Boris Rozin - Academia.edu (original) (raw)
Papers by Boris Rozin
Progress in Biophysics and Molecular Biology, 2023
The mystery of the morphogenesis of phyllotaxis has been of concern for several generations of bo... more The mystery of the morphogenesis of phyllotaxis has been of concern for several generations of botanists and mathematicians. Of particular interest is the fact that the number of visible spirals is equal to the number from the Fibonacci series. The article proposes an analytical solution to two fundamental questions of phyllotaxis: what is the morphogenesis of patterns of spiral phyllotaxis? and why the number of visible spirals is equal to number from the Fibonacci series? The article contains videos illustrating the recursive dynamic model of spiral phyllotaxis morphogenesis.
непрерывные функции для обобщенных чисел Фибоначчи и Люка, матрицы Фибоначчи и «золотые» матрицы.... more непрерывные функции для обобщенных чисел Фибоначчи и Люка, матрицы Фибоначчи и «золотые» матрицы. Статья опубликована в международном электронном журнале “Visual Mathematics”, 2006,
This article presents the results of some new research on a new class of hyperbolic functions tha... more This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into ''continuous'' theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers. Taking into consideration a great role played by the hyperbolic functions in geometry and physics, (''Lobatchevski's hyperbolic geometry'', ''Four-dimensional Minkowski's world'', etc.), it is possible to expect that the new theory of the hyperbolic functions will bring to new results and interpretations on mathematics, biology, physics, and...
Chaos, Solitons & Fractals, 2006
The new continuous functions for the Fibonacci and Lucas p-numbers using Binet formulas are intro... more The new continuous functions for the Fibonacci and Lucas p-numbers using Binet formulas are introduced. The article is of a fundamental interest for Fibonacci numbers theory and theoretical physics.
Chaos, Solitons & Fractals, 2005
The goal of the present article is to develop the “continues” approach to the recurrent Fibonacci... more The goal of the present article is to develop the “continues” approach to the recurrent Fibonacci sequence. The main result of the article is new mathematical model of a curve-linear space based on a special second-degree function named “The Golden Shofar”.
Chaos, Solitons & Fractals, 2006
The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1,2... more The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1,2,3,.. .) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions s p , special irrational numbers that follow from PascalÕs triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6), this fact is proved by the famous physicist Richard Feynman. Ó 2005 Elsevier Ltd. All rights reserved. ''What miracles exist in mathematics! According to my theory, the Golden Proportion of the ancient Greeks gives the minimal power condition of the butadiene molecule.'' Richard Feynman
Chaos, Solitons & Fractals, 2006
Modern natural science requires the development of new mathematical apparatus. The generalized Fi... more Modern natural science requires the development of new mathematical apparatus. The generalized Fibonacci numbers or Fibonacci p-numbers (p= 0, 1, 2, 3, ), which appear in the diagonal sums of Pascal's triangle and are assigned in the recurrent form, are a new ...
Chaos, Solitons & Fractals, 2005
This article presents the results of some new research on a new class of hyperbolic functions tha... more This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into ''continuous'' theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers. Taking into consideration a great role played by the hyperbolic functions in geometry and physics, (''Lobatchevski's hyperbolic geometry'', ''Four-dimensional Minkowski's world'', etc.), it is possible to expect that the new theory of the hyperbolic functions will bring to new results and interpretations on mathematics, biology, physics, and cosmology. In particular, the result is vital for understanding the relation between transfinitness i.e. fractal geometry and the hyperbolic symmetrical character of the disintegration of the neural vacuum, as pointed out by El Naschie [Chaos Solitons & Fractals 17 (2003) 631].
European Journal of Operational Research, 2008
Consider a problem of minimizing a separable, strictly convex, monotone and differentiable functi... more Consider a problem of minimizing a separable, strictly convex, monotone and differentiable function on a convex polyhedron generated by a system of m linear inequalities. The problem has a series-parallel structure, with the variables divided serially into n disjoint subsets, whose elements are considered in parallel. This special structure is exploited in two algorithms proposed here for the approximate solution of the problem. The first algorithm solves at most min{m, ν − n + 1} subproblems; each subproblem has exactly one equality constraint and at most n variables. The second algorithm solves a dynamically generated sequence of subproblems; each subproblem has at most ν − n + 1 equality constraints, where ν is the total number of variables. To solve these subproblems both algorithms use the authors' Projected Newton Bracketing method for linearly constrained convex minimization, in conjunction with the steepest descent method. We report the results of numerical experiments for both algorithms.
Chaos, Solitons & Fractals, 2007
This article presents a review of new mathematical models of the hyperbolic space. These models a... more This article presents a review of new mathematical models of the hyperbolic space. These models are based on the golden section. In this article, the authors discuss the hyperbolic Fibonacci and Lucas functions and the surface of the golden shofar, which are the most important of these models. The authors also introduce, within this article, the golden hyperbolic approach for modeling the universe.
Информатика, Apr 5, 2018
Предлагаются математическая модель и декомпозиционные методы оптимизации режимов параллельной обр... more Предлагаются математическая модель и декомпозиционные методы оптимизации режимов параллельной обработки группы деталей на многопозиционном многоинструментальном оборудовании непересекающимися блоками инструментов с учетом требуемой производительности и основных конструктивно-технологических ограничений. В качестве целевой функции может выступать один из следующих показателей: себестоимость обработки группы деталей, время ее обработки, суммарные затраты на инструмент.
