Natural Definition and 1000 Threads

How is the net driving pressure difference within a PWR a function of T and H delta P = delta T(Core) * g * partial Rho(T, P(RCS))/partial T * delta H I get how this correlates to the pressure differential and is found with bernoulli's equation but how does the temperature dependence get...

Homework Statement Prove by natural deduction ((X \Rightarrow ¬Y)\vee(¬X\RightarrowY))\Rightarrow(¬(X\wedgeY)\wedge¬(¬X\wedge¬Y)) Homework Equations The Attempt at a Solution i understand basic natural deduction and how to prove via it but this one has me stumped as there is no...

Homework Statement Prove by both natural deduction and by resolution ((X \Rightarrow ¬Y)\vee(¬X\RightarrowY))\Rightarrow(¬(X\wedgeY)\wedge¬(¬X\wedge¬Y))Homework Equations The Attempt at a Solution as far as natural deduction on this goes i have no idea since there is no ' I- ' looking symbol so...

Find the largest natural number m such that n^3 -n is divisible by m for n element N. Prove your assertion. How exactly do you begin this im thinking the largest m could possible be is n^3 -n, but I am not sure. To be divisible we know that mk=n^3-n for some k

Hi, I was reading Lemon's Perfect Form and it talked about "natural boundary conditions". But I don't understand exactly how one determines them. It seems to me that one imposes some random condition then deduce stuff from it...?! Advanced thanks for any enlightenment!

Homework Statement Describe Lack's experiments with Swiss starlings, and state what these experiments tell us about the effect of natural selection Homework Equations Lack's studies / experiment was that he marked the nestlings of the starlings and then he recaptured them months later...

Most public intellectuals who are critics of society and speak out about their knowledge often come from the social science realm. Why aren't there any from the hard sciences?

i have a basic question about the natural frequency of a system. for a mass (M), spring (k constant) undamped system the natural frequerncy is: w_n=sqrt(k/M) the units of w_n according to a lot of resources i found on the internet & textbooks are [rad/sec], my question is why? if i use...

Hey, I was having this very silly problem in heat transfer. Please could you see what's going wrong ! I am working on defrost water tray modelling. In that, the water collected during defrost is heated by the compressor o/p coil so as to aid evaporation. I was trying to find out the heat...

I found two different versions of equations to find natural frequency of a cantilever beam. I am not sure which one is right. I would appreciate if someone could make things a bit clear here F1= k^2*sqrt(E*I/(mpl*L^4))/(2*pi) where k=1.875 for first natural freq and I= b*d^3/12; OR is...

Homework Statement Let log z be the principal branch of the logarithm function defined −pi < arg z < pi the domain to define f(z)=loglog z?? Homework Equations The Attempt at a Solution I already know how to represent the arg z by arctanb/a+2pi*k how can I get arctan [Re (log...

A natural draught cooling tower is designed to have a 3% loss of the mass of the water entering the tower by evaporation into the atmosphere. Atmospheric air enters the tower at a volume flow rate of 4 m^3/s a temp of 10C and a relative humidity of 50%. Air leaves the tower in a saturated...

Hi all ! i want to know some of the devices that measure natural frequency of solids/vessels, etc ! with regards! take care !

Homework Statement [PLAIN]http://img840.imageshack.us/img840/553/unled0016.jpg Homework Equations The Attempt at a Solution can you sujjest me some articals to read (what knowladge do i need) before attemptiong this question?

Homework Statement For every epsilon > 0, there exists an N\in N such that, for every j >= N, |f(i,n) - g(n)|<epsilon for every n\in N. In addition, for every fixed j\in N, (f(i,n)) converges. Prove that (g(n)) converges. Homework Equations f: N x N --> R, g: N --> R The Attempt at...

natural isomorphism from V to V** It is known that there is a natural isomorphism \epsilon \rightleftharpoons \omega^\epsilon from V to V**, where \omega: V \times V* \rightarrow R is a bilinear mapping. So given a certain \epsilon \in V, its image under the isomorphism is actually a set of...

