Expression Definition and 999 Threads

Mind-controlled transgene expression by a wireless-powered optogenetic designer cell implant. Kind of a sensationalized title, since it's really just interpreting brain waves through a BCI, but neat anyway. http://www.nature.com/ncomms/2014/141111/ncomms6392/full/ncomms6392.html

Homework Statement Between two metal plates a metal strip is inserted as shown on the figure. a) Calculate the electric potential anywhere inside the capacitor. b) Simplifly ##U(x,y)## for ##x>>a##. c) Calculate the electric field in the middle of the capactior. Homework EquationsThe Attempt...

Homework Statement Q. How to find Remainder of the following expression ##32^{32^{32}}\mod{}6=?## Homework Equations The Attempt at a Solution ##32^{32}\mod{}2=0 \implies 32^{32}=2x## ##32^{32}\mod{}3=1 \implies 32^{32}=3y+1## would it help to find the remainder of ##32^{32^{32}}\mod{}6##

Hi, I'm trying to covert a NFA to a regular expression and I've manged to come up with an answer but I don't think that it is right. Here's the question - http://i.imgur.com/NUHxTXY.png And here's my workings -...

PROBLEM SOLVED - the worked example I was referring too was wrong :/ ---------------------------- Hello, I've been stuck on a question in one of my SR problem sets for some time now, and managed to find a worked solution to a similar problem online. I've attached an image of the problem (the...

I have heard different things and want to get a "professional" opinion on this. It seems like the words "term" and "expression" are technical terms with specific definitions in math and I want to know what they technically refer to (not just the personal slang or informal definitions someone...

transform the first member to the second member $\sqrt{\frac{\sec^{2}(\phi)-1}{\sec^{2}(\phi)(1+\cot^{2}(\phi))}}+\frac{\csc^{2}(\phi)}{\csc(\phi)}\sqrt{\frac{\csc^{2}(\phi)-1}{\csc^{2}(\phi)}} = (1+\cot(\phi))(1-\sin(\phi)\cos(\phi))$this is what I tried so far...

Find the coordinates of the expression (cos x + sin x)^3 in the basis {1, sin x, cos x, sin 2x, cos 2x, sin3x, cos3x}. I don't understand where to start since I am dealing with cos and sin now. :confused:

Please, I'm stuck. How to get the rhs from the lhs? X^{\alpha}_{\ \ \alpha^{\ \prime}}X^{\beta}_{\ \ \beta^{\ \prime}}\epsilon^{\alpha^{\ \prime}\beta^{\ \prime}}=det X\epsilon^{\alpha\beta}

Homework Statement If a car has p litres of petrol in the tank it can travel a kilometres. With v litres of petrol in the tank it can travel b kilometres. Find an expression in terms of v in terms of p, b and a. 2. The attempt at a solution I just cross-multiplied how I was shown in class...

Homework Statement Evaluate the following: A XOR (B XOR C) = A XOR (BC' + B'C). Using Boolean expressions. [This question came up in my test today (as part of a review of 'Digital Logic Design') for my 'Computer Architecture' course. It was worth 6 marks. The total test was marked out of 15.]...

Homework Statement Assume you have a fully charged capacitor with initial condition V(0) = V_0 connected in series to two resistors R_1 and R_2. Derive an expression for the voltage over the capacitor with respect to time. Homework Equations 1. Kirchhoff's voltage law \sum_n V_n = 0 2. Ohm's...

Homework Statement Hello guys, I fail to understand a mathematical approximation I see in a solved exercise. The guy reached a partition function of ##Z=\sum_{l=0}^\infty (2l+1) \exp \left [ -l(l+1) \frac{\omicron}{T} \right ]## and he wants to analyze the case ##T>> \omicron##. He states...

I'm sure this is a trivial notation question. I just can't seem to find the notation in my texts. Let L_a(g) = ag~\forall a, g \in G where a is fixed in G and G is a Lie group. (This defines the left action of G on itself.) A vector field X on a Lie group G is left invariant if (dL_g)(X(x))...

Help to obtain a simple form of the following expression: \frac{\sqrt[3]{a^2} -\sqrt[3]{ab}+\sqrt[3]{b}}{a+b}

Homework Statement Consider a system of N particles contained in a volume V. The Hamiltonian of the system is ##H=\sum{i=1}^N \frac{\vec p_i}{2m}+\sum _{i<j}u(|\vec r_i - \vec r_j|)## where p_i and r_i are the momentum and position of the i-th's molecule. 1)Show that the state equation of the...

