Properties Definition and 1000 Threads

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...

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...

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...

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"...

Trying to determine the "Safe" properties of Face Guards I work in a sports science laboratory and I've been set the task of trying to create a simple and inexpensive test to determine which face guards are safe when two field hockey players clash heads (one wearing a face guard the other...

Was wondering how Jupiter's hydrogen liquid core converts the energy to create a magnetic field? and How exactly do these properties behave? I understand that my phrasing of the Question might be odd and may be wrong but i was just wondering how it worked

https://www.physicsforums.com/attachments/42263 https://www.physicsforums.com/attachments/42264 how we doing? i was just wondering does anyone have the properties of the following similar to the images attached.Natural gas, Water, standard oil. say motor oil properties.any oil properties...

Homework Statement Find the laplace transform of f(t)=(t-5)e^{-17(t-5)}u(t-5) The Attempt at a Solution The answer I got was \frac{e^{-5(s+17)}}{(s+17)^{2}}. I thought I finally understood the process, but when I plugged it into wolfram alpha, the answer I got was different...

I am wondering what are the possible homomorphisms \tau : Z\overline{+} -> Z\overline{+} From this it should be possible to determine which is injective, surjective, and which are isomorphic. Homomorphisms between Z plus to Z plus will all be of the form \tau(x) = nx since \tau(x) =...

So I need to find a vector v with these properties 1. magnitude of 10 2. angle of 45° with positive x-axis 3. angle of 75° with positive y-axis 4. positive k component. I understand basically just that the k component has to be positive. Any help would be appreciated.

Homework Statement Express in terms of logarithms x, y, z or w. Problem: loga(x8w/y2z4) Homework Equations log(u/w) = log u - log w log(uw) = log u + log w The Attempt at a Solution Here are my attempts: As you can see, the answers are pretty similar. I'm assuming...

Say a core collapse event of a massive star occurs, forming neutron star matter in its core. However, the explosion manages to eject enough core mass such that the remnant is below the Chanrasehkar limit. At this point, gravity would no longer be able to overcome electron degeneracy pressure...

Hi everybody, This is my first post in this forum although I started following it some time ago. My question is related to rotational properties involving harmonic oscillator model. Homework Statement We are told to evaluate the expectation value of the rotational constant of a...

Homework Statement Prove that the group Q/Z under addition cannot be isomorphic to the additive group of a commutative ring with a unit element, where Q is the field of rationals and Z is the ring of integers. Homework Equations The tools available are introductory-level group theory and...

Hi! I need a reference (book, webpage) that explains how the structure of a polymer affects its properties. I've found plenty of material over how structure changes its mechanical properties, but I could not find how it changes other parameters (e.g. electrical conductivity, boiling point...)

Antioxidants react with reactive oxygen species (such as hydrogen peroxide) to produce water. And example of this is catalase which is present in bacteria such as E. coli and P. aeruginosa. It is also known that Honey has antibacterial properties. One factor is hydrogen peroxide that kills...

I am aware of the theorem |G/Z(G)|=p with p prime implies G/Z(G) is cyclic and thus G is abelian, but I do not understand why. Is there not a theorem that says G abelian \Leftrightarrow Z(G)=G? So what if |G|=p^{3} and |Z(G)|=p^{2}? This implies |G/Z(G)|=p implying G is abelian however...

Homework Statement A solid cone is obtained by connecting every point of a plane region S with a vertex not in the plane of S. Let A denote the area of S, and let h denote the altitude of the cone. Prove that: (a) The cross-sectional area cut by a plane parallel to the base and at a distance t...

Hey guys, I'm working on calculating the enthalpy, entropy and internal energy of substances. treating them as an ideal gas. I wonder if I could be pointed in the right direction with some calculations. Enthalpy change: h2-h1=∫cp dT+ ∫[v-T(∂v/∂T)P]dP At ideal gas the pressure integral...

because the only thing the definition asks to check is the closure and inverse axioms? this arose from a problem I was working on. elements with infinite order of an abelian grp G do not necessarly make a subgrp with 0. counter example: Z x Z3 consider (1,1),(-1,1) both with inf. order but...

