Applied Mathematics

How can we make a mathematical model for tracking micronutrients in an anaerobic system (Bioreactor) that has different chambers. The feeding ( Sargassum spp.) inters in the first chamber and should pass through the system 'til the last chamber. We know the concentration of micronutrients( Fe, Ni, Co, Mo, Zinc, Mg, Mn) in the feeding. And we have data (measure the concentration of micronutrient at the end of the system) on the effluent(out). We know normally how long takes(times) the feeding(HRT: hydraulic retention time) comes from the first chamber to the last chamber. How can we make a math model for this system if it is not stable(we never reach the steady state? Than…

Hi all! At the moment I'm looking at some huge array of geological data and need to quickly analyse it. What I'm mostly looking at is partitioning the data set into smaller chunks, while ensuring that the particular way this splitting is done would give me chunks of data with lowest variability possible. I have some statistical software in the office, but I'm in the middle of nowhere and won't have access to it before the due date. Any thoughts on what statistical measure I can use? Thanks in advance!

https://www.google.com/url?hl=en&q=https://docs.google.com/document/d/1mBEbHfJgCy8HLVEhKYf5wqDGAXD1AkIb7veqkaOxGhg/pub&source=gmail&ust=1475623385111000&usg=AFQjCNF_n-qqofZTxqxXaquht5MtHTrMkg Here's the general established theoretical base: http://article.sapub.org/10.5923.j.ijtmp.20140401.01.html . . . in other words, history really does repeat itself - down to the precise numeric digital level. The most complex and abstract of theories of combinatorics and chaos theory elements determine statistics to recur within a confined frame with respect to the most rarefied, optimal, and limit-oriented intelligentsia printing press knowledge and…

I'm trying to figure out how likely it is that abbreviations would get picked out of a dictionary by a particular sampling method. We can limit ourself to one section (one letter). The sampling method is that you pick every fifth word out of a double page of the dictionary, By double page I mean that when you reach the end of one page you don't restart the count on the next page, but you keep counting up to five. Now, my question is, if you list all the abbreviations at the beginning of the section rather than listing them alphabetically like other words, does that make them less, more or equally likely to get picked than any other word?

Let M ⊂ H be a closed linear subspace that is not reduced to {0}. Let f ∈ H,f /∈ M⊥. Prove that m = inf (f, u) is uniquely achieved. u∈M |u|=1 I have approached it with the cosine definition for inner product but that only works with Euclidean spaces. I want to know how to apply this using the Cauchy-Schwartz inequality so it works for Banach Spaces. Can anyone help? I have placed my work below. The Hilbert Projection Theorem says that there exists a unique object in M that minimizes the distance to f. It also happens to be the projection. So let f = p + q, where p is in M, and q is in Mperp. (We use the projection theorem on M and Mperp s.t. p is the projecti…

Kinda struggling with this one.

Hi, I have a number of measured data consisting of 10 numerical values. Let’s call these x1 to x10. x1 to x10 have a certain standard deviation, which I calculated by using the formula for the standard deviation for samples (see for example here: https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php). Then, I need to convert these values to new values according to the following formula: 2^(-x) From this, I get 10 new numerical values. I can calculate the new sample standard deviation for these based on the formula above or I can use the rules for the Gaussian error propagation to calculate the new standard deviation (see att…

Hi all. My speargun takes 80 lbs-force (355 Newton) to pull its elastic rubber band that will impulse a 0.4Kg spearshaft when pulling the trigger. Assuming no friction nor drag by water, when 'firing', the elastic band applies its force to the spearshaft while contracting during -say 0.02 seconds- The push force decreases linearly? to zero by the moment the spearshaft 'takes off'; I believe as a compressed spring pushing a streamlined object. Is it rational to say that a lightweight spearshaft will have little penetration into a target; and if it is too heavy, lacking initial and final velocity will also have little penetration into target ? How to determine the opti…

I have a bandwidth-unlimited periodic signal. All I know about this signal is its finite peak amplitude. I pass this signal through a known and simple low-pass filter (gain = 1 within the pass band; say 2nd-order Butterworth or Bessel type filter). I am interested to estimate the maximum change rate of the resulting signal (that is, absolute maximum / minimum of the derivation of the resulting signal) for the worst case. 1. Does the ‘worst case’ (that is the case where the resulting signal changes most rapidly) happens if (and only if?) the original signal has peak-to-peak discontinuities? For example, when the original signal is a square-wave signal. 2. What is a good …

Gratitude and credit go to Hans Milton for creating this model in Mathematica. http://community.wolfram.com//c/portal/getImageAttachment?filename=NSTF.gif&userId=93385 The first angle that we are concerned with is the elevation angle E. It is the angle that is formed between the equatorial plane (beige) and the elevation plane (yellow). The second angle is more complicated. It is formed between a plane of longitude (green) and a "tangent" plane (blue) which lies in a conical orbit. The construction of the longitude plane is not too complicated, but its orientation is very specific. The orientation of the longitude plane is such that it intersects a poi…

Hi guys, Currently, trying to determine the percentage chance of winning an imaginary giveaway for 500 prizes. It uses a single entry per person. Say there is 10000 entries and a total of 500 can win with each winner being unique (1 per person). So far I figure that since you can only win once the odds would be: 1/10000 + 9999/10000 * 1/9999 + 9999/10000 * 9998/9999 * 1/9998 + 9999/10000 * 9998/9999 * 9997/9998 * 1/9997 + ... etc How would I go about calculating that if one person was to have 1000 entries instead of just one? For example, say one person cheats and gets 1000 tickets in a raffle instead of just one with the same prize po…

There's a new blog on Applied Maths! Its name is "Math Is In The Air": have a look if you like url deleted We are a group of Italian people and we have started a few days ago our new adventure trying to write in English. I hope you like our trial and I strongly suggest to share! Then you can also like our facebook page: url deleted ! Don't be scared of the name in Italian, you can also find posts in English! And don't be shy too, so share share share! See you Francesco

Does mathematical operations has to follow the observed reality?

