General Mathematics

1502 Submissions

[18] viXra:1502.0185 [pdf] submitted on 2015-02-21 08:45:39

Новые методы оптимизации и их применение v3 (New Methods of Optimzation and Their Applications V3, in Russian)

Authors: Bolonkin A.A.
Comments: 226 Pages. Это более качественная версия сканирования 3. Старые версии 1,2 можно удалить.

Краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана. Автор излагает принципиально новые методы оптимизации, поиска и оценки глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п. Краткое оглавление: Математические основы методов оптимизации. Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления. Приложение методов α – , β –функционалов и максимина к техническим задачам. Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием.
Category: General Mathematics

[17] viXra:1502.0137 [pdf] submitted on 2015-02-16 19:07:44

Новые методы оптимизации и их применение v3 (New Methods of Optimzation and Their Applications, V3)

Authors: Bolonkin A.A.
Comments: 223 Pages. This is better scanning than previous copy (Эта версия имеет лучшее качество сканирования)

This is a brief summary of lectures for the course "Theory of optimal systems", read by the author for senior students, graduate students, engineers and lecturers in 1962-1969 at the Moscow Aviation Institute of Technology and in 1969-1971 at MVTU. named Bauman. The author presents the fundamentally new optimization techniques, search for the global minimum and applies them to the technical problems of automation, flight dynamics, aviation, aerospace, combinatorics, game theory, problems with resistance, etc. Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана. Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п. Оглавление: Часть 1. Математические основы методов оптимизации. Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления. Часть 2. Приложение методов α - и β –функционалов и Максимина к техническим задачам. Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием.
Category: General Mathematics

[16] viXra:1502.0122 [pdf] replaced on 2015-04-06 11:32:09

Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 1 Gossamer Numbers

Authors: Chelton D. Evans, William K. Pattinson
Comments: 22 Pages.

The discovery of what we call the gossamer number system ∗G, as an extension of the real numbers includes an infinitesimal and infinitary number system; by using ‘infinite integers’, an isomorphic construction to the reals by solving algebraic equations is given. We believe this is a total ordered field. This could be an equivalent construction of the hyperreals. The continuum is partitioned: 0 < Φ+ < R+ + Φ < +Φ−1 < ∞.
Category: General Mathematics

[15] viXra:1502.0121 [pdf] submitted on 2015-02-15 07:58:51

Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 2 the Much Greater Than Relations

Authors: Chelton D. Evans, William K. Pattinson
Comments: 18 Pages.

An infinitesimal and infinitary number system the Gossamer numbers is fitted to du Bois-Reymond’s infinitary calculus, redefining the magnitude relations. We connect the past symbol relations much-less-than and much-less-than or equal to with the present little-o and big-O notation, which have identical definitions. As these definitions are extended, hence we also extend little-o and big-O, which are defined in Gossamer numbers. Notation for an reformed infinitary calculus, calculation at a point is developed. We proceed with the introduction of an extended infinitary calculus.
Category: General Mathematics

[14] viXra:1502.0120 [pdf] replaced on 2015-04-06 11:41:31

Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 3 Comparing Functions

Authors: Chelton D. Evans, William K. Pattinson
Comments: 16 Pages.

An algebra for comparing functions at infinity with infinireals, comprising of infinitesimals and infinities, is developed: where the unknown relation is solved for. Generally, we consider positive monotonic functions f and g, arbitrarily small or large, with relation z: f z g. In general we require f, g, f − g and f/g to be ultimately monotonic.
Category: General Mathematics

[13] viXra:1502.0119 [pdf] replaced on 2015-04-06 11:47:02

Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 4 the Transfer Principle

Authors: Chelton D. Evans, William K. Pattinson
Comments: 14 Pages.

Between gossamer numbers and the reals, an extended transfer principle founded on approximation is described, with transference between different number systems in both directions, and within the number systems themselves. As a great variety of transfers are possible, hence a mapping notation is given. In ∗G we find equivalence with a limit with division and comparison to a transfer ∗G → R with comparison.
Category: General Mathematics

[12] viXra:1502.0118 [pdf] submitted on 2015-02-15 08:14:36

Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 5 Non-Reversible Arithmetic and Limits

Authors: Chelton D. Evans, William K. Pattinson
Comments: 13 Pages.

