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The problem of identification of parameters of nonlinear system of differential equations is considered in this article. It's reduced to the problem of stabilization. To solve it, we use the method which has been developed in the last decade for nonlinear systems. The original system is transformed into a form suitable for the application of the proposed method. An algorithm for identifying data is presented, a numerical experiment for searching the parameters is shown.

https://www.researchgate.net/publication/301700299_On_Algorithm_of_Identification_of_Nonlinear_System_Parameters
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Carlos Sepulveda's profile photo
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Few days before I have posted the below link which describes the sum of power of consecutive natural numbers. But somehow I found that it was inconsistent with higher powers and higher numbers. I don't know that I calculated wrongly or the method cannot be applied for higher powers and higher consecutive numbers. I realised the error whine I compared the result of the method and actual result on the scientific calculator.

But when I calculated the sum of powers with Faulhaber's formula It was same as per the result I get on my calculator. Still I do not know the method which I have developed is correct since there is very huge number of terms to be calculated I may have calculated wrongly. Is any one can prove that the method which I have found is right or wrong.

http://mathworld.wolfram.com/PowerSum.html

http://www.maa.org/press/periodicals/convergence/mathematical-treasures-johann-faulhabers-academia-algebrae
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Bruce Mincks's profile photo
 
Why would a number of consecutive numbers total a different number of powers for the same numbers in series?  An infinite series would only allow you to extrapolate some difference between squares (Gauss), not to accumulate quadratic roots into greater cubes, and any intervals in the difference would contradict the assumed "infinite" distance from the "zero" origins that include all numbers but not any power.  Serial powers assume quantum states.
 
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Stumbled across the greatest prime factor function recently, and it turns out that the internet seems to know very little about it. So I thought I would remedy that, by applying some analytic combinatorics to generate some pretty pictures!   
https://linas.org/art-gallery/gpf/gpf.html
Greatest Prime Factor. It would appear that very little is known about the greatest prime factor function gpf(n) that returns the largest prime divisor of n. Some values are given in OEIS A006530. I was unable to find anything at all discussing the typical analytic formulations of this sequence, ...
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Mohamud Abdirisak's profile photoNathan Martin's profile photo
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Generalizing the algorithm for computing powers of 2 mod n without using multiplication or exponentiation to work for all k mod n such that GCD(k,n) = 1
Previously I showed an algorithm for generating powers of 2 mod n without using multiplication or exponentiation. The algorithm can easily be modified to generate powers of any integer k mod n where the greatest common diviso...
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Daniel Carvalho's profile photoAndrew Amgad's profile photo
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Alex Alaniz

Research  - 
 
Precision colorectal cancer model incorporates 19 known environmental and lifestyle risk factors for the disease, as well as 64 common genetic risk factors to save lives.
Experts have debuted their latest progress in precision prevention -- an in-the-works method to predict risk of colorectal cancer that integrates genetic, lifestyle and environmental risk factors.
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MYVALK's profile photo
MYVALK
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Wow you truly and literally have math up your a$$ lol. 
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Define "whole number". Please.
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Lee Creighton's profile photoIwuchukwu Obieze's profile photo
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"whole number" is only part of "number". the definition is for only 'whole number'. 'number' is a larger set.
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Definition: Given two distinct odd primes p and q and an integer a < p*q such that GCD(a, p*q) = 1 and a2 = 1 mod p*q then a is a lonely square mod p*q. Clearly, a = 1 is the most trivial example of a lonely square. In Types ...
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Eric S. Harris's profile photoManuel Alzurutt's profile photoDaniel Carvalho's profile photoMonica Bellucci's profile photo
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With these graphs and a modest amount of self-deception (normal levels will do) you can find patterns in the stock market or roulette wheel or dice that will for sure make you rich.

The math-y way out of this pickle is?
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The following thesis---challenging the accepted Goedelian-Tarskian textbook wisdom that mathematical truth (which is the basis for asserting that any scientific proposition may be treated as true) is not definable objectively---has been accepted for dissemination by the Editors of 'Cognitive Systems Research'.

Title: The Truth Assignments That Differentiate Human Reasoning From Mechanistic Reasoning: The Evidence-Based Argument for Lucas' Goedelian Thesis

The paper is also freely downloadable till 8th May 2016 from:

http://authors.elsevier.com/a/1SkGv4xrDw50dQ

(The author's updated version is always accessible at: http://alixcomsi.com/28_Human_Reasoning_v_Mechanistic_Reasoning_Update.pdf)
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Bruce Mincks's profile photo
 
We might distinguish truth from satisfaction analogously with care or desire (divine or carnal love) conceptually; then historically, in psychological or metaphysical terms, still find that the issue of whether something is true or not depends largely on what something is.  Given "that" as data, then some correspondence between number theory and axiomatic logic may prove more technical in science than necessary for reasoning (such as found in this link).  

