Property Definition and 608 Threads

It is said on wiki* that "Maximal compact subgroups are not unique unless the group G is a semidirect product of a compact group and a contractible group, but they are unique up to conjugation, meaning that given two maximal compact subgroups K and L, there is an element g in G such that...

Homework Statement We are supposed to prove that sin(x+y) = cos(x)sin(y) + sin(x)cos(y) Homework Equations cos(A-pi/2) - sin(A) sin(pi/2 - A) = Cos(A) sin(A-pi/2) = -cos(A) The Attempt at a Solution We had to prove all of the relevant equations but were allowed to work in groups...

[for all of the following, "lim" means the limit as n->∞] Let an be a sequence of real numbers. Theorem: if lim an = L and lim an = M, then L=M. (Incorrect) "Proof": lim an = L and lim an = M Thus, L = lim an = lim an = M (transitive property) Therefore, L=M. To me, every step in...

Hello, Saw this expression: ^{inf}_{-inf} \int e^{x^{2}} = 2 \times ^{inf}_{+0} \int e^{x^{2}} I am unable to understand this change of base. You can change from -inf to 0 and 0 to +inf but do not see how that equals to 2 * the integral from 0 to infinity. I hope someone will help me...

Homework Statement Warren Siegel, Fields, ex. IA2.3(b) Define the eigenstate of the fermionic annihilation operator as a|\zeta\rangle=\zeta |\zeta\rangle. \zeta is a Grassmann (anti-commuting) number. Show that a^\dag|\zeta\rangle=-\frac{\partial}{\partial\zeta}|\zeta\rangle. Homework...

Hi, I am actually not really concerned about what the whole details are but more whether my approach is correct to show the following statement: Let f be continuous on a closed bounded region \Omega and let (x_0 ,y_0) be a point in the interior of \D_r. Let D_r be the closed disk with center...

What is the essence of space? Is it a property of matter? If not, is it an entirely new stuff distinct from matter? If the former is true, why does space seem so homogeneous to us while the distribution of matter seems so uneven. If the latter is the case, what does it mean by the matter without...

Homework Statement Hello. I am relatively new to this subject please forgive my incompetence. Please correct me if I have misunderstandings. I understand that the cross product of two vectors (say A and B) in R3 is a vector that is orthogonal to both A and B. But how A x B be...

Use determinant property to evaluate matrice determinant Homework Statement 3x3: A = 12 27 12 28 18 24 70 15 40 What determinant property can I use to find the determinate of this matrix? I cannot see any relationship between the rows or columns. Apparently 720 comes into it somehow, but I...

Homework Statement Let X have a geometric distribution. Show that P(x>or= k+j|x>or=k) = P(X>or=j) where k and j are nonnegative integers. The Attempt at a Solution P(x>or= k+j|x>or=k) = P(x>or= k+j intersect x>or=k)/P(x>or=k) = P(x>or=k+j)/P(x>or=k) for j>or= 0 =...

Homework Statement For the construction of a thermometer, one of the essential requirements is a thermometric substance which a. remains liquid over the entire range of temperature to be measured b. has a property that varies linearly with temperature c. has a property that varies with...

Homework Statement Find the eigenfunctions and eigenvalues of the translation operator \widehat{T_{a}} Translation operator is defined as \widehat{T_{a}}\psi(x)=\psi(x+a) (you all know that, probably you just call it differently) Homework Equations The eigenvalue/eigenfunction equation is...

What is the \int(u)-1 where u is a fonction of x , forming a quadratic equation. As in: \int(u)-1 where u = x2+2ax+a2 for example. Is there a basic property for this... or do I have to play around with the fonction u , in order to integrate? ---- I know that \int(x)...

Homework Statement A characteristic property is a property that can be used to help identify a substance since it is the same for all samples of the substance. We have now studied mass, volume and density. Which of these is a characteristic property of substances? Explain. Homework...

I am confused regarding the heat properties of electromagnetic radiation. Wiki states "Any electromagnetic radiation can heat a material when it is absorbed.". Does this imply radiation with wavelengths in the visible light region can also heat a material, that is, increase its temperature? From...

