Form Definition and 1000 Threads

Hi, I'm trying to solve this problem and I'm stuck. What I want to do is determine the kind of surface from this equation: x2-2y2-3z2-4xy-2xz-6yz = 11 Matrix representation: 1 -2 -1 -2 -2 -3 -1 -3 -3 I want to find the eigenvalues so I write the characteristic equation like...

Is it possible to reduce moisture content in Polyethylene glycol or propylene glycol by applying vacuum to around 15000 mTorr for 24 hours. If anyone has any idea please let me know

Homework Statement Grammar 'G' is any context-free grammar without any λ productions or unit productions. Let k be the max number of symbols on the right side of any production in P. Prove that there's an equivalent grammar in Chomsky Normal Form with no more than (k − 1)|P| + |T| production...

I was watching Nova Science Now and they were talking about how stars form when gas clouds are compacted when hit by supernova shockwaves, which then allows them to compress further by their own gravity and eventually they ignite. But I was left wondering how then the first stars were able to...

Hey! :o I have to write a RAM program to accept all inputs of the form $1^n 2^{n^2} 0$. The instructions of the RAM machine are the following: I have done the following: Read x from input d=0, s=0 while x!=0 if x-1=0 d=d+1 else s=s+1 Read x from...

Homework Statement I need to calculate interference peaks using the atomic form factor for several lattice types for a lab report. I was given the expected answers but told I should also be able to calculate them.Expected results for rocksalt (eg NaCl): h+k+l = 2n fh+k+l = 4(fa+fb) h+k+l =...

I know aqueous Ammonium Bicarbonate forms when NH4+ and HCO3- ions are present in water after they've dissolved from their gaseous states of NH3(g) and CO2(g). This occurs in the reaction: NH3(g) + H2O(l) + CO2(g) => (NH4)HCO3(aq) If Ammonia gas and CO2 are present above a polar organic...

I saw somewhere that an alternate form of cos(n×π) was cos(n×π) = -1n+1 But to me this does not make sense. Am I wrong? For n = 0 cos(n×π) = 1 -1n+1 = -1 For n = 1 cos(n×π) = -1 -1n+1 = 1 etc. Is there another way to express cos(n×π) in an alternate form? PS. This is related to Fourier series.

In Alaca and Williams' (A&W) book: Introductory Algebraic Number Theory , Theorem 1.2.1 reads as follows:Without any earlier definition or clarification, A&W refer to $$a/p$$ and $$b/p$$ (see text above) ... BUT ... how should we regard such elements? What exactly do they mean and how do we...

Hi all, I'm wondering if anyone knows of a way to obtain elasticity properties (Ex, Ey, Ez, Gxy, Gxz, Gyz, vxy, vxz, vyz) from the terms of a 6x6 anisotropic stiffness or compliance matrix. I'm looking for a closed form solution, preferably. I would think that there should be a closed form...

Homework Statement Calculate ##(4.3 \times 10^8)+(2.5 \times 10^7)## Give your answer in standard form The total marks for the question is 2 Homework EquationsThe Attempt at a Solution The answer is ##4.55 \times 10^8## because that's what my calculator gave. That will score me one mark. I am...

Homework Statement Write down number 1+i and 1+i\sqrt{3} in trigonometry form.[/B]Homework Equations For complex number z=x+iy \rho=|z|=\sqrt{x^2+y^2} \varphi=arctg\frac{y}{x} And [/B]The Attempt at a Solution Ok. For z=1+i \rho=\sqrt{1+1}=\sqrt{2}...

In galaxy formations/collisions and planetary dust from newborn solar systems, they begin with an irregularly shaped cloud of matter. But why, over their lifetime, do they form a disk shape? In the case of spiral galaxies and planet orbits.

Homework Statement I am trying to calculate the atomic form factor for various crystals (NaCl, LiF, GaP, Si) in an x-ray diffraction experiment. There seems to be very little information on this topic anywhere.Homework Equations [/B] I understand how to derive the geometric form factor Sk =...

I've learned that vectors can be defined in,basically, two ways. (1) Unit Vector Form (xi+yj+zk) (2)Magnitude angle form. The second form always adds a confusion in problems. For instance let's define a function A and B as: When we define -B why do we do it as follows: I mean why do we...

