Natural Definition and 1000 Threads

Hi guys. I have been a mathematical physicist and have recently been taking great interest in theoretical particle physics. With some effort I can do calculations in the International System of Units (SI) with complete success if I focus very carefully. With the particle physics natural units...

I'm trying to prove that there are no natural numbers x and y that satisfy the equation x^2 - y^2 = 2. I tried to solve it by contradiction and so I assume that x and y are rational numbers and both x and y can be written in the form (a/b) where it's in its simplest form and a and b are both...

Natural Orbitals for "Particles in a Box" Hi, Are Sine waves the natural orbitals for particles in a box when electron-electron interactions are considered? Or is it only true for non-interacting electrons?

Homework Statement I'm having trouble calculating these limits. Homework Equations none The Attempt at a Solution 1. lim...((lnx)^5)/(x)= x->infinity (((lnx)^5)/x)/(x/x)= (((lnx)^5)/x)/1= How do I calculate from here? 2.lim ...(14lnx^2)/(6lnx^3)=...

Homework Statement I have a problem that I'm working on that I have almost solved, yet I am just a tad off of what the book says the answer is. I will show the way I'm doing it, and where I depart from the steps the book takes. The graph of y=(x^2)^x has two horizontal tangent lines. Find...

Homework Statement I'll try to restate it more clearer (I'm sorry I'm not good with using the more mathematical text type. Prove that if lim (Xn) = x and if x>0, then there exists a natural number M such that Xn > 0 for all n≥M. Homework Equations Just to be clear, this limit...

So I've come across a derivative problem that I need to solve that is showing me some of my weaknesses in my understanding/solving of Ln and e. This is what I've done so far. \(Q = 350\frac{1}{2}^{(\frac{t}{13.1})}\) \(Q = 350 * \frac{1}{2}^{(\frac{t}{13.1})}\) \(ln{Q} = \ln{350} *...

My teacher was saying that we can't have a set of infinitely decreasing natural numbers. What if we started at ω and then worked our way backwards. I realize that is ill defined. And where ever we start will be a finite number. But if we can have an infinitely increasing set in the...

Greetings, comrades! In a previous thread, a user articulated a common argument: His analogy mapping knights to horses makes intuitive sense, but how can we apply this idea to two infinite sets of knights and horses? How can we treat finite and transfinite sets equal in that sense and...

Find the $\displaystyle\lim_{n\to\infty}\frac{2ln(2)+3ln(3)+...+nln(n)}{n^2ln(n)}$

If you force a one-dimensional discrete lattice to vibrate at the mass at the origin sinusoidally with forcing frequency w0, what will the frequency of vibrations be for the lattice points, NOT at the origin ? Will it be the natural frequency ? Or will it be close to the forcing frequency near...

Homework Statement I'm trying to find a natural definition for V[X|Y], but I'm not sure what a natural definition is. Any help?

Homework Statement Find y' of y= 1-3ln(7x)/x^4 Homework Equations The Attempt at a Solution I used the quotient rule and got: y'=x^4*d/dx(1-3ln(7x)-(1-3ln(7x)*d/dx(x^4)/(x^4)2 which is: x^4*(0-3*1/7x*7)-(1-3ln(7x))*4x^3/x^8 simplified to: 3x^4/x-1+3ln(7x)*4x^3 3x^3-4x^3+12x^3ln(7x)/x^8 take...

Logic: Natural Deduction Can anyone lead me off here? I've broken down the three premises using 'for all' elimination, now I need to start a subderivation with an assumption, but I'm not sure what! Right now I'm unsure of the strategy I need to use to get to the conclusion, what do I...

Homework Statement I don't see why it's -LN it should be positive LN

Determine the infinite limit. lim x->4+ ln(x^2-16) I know from graphing the equation and doing a table that the limit is -infinity, but my book is saying to do the following. Let t = x^2-16, Then as x->4+, t->0+, and lim x->4+ ln(x^2-16)=lim t->0+ ln(t) by 3

Homework Statement Solve the compound interest formula for r by using natural logarithms. Homework Equations A=P(1+r/n)nt The Attempt at a Solution 1400 = 1000(1+r/360)(360*2) 1.4 = (1+r/360)720 ln(1.4) = 720ln((360+r)/360) I'm not sure where to go after this. Did I...

