Properties Definition and 1000 Threads

Homework Statement Simplify. \sqrt[3]{\frac{5}{4}} The answer according to the textbook is: \frac{\sqrt [3]{10}}{2} Homework Equations -- The Attempt at a Solution Separated numerator and deonominator into individual cube roots and multiplied both by \sqrt[3] {4} ...

Homework Statement Use the properties of the determinant of a matrix to show that\begin{vmatrix}1+x^2 & x & 1 \\ 1+y^2 & y & 1 \\ 1+z^2 & z & 1\end{vmatrix}=(x-y)(x-z)(y-z) Homework Equations Properties of determinants. There's 10 of them, according to my notes.The Attempt at a Solution I used...

Let us take a function defined by y=cx To differentiate that, we use the operator d/dx \frac{d}{dx} y = \frac{d}{dx} cx^{-1} By the chain rule/implicit differentiation on the left and normal differentiation on the right we get, \frac{dy}{dx} = -1c x^{-2} What confuses me is the proper...

Homework Statement The hamiltonian for a given interaction is H=-\frac{\hbar \omega}{2} \hat{\sigma_y} where \sigma_y = \left( \begin{array}{cc} 0 & i \\ -i & 0 \end{array} \right) the pauli Y matrix Homework EquationsThe Attempt at a Solution So from the time dependant schrodinger...

Hi, I am looking for the thermophysical (viscosity, thermal conductivity, diffusivity, linear expansion, dansity) values of gases and liquids at various pressure. Can anyone tell me any useful resource of finding this data. Thanks Misbah

Hello, I would like to check my arguments for this problem. Homework Statement Consider the relation R = \{(x,y) \in \mathbb{R} \times \mathbb{R}: x-y \in \mathbb{Z}\} on \mathbb{R} . Prove that this relation is symmetric, reflexive, and transitive. Homework Equations Supposing a relation...

Hey came across this question in my physics textbook. If the surface of a material is under compression, is it hot or cold relative to the body of the same piece of material? Unfortunately their explanation doesn't make any sense what so ever! Would anyone like to give an explanation that makes...

sir , my doubt is that are than any ordered fields other than Real numbers,rational numbers,integers...

This isn't really homework, but I figure this is the most appropriate place to post this... Please do say if you think there is a more likely place it will get answered - I'm new! Homework Statement I am trying to calculate the muzzle velocity of an air rifle. I can find the time of flight...

How is density an intensive property? If density= mass/ volume wouldn't the density increase as the mass increases seeing that they are directly proportional? I'm seeing this in my Uni lecture slides on thermodynamics; that density is an intensive property which means it is mass...

i need some conceptual help for my final year project... what are the thermal properties of ice cream?? Specifically the thermal conductivity and latent heat and the relation of it's variation with temperature... i'll be adding a copy of my abstract for better understanding. oh and yeah I'm a...

Hi i am carrying out CFD analysis on a valve and i would like to use a material of OIL as the fluid body. i have already carried out simulations with water and air, can anyone tell me were i can find the properties of oil (ie density 918kg/m³) in the materials library as at the moment this...

Hello. I need help with some thermo basics. I can't understand the concept of constant volume compression/expansion. Please help me understand how it occurs. Also, I am not clear on how pressure is an intensive property. To my understanding it IS a quantity dependent on system size (eg...

Homework Statement A well lagged calorimeter of mass 120g contains 200g of water and 50g of ice, initial at 0°C. A jet of steam is blown through the water until the water temperature reaches 30°C. Calculate the mass of steam that must condensed. The specific heat capacity of Copper...

If two elements in a group operate together and can create more then 1 answer (this answer is still a part of set, not foreign) is it still a group, if so why?

Homework Statement Homework Equations The Attempt at a Solution I tried to see if the problem has any properties with determinants that i can apply but the properties i learned didn't involve the use of adjoint matrices so I'm kind of stumped on this one. Any hints would be...

Hello there. I have been reading G.H. Hardy's book "A Course of Pure Mathematics". It is a fantastic introduction to Analysis. I have no problems with the book so far, however, it does assume some knowledge in number theory. I just want to make sure that the following proofs for properties of...

Hey all, I'm doing an investigate into lock-in amplifiers and am looking for a book, or journal, which has a collection of properties/ characteristics for cables? For example, I'm particularily looking for a reliable source to quote the speed of propagation of a particular co-axial cable...

