Natural Definition and 1000 Threads

I wish to show that the sum of 9 consecutive natural numbers: n(n+1)(n+2)(n+3)...(n+8) will not be a perfect square. This problem came by as a result of another problem I was doing and I'm wondering if anyone knows/has come across this already. After some searching I found that n! is not a...

Hi, I had been reading the book on 'Dynamics of Structures' authored by Prof.Anil K Chopra of University of Berkeley. In his book, the author has provided the natural period of vibration of some buildings like: 1) Transamerical building of San Francisco- California which is 2.90 seconds...

How can I convert an equation in units where hbar = c = 1 into an equation with hbar and c in SI units? I searched around a bit and wasn't able to find anything (I'm probably not asking the right question). Is there some general way to do it rather than just intuition from having seen the...

I am trying to understand Ritz method, but i have troubles wtih determining the boundary conditions. After weak formulation of a differential equation how do we determine natural and essential b.c.? What are boundary terms, secondary variables, primary variables, natural and essential...

Hello, I'm re-studying calculus using Spivak's Calculus 4ed and I'm stuck in one of the problems. Any help is appreciated. Homework Statement The theorem to prove is "every natural number is either even or odd". The definition of even given by Spivak is the following: A natural number n is...

Is it possible to define an abelian group on the natural numbers (including 0)? It's just that for every binary operation I've tried, I can't find an inverse!

Homework Statement if n is a natural number and n2 is odd, then n is odd Homework Equations odd numbers: 2k+1, where k is an integer even numbers: 2K, where k is an integer The Attempt at a Solution ok so take the opposite to be true, or n2 is odd and n is even. Then we would have...

For example the microcanonical ensemble uses a dirac delta distribution on a certain energy shell E, which is not actually a uniform distribution (even on the energy shell), but it comes close. Why is uniformity (in phase space, or a relevant restriction thereof) natural for equilibrium...

Natural selection: What do they mean by "average" individual? You know how they say stabilizing selection favors the "average" individual - i.e, it is centered around the mean? I have a question. How do they calculate this "mean"? I'm confused. All I know is that if pure-white rats mate...

If 'n' is a natural number such that n>1, prove that there exists a natural number k such that n-k=1. It raises the question: What is the definition of a natural number? Could you say that because n is natural, n-1 must be natural so that if k = n-1, n-k = 1? BiP

Homework Statement A musicians tuning fork rings at A above middle C, 440Hz. A sound meter level meter indicates the sound intensity decreases by a factor of 5 in 4 seconds. What is Q of the tuning fork? Homework Equations Q=\frac{\omega}{2\beta}...

So a human is made of cells. It is essentially a city or society of cells that live together. There is no such thing as human, it's just a bunch of cells. So human is just a natural phenomenon, an emergent property. In addition, a cell is just a bunch of atoms. I.e. a collection of atoms...

Hi all, A fixed-free bar has a single natural frequency. When we discretize such a bar in the finite element method, then the natural frequencies are the eigenvalues and an nχn matrix where n is the number of the degree of freedom which is usually large. Thus we obtain up to n natural...

I had this posted under the wrong field earlier until I realized it's an applied mathematics question An excerpt from The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner "There is a story about two friends, who were classmates in high school, talking...

An excerpt from The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner "There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a...

I want to prove the next assertion in Jeffrey M. Lee's Manifolds and differential geometry. If \mathcal{D}_1, \mathcal{D}_2 are (natural) graded derivations of degrees r_1,r_2 respectively, then the operator: [\mathcal{D}_1,\mathcal{D}_2] := \mathcal{D}_1 \circ \mathcal{D}_2 - (-1)^{r_1 r_2}...

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

Hi people, we were doing an experiment in lab where we excite a plate clamped at the circumference at various frequencies to detect natural frequencies. My questions are: 1. Sometimes at certain frequencies, we were observing multiple mode-shapes (an overlap of two mode shapes, to be exact)...

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...

Homework Statement I wish to show {m+1/n|n is a natural} given m a natural has M as ONLY limit point Homework Equations Rationals dense in reals The Attempt at a Solution Let M = {m+1/n|n is a natural}. I can easily show, by archemidean principle of Reals that m is a limit point...

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...

This is my first proof and post. I'll eventually get better at tex. Homework Statement If n \in N, then n ≥ 0. Hint: N \subset N (thus not any empty set) and has least member by the well-ordering principle. 2. Relevant (i) 0 \subset N (ii) n+1 \in N for all n \in N...

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...