I came across this formula by Blevins for calculating the natural frequency of a hollow cylinder and was hoping that someone could answer a question I have for calculating the mass per unit length (m). Here's the formula: f = A/(2*pi*L^2)*sqrt(E*I/m) A= 9.87 for first mode I = Area Moment of...

I am having trouble understanding resonance. But before that I need to understand natural frequency of an object. I saw similar questions posted in the forum, but I don't understand the answers fully. So what exactly is a natural frequency? One answer which I have read says "Nearly all...

I found this equation for predicting the bending natural frequency of a tube but am having trouble working it out. I was hoping that someone might be willing to steer me in the right direction. First the equation and the info provided on the website: w = (B*l)2 * SQRT (E*I/(rho*l4)) w -...

Prove that n^n (is less than or equal to) 1*3*5...(2n-1).Where n is any natural no. Homework Statement Prove that n^n (is less than or equal to) 1*3*5...(2n-1) n^n ≥ 1*3*5...(2n-1) .Where n is any natural number.I think Arithmetic or Geometric progression is used (A.P.>G.P.) The...

I decided from the start of this year i would work harder and study more maths not that I am bad I am actually very good for a 14 year old turning 15 because i want to be a theoretical physicist one better than einstein but no matter how hard or how long i study maths or work on it it always...

I was reading in George Gamow's book and he talks about drawing a one-to-one correspondence between the natural numbers and their squares and how these sets have the same size. But could I take each natural number to \aleph_{0} like 1^{\aleph_0}, 2^{\aleph_0} and draw a one-to-one...

If I have a convolution of two variables, say x * y, and I take the natural logarithm of this operation, ln(x*y), do the same properties of logarithms apply? So, does ln(x*y) = ln(x)+ln(y) ?

What are the "natural" generalizations (if any) to Bose and Fermi statistics? fermions: 1 particle per state Bosons: unlimited number of particles per state do people consider things in between like states with a capacity n? are there other generalizations of these statistics? Thanks!

Homework Statement Solve the Equation, Check for extraneous solutions. (ln x)^2 = ln (x^2) Homework Equations -None- The Attempt at a Solution I tried simplifying it down for myself but got stuck and don't know what to do next. (ln x)^2= ln x^2 (loge x)^2 = loge x^2...

Homework Statement I need to find whether or not the Ʃ1/(n(ln n)(ln(ln(n)))) (from 2 to infinity) converges or diverges using the Integral test. I think the best question to ask is where to start with the integral? Homework Equations None. The Attempt at a Solution I've...

Trig identity with natural logs and absolute value?? Homework Statement -ln|csc(x) + cot(x)|= ln|cscx(x)-cot(x)| Homework Equations The Attempt at a Solution I got that csc(x)=1/sin(x) and cot(x)=cos(x)/sin(x), giving me a common denominator, added together I have...

Homework Statement Use the form of the definition of the integral to evaluate the following: lim (n \rightarrow ∞) \sum^{n}_{i=1} x_{i}\cdotln(x_{i}^{2} + 1)Δx on the interval [2, 6] Homework Equations x_{i} = 2 + \frac{4}{n}i Δx = \frac{4}{n} Ʃ^{n}_{i=1}i^{2} =...

Metal pipe and electric field Hello, Consider a metal pipe in which a natural gas and oxygen is flowing. One end of pipe is connected with high potential electric wire from grid station and other end is earthed. Whether explosion would result from it? please explain this to me. Thanks

Not really sure whether this question belongs here or not (if it doesn't, help move?). So I was reading my electronic circuits textbook and am at the section of underdamped RLC unforced response, and the book mentions the natural response as v_{n} = e^{-\alpha\cdot t}(A_{1}\cdot...

So, I was reading a book on Nikola Tesla the other day, and it said that he said that he could theoretically split the Earth in two with resonance. If I had a variable frequency oscillator, and I knew the natural frequency of an object, obviously I could create a standing wave. But, could I, as...

https://www.physicsforums.com/attachments/42263 https://www.physicsforums.com/attachments/42264 how we doing? i was just wondering does anyone have the properties of the following similar to the images attached.Natural gas, Water, standard oil. say motor oil properties.any oil properties...