Okay, I have read all the threads on this site that I could find about Bernoulli's equation and blood pressure, but I am still really confused, and the more I think about it the more confused I get. I get that bernoulli's doesn't take frictional losses into account, but at a short section of...

Homework Statement If the limx→b f(x)=c, then limx→b ex= ec. What property of the function g(x)=ex allows this fact? The Attempt at a Solution Is it just because e is a constant?

Hello 1- I calculate optical properties of a pure compound in framework of DFT with pseudopotential by software. I get several picks in loss function. Does only the highest , determine plasma frequency or all of them with different density of valence electrons? 2-can we conclude the...

Homework Statement Determine whether the assertions are true or false, explain. (a) If (f * g)(t) = f(t), then g(t) must be an impulse, d(t). (b) If the convolution of two functions f1(t) and f2(t) is identically zero, (f1 * f2)(t) = 0 then either f1(t) or f2(t) is identically zero...

Homework Statement I solved a problem that asked me to show that the sum of the eigenvalues of A+B equals the sum of all the individual eigenvalues of A and B, and similarly for products. I just would like to know why is this so... Homework Equations The Attempt at a Solution Is...

I googled this and surprisingly no one seems to have an answer. What would have to be done to the water to make it change chemically?

I am curious to know using scientific information what color lightsaber is the strongest? I have done some minor research and cannot figure it out on my own. I have come up with that violet produces the highest frequency while red produces the lowest frequency. Using Planck's Law E=hv I gather...

I have read in a lot of places the PAN acts as a very good reservoir of nitrogen dioxide. I can't find much information on why though. All I have found is that PAN is thermally unstable and has a very short lifetime at typical tropospheric temperatures, but becomes much more stable at lower...

Hey all..so Ill go ahead and say that I recently discovered passion for math..I didnt really learn too much in high school when graphin y=-f(x) -how would I input on ti83? how do y=2f(x) differ from y=f(2x) -when it comes to input and output..how would the outputs differ? I am basically...

Give a formula for a rational function having the following properties: • Horizontal Asymptote: y = 2 • Vertical Asymptotes: x = − 3 and 1 • x-intercepts: -1 and 5 Here is what I've done so far \frac{2x^2}{(x+3)(x-1)} I basically get stuck when trying to come up with something for the x...

Homework Statement Demonstrate that \int_{-\gamma} f(z)|dz|=\int_{\gamma} f(z)|dz| where \gamma is a piecewise smooth path and f is a function that is continuous on |\gamma|. Homework Equations The Attempt at a Solution This proof seems like it should be very simple, but I am...

The properties arise from infinitely nested functions such as: x=\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}...}}}} You can solve it algebraically to verify that x is equal to the nested function (all of the following functions can be solved in a similar manner)...

Who discovered the Hadron and when? What properties does the Hardron have? What are all the interesting facts about the hadron?

A piston cylinder device contains .85kg of refrigerant-134a at -10°C. The piston is free to move and has a mass of 12 kg and a diameter of 25cm. The local atmospheric pressure is 88 kPa. Now, heat is transferred to refrigerant-134a until the temperature is 15°C. Determine (a) the final pressure...

Hi everybody, I'm looking for a free software (or web link) for calculation of thermodynamics properties (enthalpy,entropy,density,viscosity,etc.) of a wide range of substances.Does anyone have any suggestions about ? Thanks in advance.

Hello All, I'm hoping someone can assist me in locating a stress amplitude vs. cycles curve (S N curve) for a Duplex Stainless Steel. The particular material I'm using is SAF 2205. I have been searching far and wide, including the Atlas of Fatigue Curves, but I have not been able to find...

how would I show that y'(t) = x(t) * h'(t) and y'(t) = x'(t) * h(t) I know that in an LTI system y(t) = x(t) * h(t) = \int x(\tau) * h(t-\tau) from \infty to -\infty But how would I go about trying to prove the first two equations?