Applied Mathematics

Hi. Trying to create an equation, what is left from my brain gets twisted and stuck there. With a flat mirror I have no problem, but with a convex one is different. Can anyone please try, or provide heavy guidance ? It is necessary to take a look at this mirror and its reflection : ----> http://www.cleardomesolar.com/solareflexpanels.html The variables are The mirror arc (mirror lenght or size) A The mirror curvature (its radius) R The illuminated target span S The illuminated target position P Time of day (or sun azimuth angle) T The target-to-mirror distance D I see the relationships as: A (larger) curvature radius R is inversely proportional …

i understand the binomial series but i dont under what is meant by to calculate o the nearest hundreth the values for example : q)(0.98)^6=(1-0.02)^6 i solve this question by binomial series but i dont understand how to calculate to the nearest hundreth the value

I'd be grateful for advice and guidance on this question please. Given - that in 1984, London ("chief city of Airstrip One") is being subjected to a sustained bombardment by rocket-bombs, and: 1. The rocket-bombs are falling at the rate of 20 to 30 a week (say, 4 each day); 2. Each bomb destroys buildings within a 50-metre radius of the impact-point; 3. No rebuilding is undertaken; 4. London has an area of 40 x 40 kilometres, ie 1,600 square kilometres; Then - is it possible to calculate how long it would take for London to be completely destroyed? The difficulties in such a calculation seem to be as follows: A. As the bombardment goes on, there's an…

Hi all I am new to DOE. I wonder if for a very costly experiment that sampling is impossible in practice, we can implement DOE methods and find the optimum parameters just by using the mathematical model (that simulate the process) of that process (for example generating data by using the model not by experiment). And which designs are usually used for costly experiments? Thanks

Hi guys, I'm looking for a function [latex] b(x,y) [/latex] that satisfies: [latex] \int_0^L \int_0^H b(x,y) \, dx \, dy = 0[/latex] and [latex] \int_0^L \int_0^H b(x,y) \cos \left(\frac{n \, \pi \, x}{L} \right) \cos \left(\frac{m \, \pi \, y}{H} \right) \, dx \, dy \ne 0[/latex] for [latex] n=1,2,3,... [/latex] and [latex] m=1,2,3,... [/latex] Thank you in advance...

I understand that anything other than zero to the zero power equals one. But this doesn't seem to make sence to me. Could someone explain how this is, rather than that it is? I'd like as much feedback on this as possible. Thank you.

What is the smallest sample size that we need for a statistical study to be representative of a real population? eg. if there is a population of 100 and my sample size is 10 then even if 8 out of 10 responses are positive what is the possibility that 80 out of 100 people would adhere to the same norms? Are percentages inaccurate in this case? Please advise.

Hi, My sincere apologies if this forum is not for my below query.... I have always been interested in applied mathematics and physics and have done well in Math from my school days till bachelors. I have now decided to do what I like till date and have enrolled for a Bachelor of Science - Mathematics, which has more of applied math syllabus. This degree also covers Mechanics & Dynamics to the required levels and I want to capitalize on this degree and see if I can get into a MS Aerospace/Aeronautical Engineering program. The crude reality is that I am 33 yrs now and will at least be 38 if I get my admission. Please advise if Universities take such cand…

Hello, I have a DoE question about a 3^(7-1) fractional factorial design matrix. For the 7th factor, I used the generator function G=ABCDEF, and I'm wondering what its resolution and the associated confounding structure is. Can anyone help? I'm using DoE to analyse the effect of 7 input factors on a response variable and expect a nonlinear relationship, hence all factors have 3 levels. I appreciate that 3^6 (=729) experiments may seem 'a lot' but they're reasonably quick to do since they're computer experiments rather than physical experiments. However, the full 3^7 experiments would take too long. To determine the design matrix's resolution and the confoundin…

A particular problem must be diagnosed. There are different hypotheses h1,h2,....hj as possible solutions, with required probabilities for acceptance p1, p2, ..., pj. The hypotheses are mutually exclusive and exhaustive, that is P(h1) + P(h2) + ... + P(hj) = 1 at all times. There are different tests that can be performed, t1,t2,....,tk to provide information to assist in the diagnosis. The tests cost c1,c2,....,ck. The result of each test r1,r2,...,rk is qualitative taking on only three possible values: true, false, or not yet performed. The probability vector that a given hypothesis is correct <P(h1),P(h2),..,P(hj)> is a known function f(r1,r2,...,rk)…

How do we define a 4D object like a Klein bottle in 3D topology? And does such matter exist in space?

Hi everyone, my name is Can studying at Aerospace Engineering I want to minimize objective function shown below ' F' which calculates the wave drag of an aircraft. S is the cross sectional area, S" is the 2nd derivative of x-sectional area, n is the number of cross sections My questions are how can we minimize F ? What type of optimization method can we use ? if gradient based, then how can we calculate gradient? How can we perturb and see the result for all n x-sections ( n is about 100) Thanks for your time and attention C C

Hello, I have obtained data from experiments, and when I plot the values I obtained vs the time, I can see that at large t, it's going towards something constant. I would like to prove that it converges (or find a criterion to determine "from this t, we can already see that the data will converge, so we can stop the measurement at time t"... something like that ). I have never tried to do a "convergence proof" with real data, so I am a bit lost... Thanks for your help!