Is it known if space: 1. is "grainy" or smooth ?, 2. has singular points ?, 3. is like R^3 ?

Let p be an odd prime. Let f(a) be a function defined for a prime to p satisfying the following properties: (i) f(a) only takes the values ±1. (ii) If a=b (mod p), then f(a)=f(b). (iii) f(ab) = f(a)f(b) for all a and b. Show that either f(a) = 1 for all a or that f(a) = (\frac{a}{b})

Homework Statement Canada Post will deliver parcels only if they are less than a certain maximum size: the combined length and girth cannot exceed 297 cm (Girth is the total distance around the cross-section of the parcel). Canada Post delivers a crate with the smallest SA to your house. What...

Homework Statement 1 1 1 a b c = (b-a)(c-a)(c-b) a^2 b^2 c^2 (above is a 3x3 matrix equaling to a equation) question:"Show by applying property of the determinant"Homework Equations N/AThe Attempt at a Solution read through the whole chapter of...

Just a couple of numbers I'm having trouble finding. Does anyone know what a typical energy for a nuetrino ejected from the sun is? Any number on a guess-timate of what the density of nuetrinos is in deep space? Also, same two questions for electron nuetrinos and Tau nuetrinos. A 1...

i need the material properties of Tungsten Nitride. Here is a list of properties i need: 1.band gap at 300k 2.work function 3. electron and hole mobility 4. permittivity 5. thermal conductivity 6. heat capacity 7.SRH recombination rates(tau-n and tau-p) 8.density of states(conduction...

My friend and his brother were trying to work out what affects the size, power and height of a wave and why? Is it the moons gravity or fetch? Can anyone help?

Homework Statement the ques says: lim x tending to 0 [f(x)g(x)] exists. Then both lim x tending to 0 f(x) AND lim x tending to 0 also exist. True or False Homework Equations The Attempt at a Solution lim f(x)g(x) =lim f(x) * lim g(x) so if LHS exists then limf(x) and lim g(x) must exist so it...

Ok, so the wavelength is the length between two crests. Is it also the length of a complete wave? (sorry if I sound really stupid) The period is the time taken for one particle that makes up the wave to complete its oscillation, and it is also the time taken to make one complete wave. But I...

Homework Statement Suppose f is differentiable in \mathbb{C} and |f(z)| \leq C|z|^m for some m \geq 1, C > 0 and all z \in \mathbb{C} , show that; f(z) = a_1z + a_2 z^2 + a_3 z^3 + ... a_m z^m Homework EquationsThe Attempt at a Solution I can't seem to show this. It does the proof...

hi all, what happens if we employ two devices such that one measures position and another measures momentum but that they measure at the same time.

I'm researching solar cells, some of which use TiO2 as a semiconducting film. Modern solar cells use TiO2 nanoparticles to increase the surface area of the film. Somehow this is advantageous to the solar cell. From my limited understanding of semiconductors, I know that to get a current...

Hey guys, I have a butterworth high-pass filter, and I was asked to find it's temporal response equation to the u(t) function. That part was easy, using basic Laplace tables I was able to find the following equation: y(t)=√2 e^(-31100t) *cos⁡(31000t+π/4)u(t) However, I'm supposed to be able to...

Hey guys, I've been trying to work out this question, http://img189.imageshack.us/img189/2954/asdagp.jpg so the identity theorm is just that if the power series = 0 then the coefficient of the series must be zero. Im having trouble seeing how that negative has any influence over...

1. Homework Statement Prove that there is an additive identity 0∈R^n: For all v∈R^n, v+0=v2. Homework Equations Axiom of Real Numbers: There is an additive identity 0∈R : For all a∈R, a+0=a and o+a=a 3. The Attempt at a Solution Solution 1 (My own attempt) : Let v=(v1, v2, v3... vn). Then...

Homework Statement Matrix A is a 4 row by 5 column matrix. Matrix B is a column vector in R^{4}. We are supposed to decide whether the following are (a) no solution, (b) one solution, or (c) infinitely many solutions, or whether (d) the data do not give enough information to tell, or (e) the...

Disclosure: I am studying biochemistry so my thermodynamics education is lacking and I'm likely misinterpreting some of these concepts (that's why I'm here for help). I have always had trouble defining some properties as either intensive or extensive. I understand that extensive are...

