Properties Definition and 1000 Threads

Good afternoon, I am performing an experiment involving a SEM and I am using Macor glass as insulators between the metal components. I am writing a small paper on the breakdown voltage. The problem I am having is that the information for the values of the dielectric constant are clear and...

1.prove that for any set X: |X|<c <=> in P(X) exist such countable set family F, that sigma algebra generated by F contains all points. 2.let (X,E,u) be probability space and A_1,...,A_2009 in E have property u(A_i)>=1/2. Prove that there exist x such is in A_i for atleast 1005 different i. i...

Homework Statement The given function is an even function. I tried using properties but did not get any satisfying result.

I recently posted a comment about the properties of electromagnetic fields in an article about electric fields in the library. But it was deleted, could someone please point out the errors in the article so I can refine my understanding of this phenomena? The article is written below and...

Homework Statement Our lab was to find the spring constant of the springs that we were using, and then verify the properties of SHM. We used a vertical spring system AND an inclined spring system. We used 3 different springs for both systems. For the vertical system: We hung the 3...

Homework Statement For a,b > 1 prove that: \int_{1}^{a} (1/t) dt + \int_{1}^{b} (1/t) dt = \int_{1}^{ab} (1/t) dt Homework Equations Hint: This can be written \int_{1}^{a} (1/t) dt = \int_{b}^{ab} (1/t) dt "Every partition P = {t0, ..., tn} of [1,a] gives rise to a partition P' = {bt0...

Hello PF! I was having a debate with a coworker of mine. We were talking about the properties of springs underwater. He was convinced that it doesn't change, at least when in water. I thought otherwise. Does a spring's spring constant change if fully submerged underwater? Does the...

Can someone help me with this? When two linear operators commute, I know how to show that they must have at least one common eigenvector. Beyond this fact, what else can be said about commutative operators and their eigenvectors? Further, can they be diagonalized simultaneously (or actually, can...

Hello. I am writing an encryption algorithm for a program and have decided to use a hill cipher. My problem is that for the hill cipher, I have to have matrices with very specific properties. How might I go about finding 3 matrices of size 4x4 such that all of the matrices are integer-only and...

Hey everyone, I'm currently taking a thermal physics course and have been assigned a research paper about the thermodynamically arguable aspects of experimentally observed properties of the 3He superfluid. I have been searching for many different sources but have only found a few worthwhile...

I am doing a heat exchanger report for a domestic boiler, and would anyone know what the specific heat capacity for diesel in its liquid and gas(having been combusted) state. In J/kgK please thanks

Assuming that super-heavy atoms were stable (at least up to 118), what would be some interesting chemical properties of some of them?

I am researching electric and magnetic fields, and so far from my understanding each electron produces its own electric field, negatively charged, and thus the atom has its own electric field, am I right so far? Some atoms have better current than others, this is related to the number of valence...

Quick Analysis Problem -- Related to properties of cont functions Homework Statement This problem assumes that f: R ----> R is continuous on all of R. I need to determine if the following set is guaranteed to be closed, regardless of f(x). A = {x in R | 0 <= f(x) <= 1} Homework...

Show the following: If A and B are n x n matrices such that A - B is singular then A2 - AB + BA - B2 is also singular. I really have no clue how to solve this, but I am guessing that AB does not equal BA, I don't know how that can help or be relevant but just in case Thanks alot...

Matrix Properties Hello, I am having difficulties with this question. A^2+6A+9I3 = 0. A is a 3x3 matrix. I must show that A is invertible. I am tempted to factor but this problem deals with matrices. I know this is wrong but I come to A2+3A+3A+9=0 (does 9I3 = 9, since 9 is a constant?), then...

I am planning to use natural sources of citric acid-lemons preferably-to demonstrate a flame retardant mixture using chiefly sodium benzoate(preservative) and ammonium phosphate besides citric acid.Will a natural source work? I suspect the other chemicals in the lemon extract will spoil the...