Homework Statement A 20 kg rock falls with the force of gravity acting on it. Another force acts on the rock (same direction as gravity) that is proportional to the velocity squared, 100v^2. Come up with an expression of the rock's velocity at any time t. Homework Equations Hint...

Homework Statement Use Netwon's laws to find an expression for the angle of incilination theta at which the refrigerator starts to slide. Express your answer in terms of possible g, Us, Uk and m. Homework Equations Fnet=ma Ff=UFn The Attempt at a Solution I attached my attempt...

Homework Statement A projecticle launced at an angle of θ to the horiz

List all values of x for which each rational expression is undefined: \frac{x^2-9}{x^2-3x-10} Answer is 3, -3 q1) Are these -, and positive answer interchangeable ones because it is a rational expression so when I see rational that's going to signal it's going to need 2 answers (either...

Hello, I am having difficulty solving my math problems. Simplify the Expression and show how.. And kalkulate z²+w(2wz)²-(w+4z²-1)w³-(z+w²)(x-w²) And w=2 I know we have many ways doing it, an the more ways i can study, the bether i can understand this..

Hello everyone! I'm trying to design an NFA and then turn it into a DFA, and I'm not sure if I've done it correctly so far. Here is the question: "Present a transition diagram for an NFA for the language associated with the regular expression (1001 + 110 + 11)*. Your NFA must have no more than...

Homework Statement Both Newton's gravitational law and Coulomb's law are inverse-square laws: The force of attraction between the sun (S) and Earth(E) has (G*m_S*m_E)/r^2, whereas the force of attraction between an electron and a proton in a hydrogen atom is (e^2)/(4*pi*epsilon_0*r^2). Derive...

Hello, I am having difficulty solving my math problems. Simplify the expression: (12+r-r^2)/(r^3 +3r^2) The answer is (4-r)/r^2 I know that i can expand 12+r-r^2 as (-r+4)(r+3) But i cannot figure out the rest. Please help me. Thanks

Homework Statement Hi guys, I'm getting confused trying to manipulate an expression. Any help here would be hugely appreciated. How do I manipulate the expression -4 / (4x + 1)1/2 to become (1/4 + x)-1/2 The Attempt at a Solution I've tried dividing by -4 to get and used an index...

Edit: well this is frustrating, not sure why the itex things aren't working.. Edit2: I've attached a picture of the question at the bottom as well. Homework Statement The cohesive energy of a solid noble gas may be written as (See picture below) Derive an expression for the...

I have this expression: f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1] where P_2 is a second order Legendre polynomial, and P(\omega) is some distribution function. Now I am told that, given a data set of f(\tau), I can solve for P(\omega) by either...

I am trying to find a general expression for radicals, for example, √k=f(k) Does anyone know of any? Thanks!

Hi all, I have this integral, and I wish to write it in a closed-form in order to be able to program it. The integral is: \int_{-\infty}^{\infty}e^{j2\pi f_c[a^{(u)}-a^{(m)}]}g(t[1+a^{(m)}]-kT_s-\tau_p^{(m,n)}) g(t[1+a^{(u)}]-lT_s-\tau_q^{(u,n)})\,dt where...

I am trying to simplify the expression \not p \gamma^\mu \not p. I believe the answer should be - \frac{1}{2} \gamma^\mu p^2, but I am not sure. Tom

2x^2+9x = -5 Solved, you can banish this thread now mods. 2x^2+9x = -5 With the given answers, nothing I can come up with matches it. I can't solve it like a normal quadratic, as it gives me no answer that matches those. And I can't factor it. Nothing that adds up to 9, that when you...

The expression gives time taken to reach a a distance ds in a medium. The expression has the dimension of time, But my question is how come the denominator is (c/n)? why it can't be (cn)? explain me.

Homework Statement Factor the expression ac-bd+adi+bci Homework Equations The Attempt at a Solution We can factor the variable 'a' which gives: a(c+di)-bd+bci The common factor in the remaining terms is b, and if we also factor out b we get a(c+di)-b(d+ci) But this is not the...