Progress in Biophysics and Molecular Biology, 2023
The mystery of the morphogenesis of phyllotaxis has been of concern for several generations of bo... more The mystery of the morphogenesis of phyllotaxis has been of concern for several generations of botanists and mathematicians. Of particular interest is the fact that the number of visible spirals is equal to the number from the Fibonacci series. The article proposes an analytical solution to two fundamental questions of phyllotaxis: what is the morphogenesis of patterns of spiral phyllotaxis? and why the number of visible spirals is equal to number from the Fibonacci series? The article contains videos illustrating the recursive dynamic model of spiral phyllotaxis morphogenesis.
непрерывные функции для обобщенных чисел Фибоначчи и Люка, матрицы Фибоначчи и «золотые» матрицы.... more непрерывные функции для обобщенных чисел Фибоначчи и Люка, матрицы Фибоначчи и «золотые» матрицы. Статья опубликована в международном электронном журнале “Visual Mathematics”, 2006,
This article presents the results of some new research on a new class of hyperbolic functions tha... more This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into ''continuous'' theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers. Taking into consideration a great role played by the hyperbolic functions in geometry and physics, (''Lobatchevski's hyperbolic geometry'', ''Four-dimensional Minkowski's world'', etc.), it is possible to expect that the new theory of the hyperbolic functions will bring to new results and interpretations on mathematics, biology, physics, and...
Chaos, Solitons & Fractals, 2006
The new continuous functions for the Fibonacci and Lucas p-numbers using Binet formulas are intro... more The new continuous functions for the Fibonacci and Lucas p-numbers using Binet formulas are introduced. The article is of a fundamental interest for Fibonacci numbers theory and theoretical physics.
Chaos, Solitons & Fractals, 2005
The goal of the present article is to develop the “continues” approach to the recurrent Fibonacci... more The goal of the present article is to develop the “continues” approach to the recurrent Fibonacci sequence. The main result of the article is new mathematical model of a curve-linear space based on a special second-degree function named “The Golden Shofar”.
Chaos, Solitons & Fractals, 2006
The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1,2... more The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1,2,3,.. .) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions s p , special irrational numbers that follow from PascalÕs triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6), this fact is proved by the famous physicist Richard Feynman. Ó 2005 Elsevier Ltd. All rights reserved. ''What miracles exist in mathematics! According to my theory, the Golden Proportion of the ancient Greeks gives the minimal power condition of the butadiene molecule.'' Richard Feynman
Chaos, Solitons & Fractals, 2006
Modern natural science requires the development of new mathematical apparatus. The generalized Fi... more Modern natural science requires the development of new mathematical apparatus. The generalized Fibonacci numbers or Fibonacci p-numbers (p= 0, 1, 2, 3, ), which appear in the diagonal sums of Pascal's triangle and are assigned in the recurrent form, are a new ...
Chaos, Solitons & Fractals, 2005
This article presents the results of some new research on a new class of hyperbolic functions tha... more This article presents the results of some new research on a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring Fibonacci and Lucas series. The hyperbolic Fibonacci and Lucas functions, which are the being extension of Binet's formulas for the Fibonacci and Lucas numbers in continuous domain, transform the Fibonacci numbers theory into ''continuous'' theory because every identity for the hyperbolic Fibonacci and Lucas functions has its discrete analogy in the framework of the Fibonacci and Lucas numbers. Taking into consideration a great role played by the hyperbolic functions in geometry and physics, (''Lobatchevski's hyperbolic geometry'', ''Four-dimensional Minkowski's world'', etc.), it is possible to expect that the new theory of the hyperbolic functions will bring to new results and interpretations on mathematics, biology, physics, and cosmology. In particular, the result is vital for understanding the relation between transfinitness i.e. fractal geometry and the hyperbolic symmetrical character of the disintegration of the neural vacuum, as pointed out by El Naschie [Chaos Solitons & Fractals 17 (2003) 631].
European Journal of Operational Research, 2008
Consider a problem of minimizing a separable, strictly convex, monotone and differentiable functi... more Consider a problem of minimizing a separable, strictly convex, monotone and differentiable function on a convex polyhedron generated by a system of m linear inequalities. The problem has a series-parallel structure, with the variables divided serially into n disjoint subsets, whose elements are considered in parallel. This special structure is exploited in two algorithms proposed here for the approximate solution of the problem. The first algorithm solves at most min{m, ν − n + 1} subproblems; each subproblem has exactly one equality constraint and at most n variables. The second algorithm solves a dynamically generated sequence of subproblems; each subproblem has at most ν − n + 1 equality constraints, where ν is the total number of variables. To solve these subproblems both algorithms use the authors' Projected Newton Bracketing method for linearly constrained convex minimization, in conjunction with the steepest descent method. We report the results of numerical experiments for both algorithms.
Chaos, Solitons & Fractals, 2007
This article presents a review of new mathematical models of the hyperbolic space. These models a... more This article presents a review of new mathematical models of the hyperbolic space. These models are based on the golden section. In this article, the authors discuss the hyperbolic Fibonacci and Lucas functions and the surface of the golden shofar, which are the most important of these models. The authors also introduce, within this article, the golden hyperbolic approach for modeling the universe.
Информатика, Apr 5, 2018
Предлагаются математическая модель и декомпозиционные методы оптимизации режимов параллельной обр... more Предлагаются математическая модель и декомпозиционные методы оптимизации режимов параллельной обработки группы деталей на многопозиционном многоинструментальном оборудовании непересекающимися блоками инструментов с учетом требуемой производительности и основных конструктивно-технологических ограничений. В качестве целевой функции может выступать один из следующих показателей: себестоимость обработки группы деталей, время ее обработки, суммарные затраты на инструмент.