If you have, as an example, a 3x3 matrix: A = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} } Such that Ax = 0 and you perform row reductions on it and at a certain point it reduces to: { {1, 2, 3}, { 0, 1, 2}, {0, 1, 2} } Then you could legitimately remove one of {0, 1, 2} from the system...

hello, I have a very simple question: a hollow sphere has the propertie that in the sphere the electric field, due to being charged , is zero is it in the whole sphere? for example, near the inside surface of the sphere, the the electric field of the nearest charge will be geater than the...

Hello, I have been doing some research with self assembled monolayers. I was wondering if a molecule terminating in -OH was able to bond with a silicon wafer in atmospheric conditions?

A couple of days ago I burnished a very rusty old piece of steel with a fine steel wool. It's now very smooth, and there is no loose rust scale. It has a finish somewhat like a century-old doorknob in some old building at a university. Some place where hands have rubbed it many thousands of...

Partition separates two gases in a rigid well-insulated container. Q=0, W=0. State 1: Air: m=1kg P=500kPa T=350K CO_2: m=3kg P=200kPa T=450K Assume constant specific heats. Assume kinetic and potential energy changes are negligible. Assume the partition between the two gases...

Homework Statement A*certain*soil*has*c’*=*12kPa*and*φ’*=*32°.*The*major*and*minor*principal*stresses*at*a*point*in*this* soil*are*348*and*160*kPa*respectively,*and*the*pore*water*pressure*at*this*point*is*96*kPa.*Draw*...

By increasing the hydrophobicity of canoe hull material, will drag be reduced? Have hydrophobic materials been used on boats? My thoughts: Yes, there is less surface contact with the water. Thus less viscous (friction) forces.

Homework Statement Orbital angular momentum L is given by L = mr x v Linear and angular velocity are related by the eqn. v=w x r Solve for L in terms of m, r, and w. Homework Equations I was thinking of using Lagrange's formula. A x (B x C) = B(A*C)-C(A*B) The Attempt at a...

So I was recently learned that for some square integrable position wave-functions in Hilbert Space have the momentum function is not square integrable. Thus the momentum function are not in hilbert space. However, due to "Fourier's Trick" Dirac discovered for quantum mechanics, the momentum...

Homework Statement If F is an ordered field the the following property holds for any elements a and b of F. If b<a, the -a<-b. My task is to prove this property. My question is whether I need to use the definition of an ordered field. I used the basic axioms but I didn't use the definition...

Hello, I wanted to know which properties a foam plastic have in general and how it works in a Mattress. I have a Foam mattress is there any difference between hot and cold foam? My Mattress is a Foam mattress not a Spring mattress and it feels too hot after a while you lie on it...

What are the "key image properties" of an image? Homework Statement Hi, I'm been assigned a project to capture images of laser speckle and do some image processing in Matlab. The directions say to "measure key image properties". Homework Equations The Attempt at a...

Homework Statement There are two log properties that I have to prove: 1) Explain why ln(b1/n)=(1/n)ln(b) for b>0, set b=an 2) Explain why ln(ar)=rln(a) for any r in Q and a>0, ie r is rational. Homework Equations ln(an)=nln(a) The Attempt at a Solution In a previous question...

When a block of mass M is suspended by a long wire of length L, the elastic potential energy stored is given by 1/2 x Mg x l, where l is the elongation produced. The loss in gravitational potential energy of the mass-earth system is Mgl. I wonder where does the other Mgl/2 go?

Homework Statement Let An be the nth term of an A.P. and if A7 = 15, then the value of the c.d. that would make A3 x A7 x A12 greatest is : 1)9 2)9/4 3)3/8 4)18 Homework Equations The Attempt at a Solution Applying AM>=GM A3+A7+A12/3 >= (A3 x A7 x A12)^1/3 given that...

Homework Statement A and B are n x n matrices, so their Jordan Product is (AB + BA)/2. Show that this product is commutative but not associative. Homework Equations The Attempt at a Solution I understand the logic behind the answer, but I don't know how to show it. Where would...

