Sergey P. Klykov

Alpha-Integrum, Ltd. · Science and technology

ABSTRACT. This article shows that the FLT equation, a^n+b^n =c^n and the equation derived from it, (bc)^(-n)+(ac)^(-n) =(ab)^(-n), are showing different numbers of possible rational and irrational solutions. Taking into account the proof of the Pythagorean theorem and the previously published symmetry for the solutions of the Pythagorean theorem, t...

It was shown within the framework of elementary algebra, which corresponds to the Pythagorean theorem, PT, that the assumption of the existence of certain "Fermat's triples", FTs, as integer solutions of Fermat's Last Theorem, FLT, can not be possible due to some fatal inconsistencies for the PT and found by means the PT. The impossibility of integ...

It was shown that for any sum of any p-adic numbers from any number system, x+y=z, such Zp can be found, where this sum can be represented by triples of integers a, b, and c, as squares, i.e., x=a 2 , y=b 2 , z=c 2. In other words, each Zp contains unlimited sets of number triples, which are analogous to Pythagorean triples in the decimal number sy...

http://www.socionauki.ru/book/files/evolution_3/249-256.pdf Abstract For the first time, the growth rate of minimal animal genome size is shown to slow down in the course of evolution from prokaryotic forms to mammals after the Cambrian explosion. There is proposed an original mathematical model which takes into account a multiphase character of de...

ABSTRACT. An elementary and short proof of Fermat's Last Theorem, FLT, is presented, which is understandable even to a student. Perhaps this proof is precisely the lost proof, which could similar to own Fermat's proof. Restricting some coefficients of polynomials by value 0, except for the first term, allows to prove the Fermat's Last Theorem for d...

A simple proof for Fermat's Last Theorem, FLT, x p +y p =z p , has been shown for the set of integers Z using polynomials having two terms on the right and by a simple algebraic way, mostly. The logic of the proof is shown in the definition of residues from z p , which could provide the presence of roots for the FLT equation. However, the presented...

A simplified method for calculating polynomials coefficients without explicit application of power for p for representation of fractions is proposed.

The possibility of solutions existence for equations α n +β n =γ n in Qp for n=3 examples was shown. It was shown, that each number from any Pythagorean triple is a square in certain Zp for equations, i.e., A 2 +B 2 =C 2 = a 4 +b 4 =c 4 , where Pythagorean Triples, A, B, C, are defined as follows: A=a 2 , B=b 2 , C=c 2. It was shown that there is a...

Waste to the product approach was proposed for tuning environ-threat soybean husk towards lipolytic enzyme by integrating the invasive weed optimization with biomass and product dynamics study. The invasive weed optimization constitutes based on the non-linear regression model results in a 47 % enhancement in lipolytic enzyme using the optimization...

Remarkable highlight of microcosmic configuration of matter, especially the factuality that discretionary particles in cosmos are mutually convertible is always in orientation towards complete induction day by day has made the homogenous profile of cosmos more and more explicit in our rational purview. Whereas, is cosmos really homogenous originat...

Based on the previously obtained proof of the Fermat's Last Theorem using the Pythagorean Theorem, it is shown, that the equations of Beal's Conjecture are a kind of equations of the Pythagorean Theorem too: a p +b q =c r → a (p/2)2 +b (q/2)2 =c (r/2)2 →A 2 +B 2 =C 2 , with integers a, b, c, p, q, r, and p,q,r >2, where are A= a p/2 , B= b q/2 , C=...

An attempt was made to use the Diophantine equations for the analysis of S-shaped curves of the growth of microorganisms. The most famous of such equations are the equation of the Pythagorean Theorem and the equation of Fermat’s Last Theorem, FLT. The article does not claim to prove FLT, but it shows interesting facts for biological objects - there...

The invention relates to biotechnology, in particular, to the cultivation of microorganisms in an industrial environment. A method for obtaining biomass of Enterobacteriaceae for Escherichia coli or Salmonella is proposed. The method includes preparing a nutrient medium based on 0.9% sodium chloride solution and a nutrient medium concentrate contai...

