Analysis and Calculus

1. +y coordinate as a, +x as b, C is the found by pythagorean, we need to make C a curve so we have in quadrant 1 three x coordinates and 3 y coordinates, x1 = 2C/pi, y1=C/pi, x2 & y2 = (x1+y1)/2, x3=y1, y3=x1. Of course quadrant 3 is all negatives, quadrant 2 x are positive and y are negative, quadrant 4 y is pos x is neg (Did the math on that it works to make a perfect circle) 2. a 45 degree angle or C can be found by starting at the top corner of quadrant 4 and bottom corner of quadrant 2 and having C be crossing (0,0), so a and b are doubled. Then you can get the other diagonal through 3 and 1 quadrants using the same formula for a curve, n…

Hello, any help with these questions would be greatly appreciated.🙂

could someone help me please,I need this object's mathematical expression in cartesian coordinates.(The drawn area 3d coordinates please) Thanks in advance.

I'm wondering what the general process is for this. In general being well defined means there is only exactly one output for each input or that if x=y, f(x) = f(y) which looks like the reverse of proving injectivity, I don't know if that is a coincidence or not. Is a Fourier transform of a real function is still always real? I suppose the idea is that the imaginary component decays to 0 as you take the integral from -infinity to infinity so that it evaluates to a single finite real number, or actually, does the output of a the Fourier transform of a real valued function need to be real? Why do I generally see absolute value arguments in proving well-defined propertie…

If we have two objects Obj1 and Obj2 along with we have two Methods for weight calculation of theses objects i.e. Method1 and Method2. If Obj1 have weight X1=0.7 from Method1 and weight Y1=0.5 from Method2 similarly, Obj2 have weight X2=0.5 from Method 1 and weight Y2=0.7 from method2 My objective is to Rank the obj1 and Obj2 according to there weight values determined from Method1 and Method2. Can anyone help me to tell the defined mathematical formula to get the, Rank of Obj1 = ? Rank of Obj2= ?

hi. how to solve the integral that i attached in this post? i tried to solve it but seems its too hard for me 😕 plz help me

Is it possible to define the second derivative of f(x) in this way: \[ f''(x) = \frac{f(x+2dx) -2(f+dx) + f(x)}{(dx)^2} \] I am using a finite difference approximation called "Second order forward" from the link, I use dx instead of h: https://en.wikipedia.org/wiki/Finite_difference#Higher-order_differences

I am hoping that people here might be able to provide insight into what context/s this equation might be relevant, particularly the contents of the brackets. I am aware it is a strange request, related to puzzle solving, but perhaps someone can help guide me in an interesting direction.

Hi everyone, I have a problem when doing an approximation. The problem comes in the final results that I have to demonstrate two functions below equal each other frac{1}{8\sqrt{2}\cos{\frac{\phi-\phi_0}{2}}(1-\sin{\frac{\phi-\phi_0}{2}})\sqrt{1-\sin{\frac{\phi-\phi_0}{2}}}} = \frac{1}{[1+\cos{(\phi-\phi_0)}]^2}. \begin{equation} \frac{1}{8\sqrt{2}\cos{\frac{\phi-\phi_0}{2}}(1-\sin{\frac{\phi-\phi_0}{2}})\sqrt{1-\sin{\frac{\phi-\phi_0}{2}}}} = \frac{1}{[1+\cos{(\phi-\phi_0)}]^2}. \end{equation} I have checked the two functions by numerical calculation to a graph and see that two functions give exactly the same shape with the $\phi\leq \pi$ as shown in the figur…

Hi, I am trying to read a research paper: PrivateJobMatch: A Privacy-Oriented Deferred Multi-Match Recommender System for Stable Employment : https://faculty.ucmerced.edu/frusu/Papers/Conference/2019-recsys-private-job-match.pdf On one hand it says: And on the other hand it says: I feel the above two views are conflicting because on one side it says that PrivateJobMatch does not generate recommendations and on the other hand, it says, it is adapting DAA into recommender system. I can't understand how PrivateJobMatch utilizes the features of decntralized markets. Somebody please guide me. Zulfi.

Hello, I am modelling the length of the growth season for 120 different years based on estimated daily temperature. The temperature is estimated from a periodic function: f(x)=D+A*sin(B(x+C), where the constants B and C are the same every year and A and D varies. So I would like to know when the area under each function equals 1200 as shown in the figure. I think it can be solved by finding the upper limit b in equation 1 when the lower limit a is known. For the year 1990 it would look like equation 2, and b will take a value between a and 365. Do you know how I can calculate this using Excel? Thanks in advance,

Every point of a number line is assumed to correspond to a real number. https://en.wikipedia.org/wiki/Number_line Is it possible to find points corresponding to infinitesimals on a number line? I mean finding an infinitesimal between two neighbouring points (between two real numbers). I am assuming that every point is surrounded by neighbourhood. I got this idea of neighbouring points from John L . Bells' book A Primer of Infinitesimal Analyis (2008). On page 6, he mentions the concept of ‘infinitesimal neighbourhood of 0’. But I think he would not consider his infinitesimals as points because on page 3 he writes that "Since an infinitesimal in …

Hi everyone, I was looking on the post about the reliability of published research. And I was wondering if we could know, a posteriori, if a study is dependable or not. Do you know any statistic test to improve our understanding of already published paper? In biology I have seen a lot of people doing three or four different tests to see if their results are meaningful. Isn't it a kind of fraud? Thank you very much.