Homework Statement let u be a nonzero vector in space and let v and w be any two vectors in space. if u.v = u.w and u x v = u x w, can you conclude that v=w? give reason for your answer. Homework Equations The Attempt at a Solution v is not necessary equal to w since u is nonzero...

Hello, Am I missing something or is R^2 a field with the obvious component wise addition and multiplication (a,b)*(c,d)=(ac,bd)?

Hi, I would like to find the properties of humid air at different humidities and different temperatures. What sort of charts should i consult? I tried looking at psychrometric charts, I'm not sure if I'm reading the correct thing. Thanks

Problem: Show, without evaluating directly, that \left|\begin{matrix} a_1+b_1t&a_2+b_2t&a_3+b_3t \\ a_1t+b_1&a_2t+b_2&a_3t+b_3 \\ c_1&c_2&c_3 \end{matrix}\right| = (1-t^2)\left|\begin{matrix} a_1&a_2&a_3 \\ b_1&b_2&b_3 \\ c_1&c_2&c_3 \end{matrix}\right| Clearly, here I'm...

Just some thought on dark matter/energy, please correct me if I am wrong in any case: Is it possible to explain the difficulty in detecting the dark matter from Earth due to 1)the relative Size and Scale of space it's occupying, or 2) the Mass it's affecting, in order for them to have...

How does a difference in the number of protons in an element lead to such a difference in the properties (color, texture, form, etc.) of elements? I.E Gold and Mercury. This question has been driving me crazy and I would really appreciate any answers. Thank You.

Hello all, I am a layman who is interested in nuclear fusion via magnetic confinement (the Tokamak setup). I recently read in a book about how the (a) transformer in the device could operate only for some number of "volt-seconds" before it had to be "recharged". This requires an additional...

Homework Statement i have read in my 7th grade textbook, "LIGHT TRAVELS IN STRAIGHT LINE". But in my 12th grade textbook, it has been mentioned " Light is an electromagnetic wave and transverse in nature". Transverse means the vibrations are perpendicular to the direction of propagation...

So I'm doing research with MEMs so we're going to be making silicon wafers that will have little cantilever beams on them which will act as an accelerometer. I need to design it so the beams break at certain forces but to do that I need the yield strength of silicon (that is the correct...

Homework Statement dx/dt = 9-4x^2 , x(0) = 0 when I integrate, am I supposed to use the property below? int du / (a^2 - u^2) = 1/2a ln(u+a / u-a) + c or how do I integrate this by using partial fraction? tips anyone? Homework Equations The Attempt at a Solution

Hey, I have been looking around for a good resource explaining the analytic properties of Feynman diagrams and their resulting amplitudes. I think I understand in general what to expect (branch cuts for multiparticle states, poles for single particle states and bound states), but I'm not...

Why are S orbitals referred to as "non-directional"? Shouldn't their direction be referred to as "all directions"?

Hi. It is relative easy to find mechanical properties for woods that can be used in building construction. But I would like to find mechanical properties for woods that can be used in bow building. That would be properties for woods such as hard rock maple, yew, bamboo, cocobolo, bolivian...

Hi, everyone: I am going over J.Lee's Smooth Manifolds, Chapter 3; specifically, Lemmas 3.1, 3.4, in which he states properties of derivations. Lee calls linear maps L with the Leibniz property (i.e L(fg)(a)=f(a)L(g)+g(a)L(f) ) derivations, when these maps are defined in a...

Hey folks, I am looking for something free to help me out here. I have experimental data that consists of the temperature and pressure of a gas over time. That is I have (T1,P1), (T2,P2),...(Tn,Pn) where n might be upward of a 500. I would like to be able to determine the specific volume...

im having diificulty in solving Equations in this research paper how ohms law has been witten in Eq (1) how can we write microscopic form of ohms law for non linear meta materials?

Homework Statement Let [G,+,0] be a non-abelian group with a binary operation + and a zero element 0 . To prove that if both the zero element and the inverse element act on the same side, then they both act the other way around, that is: If \forall a \in G , a + 0 = a , and a + (-a)...