Analysis and Calculus

I seek a proof, (using the properties of the h.c.f.), that if k divides nr then k = k1k2 where k1 divides n and k2 divides r

This question is inspired by one question, which was about representations that can be realised homologically by an action on a graph (i.e., a 1-dimensional complex).Many interesting integral representations of groups arise via homology from a group acting on a simplicial complex that is homotopy equivalent to a wedge of spheres. A classical example is the action of groups of Lie type on spherical buildings. On homology this gives an integral form of the Steinberg representation.One may ask if there exists a complex of lower dimension than the Tits building that realises the (integral) Steinberg representation in this way. I am guessing that the answer is No, but how to p…

Can someone give me an example of a topology, which is not sigma algebra?

The two transcendental numbers, pi and e, are derived in totally different ways. Pi is the ratio of circumference to diameter of a circle. There is no reason to believe that it is different in any other part of the universe, or that it changes with time. We understand it to be a universal and eternal constant. Similarly, e, first calculated by Euler, is accepted as a universal constant and assumed to be eternal. Exponential relationships have existed since the origin of the universe; radioactive decay, first order chemical reactions, etc. There appears to be no physical reason to connect pi and e. However, we have Euler's Identity e^ipi+1=0 which can be rewritten e^ipi=-1…

I do not know how to find the sum of factorials: My attempt: I do not know how correctly I chose the method, but I do not know what to do next. If anyone helps, I will be grateful.

Here is the paper: http://vixra.org/abs/1703.0073 Also testing if the "lol XD you so fahnny posting you schizo viXra maymays xD XD XD" people are active in this forum.

hi, I wonder if you can help me please? I am not a mathematician, but used to teach science, so I have a little knowledge. I am now disabled and use mobility scooters, I am trying to reasonably accurately predict the discharge of my batteries. way back in the day, I used to use a Dos program called XY math ( I think). It allowed you to enter experimental results and plot them. an algorithm would then test the data against about 20 equations of various types. it would then give an indication of correlation and display the line (curve) of best fit. I have searched Google that I can only find a program in French. does anyone know of a…

ok i dont know how to do this and was wondering if anyone would educate me in this i have formula to get the length(l) of fish in relationship to time elapsed(t) ( l=80*(1-0.96^t)). and those numbers below are what i got, and i got a series of Weight values for the fish at those lengths. Length(cm) Weight(g) months 3.2 1.00 10.1 15 3.31 25 236 9.18 32.6 520 12.82 35.4 660 14.31 43.8 1250 19.43 45.5 1425 20.60 55.7 2590 29.19 how do i get the formula to calculate the weight of the fish i did a bit o…

Back story-My son is gifted in math, I already knew this when the child was multiplying before kindergarten but sadly he was in less than great schools, but now he's transferred mid-year to an awesome school who noticed his sol scores and are planning to put him in gifted math and the gifted program next year (it's too late in the year at the new school) but they have a program called ixl that the school uses where you log into different math concept levels I found out my son has been logging out of his required work which he calls boring and been logging into the calculus section which he apparently absolutely loves. My problem is that I am absolutely math illiterate (I …

Can calculus solve the volume of a 3 dimensional object? Like a pile of grain on the ground that is not symmetrical?

(∫∫∫∑Wavefront Surface Areaa - ∫∫∫∑Wavefront Surface Areab ) / ∫∫∫ Volume Designated This is a simple metric for wave density of a given volume for two given wave fronts within it, which can be used as a value for mass-energy and mass-volume. As the number of separate wave fronts can be infinite within a given volume, a method for describing wave density is useful, and can also be used to distinguish between the presence of different massive particles - the changing volumes between the surface areas of wave fronts indicates both particle type and number.