If you have 50mg dissolved in 50ml, what would that be in micro moles? Have fun!

Hi there, I am a pharmacuetical PhD student, currently want to ask some advice about the statistics. We performed a DOE to study the relationship between simulated intestinal fluid (SIF) components and solubility of drugs. The DOE is composed of 7 factors (representing the components of SIF) and 2 levels for each drug. And we have done several drugs with the DOE. Now with the DOE analysis, we can tease out significant factors for each drug, and now we want to compare all those drugs by correlating the significant factors with the drug properties (multivariate). At the beginning, we want to see how each factor can affect the solubility. Actually the increase/d…

Hello, I have a doubt about the distribution of random variables that maximize the differential entropy in a set of inequalities. It is well known that the Normal distribution maximizes the differential entropy. I have the following set of inequalities: T1 < I(V;Y1|U) T2 < I(U;Y2) T3 < I(X1,X2;Y3|V) T4 < I(X1,X2;Y3) where, Y1=X1+N1, Y2=a*X1+N2, Y3=b*X1+X2+N3. N1,N2,N3 are Gaussian ~ N(0,1). The lower case a and b are positive real numbers a < b. U, V, X1 and X2 are random variables. I want to maximize that set of inequalities. I know the following: (i) From T4, h(Y3) maximum is when Y3 is Gaussian then X1 and X2 are Gaussian. (ii) From T2 we maximize it…

I have entered this into my calculator several times and I keep getting the same answer could someone tell me why? c^2-(1/c)^2 = 8.987551787e16 Then I enter c^2-(1/c^2)^2 = 8.987551787e16 c is the speed of light 299792458 I am hitting the enter key at the = sign I was expecting the second calculation to have a different result.

For instance if x is one bit of information, how many similar bits (y) are necessary to describe x ? *It seem obvious that y > x, I just wanted to know had any rules been established. This would be done without using compression, predictions, sets or subsets, and each bit of information must be individually described. *Could a clone be considered as a valid description, in the physical or theoretical sense? Would this mean the smallest possible uncompressed description of a system can be no smaller than the system itself? Btw I know very little about computer science, physics or maths so a link to a '________ for dummies' site would not be considered inapp…

Anyone that can help me with enclosed problem ? AccumulatorProblem.doc

An interesting application of the geometric mean of 2 numbers would be calculating the vertical distance to the roof of a sports dome from any point on the playing field, provided the dome is a hemisphere and the playing field lies on the equatorial plane. The distance from any point to the roof is the geometric mean of 2 distances. The 2 distances would be any 2 OPPOSITE distances to the wall. But what's an application for the geometric mean of 3 numbers? (the cube root of their product) Also, how about 4 numbers? (the 4th root of their product)

please someone should help me out of this. solve the heat equation using inverse laplace transform. dw/dt=c^2d^2w/dx^2. subject to the d following boudary conditions W(x,0)=To W(0,t)=0 W(x,t) goes to 0 as X tends to infinity.

I'm interested in establishing a framework to dynamically reduce explicit/classical representations into various orders of abstraction with intent to simplify computation necessary for the simulation of systems. If you prefer that I specify how I imagine these systems might be, consider a very large set of points which may exhert various forces upon each other (classically, like particles) within the system e.g. exhibits contact dynamics and supports modelling external forces and fields from outside the system of points. Consider a large number of these points behave like a fluid, and they're contained in a way that can be approximated using a planar-surface fluid approxi…

Hello all, I am looking into designing an experiment and am considerable stumped/ confused. I have limited knowledge on statistics, consisting of one undergrad and one graduate course, not covering DOE. Basically I am doing my experiment to investigate 10 factors on a particular process and its corresponding output. The complicating issue in this case is the fact that the factors have different levels (two, three, or four). As well, complicating things greater, three of the factors are nested within one factor. This issue is slightly hard to explain so I'll explain it differently: a,b,c are nested within x; 'a' under x1, and 'b', 'c' under x2. x = x1,x2 …

some Qs look simple, but it is not easy to get the right answer, here is the one below : you and your 27 classmates go to buy coca cola. the promotion is: buy 3 free 1, ask: how many bottles of coca cola you and your classmates need to buy ? (only one bottle per classmate)

As we know, now there is efficient algorithms to find the overall min-cut in a directed graph, e.g. Hao and Orlin (1994). Now my problem is to find an overall min-cut just separating some given node pairs, not all the node pairs. For example, I have an 8-node digraph with capacities on each arc and want to find the overall min-cut separating only some node pairs such as 8 and 1, 6 and 3, 7 and 1. The algorithm of Hao and Orlin (1994) cannot solve my problem. Thanks a lot. Shaon