Investigate and define non-reversible arithmetic in ∗G and the real numbers. That approximation of an argument of magnitude, is arithmetic. For non-reversible multiplication we define a logarithmic magnitude relation. Apply the much-greater-than relation in the evaluation of limits. Consider L’Hopital’s rule with infinitesimals and infinities, and in a comparison f (z) g form.
Category: General Mathematics

[11] viXra:1502.0117 [pdf] replaced on 2015-04-06 11:51:07

Extending du Bois-Reymond’s Infinitesimal and Infinitary Calculus Theory Part 6 Sequences and Calculus in ∗G

Authors: Chelton D. Evans, William K. Pattinson
Comments: 15 Pages.

With the partition of positive integers and positive infinite integers, it follows naturally that sequences are also similarly partitioned, as sequences are indexed on integers. General convergence of a sequence at infinity is investigated. Monotonic sequence testing by comparison. Promotion of a ratio of infinite integers to non-rational numbers is conjectured. Primitive calculus definitions with infinitary calculus, epsilon-delta proof involving arguments of magnitude are considered.
Category: General Mathematics

[10] viXra:1502.0116 [pdf] submitted on 2015-02-15 08:25:09

The Fundamental Theorem of Calculus with Gossamer Numbers

Authors: Chelton D. Evans, William K. Pattinson
Comments: 11 Pages.

Within the gossamer numbers ∗G which extend R to include infinitesimals and infinities we prove the Fundamental Theorem of Calculus (FTC). Riemann sums are also considered in ∗G, and their non-uniqueness at infinity. We can represent the sum as a continuous function in ∗G by inserting infinitesimal intervals at the discontinuities, and threading curves between the sums discontinuities. As the FTC is a difference of integrals at the end points, the same is true for sums.
Category: General Mathematics

[9] viXra:1502.0115 [pdf] submitted on 2015-02-15 08:31:38

Convergence Sums at Infinity with New Convergence Criteria

Authors: Chelton D. Evans, William K. Pattinson
Comments: 40 Pages.

Development of sum and integral convergence criteria, leading to a representation of the sum or integral as a point at infinity. Application of du Bois-Reymond’s comparison of functions theory, when it was thought that there were none. Known convergence tests are alternatively stated and some are reformed. Several new convergence tests are developed, including an adaption of L’Hopital’s rule. The most general, the boundary test is stated. Thereby we give an overview of a new field we call ‘Convergence sums’. A convergence sum is essentially a strictly monotonic sum or integral where one of the end points after integrating is deleted resulting in a sum or integral at a point.
Category: General Mathematics

[8] viXra:1502.0114 [pdf] submitted on 2015-02-15 08:36:32

Power Series Convergence Sums

Authors: Chelton D. Evans, William K. Pattinson
Comments: 7 Pages.

Calculating the radius and interval of convergence with power series at infinity. By using non-reversible arithmetic, either by factoring, comparison or application of the logarithmic magnitude relation, convergence or divergence may be determined. We interpret uniform convergence with a convergence sum.
Category: General Mathematics

[7] viXra:1502.0113 [pdf] submitted on 2015-02-15 08:41:48

Convergence Sums and the Derivative of a Sequence at Infinity

Authors: Chelton D. Evans, William K. Pattinson
Comments: 10 Pages.

For convergence sums, by threading a continuous curve through a monotonic sequence, a series difference can be made a derivative. Series problems with differences can be transformed and solved in the continuous domain. At infinity, a bridge between the discrete and continuous domains is made. Stolz theorem at infinity is proved. Alternating convergence theorem for convergence sums is proved.
Category: General Mathematics

[6] viXra:1502.0112 [pdf] submitted on 2015-02-15 08:47:05

Rearrangements of Convergence Sums at Infinity

Authors: Chelton D. Evans, William K. Pattinson
Comments: 12 Pages.

Convergence sums theory is concerned with monotonic series testing. On face value, this may seem a limitation but, by applying rearrangement theorems at infinity, non-monotonic sequences can be rearranged into monotonic sequences. The resultant monotonic series are convergence sums. The classes of convergence sums are greatly increased by the additional versatility applied to the theory.
Category: General Mathematics

[5] viXra:1502.0111 [pdf] submitted on 2015-02-15 08:51:41

Ratio Test and a Generalization with Convergence Sums

Authors: Chelton D. Evans, William K. Pattinson
Comments: 9 Pages.