Homework Statement Convert 2cis(-pi/3)cis(pi/6) into cartesian form. Show all working to obtain full marks Homework Equations I know that the equation for it is 2((cos(theta) +isin(theta))+(cos(theta)+isin(theta))) The Attempt at a Solution Okay so cos of (-p/3) = 1/2 Sin of (-p/3) =...

Hello everyone! Here is a question I am working on: Consider the context-free grammar G = ( { S, B, E }, { 0, 1, i, e, s }, R, S ), where R is: S --> iBSE | s B --> 0 | 1 E --> lambda | eS Convert this to Chomsky Normal Form, showing all steps. Alrighty, so I removed the lambda and got: S0...

Hi Folks, I have the following forced torsional vibration problem of the form ##\displaystyle J_0 \ddot{\theta}+k_t\theta=\frac{a_0}{2}+\sum_{n=1}^{\infty} (a_n \cos n w t+b_n \sin n w t)## I assume the solution of the CF is in the form ##\theta=A \cos nwt+B\sin nwt## but I am not sure what...

Moderator note: The OP was warned that he needed to do more research before asking questions like this. So mild steel appear to have black mild steel or bright mild steel... What are the differences between them... And bright mild steel appear to have higher quality than black mild steel... In...

Mod note: This post with template not used and no effort shown received a warning. Okay I am totally confused in this. This is not a homework question but rather one I saw online and was wondering for example how to solve it The question was -3-i/-8+6i to be expressed into Cartesian form...

Does anybody knows how you can reach one form of the divergence formula from the other? Or in general, why is the equivalence true?

I don't understand what charge density is meant in the equation: div E = constant times charge density. I have the derivation in front of me and the last step follows from accepting that the rate of change of the integral of the field divergence per change in volume is the same as the rate of...

Homework Statement This problem just has me find an atomic form factor for some arbitrary basis atom in a bravais lattice where the electron wave function is given (it has a dependence on the Bohr radius in an exponential). I calculated the form factor (a very long, nasty integral that...

This isn't a homework problem, a classmate asked for a challenging proof to try and do and this was the one we were given. We started by trying to derive some rules from un-integratable functions but realized that that would take a long time and a lot of work. After some thinking we came up with...

Homework Statement Hi. I have convert the following equation (which is in ionic form) into neutral form: 4S2O32-+O2+2H2O=2S4O62-+4OH- The question tells me to use calcium as a counterion for all anions. Homework Equations N/A The Attempt at a Solution I basically just added calcium to the...

Homework Statement Hi all - I have been trying to evaluate part II of this problem for a long time now... For a simplified model of a proton's charge distribution, Find the constant of proportionality required to normalise ρ correctly. Show that Homework Equations N/A The Attempt at a...

Homework Statement Problem 29. Use the subtraction trick U(tilda) = U−U1 to reduce the following problems with non-canonical boundary conditions to the canonical ones and write down the equations in terms of the variable ˜u (do not solve them). Note that there are infinitely many u1’s that...

I am given a formula in explicit form and as a recurrence relation. It is asked to derive the recurrence relation from the explicit form. How is this done?

Let function $f(t)$ is represented by Fourier series, $$\frac{a_0}{2}+\sum_{n=1}^{\infty}(a_n\cos{\frac{2n\pi t}{b-a}}+b_n\sin{\frac{2n\pi t}{b-a}}),$$ $$a_0=\frac{2}{b-a}\int_{a}^{b}f(t)dt,$$ $$a_n=\frac{2}{b-a}\int_{a}^{b}f(t)cos\frac{2n\pi t}{b-a}dt,$$...

The Attempt at a Solution Let x=tan u dx=sec^2(u)*du When x=3^0.5,u=pi/3 x=-3^0.5,u=-pi/3 S sec^2(u)d(sec u) =1/3[2^3-2^3]=0

Can some one write for me the Symmetric part of a third order tensor (as a tensor form) Thanks .

Homework Statement Given a strong form boundary value problem, derive the weak form using weighted residuals. Homework Equations ##(2-x)u''(x)-u'(x)+u(x)=f(x)## for ##x\in(0,1)## with $$u(0)=u(1)=0$$ The Attempt at a Solution I must multiply both sides of this equation by an arbitrary test...

Hi, I am not a native English Speaker, so some words might not be appropriately used below, but I will try my best to explain what I was thinking about. In general, I have never learned how acoustic waves emerge microscopically. The application of the theoretical knowledge I acquired was always...