Suppose we have two mirrors in a gravity free vacuum. Both are shaped identically and ,why not circular and extremely thin.(and rigid) They are very close to each other (separation is zero for practical purposes) Mirror A emits a signal (any practical kind that would work in a vacuum) from its cog in the direction of Mirror B's cog. The signal is reflected back and forth between the two mirrors cross from that point onwards The 2 mirrors move apart as a consequence. (the signal carries energy) Is there a mathematical /physical description of this increasing separation over time as a function of the speed of the s…

Hi everyone, Just like the Abel-Ruffini theorem limits the solution to polynomial equations upto fourth degree, is there any such check on the solutions of a differential equation? Can a complete general solution be framed for any n-th order differential equation ? Thanks in advance

Just wondering what people might say... In nature we never see perfect circles, perfect triangles or perfect polygons such as the Platoic solids? Everytime we see thing that resemble these figures but are in some way flawed, like a crystal for example. I know theoretically we can describe such figures, but why are they not met in the real world? Or are they?

why isnt (-1/n,1/n) not an open in the product topology but open in the box topology ?

Gauss periods, used to solve the heptadecagon, are defined in such a way that each level can be determined from the one above. For example Gauss periods of length 4 determined from those of length 8. Can anyone suggest how Gauss came to this conclusion. Or offer a proof ? Thanks

I am trying to find an equation for biorhythms. I have the answers Physical=63% Emotional=-22% Intellectual=-81% I just don't know how to write the equation into y=asin(Bx+C)+D Answers would really be appreciated. Thank you

Hi everybody ! I have the follow equation : \qquad \mathbf{v}_l = \frac{1}{(1+A^2)}[\mathbf{B}-\mathbf{A}\times\mathbf{B} + (\mathbf{A} \cdot \mathbf{B} ) \mathbf{A} ] look the pdf I would verify (but I don't have Mathematica or other symbolic computing package license) that is correct and if yes how to get this (the step) thanks in advance Marco post2.pdf

Determine the solution to the following differential equation: dA/dt = -0.3A and A(2) = 400

I have 3 variables: v, b and h. I know how to calculate v’, b’ and h’. Starting the simulation from an initial condition, I need to calculate v, b and h after a given time using a numerical integrator (say RK4). If I use the simple Euler method, I write; v= v + dt * v’ b= b + dt * b’ h= h + dt * h’ but when I switch to RK4, I don’t know what to write. The simulation is explained here: https://mintoc.de/index.php?title=Gravity_Turn_Maneuver For example, h’= v * cos(b) doesn’t seem a differential equation; does it mean that h= h + dt * h’ is correct and that there is no reason to use RK4? Also, the second RK4 step is: k2 = f(x + dx / 2, …

Hello! I want to integrate the area between the function y(x)=x^2+y^2=1 and h(x)=|x|. Can you help me? Thank you!!

A % change for stomach patients within a year from 300 to 360 is: [math] \frac{360-300}{300}*100= [/math] 20% A % change for liver patients within a year from 200 to 260 is: [math]\frac{260-200}{200}*100 =[/math] 30% Hence Total % change in stomach and liver patients within a year is: [math] \frac {620-500}{500}*100=[/math] 24% But it should be 50% shouldn"t it ??

I want to use a quadratic equation that uses not constants, but variables, like 0=xz^2+yz+w. Does the regular formula work for that?

How does one determine with 100% certainty that a certain function can't ever possibly be put into terms of elementary functions, or really any arbitrary list of functions? Take the gamma function for instance, [math]\Gamma(x)[/math]. I am fairly confident the gamma function cannot be put into terms of elementary functions, but on the other hand, I've never ever seen anything remotely resembling a proof of that statement or any statement of that nature about any special function. How would I determine it can't be put into terms of other non-special functions or a mix of special functions and elementary functions?

I am reading Schaum's Outlines, Electric Circuits Fifth Edition having taken both precalculus courses but not calculus. Firstly, I am confused by the definition of power as the time derivative of watts (p = dw/dt) even though watts is a unit of power. More importantly, I am confused about how this derivative is reversed into an integral of power as below: [math]w = \int_0^t p dt[/math] I recognize that both have an undefined variable t, but I am baffled at why the below should be true regardless of the value of t: [math](\int_0^t p dt) \div w = \frac{dw}{dt} \div p = 1[/math] I get even more confused by some equations given to describe the behavior of an…