Unit Definition and 1000 Threads

Homework Statement I would like to use the Weierstrass M-test to show that this family of functions/kernels is uniformly convergent for a seminar I must give tomorrow. H_{t} (x) = \sum ^{-\infty}_{\infty} e^{-4 \pi ^{2} n^{2} t} e^{2 \pi i n x} . Homework Equations The Attempt at a...

Hello, In my lab report, I am trying to discuss what the units of resistivity mean. For instance, the unit of speed m/s second can be described as the time it takes to travel 1 m; specifically, 50 m/s would say that it would take 1 s to travel 50 m, or, we travel 50 m every second. Could...

So I'm busy struggling with some worked examples in my signals class. I understand the theory from the notes and textbook but I cannot seem to apply them to proper examples. We are asked to find the derivative of g(t) = (1-e^(-t))*u(t) where u(t) is a unit step function. I know the...

I'm completely stuck here, can anyone help me?

Homework Statement Is (x^2-1) a unit in F[x]? where F is a field. 2. The attempt at a solution I might say yes, cause we can find the taylor expansion of 1/(x^2-1), is my idea right?

Homework Statement The problem states to find a unit vector that is orthogonal to \left\langle1, 1, -2\right\rangle, forms an angle of \frac{\pi}{4} with \left\langle1, 1, 1\right\rangle and has v1 > 0. Homework Equations cos\theta = \frac{\vec{u}\bullet\vec{v}}{|\vec{u}||\vec{v}|}...

"find a unit tangent vector and the equation of the tangent line to the curve r(t) = (t, t^2, cost), t>=0 at the point r(pi/2)." NOW, what I don't get is, how is that a curve? This is not like the example I have studied and I don't really get the question. So I don't know where to start. Once I...

Homework Statement Not sure if this belongs in homework or general discussion - I found this in reading In studying the divergence and curl of the magnetic field (B), I found a statement that I need some help with. In the derivation of the divergence of B using the Biot-Savart, I have...

Hello, now I'm reading Peskin Shroeder. I have a question about the Casimir operator on page 500 in Chapter 15. From the following eq, ## \ \ \ [T^b , T^a T^a ] = 0 \ \ \ \ \ \ \ (15.91) ## ## T^2(=T^a T^a) ## is an invariant of the algebra. Thus the author concludes that ##T^2## is...

I seem to recall when taking college Trigonometry my professor saying that the unit circle and sinusoidal curves were basically a mathematical represention of a slinky in that the unit circle was the view of a slinky head on, so that what you saw in the two dimensional sense was a circle, and...

OK, I'm really rusty on this. I need to convert a unit vector to right ascension and declination. I believe I recall the formulae correctly, as I seem to have gotten 1 as my radius. So, that's good. In the pic I have my unit vector (P2), my actual answer below, my expected answer in...

Hi all, How do I compute the Fourier series coefficients for unit periods for cos(pi)x, the interval is from -1/2 to 1/2. I know the formula but I am getting a wrong answer ?

Homework Statement Find all the unit vectors orthogonal on the line L. Homework Equations L passes through the vectors u = [9; 7] and v = [1; -5] The Attempt at a Solution I found the slope of L from the two vectors: 3/2. I know that to be orthogonal, the vector will have a...

hi... we know the unit of velocity is m/s2 and while calculating the mean square velocity we find the average(or mean) of the 'squares' of the given velocities. then the unit of MEAN SQUARE VELOCITY should be 'm2/s4' then how come its unit is also m/s2 and not m2/s4 ?

Today I came across a statistical report of world energy consumption. There was a tab named energy generated and the values were given in TWh. There was a tab named Primary energy consumed and the values were given in Mtoe. I saw that the energy generated by the world is around 20000 TWh and the...

I have been wondering what type of measurement is used to measure the space inside of a four dimensional (space, not time) object. For example, a one dimensional line's distance gets measured, a two dimensional object's area gets measured, and a three dimensional object's volume gets measured...

Homework Statement Hi,can someone explain to me through real world examples what the unit step and unit impulse means in systems control?How are they related to the system's input? Thank you.Homework Equations δ(t) = unit umpulse u(t) = unit stepThe Attempt at a Solution

Homework Statement f(t) = cos (pi*t) if 1\leq t <4 and 0 elsewhere using unit step functions to find Laplace TransformHomework Equations The Attempt at a Solution I came up with the unit step function f(t) = cos(pi*t) u(t-1) - cos(pi*t) u(t-4) in order to use the second shifting theorem f(t)...

