Analysis and Calculus

The common way to calculate logarithm involves tables of logarithm, the mantissa and the characteristic. What is needed is a global, explicit formula for the logarithm. LN V = 2n x (V1/2n+1 - 1/V1/2n+1)This is the first explicit global formula for the natural logarithm, which can be used immediately to find LN V without resorting to logarithm tables, or calculators which feature the logarithm key: all we need is a calculator which has the four basic operations and the square root key. It links algebraic functions with elementary and higher transcendental functions.For a first approximation,LN V = 2n x (V1/2n - 1)First results appear for n = 8 to 12, all the remaining…

I need someone to tell me what u(.,t) means when u is a function of x and t. x is in Rn

I have an ordinary differential equation in the form of dp/dt=p-f(p). Since p and f(p) are bounded, any equilibrium of this ODE should satisfy p*=f(p*). I have another ODE in the form of dw/dt=g(w). I know this ODE diverges and because w is bounded between zero and one, at the equilibrium w* is zero or one. Now I consider a system that has p and w and both of them are changing which gives me two ODEs, dp/dt=p-f(p,w) and dw/dt=g(w,p). I know for any fixed w, we have p*=f(p*,w) at the equilibrium and for any fixed p, w* equals zero or one. Does anyone know if I can claim there is any equlibrium for general case and at the equilibrium p*=f(p*,w*) and w* equals zero or one?

In the example above they use the cramer rao minimum variance estimation. I have one problem. For the mean they use the pdf of exponential. However the mean of exponential follows gamma. And the median distribution can be shown to be normal distributed in general. Why do they use the exponential pdf in Cramer Rao when the mean is gamma distributed? And how can they compare the median and the mean with Cramer Rao when they follow different distributions. I have a derivation in my book of Cramer Rao that starts with mle and uses the pdf until it shows that the covariance between the estimator and the fisher information of the pdf is bounded. But is it not so that you must u…

I want to calculate the number of labels in a roll according to the following parameters: 1.width of the label 2.length of the label 3. Total diameter of the roll 4.Chuck diameter 5.Distance between 2 labels Thanks

Hi there, Everyday I am reading articles besides doing experiments in the lab and I was joking with one of my friends that it is going to take me forever to read all 90 articles I still have on my desk, because on average I add 0.7 more articles per article that I read. So then I was wondering what type of mathematical function this would. I have written a quick python program which approaches the limit of whatever this function would be (I think it approaches 300 articles). I however still haven't been able to think of what the actual function would look like. Could anyone help me out, thanks! -Dagl PS. the python code (I know this can be written a lot bette…

Hello all, I have a dataset which I am using to perform some allometric analyses. It's straightforward enough when taking the log10 of single values to plot against each other, but when using the formula for Fulton's condition factor K=(Ms/LT3)*100 where Ms is the somatic body mass and LT is total body length, I am uncertain whether the log transformation should be done on the data being plugged into the formula or on the resulting output from the formula. Thank you in advance.

Okay bear with me, I work for a company that delivers food. One of my jobs as a manager is to achieve the lowest average delivery time across all orders each week. Before I became the manager, my boss who used to do my job used to be able to achieve an average delivery time of around 40 minutes each week. This was years ago when we did less orders and had less drivers. Once I became the manager most weeks our average delivery times is in the high 40s. Even on our best weeks with very little order issues or order delays I can only get our average delivery time around 43 to 45 minutes. My boss often wants to know why I can’t consistently achieve the low 40s that he was able…

No math background... But need help. What is the "?-ft." measurement? Any questions? Thanks!

I have developed formulas to calculate the square root of real numbers discovered from a pattern you can read details at : https://www.researchgate.net/project/Square-root-of-positive-real-number-sequence-and-calculation-methods Looking for your scientific opinion

For anyone who has a little bit of time to spend and likes a challenge, I would be thankful if you went to: https://member.expireddomains.net/domains/combinedexpired/?start=0 And took a good look at the results. Make sure there are no filters and they are sorted by ''dropped''. You are looking at domains which have most recently expired. We want to see if there is pattern to expiration of those domains and maybe, be able to estimate when a certain domain would expire given its name or whatever other metric might be relevant. It's a longshot and probably impossible to figure out, but feel free to give it a go. Thanks.

Let's consider unit circle with central point x=0 ;y=0 a is an angle in rad x is cosine of angle a y is sine of angle a Area of tryangle is At=y*x/2 Area of segment a = a/2 Area of half of sector 2a =area of segment of a - area of tryangle = a/2 - yx/2= a - y(1-y2)1/2 Can area of half of sector 2a be calculated by integration if x=31/2/2 then x2=1 (3^1/2)/2f1 (1 - x2)1/2 dx How to calculate the integral?

Is there any way to pre-determine whether a series exists which will satisfy the requirement of fulfilling a given chosen function? For example, given Sin 3X - Cot 5X / Csc X , does an infinite series exist which satisfies it? How does one know? Perhaps my question is naively foolish; I studied LaPlace Transforms, Test Ratio Tests, etc., but never truly understood.

Hello,I am trying to calculate Hurst exponent using as an input FX Tick Volume. However being not educated in advanced math and physics, I struggle to obtain clear and objective results. I am not sure whether I get reliable Hurst exponent calculation.One Tick is each change of price, which can occur a few times a second. As there is no source for the Real Volume(in USD etc.), Tick Volume is the only reliable data available for research purpose.What I do is I take a sample of Tick Volume(below you will find just a fraction, I attached full sample in file "DATA"):1.141281.141331.141271.141321.141381.141421.141361.141411.14137and then I change it into a binary system, tick h…

Does the constant in a polynomial equation f(x) moves it up and down or does it does something more to the graph. Ex x^2 + 3x + a = f(x)

The set of values of a for which the equation x^3 - 3x + a has one negative and two positive roots is ? I know that a>0 and i also know that the turning point of the graph is at x=-1 and x = 1 but how to proceed further??

Derivative is defined as the limit of a finite difference \[\frac{dy}{dx} = \lim_{h\to\0}\frac{f(x+h)- f(x)}{h}\] where h is finite. Is it possible to define the derivative by \[\frac{dy}{dx} = \frac{f(x+dx)- f(x)}{dx}\] where dx is not finite but infinitely small, infinitesimal ?

[math] \lim_{\left(n \rightarrow \infty \right)} \sum_{i=1}^{i=n} i= - \dfrac{1}{12} [/math] I've seen it on the next page. https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_⋯

Thank you,

I need help with an equation. If I put an empty half gallon jar on a scale before plugging it in so that the beginning weight including the empty jar is zero, then fill the jar with fresh chopped herbs and note the weight, then leaving the jar of herbs on the scale, cover the herbs in 100 proof vodka to the top of the jar and note the weight again, what is the ratio of herb to vodka? This assumes the temperature in the room is 68 degrees F. I will be putting this equation into an excel spreadsheet. Thanks to all who attempt to help. I am terrible at math. 10/2/18 If I need to post this in a different section, please advise.

Can this equation find the derivative of any given function

Hi, I came across this integral doing some research which I could not integrate. May need to do some sort of substitution?? Any help will be appreciated. I have attached a microsoft word document with the integral. Math_Help_Integral.docx

This is a simple but elusive problem that has been around for years and defeated some of the best mathematicians who have attempted it. It is also known as the hail stone problem, for obvious reasons. I think I might have a proof of it but need to check that I have not missed anything. For those who are interested i believe that i have proved it in the affirmative and that no counterexamples exist. Are there any experts out there who can lend a hand checking my work?

what is the calculus?