Applied Mathematics

Hello all, I'm trying to solve analytically a differential equation and I encountered the following integral, Integrate [1/((Sqrt(x))*(atan(x)), dx] The change of variable u = sqrt(x) brings this integral to, 2 * Integrate [1 / atan(u^2), du] Now what ... ? Any help will be highly appreciated. P.S. I attached a PDF file with the problematic integral. Question.pdf

I would like to implement the support vector machine-recursive feature elimination algorithm to a biomedical dataset. I am a beginner in machine learning, and would like to know how I can implement this algorithm. I currently have a proteomics dataset comparing two cell lines (WM and 1205) that have been analyzed in triplicate. I was hoping to apply the support vector machine with recursive feature elimination to classify on the basis of cell line. Is this algorithm appropriate for data of this type, or are more samples (I only have 3 per cell line) necessary for accurate classification? What would be the appropriate method to train the SVM? I was thinking…

Dear forum members, I am encountering the problem related to finding derivations of Hankel functions presented below and would you please suggest me any idea for the problem if possible? I would like to find derivations of H0(2)(k0.r) respect to k0 and I found a recursive relation to find its derivatives can be found in the attachment. And then I will calculate H0(2)(k1.r) by using Taylor expansion: H0(2)(k1.r) = ( H0(2)(k0.r))[0] + (k1-k0). ( H0(2)(k0.r))[1]/1! + (k1-k0)2. ( H0(2)(k0.r))[2]/2!+ .... However, the result only converge with small value of r (0.3 - 1.2) and it will diverge if r is large (100-1000) k0=21 k1=27 Could you please pro…

Using the values L=50*10^-3, R=100 ohms, C= 1600 microF, peak to peak voltage= 200V, and frequency=100Hz, how do I set up and solve the second order differential equation to find the voltage across the capacitance? I know the equation to use is: L*(d^2i/dt^2)+R(di/dt)+(1/C)i=wVcoswt But I am unsure how to solve it to obtain the voltage across the capacitor Oh, and the intitial conditions are that both the initial voltage across the capacitor and current through the inductor are zero

Hello, I am a new member here... I need help in solving a huge homework, there are 4 exercises, each exercise contain many problem solving that I need to solve, I don't really know some of my answers are true or not, I need someone who is professional in Applied Math to help solve the problem before the exam starts (13/3/2012) and thanks

Hello bright minds! I've recently started on a project to help somebody to track employee shifts data in a database in FileMaker Pro. And while the database itself is going just fine, nothing fancy here I wanted to take it further just because the improvement I have in mind is exciting to implement. I'm not familiar with advanced mathematics so I will need more down to earth explanations. In a way this call for help is almost like saying "do this for me" and I'm sorry about that, but it's a very interesting problem to tackle nonetheless. So with all that out of the way here's what I'm looking to implement: We have a table with columns of days in a given month and ro…

Hello All, I have a question related to the fascinating topic of "Boundary Layer Theory". Take for example the simple equation mx'' + kx' + cx = 0 where k and c are finite constants and (m -> 0), (The derivative sign (') is by t) x(0) = 0 x'(0) = A > 0. In order to achieve a comprehension on what's going on near the point t = 0 when (m -> 0), it is suggested to take the change of variables t* = t/m. By that the former equation becomes, x'' + kx' + mcx = 0 (Now, the derivative sign (') is by t*). Now, moving into the limit or alternatively noticing that mcx is negligible, we can drop it and we get, x'' + kx' = 0 and now the solution i…

Is there a listing somewhere with all the formula of science recorded - something like the guiness book of world records except for all known scientific formuli?

if a baseball manager has 5 pitchers and catchers, how many different possible pitcher-catcher combinations can he field

