tendency to contract in length (longitudinal contraction )like a...

Homework Statement I'm a bit at a loss - I thought the last row with '1's would be useful, but it just gave me: (b2c - bc2) - (a2c - ac2) + (a2b - ab2) and bc(b - c) - ac(a - c) + ab(a - b) But then it is a dead end. I am probably doing something stupid again ... Any help appreciated.

I am studying this in the context of group/ring theory, ideals etc. So I post it here and not in the number theory section. 6. Suppose gcd(a,b)=1 and c|ab. Prove That there exist integers r and s such that c=rs, r|a, s|b and gcd (r,s)=1. One of my attempts: From gcd(a,b)=1 there exist s',t'...

Elements like Silicon, Germanium and Gallium can be used to make solar cells but platinum can not be used. What is the exact reason? Is it related to threshold frequency? Tried to search for the answer through many sources, but couldn't get a satisfactory one. Your views and answers are really...

In the usual derivation of time dilation in special relativity, we have two frames of reference, A and B, moving relative to each other with velocity v. In A's frame, a light beam is directed vertically upward toward a mirror and reflected vertically back down. In B's frame, the light follows a...

Hi Everyone. I want to know what do you think about this Transfer function: T(\omega) = \frac{e^{i\omega\tau}}{1-\rho e^{i2\omega\tau}} If\tau is Real, this function is "good and pretty"(?), because it has a "nice" representation in time with its inverse transform: a delay plus a series of...

Two particles cannot be entangled in respect to position and momentum, I've read. But can particles be entangled by all other properties, including either position or momentum? For example by energy, momentum, spin and polarization (+some other(s)?) between two photons. I've read in some other...

Homework Statement 1. wave properties of light in a prism experiment? 2. wave properties of diffraction in a prism experiment? 3.name one apparatus that uses diffraction Homework Equations The Attempt at a Solution 1. The wave properties of light are dispersion and recombination 2. The wave...

Is there a mapping of macroscopic properties of a substance and its atomic properties? We know that colour is associated with the electron shells. What about other properties of matter like mercury liquid at room temp vs gold its neighbour on the chart a solid? Is there a mapping like...

\log_{b}\left({a}\right) =c ,0<a<1<b What can you conclude about c? explain.

Dear all, I would like to study more about the optical properties of scintillator detector in nuclear physics experiment. Is there any good reference for this? If the reference is discussed deeply in solid-state-physics, that is really nice. Actually, I am attending a "optical properties of...

Hi, I am making a faraday cage to be used in reactive ion etching of silicon. I was wondering if the size of the cage, or the surface area has any impact on it's effectiveness or how it works? I know the size of the mesh and the material I use, as well as whether or not it is grounded all...

I'm looking at the simplest example of an interacting theory, and this is the theory of a neutral scalar boson $\phi$ with $\lambda \phi^4$ interaction term. Can I ask: is there a physical interpretation of the `charge' through which this field interacts with itself? In particular, is \lambda...

Trying to an invent a fictional element/metal. I need something that could enable FTL travel and anti-gravity cars. And also biological immortality. I'm thinking something similar to this: http://masseffect.wikia.com/wiki/Element_Zero I need some help coming up with techno-science-magical...

Does anyone have a source for 303 stainless steel mechanical properties (YS, UTS, modulus, poisson's) with variation to temperature, especially around 800C? I've been searching a lot of sites... Or would it be fine to assume 303 has "good resistance to scaling at up to 871C" from...

The problem states, Show that: a) |e^(i*theta)| = 1. Now, the definition of e^(i*theta) makes this |cos(theta)+isin(theta)| If we choose any theta then this should be equal to 1. What can help me prove this? If I choose, say, pi/6 then it simplifies to |(sqrt(3))/2+i/2)| which doesn't seem to...

Use properties to show that: (question is in the attached picture) Now, it is my understanding that due to properties you can express (sqrt(5)-i) as the sqrt((sqrt(5))^2+(-1)^2) which equals sqrt(6). And (2zbar+5) can be represented as (2z+5). But this would be sqrt(6)*(2z+5) which is NOT...

Hi I want to ask which of the cast steels or forged steels provide with better shock absorption? The component has to be used in the under chassis of heavy trucks in bumpy roads. Can anyone help me with that? Thank You

Hello I was reading Spivak's calculus. It starts with discussing the familiar axioms of the real numbers. He calls them properties. At some another forum, I came across the reference to Landau's "Foundation of Analysis" as a background for analysis. So I referred to that book. On the very first...

