General Mathematics

1504 Submissions

[7] viXra:1504.0198 [pdf] replaced on 2015-04-28 21:01:24

C.K.Rajus Mistake

Authors: Subramanyam Durbha
Comments: Pages. This article appeared in the Mathematics teacher(India) volume 50.Please make a note of my e-mail address which is on my abtract and is different from the e-mail address on the pdf document
Category: General Mathematics

[6] viXra:1504.0131 [pdf] submitted on 2015-04-17 00:40:25

Factorization Method Devised from Fermat Method

Authors: Bojan Vasiljević
Comments: 1 Page.

Here we have very slight improvement of Fermat factorization method, where instead for looking off odd N, we are looking for odd or even B.
Category: General Mathematics

[5] viXra:1504.0027 [pdf] submitted on 2015-04-02 15:32:08

On the Exact Solution of Burgers-Huxley Equation Using the Homotopy Perturbation Method

Authors: S. Salman Nourazar, Mohsen Soori, Akbar Nazari-Golshan
Comments: 10 Pages.

The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley equation. Also, the results prove that the method is an efficient and powerful algorithm to construct the exact solution of non-linear differential equations.
Category: General Mathematics

[4] viXra:1504.0026 [pdf] submitted on 2015-04-02 15:36:11

On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method

Authors: S. Salman Nourazar, Mohsen Soori, Akbar Nazari-Golshan
Comments: 11 Pages.

In the present work, we use the homotopy perturbation method (HPM) to solve the Newell- Whitehead-Segel non-linear differential equations. Four case study problems of Newell-Whitehead- Segel are solved by the HPM and the exact solutions are obtained. The trend of the rapid convergence of the sequences constructed by the method toward the exact solution is shown numerically. As a result the rapid convergence towards the exact solutions of HPM indicates that, using the HPM to solve the Newell-Whitehead-Segel non-linear differential equations, a reasonable less amount of computational work with acceptable accuracy may be sufficient. Moreover the application of the HPM proves that the method is an effective and simple tool for solving the Newell-Whitehead-Segel non-linear differential equations.
Category: General Mathematics

[3] viXra:1504.0015 [pdf] submitted on 2015-04-01 18:57:33

Optimal Trajectories of Air and Space Vehicles

Authors: Alexander Bolonkin
Comments: 28 Pages.

The author has developed a theory on optimal trajectories for air vehicles with variable wing areas and with conventional wings. He applied a new theory of singular optimal solutions and obtained in many cases the optimal flight. The wing drag of a variable area wing does not depend on air speed and air density. At first glance the results may seem strange, however, this is the case and this chapter will show how the new theory may be used. The equations that follow enable computations of the optimal control and optimal trajectories of subsonic aircraft with pistons, jets, and rocket engines, supersonic aircraft, winged bombs with and without engines, hypersonic warheads, and missiles with wings. The main idea of the research is to use the vehicle’s kinetic energy to increase the range of missiles and projectiles. The author shows that the range of a ballistic warhead can be increased 3–4 times if an optimal wing is added to it, especially a wing with variable area. If we do not need increased range, the head mass of rockets can be increased. The range of large gun shells can also be increased 3–9 times. The range of an aircraft may be improved by 3–15% or more. The results can be used for the design of aircraft, space ship, head of rockets, missiles, flying apparatus and shells for large guns. ------------------------------------------- Key words: Methods of optimization, optimization, optimal control, aviation, space ships.
Category: General Mathematics

[2] viXra:1504.0014 [pdf] submitted on 2015-04-01 20:40:25

List 5.1 of Some Bolonkin’s Publications in 2007-2014 (Loading is Free):

Authors: Alexander Bolonkin
Comments: 68 Pages.

List 5.1 of some Bolonkin’s publications in 2007-2014 (Loading is free):
Category: General Mathematics

[1] viXra:1504.0011 [pdf] submitted on 2015-04-01 12:28:39

New Methods of Optimization and Their Aplication, v4 (Russian). Новые методы оптимизации и их применение, V.4.

Authors: Bolonkin A.A.
Comments: 113 Pages.

Болонкин А.А. Новые методы оптимизации и их применение.v4. Краткий конспект лекции по курсу "Теория оптимальных систем". — М.: Издание МВТУ им. Баумана, 1972. — 220 стр. 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. 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 комбинаторного типа. Задачи с противодействием.
Category: General Mathematics