I downloaded the Crysis natural mod, installed it, and not only does the game look mind-blowingly spectacular, But I think the framerates increased very slightly. Beforehand, playing Crysis on very high spec/1920x1080 gave me 25-45 fps. Now it's at 35-60+ fps with the natural mod installed. Did...

SORRY FOR THE LACK OF FORMATTING, I SPENT 30 MINUTES TRYING TO FORMAT AND IT KEPT GETTING MESSED UP. Homework Statement Evaluate by substitution. Integral of dx/xln(x^2) Homework Equations integral of 1/u du = ln(u) + C The Attempt at a Solution u = ln(x^2) du = 2/x...

Homework Statement Evaluate the derivative of the following function: p(x) = (5x)-ln(5x) Homework Equations \frac{d}{dx}lnx = \frac{1}{x} Not sure what else... The Attempt at a Solution I know that I will have to use the chain rule in this problem, but actually...

Hi everyone, Say, I was wondering if you could explain something to me. I have two examples to share: 1) I drive by several enclosed bus stops on my way to work. The enclosure consists of a solid roof, but the sides are a metal mesh screen with circular holes less than the diameter of my...

Homework Statement Find the area under the given equation using definite integration. y = 4ln(3-x) from 0 to 2 The Attempt at a Solution Integration from 0 to 2 4 (integration from 0 to 2) (3-x) Let u = 3-x du = -dx -du = dx -4(integration from 0 to 2) du Idk where to go from there :/...

if a free-free bar has a crack located somewhere along it's length, in order to find the natural frequency of the bar do you split the bar on either side of the crack and assume each bar is free/excited? What would the equation for natural frequency be in this situation?

Hey there I need to find the natural frequency of a Cantilever Beam. The beam is tapered in breadth, but has a uniform thickness. So basically the end goal is an equation for f as a function of the angle of the side cut. Clamped at one end L=constant B=changes though the length of the...

EDIT: finite dimensional only! Hello, I would like to ask a question; I understand that the cannonical "evaluation map" ( (p(v))(f) = f(v) , f is a functional, v in V ) from V -> V** is a "natural" isomorphism ( we don't have to select any bases, the isomorphism relies on no choices ), so V...

Homework Statement Model the above beam with 3 elements(image provided in attachment). Calculate and list the first 6 natural frequencies Plot the mode shapes corresponding to each of the natural frequencies Homework Equations DET(M^{-1}*K + [I] \omega^2)=0 shape functions...

\ Is \ \mathbb{N} \ dense \ in \ itself.

I got this question and I know a bit on how to start it, but not sure which direction is best: By considering the power series 1/(1 + x) and 1/(1 - x) show that: so I do the differentiation - ln(1 + x) = x0 du/1 + u = x - x2/2 + x3/3 - x4/4 ... which equals - = sigma (upper infinity and...

Well I've been doing fairly complex thermodynamics in classical mechanics lectures with a bit of medium to advanced class, first of all , it took me a very long time to wrap my head around the concept of Entropy, however I still don't understand why we use ln (Natural Log) to calculate the...

Show there exist a natural number n... 1. Let {xn} be a sequence of reals which converges to x > 0. Show that there is a natural number n0 such that xn > 0 for all n >= n0 . I tried this but cannot approach the answer. Can anybody?

I am just learning about the theory of Evolution and wonder how parallel evolution of unrelated species during the same period of time is explained.

Hi I want to derive a natural frequency equation for a system. I saw this question in a book. so they gave us an equation frequency = (1/2pi) * ( sqrt( k/m1+m2+m3/3+4m4+Ic/r2) ) Ic = Moment of inertia of pulley about rotational axis r = effective radius of pulley k = spring constant now the...

So I know that every smooth manifold can be endowed with a Riemannian structure. In particular though, I'm wondering if there is a natural structure for the unitary and special unitary groups. I often see people using the "trace/Hilbert-Schmidt" inner product on these spaces, where \langle X...

