Applied Mathematics

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?

A 5-year duration coupon bond has 8% annual rate, the par value is $100. It's issue date is Jan 2, 2010, the dividend paid date (is it called ex-dividend date? i forget..) is Jan 1, 2011, and the tax rate is 20% for the coupon rate $8 on dividend paid date. (note: if the buyers sell this bond before dividend paid date, he/she will avoid the 20% tax rate.) if we hold this bond till dividend paid date Jan 1, 2011, we will get $6.4 dividend after tax. Christine buys this coupon bond on Dec 29, 2010, she pays almost 108 and she will get approx.$6.4 dividend on the dividend paid date. my Q is why people says she actually pays twice 20% tax ? it is 40% tax for th…

from October 11, 2003 SAT I: Reasoning Test.

Does it go on forever approaching zero, or is it just zero?

does anyone know how to do this? my teacher said that she can prove it, she said that in ceartain instances, numbers may be forced to do things that they are not supposed to do.... alternatively, does anyone have any other simple problems like this that you could prove like 1+5=5 or something seriously, any ideas at all, no matter how absurd OR complex, would be appreciated

I want to develop a 2D random field and its change with time with constant velocity. My process: 1. Define a 2D grid (not the fields yet) [x,y] with n×n points 2. Define 1D time axis [t] with nt elements 3. Find the Lagrangian distance D between the points in space and with time [ with advection velocities in x and y , i.e., [vx,vy] ]. For now vx and vy are constants. D[t,(xi,yi),(xj,yj)]=(xi−vxt−xj)2+(yi−vyt−yj)2−−−−−−−−−−−−−−−−−−−−−−−−−−√ D has size [nt×n2×n2] 4. Use this distance matrix and the time axi…

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

found some interesting stuff about 4d cube and its visualization, please comment and reply if you have any suggestions more to visualise it http://lordofnet.blogspot.com/2006/01/experience-4d-cube.html

I recently watched the movie again and was curious if anyone has studied John Nash's theory more in-depth. Can anyone explain exactly what the theory predicts and/or how it works?

“I constructed a circle by tracing around the shape of the base of a good cylinder(such as Milk Tin): How can the centre of such a circle be obtained, in order to measure its radius? IN SUMMARY: How Can an Unknown Center of a Circle be Located? NB: With only a straight edge and a pair of compasses.

There are two statements people often make about the one-time pad that I believe are contradicting each other. The two statements are: "The key should use truly random letters, which means that each letter in the alphabet has an equal chance of occuring." "When Eve attempts cryptanalysis with unlimited computing power, she will recieve the plaintext instantly. However, she will notice that the message 'WINTER' is just as likely to occur as the message 'SUMMER'." Alright, if the one-time pad's key is supposed to have truly random letters that all have an equal chance of occuring, then won't that mean the key will most likely have an equal combination of all of …

You know these questions when they ask you to find out how many triangle are there in the diagram? Well, is there an actual formula that can be used???

This was posted by someone else on another site. It is a fin problem that I now pose to you. You have to choose randomly (with a 50-50 chance) between two people using three unfair coins. How do you do it? The coins can be unfair in any specific specified way (they just cannot be 50-50 for heads and tails). And, for a nice start (and easier problem), how would you do it with three fair coins?

There are 9 cities. The ciities ar ordered from 1 to 9 and they are always visited in order from 1 to 9. From city n to city n+1 there are 4 routes, let's call them 1, 2, 3 and 4 . The distances doesn't matter. There are 4^8 possible routes from city 1 to city 9. Is it possible to find out the minimum number of ways to go from city 1 to city 9, such that the route would differ at one and only one segment from the one considered to be the right route? In other words: Possible vectors: (1,1,1,1,1,1,1,1) (1,1,1,1,1,1,1,2) (1,1,1,1,1,1,1,4) (1,1,1,1,1,1,2,1) (1,1,1,1,1,1,2,2) . . . (4,4,4,4,4,4,4,4) Person A chooses any of those. What …

Hi: Im reading this book called "Wonders of Numbers" by Pickover and in one chapter he says that a probability simulator would help solve the problem. In case you don't know, a probability simulator simply simulates a situation where you want the computer to randomly pick some numbers. I would prefer a visual simulator but if you know of anything plz tell me. Thank-you

I'm Alexandra, and I'm a 17 year old aspiring nuclear/astrophysicist. Long story short, I was accepted on a partial scholarship to an all-girls school in 9th grade in the hopes of furthering my education. My family lost everything last year and we fell into debt with the school. Unless we pay it off, they wont even release my transcripts and I cant graduate. My sister started this campaign to help me, and with every penny raised I have more hope that I can graduate high school and attend college. Please, PLEASE, if you can donate a dollar, do. Im not past begging at this point. I just want to graduate. Thank you so much for taking the time to read this. The fu…

Most forums are rehashing the same stuff, which gets boring. Went back to a few projects started a dozen yrs ago. This is one of them. The graphic is an incomplete 'tree'. Vixra postings don't provide any constructive feedback! The PDF file is here

https://vixra.org/abs/2201.0186 Hi every body , here a solotion for the Collatz conjecture. If there is any comment , question or critic i ll be happy to discuss it (even if i am more frocophone than anglophone)

Does P(A|B) = 1 - P(A|B')?

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?

If we can climb one stair, one stair, or two stairs, two stairs, in what ways can we climb n stairs?

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 ?

There is a 4 digit number which spells like "abcd". Jack, John and James tries to find this number. Jack only know the range of the digits(biggest -smallest).John only knows a+b+c+d.James knows a*b*c*d. Jack says: I dont know all the digits but James doesn't either. James says: I dont know all the digits but John doesnt either. John says: I just found it and Jack should be just found it as well. What is the four digits ?

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…

If this is indeed what "strong emergence" means to the academic community, then I think one can confidently conclude that "strong emergence" does not exist; if you like subtle thoughts, see my paper A Universal Analytical Model of Explanation Itself". With regard to "weak emergence" (that is with regard to the definition of "weak emergence") I feel it can also be dispensed with via the following proof. That is, emergence is emergence and there is nothing either weak or strong about it! People begin to think about weak "emergence" when what they are looking at is more complex than what they can deduce from "known laws". What they seem to forget is that physics is ap…