I'm considering the problem: Given c \in \bold{F}, v \in V where F is a field and V a vector space, show that cv = 0, v \neq 0 \ \Rightarrow \ c = 0 I've been wrapping my head around this one for a while now but I can't seem to get it. Proving that if cv = 0 and v \neq 0 implies v = 0 is...

Hi, I am looking for a nonlinear equation capable of approximating a sigmoid curve that can be multiplied by another equation of the same type with different parameters and this product can be made linear in the parameters. I am an ecologist, so I hope I am using the right terms. I...

A set X is *this* iff whenever x is a subset of X, then x is also an element of X. Note that this is not transitivity.

d1 and d2 are metrics on a space X. Does min(d1,d2) satisfy the triangle inequality. I think it does not but I am having a hard time finding a counter example.

I want to show the triangle inequality, d(x,x)=0, d(x,y)\neq0 for x\neqy implies that d(x,y)=d(y,x). Note that I do not have d(x,y)>0. But I know how to show this if I can get the transitive property. I have been trying to use the triangle ineq. to establish d(x,y)>=d(y,x) and...

Does there exist an uncountable set of positive reals such that every countable decreasing sequence from that set sums to a finite number?

Hi, I am reading Baby Rudin on my own to get prepared for the analysis class that I will be taking in the fall. I got up to this theorem, and I was wondering if someone can clarify me the proof of this (i.e. Thm 1.11, the first theorem). 1.11 Theorem: Suppose S is an ordered set with the lub...

Statement: 37. Let G be a group and suppose that a * b * c = e for a, b, c \in G. Problem: Show that b * c * a = e. Thought Process Can we assume that our binary operator * is abelian. Thus, a * b * c = a * (b * c) = (b * c) * a = b * c * a. Thanks, JL

I haven't been taking math for 3 years so I have a question about the following: is 14m6n2 the same as 2mn x 7m5n basically asking this because I am not sure whether or not I can factor the terms out like this if this information is insufficient I can post the whole problem. Thanks in advance.

Hello, I'm trying to prove the time differentiation property of Laplace transform. dx(t)/dt = sX(s) http://img10.imageshack.us/img10/290/tlaplace.jpg http://g.imageshack.us/img10/tlaplace.jpg/1/ how do i continue from here ?

I saw the technique of using a mathematical system called the "Four minute clock". Basically, the clock has 4 numbers, 0, 1, 2 and 3, and only one hand. We can make a summation table which will look like the image attached. According to the text, if there is symmetry (reflection) across the...

There are certain properties of lines of force, I know they are not real, but following these 'properties', given position and intensity of magnetic/electric field sources we will be able to reconstruct these lines without any practicals. So I have a problem with lines of forces. Sources...

Hello, according to my book of 'Geometric Algebra' the operation of Left-Contraction for Blades has a distributive property in respect to addition. However the authors do not prove it, nor they give the smallest hint on how to derive it. The property says that...

Sources say if lines are parallel they will repel else try and merge which I don't agree and even see practically. Suppose we have 2 opposite charges facing each other, the lines are parallel, they should repel. Similarly if 2 equal charges are facing each other, the direction of the lines...

Hi there, i was wondering if you had any thoughts on the following question: Let (a_{1}, a_{2}, ..., a_{2n}) be a permutation of {1, 2, ..., 2n} so that |a_{i} - a_{i+1}| \neq |a_{j} - a_{j+1}| , whenever i \neq j . Show that a_{1} = a_{2n} + n, if 1 \leq a_{2i} \leq n for i = 1,2, ..., n

The derivative of arctan(x) is \frac{1}{x^2+1} The derivative of arctan(x - sqrt(x^2 + 1) is \frac{1}{2(x^2+1)} take arctan(x) to be A and arctan(x-sqrt(x^2 + 1)) to be B. A'=\frac{1}{x^2+1} B'=\frac{1}{2}*A' Why doesn't \frac{1}{2}*A=B? If you'd like, I can prove the derivative...

I'm just learning about the "spin" property of particles but I'm a little confused. What exactly is the "spin" property of particles and why is it important? Thanks for the help!