Hi everyone, So, resonance, are resonant frequencies and natural frequencies the same thing with a different name? If not could someone please explain the difference. Been searching for the answer for over an hour. Thanks in advance Peter

Homework Statement The methane in natural gas burns completely in oxygen according to the reaction equation: CH4 +__O2 → __CO2 + __H2O Homework Equations a) Complete the reaction equation by filling in the missing coefficients for oxygen, carbon dioxide and water. b) How many kilograms...

I'm not entirely sure that this question doesn't belong in the Earth sciences forum, so my apologies if I've goofed. I'm trying to figure out what academic path to take in order to best be qualified to do field research out in the natural world as often as possible, and secondarily in as...

If I am correct, crystal frequencies depend on the size, shape/cut, and purity of a crystal(?) How can you measure (what instrumentation) the frequency/ies of a natural crystal (other than just quartz)?

hi... we see this phenomenon in our everyday lilfe...:redface: in a sink, if we open its hole suddenly, the water gushes toward it in circular manner and not directly... why the water has to first circle the hole and then it passes through the hole...why it never takes the shortest...

Homework Statement what is the integral of ln(e2x-1) dx 2. The attempt at a solution I got u= ln(e2x-1) du = 2e2x-1 \ e2x-1 du = 2 dx 1/2(integral of u du) 1/2 ln (e2x-1 ) +c = 1/4 [ln (e2x-1 )]2 + c Could you please let me know if this is correct? I don't know how to integrate ln...

How can i find a bijection from N( natural numbers) to Q[X] ( polynomials with coefficient in rational numbers ). I can't find a solution for this. Can you please point me in the right direction ?

Homework Statement Given the Equation ln(x+1)-ln(x)=0 find x (If it exists. Homework Equations The Attempt at a Solution ln(x+1)-ln(x)=0 ln(x+1)=ln(x) x+1 = x 1 = x-x Solution does not exist. (My book "agrees" with me in the solutions.) However, typing up the...

Homework Statement (1) Real variables x and y are related by the equation 3ln(y +4) = 2ln(x +2) − 2ln(x +9)+3ln(x^2 − 1). Determine the range of values of x and y for which the expressions on each side of this equation are defined. Find y explicitly as a function of x, that is...

Homework Statement Evaluate. Integral of (x^5 + 1) / (x^6 + 6x) on x from 2 to 3. \int_2^3 (x^5 + 1) / (x^6 +6x) dx Homework Equations Not sure! The book only seems to give an equation for integrals in the form of du/u, which is integral 1/u*du = ln |u| + C. It also says...

May I ask how to find the E\left(ln x\right) and Var\left(ln x)? The X_{i} are random sample from the f\left(x; \theta\right) = \theta x^{\theta - 1}I_{\left(0, 1\right)}\left(x\right) where \theta > 0. I need the information in finally solving the Cramer-Rao lower bound for the variance of...

I'm calculating the natural frequency of a piping system that is spanning between two points, the formula is the square route of various terms, including the effective axial force in the piping. This is taken from a design code, see below: f = C * SQRT[(E.I/M.L^4)(1+Seff/Pcr+C.(d/D)^2] C =...

How can I show that: \sum_{i=0}^{n}2^{n-i} {n+i \choose i}=2^{2^{n}} for every natural numbers

How can I solve that type of equation: x^2+y^2=4z^2 or x^2+3y^2=4z^2

Prove that sum 1/2^(n+1)*n/(n+1), from n=0 to infinity, converges to 1 - log(2), where log stands for the natural logarithm. I know that the Taylor series for log(x) about x=1 is sum (-1)^(n+1)*(x-1)^n/n, but I don't see how these two statements are consistent. Thanks for any pointers!

Homework Statement Find v(t) across a cap. in a series rlc circuit with no driving force (initial v across cap: 24V) Homework Equations from the values of the components, \alpha > \omega_0, the circuit is overdamped, and the following equation can be used: v(t) =A_1 e^{s_1 t} + A_2...

What is natural line width of laser? how one can determine it e.g. for semiconductor lasers?

Hi, I need to estimate the sloshing natural frequency, in the three axis of a rectuangular tank, not fully filled of liquid. I need this for understading how changes the vehicle dynamics in some trucks. I have found a linear formula for the horizontal direction, but I have found nothing...