This isn't quite a calculus question, but it didn't seem right for any of the other mathematics forums, either. Does anybody if there is a closed form for the following infinite series: \sum_n x^{n^2} for 0 < x < 1

"A Mathematical Proof That The Universe Could Have Formed Spontaneously From Nothing Cosmologists assume that natural quantum fluctuations allowed the Big Bang to happen spontaneously. Now they have a mathematical proof" Okay, but "natural quantum fluctuations" is STILL something it seems...it...

Homework Statement Hello everyone, first time poster. I am in an Analytical Mechanics class and we are covering Dimensionless Form and Free Fall and am struggling with some of the concepts. The question has multiple parts, but looks like this. The equation for a damped harmonic oscillator is...

Homework Statement Find the circle segment area that has the boundaries of line segment AB and the minor arc ACB. Give the area in an exact form in terms of surds and Pi. (see attachments for annotated picture & original question). Homework Equations Equation 1: Area of a segment = Sector...

Hello there, Imagine that a nucleus consists of three atoms arranged in a equilateral triangle with the length of each side, ##R=2 \rm fm##. Our protons starts infinitely far away. What is the work required to push these protons together in order to overcome the electric force between them? I...

Osmotic power is a form of renewable energy under development which exploits the salinity gradient between fresh river water and salt sea water. The phenomenon is based in osmosis principle and called Pressure Retarded Osmosis (PRO). The two fluids are separated by a semi-permeable membrane...

General formula of a line is ax+b=0 Similarly can we have a general formula of a circle ?

Homework Statement "Put each of the following into the form Acos(ωt+θ)..." (a.) 4ejt+4e-jt Homework Equations Euler's Identity: ejθ = cos(θ)+jsin(θ) Phasor Analysis(?): Mcos(ωt+θ) ←→ Mejθ j = ej π/2 Trignometric Identities The Attempt at a Solution I attempted to use phasor analysis to...

Homework Statement limx->∞ e^5x/ln(2x) Homework Equations The Attempt at a Solution

For certain types of functions I have been using the term 'general form' as a way of stating that some function of some variable(s) is true for more than one value of the variable (usually an infinite number). Here is a simple example, 1=cos(2∏x) There have been (at times) where the use of...

Hello. I'm learning about Lie derivatives and one of the exercises in the book I use (Isham) is to prove that given vector fields X,Y and one-form ω identity L_X\langle \omega , Y \rangle=\langle L_X \omega, Y \rangle + \langle \omega, L_X Y \rangle holds, where LX means Lie derivative with...

Homework Statement I'm working on this problem: Let \hat{U} an unitary operator defined by: \hat{U}=\frac{I+i\hat{G}}{I-i\hat{G}} with \hat{G} hermitian. Show that \hat{U} can be written as: \hat{U}=Exp[i\hat{K}] where \hat{K} is hermitian. Homework Equations...

an air wave takes place in volumes of air, water takes place in volumes of water... but u can have an electromagnetic wave go through empty space using only one particle. how does this work? this to me does not seem analogous to the waves that i am used to. does this "wave" instead refer to the...

Our integral \int\limits_0^{\pi/2} \sin^{2a+1}(x)\,dx Has a Factorial Form: {(2^a a!)}^2 \over (2a+1)! What is the process behind going from that integral to that factorial form? My approach which is not very insightful: I used mathematica to calculate the integral to return...

Let e_i be a unit vector with one 1 in the i-th element. Is the following expression has a recursive presentation? $$y_N = \sum_{k=0}^N {\frac{{{X^k} e_i}}{\|{{{X^k} e_i}\|}_2}} $$ where X is a n \times n square matrix, and {\| \cdot \|}_2 is a vector norm defined as {\|z\|}_2 =...

Hi guys , I'm currently reading a book and I faced this with DEs: In the 5 attached images you'll find the textbook paragraph I'm asking about . I think I understood the first part under the title of : meaning of differential equation but I can't figure out how did he proceed with the same...

Hello, the tensor product definition of a two form is \alpha^{1} \wedge \beta^{1} := \alpha \otimes \beta - \beta \otimes \alpha \alpha \wedge \beta(v,w) = \beta(v)\alpha(w)-\beta(w)\alpha(v) But what is the definition in this sense for a three form?