I've seen a few short proofs that if that some transformation \Lambda preserves the spacetime interval, then \Lambda^\top g \Lambda = g where g is the spacetime metric. They have all relied on an argument using some simple algebra to show that (\Lambda^\top g \Lambda) x \cdot x = g x...

Homework Statement Use the Monotone convergence theorem to give a proof of the Nested interval property. Homework Equations Monotone convergence theorem: If a sequence is increasing or decreasing and bounded then it converges. Nested Interval property: If we have a closed interval [a,b] and we...

Hello, I am currently going over Nakahara's Geometry, Topology, and Physics and even though I have bumped into some typos/mistakes, there's something that I am sure is not a mistake but rather a misunderstanding I have of the basic concepts. Namely, in page 181, he describes the notion of...

Let K \subseteq F be fields and let R be a ring such that K \subseteq R \subseteq F . If F is algebraic over K, show that R is a field. If F is algebraic over K, then every element of F is a root of some polynomial over K[x]. But since K is contained in R, every element of F is thus a root...

I have seen some examples where a system has a resonance frequency, and, when the system changes, its Q factor also changes, and so the resonance frequency shifts, and this shift can be measured to detect the change in the system. An example I can think of is very sensitive mass measurement...

Homework Statement Theorem: Suppose A, B, C, and D are matrices of the same size. Then a) If A ≤ B and B ≤ C, then A ≤ C b) If A ≤ B and C ≤ D, then A + C ≤ B + D c) If A ≤ B, then cA ≤ cB for any positive constant c and cA >= cB for any negative constant c Prove this theorem. Must...

The completeness properties are 1)The least upper bound property, 2)The Nested Intervals Theorem, 3)The Monotone Convergence Theorem, 4)The Bolzano Weierstrass, 5) The convergence of every Cauchy sequence. I can show 1→2 and 1→3→4→5→1 All I need to prove is 2→3 I therefore need the proof...

Homework Statement class Person(object): """Defines a person with dob (date-of-birth, string), gender (two-value string), name (string) and age (integer).""" def __init__(self, dob, gender, name): assert (isinstance(dob,str) and dob.isdigit() and len(dob) == 8), 'dob is...

Dear all, I have a set of measurements {xm(Ti,mi)=x(Ti)+e(Ti,mi)}, where: _xm is the measured value _x is the actual value _e is a random measurement error for the measurement mi _Ti is a parameter I need to fit a curve to this data by some method. For example, if I use least squares...

Okay, so in class I learned that: 10^log(4x) = 4x But I don't understand why. I get that a log without a subscript is considered base 10, so: 10^y = 4x Is the way to understand "log(4x)", right? What if the problem was a different base? Would the "10" coefficient and 'log' in...

Homework Statement http://desmond.imageshack.us/Himg810/scaled.php?server=810&filename=screenshot20120131at923.png&res=medium The Attempt at a Solution So in particular I want to look at the last part of this problem. That is, "Show that S^n = 0" I know that dim(KerS^k) = k and...

Homework Statement http://s1.ipicture.ru/uploads/20120130/fcGLnUw5.png The attempt at a solution I have been trying to understand how to obtain the R.H.S. of each property from its L.H.S. but i can't find how, although i know that it's somehow related to differentiating the L.H.S. I am...

Thermal Properties -- Energy and velocity of molecules Hello all, Homework Statement (a) Calculate the total rotational kinetic energy of the molecules in 1.00 mol of a diatomic gas at 300K. (b) Calculate the moment of inertia of an oxygen molecule. Treat the molecule as two massive...

Let S be any finite set and suppose x \notin S. Let K = S \cup \left\{ x \right\}. 1. Prove that P(K) is the disjoint union of P(S) and X = \left \{T \subseteq K : x \in T \right\}. That is, show that P(K) = P(S) \cup X and P(S) \cap X = \emptyset 2. Prove that every element of X is the...

Homework Statement The curl satisfies (A) curl(f+g) = curl(f) + curl(g) (B) if h is real values, then curl(hf) = hcurl(f) + h'·f (C) if f is C2, then curl(gradf) = 0 Show that (B) holds. 2. The attempt at a solution I'm not quite sure how to interpret the "h is real valued"...