Hello All, My question is on the problem of solving the ODE x' = A(t) x (with x(0) = x0) and A belongs to R(NXN). During my research I've encountered the question of whether the sum exp(A(t)) = sum ( I + A(t) + 0.5*(A(t))^2 + ... ) is uniformly convergenct with respect to t, where t belongs to [0, T] and T is finite. One can assumes smooth matrix A(t) and A(t) is invertible. Moreover, it can be assumed that A(t) is also skew-symmetry if it helps, and that the limit exp(A(t)) exist and finite for all t. The question comes from the problem of differentiating exp(A(t)) term by term. ... So, is it true that "sum ( I + A(t) + 0.5…

Greetings, I'm working on a project where Stocks data are managed in order to be analyzed for an investor, 1. what statistical distribution\s should I use for this type of data ? 2. should I only consider the final price of the stock during the day, or include more detailed variables ?

Hi, I want to covert between global and local coordinates when rotating 3D object because some program only allow to rotate by global or local coordinate. Example in this image, if I rotate Y by global coordinate (black coordinate) then the red object will rotate around black y axis. But I want to rotate it around y' axis, the local axis of the object. How can I rotate object around local axis using global rotation? And how can I rotate around global axis using local axis? Thanks

Just out of pure curiosity, can anyone here give me any advice on the problem of solving the following differential equation [math]\left\{\sum_i \vec{\alpha}_i \cdot \nabla_i + \sum_{i neq j}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\psi} = K\frac{\partial}{\partial t}\vec{\psi} = iKm\vec{\psi}.[/math] where, [math][\alpha_{ix} , \alpha_{jx}] \equiv \alpha_{ix} \alpha_{jx} + \alpha_{jx}\alpha_{ix} = \delta_{ij}[/math] [math][\alpha_{i\tau} , \alpha_{j\tau}] = \delta_{ij}[/math] [math][\beta_{ij} , \beta_{kl}] = \delta_{ik}\delta_{jl}[/math] [math][\alpha_{ix}, \beta_{kl}]=[\alpha_{i\tau}, \beta_{kl}] = 0 \t…

Hello, I have thought of this math problem I haven't been able to solve, but it must have a simple solution. We have an undefined (either even or odd) number of line segments and we want to connect their end dots except two of them (for all the set -like if a fluid could get in by the unconnected dot, pass through all the segments and connections and them go out by the other unconnected dot).But there is an imposition: the connection cannot connect two segments that are side by side. Here is an uncompleted sketch -How can we know wherever it is better to have an odd number of line segments or an even one as to use the less length of connection? -What is,…

I have a problem which I will first state formally and then give some real-life context. Any help appreciated! Suppose I have a set with T members. I randomly choose a subset with X members. Independently of that, someone else randomly chooses a subset with Y members. Without loss of generality, assume X <= Y. Given a number N (N <= X), what is the probability that the two subsets have exactly N members in common? Now for the real-life context. Historians often find multiple copies of very old manuscripts but don't know how they came into existence. One technique they use is to look for common mistakes. If two documents have exactly the same mistake, then the s…

Hi all. I'm new to the forum and came here for a specific issue with stats. I am a third semester masters student and will be finishing in May. I work with a woodwasp that oviposits within pine trees and am trying to look at ovipositin behavior. I allowed them to oviposit in regular logs and another set to oviposit in logs that had already been infested with a known competitor/predator. (n=10 in both cases). So my question is how to go about showing that these are different. In the regular logs there was anywhere from 5-150 drill holes. In the infested logs, there were never more than 10 drills, usually there was total avoidance. Initially, I had expected an aggregat…

Hi there, I have a quick question regarding pseudo-arclength continuation. As some background, I am a chemical engineer, not a mathematician, applied or otherwise, so my knowledge of numerical methods is limited to the "standard" stuff. I've been reading up as extensively as I can on pseudo-arclength continuation, but unfortunately, it's all from second-hand sources; I don't have access to Keller's original paper. Here's what I understand at this point: We want to solve a problem [math]F(x,\lambda)=0[/math]. We assume that the solution is known at [math]x^0[/math] and [math]\lambda^0[/math]. To avoid the singularity of the Jacobian, and therefore the breakdown…