For positive series convergence sums we generalize the ratio test in ∗G the gossamer numbers. Via a transfer principle, within the tests we construct variations. However, most significantly we connect and show the generalization to be equivalent to the boundary test. Hence, the boundary test includes the generalized tests: the ratio test, Raabe’s test, Bertrand’s test and others.
Category: General Mathematics

[4] viXra:1502.0110 [pdf] submitted on 2015-02-15 08:55:18

The Boundary Test for Positive Series

Authors: Chelton D. Evans, William K. Pattinson
Comments: 14 Pages.

With convergence sums, a universal comparison test for positive series is developed, which compares a positive monotonic series with an infinity of generalized p-series. The boundary between convergence and divergence is an infinity of generalized p-series. This is a rediscovery and reformation of a 175 year old convergence/divergence test.
Category: General Mathematics

[3] viXra:1502.0100 [pdf] submitted on 2015-02-14 03:41:23

The Prime Sequence Generating Algorithm

Authors: Ramesh Chandra Bagadi
Comments: 2 Pages.

In this research paper an algorithm to find the Prime Sequence is presented.
Category: General Mathematics

[2] viXra:1502.0055 [pdf] submitted on 2015-02-06 19:25:22

Новые методы оптимизации и их применение (версия 2). New Methods of Optimization and Its Applications (V2) V.2)

Authors: Bolonkin A.A., Bolonkin A.A.
Comments: 110 Pages. Это Версия сканирования 2. This is Version of scan 2.

Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана. Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п. This is a brief summary of lectures for the course "Theory of optimal systems", read by the author for senior students, graduate students, engineers and lecturers in 1967-1969 at the Moscow Aviation Institute of Technology and in 1969-1971 at MVTU. named Bauman. The author presents the fundamentally new optimization techniques, search for the global minimum and applies them to the technical problems of automation, flight dynamics, aviation, aerospace, combinatorics, game theory, problems with resistance, etc. Оглавление: Часть 1. Математические основы методов оптимизации. Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления. Часть 2. Приложение методов α - и β –функционалов и Максимина к техническим задачам. Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием. Версия сканирования 2.
Category: General Mathematics

[1] viXra:1502.0054 [pdf] submitted on 2015-02-06 20:04:30

Новые методы оптимизации и их применение (V.2). New Methods of Optimisations Anf Their Application V2)

Authors: Bolonkin A.A.
Comments: 111 Pages. Это более качественная версия сканирования. Старую -удалить.

Это краткий конспект лекций по курсу "Теория оптимальных систем", прочитанных автором для студентов старших курсов, аспирантов, инженеров и преподавателей в 1962-1969гг в Московском авиационном технологическом институте и в 1969-1971гг в МВТУ им. Баумана. Автор излагает принципиально новые методы оптимизации, поиска глобального минимума и применяет их в технических задачах автоматики, динамики полета, авиации, космонавтике, комбинаторике, в теории игр, задачах с противодействием и т.п. This is a brief summary of lectures for the course "Theory of optimal systems", read by the author for senior students, graduate students, engineers and lecturers in 1967-1969 at the Moscow Aviation Institute of Technology and in 1969-1971 at MVTU. named Bauman. The author presents the fundamentally new optimization techniques, search for the global minimum and applies them to the technical problems of automation, flight dynamics, aviation, aerospace, combinatorics, game theory, problems with resistance, etc. Оглавление: Часть 1. Математические основы методов оптимизации. Методы β- и γ-функционалов. Методы α-функционала. Метод максимина. Численная реализация алгоритмов α-функционала и максимина, другие численные методы. Импульсные режимы. Специальные экстремали в задачах оптимального управления. Специальные экстремали и разрешимость задач оптимального управления. Часть 2. Приложение методов α - и β –функционалов и Максимина к техническим задачам. Некоторые задачи автоматики. Некоторые задачи динамики полета. Применение методов α-функционала к экстремальным задачам кобинаторного типа. Задачи с противодействием.
Category: General Mathematics