Homework Statement So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this. The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0. The laplace transformation chart that I have has two columns, the column on the...

Hi guys, I've run across a problem. In finding the potential energy between two electrical quadrupoles, I've come across the expression for the energy as follows: U_{Q}=\frac{3Q_{0}}{4r^{4}}\left[(\hat{k}\cdot \nabla)(5(\hat{k}\cdot \hat{r})^3-2(\hat{k}\cdot \hat{r})^2-(\hat{k}\cdot...

I'm not sure that I understand the vectors \hat{r}, \hat{\theta}, and \hat{\phi} in spherical coordinates correctly. I was looking through this link earlier. I understand that \hat{r} always points radially outward from the origin. That seems to imply to me that any position in space could be...

Hi all, I need help with something basic but I'm not sure how to handle it. The doubt is about how to consider the topology of the unit interval I=[0,1] inherited of the real line with its usual topology (intervals of the type (a,b)). I think that is just to pay attention to the definition...

Homework Statement Solve for the unit vectors x-hat and y-hat in terms of r-hat and phi-hat. Homework Equations r-hat=cos(phi)x-hat+sin(phi)y-hat phi-hat=cos(phi)y-hat-sin(phi)x-hat, The Attempt at a Solution I have been working on this for a really long time, and I keep getting a...

Homework Statement http://i.imgur.com/B1hFY6E.png Homework Equations -Basic geometry -Similar triangles (?) -Pythagorean Theorem The Attempt at a Solution -I need to find the angle the bar AB makes with the horizontal, correct? And with that, I will be able to figure out the...

Homework Statement When an object falls through air, there is a drag force that depends on the product of the surface area, A (m2), and the square of the velocity, in (m/s). The equation is Fdrag = CAv2. The metric unit of force is the Newton, or (N). 1 N = 1 kg*m/s2. What are the units...

Homework Statement http://prntscr.com/p7dxt Here's a screenshot of the revision question. Homework Equations The Attempt at a Solution Co-ordinates of each point A, (0, 60, 0) B, (40, 0, 0) C, (-40, 0, 40) D, (-60, 0, -60) Position Vectors rAB, 40i + -60j + 0k rAC, -40i + -60j + 40k rAD...

hello i got to ask if the center of symmetry is specific to a unit cell or a pattern or system of specific unit cell? I mean is Cubic (Bravis Lattice) is Centro symmetric or the structures formed by it. As an example, Tetragonal unit cell appears centro-symmetric but forming structures like...

Homework Statement If one truck runs on 6000 barrels of oil per year, how many trucks could run on the oil produced in the US in one year (1.9*10^10 barrels)?Homework Equations (6000 barrels/year) used by one truck (1.9*10^10 barrels/year) for US productionThe Attempt at a Solution I simply...

If Rn = 1/2(a^n + b^n) where a= 3+ 2root2 b= 3 - 2root2 and n= 0,1,2,3,4,5,... then R12345 is an integer. Its units digit is.. I didn't have any ideas so I started to plug in numbers looking for a pattern. I am sure this is not the right approach. R0 = 1 R1 = 3 R2= 7 R3= 9 Could I get...

And what are some good examples besides humans? I'm guessing that years don't matter as much as generational cycles. edit: for example, how many evolutionary cycles for humans would be contained in 100 years? Or dogs? Do you count by total age or reproductive age?

Hi I'm trying to study over break, this isn't an exact quote but its the part of the problem I need help with. Thanks. Homework Statement Draw the unit circle and plot the point P=(3,2). Observe there are TWO lines tangent to the circle passing through the point P. Lines L1 and L2 are...

Hi How do you get a photon flux per unit wavelength curve for solar radiation? My understanding of "per unit wavelength" is that the wavelengths within a very short range are fired at a detector. The range is then gradually changed to cover higher wavelengths. The values of flux measured by...

Homework Statement Calculate the integral ∫dθ/(1+acos(θ)) from 0 to 2∏ using residues. Homework Equations Res\underline{zo}(z)=lim\underline{z->zo} (z-z0)f(zo)*2∏i The Attempt at a Solution To start I sub cos(θ)=1/2(e^(iθ)+e^(-iθ)) so that de^(iθ)=ie^(iθ)dθ Re-writing in...