Hi How can you find the natural frequency of an aircraft? It would be of great help if anybody can give me an idea of how to go about the problem.

Hi, I'm studying Roman culture and civilizations in a course at my university and I'm learning how poets and philosophers argued that the natural state of matter is in motion, that everything is always in motion and never at rest, that there is an empty void that exists between objects and...

Homework Statement Show that the two formulas are equivalent integral [sec x dx] = ln|sec x + tan x| + C integral [sec x dx] = -ln|sec x - tan x| + C Homework Equations Pythagorean ID's? Log rule of addition The Attempt at a Solution Well, I realized the formulas can only be equivalent if...

Homework Statement Show that A, the set of all increasing sequences of natural numbers is uncountable Homework Equations I know that the natural numbers themselves are countable. The Attempt at a Solution I am thinking of using some sort of diagonal argument to prove this.

1. Let f(x)=sin(e^x) a. Find 2 values of x satisfying f(x)=0 b. What is the range of f(x) c. Find the value(s) of x that maximize f on [3.8,4] (use calculus) 2. y=e^x if and only if x=ln y 3.a. x=-infinity because the limit of e^x as x approaches -infinity is 0. and also...

I'm relatively new to C programming and I am trying to make a program to take and print the natural log of a number input by the user but for some reason my program always returns incorrect answers. For example I entered 1 as my number, and the answer came back as some ridiculously big value...

Hi, I was having a flick around Google maps whilst procrastinating and came across this when I looked at some islands off the Australian coast. I'm not 100% certain that the pattern is caused by diffraction of the waves passing through the gap between Bernier and Dorre Islands, or simply...

Homework Statement I'm going to post an image due to the complex syntax in the problem... The Attempt at a Solution I'm not going to lie... I really have no idea where to even begin with this problem. Because it says total distance traveled by the particle, I'm assuming that the...

Given any real numbers a and b such that a < b, prove that for any natural number n, there are real numbers x1, x2, x3, ... , xn such that a < x1 < x2 < x3 < ... < xn < b. The hint I was given says : Define xi recursively by x1 = (a+b)/2 and x(i+1) = (xi +b)/2. Prove that xi < xi + 1 < b...

Can I say that the natural frequency is the frequency of a system vibrating without effect of forces and including all parameters of damping that could occur on the system? Resonance would occur when the forcing frequency equals the antural frequency.

This is about a little thing that I have a lot of trouble understanding, and which always bugs me when studying equilibrium. I've often tried to apply the concepts of torque in this context, but nothing ever seems to make sense. I consider a uniform rod which is initially at rest, and is not...

First of all, let me apologize if this question is in the wrong place. It's fundamentally a statistics question but it relates to computer science. I'm also not sure if this falls under the "homework" category, since it's for a class, but I need assistance on a general idea, not a problem set...

Hi. I just saw on wikipedia that natural logarithm has such a property: [x/(1+x)] < ln (1 + x) < x (http://en.wikipedia.org/wiki/Natural_logarithm) Can anyone pls tell me how to prove this? Proving [x/(1+x)] and ln (1 + x) less than 'x' is easy.. But how abt [x/(1+x)] < ln (1 + x)...

Homework Statement A lifetime of the first excited state for some atom is τ, calculate natural line width for that line. The Attempt at a Solution Well, I could use energy-time uncertainty relation ΔE*Δt=h then ΔE*τ=h , now I can use a relation E=hc/λ to obitain Δλ=c*τ , which is...

I am struggling to understand the concept of natural parametrization of pdf of exponential family. Say that we have a function with the following pdf: f(x;\theta)=exp\left[\sum_{j=1}^k A_j(\theta)B_j(x)+C(x)+D(\theta)\right] where A and D are functions of \theta alone and B and C are functions...

[PLAIN]http://img31.imageshack.us/img31/9004/screenshot20111117at720.png Proofs always get to me for some reason. It's like other problems I can do, but when it comes to proofs I don't know what to put. Can anyone show me steps? Thank you

Homework Statement Prove by Mathematical Induction that the assertion, n ∑ r^2 = n/6 (n+1)(2n+1) r=1 holds for every natural number n. Homework Equations Ok, so basically, how do you solve this question? I have got to the Induction step but I'm not sure how to do it...