Okay so I'm under the understanding that the way gravitation works is that each object warps the space around itself, and essentially objects caught in the warping are "falling" towards the object with the bigger warp in the center. So my question is, how do objects that are complete clones of...

Hello All :) I've heard it proposed that a reason for the fine tuned nature of our universe in a way to allow the existence of complexity and life could be that the universe itself is the product of evolution in a multi-verse. I don't want to debate around the anthropological principle as I am...

Hello, could you please give me an insight on how to get through this proof involving operators? Proof: Given an eigenvalue-eigenvector equation, suppose that the vectorstate depends on an external parameter, e.g. time, and that over it acts an operator that is the fourth derivative w.r.t...

hello! what are the physicochemical properties of the metals that facilitate the catalytic conversion in cars? what are their properties that make them act the way they do? ie. facilitate the reactions? I mean in electron/proton etc basics, atomic level thanks

Hello forum, I am new to group and ring theory, so exercices like this are making me problems: Let R={ab∈ℚ∣b is odd}. (1) Prove that R is isomorphic to ℤP, where ℤP is the localization at P, for a prime ideal P of R. (ii) Find U(R). Prove that I:=R∖U(R) is a maximal ideal. Determine which...

http://arxiv.org/abs/1409.0868 Holomorphy without Supersymmetry in the Standard Model Effective Field Theory Rodrigo Alonso, Elizabeth E. Jenkins, Aneesh V. Manohar (Submitted on 2 Sep 2014 (v1), last revised 6 Nov 2014 (this version, v2)) The anomalous dimensions of dimension-six operators in...

why light shows both particle and wave nature?

I am a part C Mechanical Engineering student and have been undertaking a project investigating the strain sensitivity of a particular glass filled composite. From my quasi-static results, the stress-strain curves seem to be reasonable and match that of the mechanical material properties...

Hello. Is there a way to calculate properties of a gas, given only it's composition? I.e. let's say i want to know what would a planet look like with an atmosphere of a mix of 50% gaseous sulphur and 50% gaseous mercury, at 500*C and surface pressure of half that of Earth. How would i go about...

Hey! :o I want to show the following properties of Ackermann's function: $A(x,y)>y$. $A(x,y+1)>A(x,y)$. If $y_2>y_1$, then $A(x,y_2)>A(x,y_1)$. $A(x+1, y) \geq A(x,y+1)$. $A(x,y)>x$. If $x_2>x_1$, then $A(x_2, y)>A(x_1, y)$. $A(x+2, y)>A(x,2y)$. I have done the...

Please help me with this question. Part a was good but I don't understand parts b or c. Thanks in advanced.

I don't understand how some terms are derived. How did the last term of 3-47 originate? How did 3-49 get so many terms from just one term in 3-41? Why integrate from V to infinite? That is not intuitive. Thas a functions are unusual because the absolute values of U,H,S cannot be computed...

If someone could explain some of the steps needed to work out these 2 questions it would be much appreciated!

I've been thinking about the properties of the Dirac delta function recently, and having been trying to prove them. I'm not a pure mathematician but come from a physics background, so the following aren't rigorous to the extent of a full proof, but are they correct enough? First I aim to...

Hey! :o Find the solution of the problem $$u_t(x, t)-u_{xx}(x, t)=0, 0<x<1, t>0 \tag {*} \\ u(0, t)=0, t>0 \\ u_x(1,t)+u_t(1,t)=0, t>0$$ I have done the following: We are looking for solutions of the form $$u(x, t)=X(x) \cdot T(t)$$ $$u(0, t)=X(0) \cdot T(t)=0 \Rightarrow X(0)=0 \\ X'(1)...

I've been searching the Internet high and low looking for the ELECTRICAL conductivity of R11. There doesn't seem to be much info on the subject and I'm stuck. Does anybody know its conductivity and/or where I could find it out?

Specifically I am interested in a book which talks about lenses, their types, where and how they are used. How do binoculars, telescopes work (how to construct them), what type of lenses to use... Am I asking for too much? Would really appreciate if any of you guys could suggest me of such a...

Homework Statement Find the domain, target space, image, rank and nullity of the linear transformation T(A)=Av, where v= (1, 2) and A is any 2×2matrix. Homework Equations The Attempt at a Solution I believe I know the domain (R2x2 vector space) and target space (R2), but I am not sure how to...

By properties I mean the +I or -I effect as compared to other functional groups along with whether it induces a +R or -R effect?