1. How to solve -1<1/(x+1)<2 2. Now if I switched both sign and took the reciprocal such as 1/-1>(x+1)/1>1/2 I get the right answer: x<-2 and x>-1/2. 3. Without using the reciprocal property would be lengthy and confusing, but I have very little and contradictory information found...

Considering the visual representation of an electric/magnetic field (by 'line of forces'), is this fact about the properties of lines of force true? - "Each line of force has equal strength" The websites/books are pretty timid in reviling the properties of lines of forces...at least for E.Fs.

Im a new student and I have searched high and low for a clear explanation as to why electrons and protons have something called charge. So far my basic understanding stands at 1. Charge is a fundamental conserved property of certain particles like electrons and protons. 2. This...

Orthogonality Property of Hyperbolic functions ? Hi all, I have seen Orthogonal property for trigonomeric functions but I am unsure if there is something similar for sinh() , cosh() ? . I know that the integral of inner product of the two functions should be zero for them to be...

I have a problem, in Newton's second law F=m*a in inertial frame. In the accelerated frame a mass should be affected by a inertial force, but the force in the original inertial frame don't change, so real force is just like the temperature and will be the same in different frames?

Thermodynamics: property tables HELP! Homework Statement 1 kg of R-134a fills a 0.14m^3 weighted piston cylinder device at a temperature of -26.4C. The container is now heated until the temp is 100C. Determine the final volume. The Attempt at a Solution So the boiling point is -26.1...

Crud, it looks we have a coyote nesting in the brush next to our property. I saw it this morning as I was walking down to the office. Bad news for our kitties. :frown: And right now I don't know where Little Tyke is, but she usually is out this time of the morning. I was afraid of this. Once...

Homework Statement How do you show that int[delta(t)]dt from negative infinity to infinity is 1? Homework Equations Dirac delta function defined as infinity if t = 0, 0 otherwise The Attempt at a Solution My teacher said that it has to do with m->infinity for the following...

Homework Statement The boiling points (ºC) of methanol, ethanol, 1-propanol, 1-butanol, and 1-pentanol are 64.7, 78.5, 97.2, 117 to 118, 137.5, respectively. The melting points are -97.8, -114.1, -1277.0, -90.0, and -79.0, respectively. Explain these trends with reference to molecular...

I have to prove that for all k,m,n \in N that if m+k = n+k, then m=n. The problem mentions that I must prove this by induction. I did the base case k = 0: If m+0 = n+0, by identity m=n. Then I attempt to show that m+1 = n+1 implies m=n, but I am stuck, I don't see how induction can be...

Homework Statement Give a proof for the operation * is commutative being a structural property. Homework Equations The Attempt at a Solution * is commutative I know this means that I have to show (a*b)*c=a*(b*c) I'm not sure where to go now

Homework Statement Show that : || a x b||^2 = ||a||^2||b||^2 - (a . b)^2Homework Equations The Attempt at a Solution I don't know where to start off

Hi! I wonder how to prove that if y(t)=sin(t) solves an autonomous ODE f(y,y',...,y^(n))=0, then x(t)=cos(t) is also a solution. I mean I'm a bit distracted by the fact that all derivatives of y are present here. For example in the equation for a pendulum there are just y and y'' and a...

Matrix multiplication: Commutative property. Hello, First time poster. I have got a question about commutative property of matrix multiplication. Literature says that matrix multiplication is communicative only when the two matrices are diagonal. But, I have a situation with an...

Homework Statement Let X be a topological space, a subset S of X is said to be locally closed if S is the intersection of an open set and a closed set, i.e S= O intersection C where O is an open set in X and C is a closed set in X Prove that if M,N are locally closed subsets then M...

What does orthonormality of a basis set i.e. {χ_i} stand for? I am reading the Mulliken Population Analysis and there are integrals that are simplified by this property of basis sets and I can't quite catch what is it.

Forgive me if this sounds a little uninformed but in the world of academia or engineering or work and what-have-you, how does intellectual property? When a company hires you to design something, say a motor, do they own all work that you produce in that given time? What about if I work on...

Dual "wave-particle' property of electrons I know that electrons get a dual 'wave-particle' property. I wonder if the velocity of the electrons is different, is that the diffraction pattern in the experiment proving that electrons get wave property differ? Also, is that electron gets a definite...