Homework Statement Find the partial fractions for this expression. (((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1))) The Attempt at a Solution The final answer is 1/sqrt(n) - 1/(sqrt(n+1)) My work: A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n)) I am subbing in n = -1 and n = 0 to solve for...

Homework Statement This problem is found in a chapter about rational functions in my review book. The expression is as follows: \lim_{x\rightarrow a} {\frac{2 x^2 + 5x - 3}{x - a}} = \ \text{L} where 'a' is a constant. I'm supposed to find a value of 'a' that allows the limit to...

Homework Statement Problem is posted as imageHomework Equations The Attempt at a Solution Hello, I am having some confusion over what is meant by 'type in the boxes the minimum value of the expression'. Does that mean take the derivative of the function? Or does that mean the value at which...

find integer a such that $(x-a)(x-10) +1$ can be factored as $(x+b)(x+ c)$ where b and c are integers

Homework Statement Evaluate (simplify) the following expression: y(t) = ∫0∞ e2(t + 2τ)δ(t + τ)dτ =Homework Equations Shortcut signal expression techniques, integration of an exponential signal and impulse signal, other techniques that are probably unknown to me The Attempt at a Solution...

Homework Statement I am working on problem 4 in the PDF attachment now, but I will show my code for 2 and 3 since they are related to 4. The values for 2 and 3 were given in the editor. Homework Equations The Attempt at a Solution 2. P = [1.6, 4, 2.9, -8]; N = 3; PextDown = repmat(P,3,1)...

Simplify $\tan x\left(1-\sec \dfrac{x}{2} \right) (1-\sec x)(1-\sec 2x)\cdots(1-\sec 2^{n-1} x)$ at $n=8$.

Hi everyone, :) Here's a question I got from a mailing list in our university. Interesting problem but I sill have no clue on how to solve it. Note that this is a research level question and a solution may or may not exist.

Homework Statement I want to know the expression for the round metric of an n-sphere of radius r Homework Equations I have obtained this for a 3-sphere dS^{2}=dr^{2}+r^{2}(d\theta_{1}^{2}+sin^{2}\theta_{1}d\theta_{2}^{2} +sin^{2}\theta_{1}sin^{2}\theta_{2}d\theta_{3}^{2}) The...

Homework Statement Homework Equations That is the solution: The Attempt at a Solution I think ε≠Bvl because ε = - dø/dt=- Bd(v.t)/dt, v is not constant. Why ε=Bvl?

Just a question if you had to write a boolean expression for a problem like this, A motor requires three conditons ABC to be high to start, but a manual override can start and stop it (M) what is the expression for Z so Z = ABC... how would you incorporate the overside switch.

consider the following LMM $$y_n-\frac{3}{2}y_{n-1}+\frac{1}{2}y_{n-2}=h(\frac{1}{2}f_n+\frac{1}{4}f_{n-1}-\frac{1}{4}f_{n-2})$$ which is applied to the initial value problem $$y'(t)=y(t),0\leq{t}\leq{1}\\ and\\ y(0)=1$$ How do i find an expression for $$y_n$$, if the starting values are...

Homework Statement From the 2nd TD law: TdS= d(\rho V) + P dV - \mu d(nV) find that: S= \frac{V}{T} (\rho+P- \mu n) Homework Equations \frac{dP}{dT}= \frac{P+\rho - \mu n}{T} The Attempt at a Solution TdS= d(\rho V) + P dV - \mu d(nV) TdS= d[(\rho+ P- \mu n) V] -...

Homework Statement it is capacitor charging expression..how to find its integration Homework Equations VL(t) = ∫_(T/2)^T▒〖Vme^(-T/2RC) 〗 dt The Attempt at a Solution result is 0.5...but how

Homework Statement If \frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}, prove that x^{b+c-a}.y^{c+a-b}.z^{a+b-c}=1Homework Equations The Attempt at a Solution I solved a question similar to it in a way. So I tried this in the same way. The only difference between the two questions is...

Homework Statement The thin, homogeneous bent rod has the mass m and the total length of 4b. It rotates with the angular speed of ω = ω0(24i + 12j - 6.0k) (only rotation) Determine the expression for the moment of inertia with consideration of the center of mass of the rod The figure...

Please look picture. I represented the expression with this integral : integral of (1-x)^3 from 0 to 1. I got 0, which makes no sense... How should I proceed?