Parametric synthesis of rod spatial vibroisolation system under arbitrarily directed external disturbance

A mathematical model of flexible-rod spatial vibroisolating suspension, describing the motion of protected object, is considered. An algorithm is proposed for solving the problem of spatial displacement of the object under the action of static forces applied in an arbitrary direction. The coefficients of stiffness matrix of the suspension are determined depending on the position of static equilibrium. It is demonstrated that, depending on the requirements by varying geometrical parameters of the rods, different dynamic properties of the suspension may be obtained

О решении задачи коши с помощью решетчатых функций в математической физике и химической кинетике

A polynomial method of Cauchy problem solving is presented. The method allows constructing a fundamental solution in locally analytical form for any type of function of the right part of the equation for normal form of differential equation. A test for well-known functions both for lower and higher among possible orders of polynomial method of solving is carried out. The expediency of using the method of higher order is determined.Представлен полиномиальный метод решения задачи Коши, позволяющий построить для нормальной формы дифференциального соотношения фундаментальное решение в локально аналитической форме при любом виде функции правой части уравнения. Проведено тестирование на известных функциях, как при низшем, так и при высшем из возможных порядков полиномиального метода решения. Установлена целесообразность использования метода высшего порядк

Единый подход к систематизации мультидисциплинарных многомерных нелинейных начально-краевых задач

An approach to the systematization of coupled problems of different science areas is suggested. A unified methodology for solving such problems is described. The usage of this methodology is illustrated by examples of solving the contact problem and the problem of chemical machine-building.Предложен подход к систематизации связанных задач различных областей научного знания, основанный на их математической постановке. Описана единая методология решения таких задач. Использование методологии проиллюстрировано примерами решения контактной задачи и задачи химического машиностроения

Решение прикладных одномерных линейных краевых задач с автоматической точностью

Possible basic types of applied one-dimensional linear boundary problems in problems of chemical kinetics, structures strength, aerohydroelasticity, and wave processes in continuous media are analyzed. A uniform definition of such problems based on three-parametrical formalization is formulated. With arbitrary topology problems as an example an algorithm of boundary problems solution alternative to both discrete and differential methods is suggested. Testing the algorithm with Krylov functions as an example and the problem of describing the deformation of a shell of revolution in the vicinity of a singular point are given.А нализируются возможные основные типы прикладных одномерных линейных краевых задач в задачах химической кинетики, прочности конструкций, аэрогидроупругости, волновых процессов в сплошных средах. Формулируется единая постановка таких задач, основанная на трех - параметрической формализации. На примере задач с произвольной топологией предлагается алгоритм решения краевых задач, альтернативный как дискретным, так и дифференциальным прогонкам. Приводятся примеры тестирования алгоритма на примере функций Крылова и задачи описания деформирования оболочки вращения в окрестности сингулярной точки

Application of identical transformations in Cauchy problem solving

A polynomial method of Cauchy problem solving is presented. The method allows constructing a fundamental solution in locally analytical form for any type of function of the right part of the equation for normal form of differential equation. A test for well-known functions both for lower and higher among possible orders of polynomial method of solving is carried out. The expediency of using the method of higher order is determined

A unified approach to systematization of multidiscipline multidimensional nonlinear initial boundary value problems

An approach to the systematization of coupled problems of different science areas is suggested. A unified methodology for solving such problems is described. The usage of this methodology is illustrated by examples of solving the contact problem and the problem of chemical machine-building

Solution of applied one-dimensional linear boundary-value problems with automatic precision

Possible basic types of applied one-dimensional linear boundary problems in problems of chemical kinetics, structures strength, aerohydroelasticity, and wave processes in continuous media are analyzed. A uniform definition of such problems based on three-parametrical formalization is formulated. With arbitrary topology problems as an example an algorithm of boundary problems solution alternative to both discrete and differential methods is suggested. Testing the algorithm with Krylov functions as an example and the problem of describing the deformation of a shell of revolution in the vicinity of a singular point are given

FABRICATION OF ACTIVE ADDITIVE TO SHAMPOOS BASED ON DIFFERENT NATURE NANOPARTICLES

Subject of Research.We developed additives to shampoos based on different nature nanoparticles with micro- and nanoscale spatial resolution. The effect of the obtained nano-additives on the surface structure of hair fibers were studied. The aim of this work was to fabricate additive complexes of nanoparticles with various nature for shampoos and study of their effect on the hair cuticle structure by optical and atomic-force microscopy. Methods. The methods of chemical separation of elements, centrifugation, laser ablation, optical and atomic-force microscopy were used in the work. Main Results. The various types of hair structures were studied, such as normal, greasy, dry and animal hair, using optical and atomic-force microscopes. Сolloidal solutions of metals and their compounds were prepared (Ag, Au, Cu, Fe, Zn, Si, S, MoO3). Two types of additives for shampoos were fabricated: for greasy/normal and dry hair. The effectiveness of fabricated shampoo additives with complexes of different nature nanoparticles was shown. Practical Relevance. The development of new shampoos with the complexes of nanoparticles will increase the effectiveness of traditional types of shampoos, in particular, the recovery and maintenance of normal hair structur