Hey guys, I don't post here often but I like to come here when I have a problem that really rattles my brain. I am an 'overclocker' by hobby (I tune computers), a big part of the overclocking scene is cooling the processor of the computer as far as possible. For years now the 'best' way of...

Early next year I will be beginning an Electromagnetism unit. However, I think I should refresh my maths over the summer break first. Here is the Unit Description from the uni website: A detailed treatment of electric and magnetic fields and theory sources leading to the formulation of...

hi, why electric current is a SI base unit - why not couloumb?

Homework Statement y''-4y'-32y={1 when 0<=t<1 and 0 when 1<=t y(0)=y'(0)=0 Homework Equations The Attempt at a Solution s2L(y) -4sL(y)-32 L(y)=u1(t) I am just struggling to figure out if my unit step function is correct. Solving for L(y) I get: (e-s) / (s(s2 -4s-32))...

Homework Statement a) Find the unit impulse response h(t) of an audio system that causes two echoes, one occurring at 0.5 seconds and the other one at 1.5 seconds. Please sketch H(w). (Magnitude and phase) b) Design a system that can eliminate noise coming from the 60Hz power signal (thus...

1) Show that (R,*,+) is a ring, where (x*y)=x+y+2 and (x+y)=2xy+4x+4y+6. Find the set of unit elements for the second operation. I understand that the Ring Axioms is 1. (R,+) is an albein group. 2. Multiplication is associative and 3. Multiplication distributes. I just don't understand how to...

Hi all; an easy question for you. In the following picture, what is the ventilation box in the corner near the floor? Is there a particular name for these things? I see them everywhere. http://upload.wikimedia.org/wikipedia/commons/7/76/Duracraft_pedestal_fan.jpg Thanks!

I have a worksheet that due to missing the lecture I'm now stuck on. You are given a cartesian vector and told find the polar unit vecors and hence express the original vector as a linear combination of the polar unit vectors just found. I've searched resources online but feel that there is...

Homework Statement OK first, I didn't know where to post this since it is and is not homework,anyways, posting here would be safest. Now, the attached scan is a proof from my (not so trustworthy) textbook and I have some doubts in it. The first doubt is in statement S1 : Every element...

This is the question The flow of a fluid between two large flat parallel plates normal to the y direction is fully developed and steady. The plates are a distance 2h apart in the y direction and the velocity profile, assuming y=0 is at the midpoint between the plate is V(y) = V_0(1-(y/h)^2)...

Let \vec{A} represent any nonzero vector. Why is \frac{\vec{A}}{A} a unit vector and what is its direction? If θ is the angle that \vec{A} makes with the positive x-axis, explain why \frac{\vec{A}}{A}\cdot\hat{i} is called the direction cosine for that axis. I am self-studying and this...

calculate the number of DU assuming that the entire atmospheric O3 column is at a uniform concentration of 3*10^12 molecules/cm^3 between 15 km and 30 km and zero elsewhere. I have no idea how to solve it. I don't know how to convert the 3*10^12 molecules/cm^3 to units of molecules/cm^2 that I...

Homework Statement A wire is fixed at both ends vibrating fundamentally. For what value of x (x position on the wire, with 0 being one edge and L being the other) is the potential energy per unit length has the maximum value? Known: Length of wire (L), Tension in wire (T), Mass of wire (m)...

what is a "scrumple" unit? (pressure) "what size of circular pipe is needed to produce a flowrate of 250 firkins per fortnight when there is a pressure drop of 3x10^5 scrumples per square barleycorn? the pipe is horizontal." I couldn't find what a scrumple was on google, does anyone know...

Homework Statement Consider energy generation in the Sun. Fusion through the pp cycle takes place within its core which has r = 0.2 Rs T = 1.3 x 10 ^ 7 K rho (density) = 1.1 x 10 ^ 5 kg m^-3 X (total mass fraction of hydrogen) = 0.34 The nuclear energy generation rate for the pp...

How this unit comes R = specific volume X (pressure / Temperature ) 0.9m^3/kg (1.3X10^5 N/m^2 / 408 K ) R = 286 KJ/KgK please can anyone explain to me how the unit ( KJ/KgK ) comes ??

I am reading Aschroft and Mermin and I came across the probability per unit time I have trouble understanding the concept as it is. But they do try to explain. They say that the probability that an electron will experience a collision in an ifinetismal time, dt, is just dt/τ. From this i...