Hello, I'm in a online debate with someone about some deep mathematical concepts. My opponent was trying to convince me that you can have a sequence of numbers for which there is a first element, a last element, but no second element and no second last element (where the sequence contains more than 2 elements). I thought that was absurd until he gave me an example: all the real numbers between 0 and 1. It definitely has a first member (0) and it definitely has a last member (1), but after 0 there is no "next" real number. Likewise, there is no real number that comes just before 1. Yet there are obviously real numbers between 0 and 1. That stumped me until I…

Normally limits are used instead of infinitesimals, but is it possible to calculate limits using infinitesimals? For example: \[ \lim_{x \to 0} \frac{sin(x) - x}{x^3} \] this is usually solved by applying L'Hopital's rule 3 times and the answer is -1/6: https://www.symbolab.com/solver/limit-calculator/\lim_{x\to0}\frac{\left(sin\left(x\right) - x\right)}{x^{^3}}

Hi, https://en.wikipedia.org/wiki/Logistic_map here is my question : does the logistic sequence for some choosen irrational parameter reach every real number inside a real interval, or is it always just a subset ? (I hope i'm in the right section) thanks !

Hello, I've been getting into the concept of hyperreal numbers lately, and I've got tons of questions. What I understand about the hyperreals is that they are numbers larger than any real number or smaller than any real number. I'm sure you can imagine how counterintuitive this sounds to someone like me who's new to the concept. It's like talking about numbers greater than infinity. I always thought that was impossible. So it shouldn't be surprising that someone like me would have a ton of questions. I'll start with a couple. 1) Assume that R is a hyperreal number greater than any real number. What does 2 x R equal? It's clear what 2 x n means where n is a real …

A given circle with area A = 1 has a radius = 1/sqrt(pi). In this case there exist a square with the sides of length = 1 which has an area equal to 1. This problem is referred as a "squaring the circle". Due to the "irrational" and "transcendental" nature of number pi , squaring of circle is not possible to be constructed only by ruler and compass. However, I've read in an old mathematical book, that a construction is possible only in case when circle area A=1, without any further explanation given. Is there any one who can support this claim?

This is part of my works. I have formulated a new formulation for sums of power and it works for any numbers (i.e. real & complex arithmetic progression). The generalize equation can generate any power p (it works fine also with complex p). Let the p-th power of an arithmetic series as follows [math]\sum_{i=1}^n x_i^p = x_1^p + x_2^p + x_3^p + \cdots + x_n^p[/math] The general equation for the sum is given as follows [math]\sum^{n}_{i=1} {x_i}^p=\sum^{u}_{m=0}\phi_m s^{2m}\frac{[\sum^{n}_{i=1} x_i] ^{p-2m}}{n^{p-(2m+1)}}[/math] where: [math]p-(2m+1)\ge 1[/math] if p is even and [math]p-(2m+1)\le 1[/math] if p is odd, [math]\phi_m[/math] is a coeffi…

My (overlong?) title describes the problem completely; my question is how? I realise that there can be multiple [sic] answers; I'm after the smallest integers that produce c. eg. Given 1.05; A/B = 21/20.

Hey folks, Here is possibly a neat "pattern" I've come across when studying prime numbers, or at least a different way of bucketing them. I'm looking to see if anyone can help me explain it, because I'm having a hard time wrapping my head around it. It may be that I've found something that is trivially explained away by some known information I just don't have or am not seeing. The pattern emerges with you cut prime sieves of length N > 3 into segments of 6 after separating the first 3 prime numbers (1,2 and 3). I'll explain below. We'll be working with a prime sieves with the following properties: We sieve on intervals [1, N] where N > 3. The exam…

Suppose you have an equation (I don't see a latex editor or know how to use math tags here) f'(h(t))*h'(t) = f(h(t)+ \alpha) where f' is differentiated with respect to t, following from the chain rule on f(h(t)). Is there a substitution that will transform this differential equation into the form of f'(w) = f(w+\alpha) ? It seems reasonable but I am not finding an easy way to do it.

E=mc^2 Apparently this can be used for code purposes in creating a set of numbers . This and several other specific designs ! If we take a four letter word and assign a value proportional to the number of the letter in the alphabet , we can create a set of values by placing the numbers in a c formation . In example the word scam , values of 19 , 3, 1 and 13. Now if we place these values in a c formation , we can x reference or by variations define a specific set of values . In the word scam in a c formation we can use a x alignment to create two values , 3+13 and 19+1 to give the 2 values ! NUMBERS !

Hi, Here is a math question : First I'm going to define some things (some names may already exists that I don't know of, so please take my definition into consideration) - let's call p[n] the nth-rank prime number p[0]=1, p[1]=2, p[2]=3, p[3]=5 etc - as you know, each integer >0 can be written as a product of integer powers of prime numbers.. let's call it the "prime writing" of a number... i'll write u[n] so for any integer X we have X = product( p[n] ^ u[n] ) - we can extend this to rational numbers, simply by allowing u[n] <0 My question is : can we define a set of irrational numbers in ]0 ; 1[ that extends p[n] when n<0 and are t…