Hi everyone Since I'm only just starting my second semester in Biomedicine and therefore no math expert, I thought it would be great if any of you math enthusiasts/experts could check the equation I came up with regarding the value of leisure activities is correct? I wrote sort of a "paper" which explains my thought process and here is the Excel File with which one can calculate the different activities. Here is a brief summary: Let's call the activity into which hour spent time goes medium M. M can be described through 3 variables: regret r, skill s and fun f. We can determine those variables by asking 3 questions: If you find yourself at the end of your l…

I would like to know is there an existing formula to find prime nos. ?? In either case I have come up with a formula... x/(x-1)! where x is the given no. to be checked !! the ratio x/(x-1)! should be in its lowest terms by default ... also x should not equal to 2 !! then and only then it is a prime no. !!

In goodness of fit tests (COD, R2, X2) with probability density functions, we need and use their CDFs. With wind speed, another pdf is by Maximum Entropy Principle or Method, of the form: f(vi)=exp(-a0, a1*vi - a2*vi^2 - a3*vi^3). where a0, a1, a2 and a3 are Langrange multipliers to be determined [THAT I CAN DO!!!]. vi are wind speeds, with some repetive, in the discrete sense. And if continuous: f(v)=exp(-a0, a1*v - a2*v^2 - a3*v^3). In probability theory, a normalized PDF is such that: I=Integral(f(v))dv = 1; limits from lowest (v=0) to highest (v=maxv). Furthermore, the CDF is given by: CDF=F(v)=1-I I used "Green Energy: Basic Concepts and Fundamentals" by Xianguo…

I'm not sure whether to put this in the computer science section or applied mathematics, but I've always considered cryptography to be applied mathematics, so I will post it here. I don't unfortunately know all the details behind how online transactions work, but as far as I know, you send to the merchant your credit card number and cryptogram and he uses those informations to validate the transaction. This seems to me a bit insecure, because you have to trust the merchant as you are giving him all the necessary information that can be used to pay anywhere and if someone for example steals it from him, he could reuse it somewhere else. (Yes I am aware that the commun…

Hi Guys, I have to find equation and starting condition to solve nonlinear Schrodinger Equation with periodic edge condition. This method should control the propagation of fiber optical signal. In details I need a case in which the energy conservation is discriminating. Can you help me?

I am a new member & have a problem, the subject of which has interested me for years. The solution for a in the hyperbolic function (for a catenary) y = aCosh(x/a), sometimes with +c added as a 'curve shifter'. I have managed in the past by iterative trial and error if y & x are known, but very time consuming, ineligant, sometimes unsuccessful. The Casio calculator I use has a "solver", which is useful when it can find an answer, but often can't. I have a new all singing & dancing HP 50G with several solvers, which is far to complicated for me to use at all! The problem is me. I do not understand why sometimes a cannot be found? Surely every Cosh…

I need help to calculate exact or approximated probabilities. I am interesting by the content of a new theory (view this link http://figshare.com/articles/Nokton_theory/1549720 for details). Currently, I studing the interactions of two neutral noktons in one dimension. I suspect that the probabilty of any position is periodic, but I can't prove it.

My book says on average the sampling variance [math]\dfrac{\sum (x- \bar{x})}{n} [/math] is biased because it usually gives estimates smaller than the actual variance of a population. We fix this by dividing the sum by n-1 instead of n: [math]\dfrac{\sum (x- \bar{x})}{n-1} [/math] Is there a more intuitive or formal explanation of this?

Hi, I would like to develop an integer function f (in form of a computer program) with the following properties: a) x and f(x) should both be unsigned 32-bit integer numbers b) f should be injective function and if you know f(x), it should be easy and fast to calculate x c) for any x1 and x2 with Hamming distance not greater than 2, f(x1) and f(x2) should be as unrelated as possible d) (actually extenstion of c)) for any relatively small group of values f(x1), f(x2), ... f(xn) it should not be possible to predict what f(xn+1) will be (unless one knows the program that calculates it, obviously). For example: if I tell you only the values of f(1), f(2), f(3) …

Hi there! I state that I'm an electronic engineer (undergraduate), then the my knowledges about the world of economics are almost null. A colleague asked to me an help about one point of the proof of the theorem 1 in this paper. The critical point is how to obtain [latex]\text{ d}Y_t [/latex] that at first glance it seemed to me enough trivial. Unfortunately I get a wrong result, so I ask if is possible, without using advanced tools like stochastic calculus, get the solution, and in that case, how to get it. I post my (absolutely not rigorous) calculations. [latex] \begin{aligned} \text{d}Y_t &= \lim_{\tau \to 0} \,\, [ Y_{t+\tau}-Y_{t} ] \\ &= \lim_{\ta…

I recently encountered this problem in a maths competition at school and even after days of working on it i just can't find any real way of solving it. I've attached the problem. I need to find the radius and the area of the shaded area To me it really seems like it is a variable answer and has no set number, but i'm doubting that if so it would be in this quiz. Any help????

Hi, Is there anyone who can check the attached equations are correct please? ap=p*pi/2a and bq=q*pi/2b. I would greatly appreciate every little help. IF anyone has any idea of what I could use to check these equations i would appreciate immensely. I have tried mathematica but the result is not very neat. Thanks