ABSTRACT In this work, it is shown that Fermat Last Theorem (FLT) does not and cannot have certainty in relation to the choice of numbers "0" and "1" due to the lack of symmetry between hypothetically possible solutions, which could enter/or not enter the FLT framework. This conjecture was shown without using the modern number theory methods on t...

Fermat's last theorem proof. Preliminarities were shown in the preprints,[1,2] and in the article, [3]. Let's consider x=n 2-(2m1)n+(m 2-m), (1), where m value is maximal root (integer) in each pairs n1=m-1 and n2=m-these are the investigated parameters (integers)for studying the set of "n" values by setting and investigating of the results step by...

APPLICATION OF THE FERMAT'S THEOREM FOR PRACTICAL PROBLEMS SOLUTION IN BIOLOGY. Article is under consideration for IJB. ABSTRACT It was shown by using of an elementary algebra that the solution of the equation an + bn = cn cannot simultaneously have three integer nonzero roots "a", "b" and "c" for integers n> 2. It occurs due to the fact that the...

The main idea of the attempt at this proof for the last Fermat's theorem (FLT) is to simultaneously use for analysis not all numbers at once, a, b, c and n, but in the use and comparison of logics for pairs of numbers. For example, for the pairs n and a. The absence of contradictions would favor the FLT proof. To get the simplest proof, it is impor...

ABSTRACT: A model of the growth curve of microorganisms was proposed, which reveals a relationship with the number of a ‘golden section’, 1.618 ..., for main parameters of the growth curves. The treatment mainly concerns the ratio of the maximum asymptotic value of biomass in the phase of slow growth to the real value of biomass accumulation at the...

Pyrolysate obtained from the pyrolysis of waste cotton is a source of fermentable sugars that could be fermented into bioethanol fuel and other chemicals via microbial fermentation. However, pyrolysate is a complex mixture of fermentable and non-fermentable substrates causing inhibition of the microbial growth. The aim of this study was to detoxify...

Bacillus subtilis KATMIRA1933, cultured in modified MRS (de Man, Rogosa, and Sharpe) broth without peptone (animal-free [AF]-MRS), produced subtilosin A at levels similar to, or even higher, than when cultured in MRS broth with peptone. AF-MRS medium contained 2.5 % (w/v) Martone or 2.5 % (w/v) cottonseed hydrolysate instead of peptone and 0.25 % (...

T ransgenic plants are increasingly considered a competing system for producing high-value recombinant proteins for biomedical and industrial purposes at affordable costs (1). Researchers have shown that molecular farming (or biopharming) is a secure technology that is capable of rendering valuable recombinant proteins free of toxins and animal pat...

In the last time and in the near future, the markets are demanding large recombinant proteins production capacity, due to the production levels of traditional platforms will be certainly not suffice to make available these demands (Huang and McDonald, Biotechnol Adv 30:398–409, 2012). The explore of alternative tools to assure adequate supplies for...

Our proposed structured deterministic model describes the kinetics of biomass growth. Metabolism is not worse than other models, but rather provides a simpler mathematical approach. Our model allows for analyzing the chemical stoichiometry of biological processes. Such analysis provides for the economic calculation of the industrial processes of ce...

Benefits of the Proposed Model Our proposed structured deterministic model describes the kinetics of biomass growth. Metabolism is not worse than other models, but rather provides a simpler mathematical approach. Our model allows for analyzing the chemical stoichiometry of biological processes. Such analysis provides for the economic calculation of...

We propose a new mathematical model for cell cultivation in a chemostat. Our model is based on the structuring of the biomass into two main groups: dividing and nondividing cells. The model is applicable both to existing static characteristics such as the Monod model and to the deviations from it. We determined the range of chemostat stability at...

In this paper we have proposed a new structured population growth model, further developing a model previously proposed by the authors. Based on this model, optimal growth characteristics of the recombinant strain Escherichia coli BL-21 (DE3) [pProPlnHis(6)] were determined, which allowed us to increase the output of metalloproteinase by 300%. We h...