The satisfaction OF truth can only refer to proof, it seems to me, as the idea of proof figures into the determination of "truth" in an ideal sense.  Such proofs are essentially "shown" for Aristotle (if not the algorithms of number theory) where the hypothetical rests on definitions in a formal sense and the true is really a convertible definition that may produce a theorem from a hypothesis.  The mechanistic or mechanical nature, similarly, as opposed to the formal components components (e.g., {P_n, Q_m, S_c} which imply a subjective/objective difference, not some dichotomy between determining "the" truth and its actual nature.  When we recognize that perspective becomes a factor or personality, not logic.  The SAME personal "ego" implies those modes (b = a - c) which make mathematics possible for mathematicians to propose rational explanations.  The order of such symbols is surely more arbitrary than the order of numbers for science.  Would the difference still exist if we didn't already know Calculus?  Doesn't arithmetic deserve a closer look, in terms of how number theory relates to geometry, not how geometry (as a source of concepts, unlike ideas of reasoning) should treat prime numbers or tertiary derivatives?

This method contrasts with simple arguments (x; between (2) perspectives) presumed always to resolve "something" in a definite conclusion (of some kind; the problem for prior reasoning, according to Aristotle).  The difference is semantic, perhaps, but that doesn't rule out the possibility for anything being true while some things do not really exist.

What is an "axiom"?  Does it have a definite syntax without a semantic definition?  Does it refer to some fact or relation?  How does its truth become authorized (not "does this truth matter in principle?")?
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Generating  (k^2)^1, (k^2)^2, (k^2)^3,..., (k^2)^r1, (k^3)^1, (k^3)^2, (k^3)^3,..., (k^3)^r2,... and so on given  k^0,k^1,k^2, ..., k^r,
where  k^r  ≡ 1 mod n,  (k^2)^r1 ≡ 1 mod n,  (k^3)^r2 ≡ 1 mod n, and r, r1, r2, .... are the smallest such integers
Previously I showed how to generate an array of powers of k mod n by cycling through the kth row of the multiplication table of Zn . Powers of powers of k mod n, or powers of each entry in the powers of k mod n array can also...
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Answer (1 of 9): I'm sure we'll never know, but I'd put my money on (son of) [father's name]. This is a very common surname construction: Johnson ben Gurion (Hebrew) bin Ladin (other Arabic variations — "ibn," "ben," "ibni" and "ibnu) MacArthur McDonald O'Mally ("O' " actually mean "grandson of"...
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Kalfch Kalfchy's profile photo
 
An asian one
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Gerwyn Jones

Research  - 
 
Fractal Brain Ball Manifold in MathMod 4.1
 
//Symmetric Fold
sin(10*abs(z)/((((sqrt(x*x+y*y+z*z))/abs(y)-abs(t)*(1.0-3.0/sqrt(x*x+y*y+z*z)))/sqrt(x*x+y*y+z*z))))
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Dev Lila's profile photoLeonard Verwers's profile photo
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Peter Fabo

Research  - 
 
Analog computers are back :-) ... in pse (pure python simulator based on Kivy and numpy ). Some pictures of the implementation of algorithms from time analog computers, description is here (in slovak, english version is planned) https://www.researchgate.net/publication/301542918_PSE_-_Basics_of_creating_simulation_models_Part_7
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An algorithm for generating powers of 2 mod n without using exponentiation or multiplication.
In "Lonely Squares" I showed an algorithm for generating all unique powers of 2 mod n when n is the product of two distinct primes p, q (in that example I used p = 3 and q = 7 to illustrate it) I also used this picturesque gr...
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Kurt Pattyn's profile photo
 
Very nice

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Three sequences that I submitted to the OEIS (Online Encyclopedia of Integer Sequences) have now been approved. The sequence in question is the sequence generated by powers of 2 mod n when n is the product of 2 distinct safe ...
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fizixx's profile photoRemedios Carino's profile photo
fizixx
 
Horrid website...clickbait post.
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Is this new or has this been discovered already? I tried to make a logarithmic equivalent of the standard deviation and performed simulations on the data. What I found was that I got a ratio of 0-1 and that as the data got closer to 0, the data becomes more centralised and as the data gets closer to 1, the data becomes more polarised. I call the indicator the "Polarity Statistical Indicator" as it appears to define polarity in the data. My thinking behind the indicator is that the Standard Deviation in it's form puts more weight to the far data and less weight to the close data while this statistical indicator in it's logarithmic form puts more weight to the close data and less weight to the far data. I didn't know what I would find but it seems to suggest that it is defines how polarised the data is. I haven't found evidence of any univariate statistical indicators like this and so I am curious to know if I have made a significant discovery or if somebody else beat me to this.

Also, if somebody could help me write the indicator in a more presentable form, I would appreciate the help as I am not used to writing mathematical formula in a digital format.
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Philip O'Neil's profile photoSidni Hale's profile photoMonica Bellucci's profile photoCate Blanchett's profile photo
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This is all I can do in the spare time I have today. I talked to a couple of statistics lecturers at my local university and they say they haven't seen anything like it. I will be able to have a more in depth analysis and discussion when I have the time. I just wanted to start a discussion about it today as it is fresh in the mind. I will have more time to detail it out a bit next week but for now I have a busy week.
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vz nuri

Research  - 
 
big number theory news. new property of primes discovered. recent large $ math awards for Wiles, Diffie-Hellman. etc oh! and Riemann hypothesis just solved... by a Nigerian ;)

a. primes
b. wiles
c. crypto/ diffie hellman
d. zhang/ tao
e. prime bias
f. auto thm proving
g. riemann
hi all. big news in number theory last few months and years. this is a tribute to a few years of top breakthroughs and exciting developments. the general theme is “primes” but there are…
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Jerzy Kaltenberg's profile photo
 
Sure, april fool.
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