In terms of milliseconds, how long would it take an object in a vacuum to freefall from its starting point, to the ground a meter away, accelerating at precisely 1g? Like, if NASA were to make a vacuum chamber, not a single millimeter above or below sea level, suck all the air out of it, and, using a mechanical hand, drop some kind of pellet to the ground that is precisely 1,000 millimeters beneath it, how many milliseconds later would it hit the ground? I'm pretty sure that this requires a more precise definition of 1g besides simply 9.8 meters per second squared. I read that the actual acceleration of 1g is in fact 9806.65 millimeters per second squared, so thi…

Modelling is a very specific extraordinary section in Mathematics. Although many systems can only be described by partial differential equations, and may be tensors equations, they can be modeled, approximately and even in some cases exactly, by very simpler equations, O.D.E.s and may be Vector Field Multi-Dimensional Functions, just assume the variables you are not in need for, pick up the property you are in need, and derive the equation. For example, conservative field force are described by an O.D.E. (or P.D.E. in the sense of general force form), but can be analyzed very simply by the form of Potential. If there is some thing wrong, would some one advise…

I'm trying to create a budget for a small business. I have to factor in the loan payments, but in order to figure how much they'll be, I'll need to know how much I'm going to be borrowing. Various banks have calculators on their websites that tell you these things, but as I put in the loan payments, my costs fluctuate dramatically. This requires that I modify the amount to borrow for my start up funds, and I end up having to repeat this process over and over again. Specifically, what equation do they use to factor my minimum loan payments? This way, I don't have to keep going back to this website calculator; I can do it myself.

Hi everyone, i'm a very beginner in Machine Learning and i hope that you can help me a bit. I'm working on Linear discriminants and i have to solve this problem : What are the values of weights : w0, w1, w2 for perceptron whose decision boundary is illustrated here : The decision boundary looks like a trivial function : 2/3x + 2 However, i don't know how to determine the weight. I know that : g(x) = W^t * X + w0 (where capital letters are vectors). when g(x)>0 : i decide omega1 g(x)<0 : omega2 g(x) = 0 : it corresponds to the decision boundary. In my set of datas, i have some label x1 and some label x2. (according to their positi…

Hello. Forgive my lay review here but this is the background to my question: My daughter and I were headed to school one morning earlier in the year. She was reading 101 Dalmations. While stopped at an intersection - I looked over to the vehicle next to me and surprise, surprise, you guessed it - there in the back seat was a DALMATION. This morning on the way to school we got to talking about that very event...that coincidence. It then occurred to me while trying to give my daughter a ball-park notion of the (high) odds of having those two events occurring again at random - that I ought to run the question of determining general probability of a seemingly r…

Hi. On a reverse osmosis process, If the seawater compartment on a desalination process is at 1000 psi; and the desalinated water compartment is at atmospheric pressure; Seawater @1000 psi -----> membrane -----> desalinated water @0psi What would be the equivalent pressure differential using atmospheric seawater compartment and partial vacuum to achieve same results ? Seawater @0psi -----> membrane -----> desalinated water @??? inches of Hg How is it calculated ? Thanks

I you have a savings account with 1% APY and monthly compounding interest, what's the APR? Also, what would be the APR for a 1% APY savings account whose interest compounded quarterly, bi-monthly, semi-monthly, bi-weekly, weekly, and daily?

Couldn't quite figure out whether to put this in Physics, Calculus, Applied Mathematics, Computer Science, or Engineering :/ I'm trying to come up with a good scheme for integrating something similar to a thin beam equation: Something along the lines of: [math] A\frac{d^4y}{dx^4}+\text{Possibly other x derivatives}=q(x) + B\frac{d^2y}{dt^2}[/math] But unfortunately comp-phys is but a hazy memory. I can remember/find notes on enough to do similar things which are first order in time with finite difference methods. Would the obvious thing of adding degrees of freedom to make: [math]v = \frac{dy}{dt}[/math] [math]\frac{d}{dt} \left[\begin{array}{c} v\\y \end…