On the statements of boundary conditions in models of the woven materials production

В статье обсуждаются проблемы постановка краевых задач при моделировании процессов аддитивного производства 3D материала, при учете наличия в нем дополнительных выделенных направлений (выкладки волокон в тканых материалах, арматуры в бетонных конструкциях, биоволокон в мышечной ткани и т.д.). Выводится общая форма тензорного соотношения на поверхности наращивания, при учете дополнительного выделенного направления. Определяется необходимая система независимых аргументов определяющей тензорной функции на поверхности наращивания в рассматриваемом случае. Определяется полный набор совместных рациональных инвариантов тензора напряжений и характерных директоров. Дается инвариантно-полная формулировка определяющих соотношений на поверхности наращивания. Предложены постановки краевых задач, моделирующих процессы синтеза тканых 3D материалов. Полученные дифференциальные ограничения конкретизируются для ортогональных систем координат, учитывающих геометрию процесса наращивания. The article discusses the problem of boundary value problems in models of the additive production processes of a 3D material, taking into account the presence of additional selected directions in it (laying out fibers in woven materials, reinforcement in concrete structures, biofibers in muscle tissue, etc.). The general form of the tensor relation on the growing surface is shown, taking into account the additional selected direction. The necessary system of independent arguments of the constitutive tensor function on the growing surface in the considered case is determined. A complete set of joint rational invariants of the stress tensor and characteristic directors is determined. An invariant-complete formulation of the constitutive relations on the growing surface is given. The formulation of boundary value problems that simulate the processes of synthesis of woven 3D materials are proposed. The resulting differential constraints are specified for orthogonal coordinate systems taking account of the geometry of the growing process.

RP-181: Formulation of Standard Quadratic Congruence of Even Composite Modulus modulo an Even Prime Raised to the Power n

The paper presented here, is a standard quadratic congruence of composite modulus, studied rigorously and found the formulation incomplete. It was partially formulated by the earlier mathematicians. The present authors realised that the earlier formulation need a completion and a reformulation of the solutions is done along with two more results. The author considered the problem for reformulation, studied and reformulated the solutions completely. A partial formulation is found in a books of Number Theory by Zuckerman at el. There the formulation is only for an odd positive integer but nothing is said about even positive integer. The authors have provided a complete formulation of the said quadratic congruence and presented here. Keywords: Composite Modulus, Quadratic Congruence, Reformulation.

A Computationally Efficient, Mass Conserving Generalized Short Bearing Formulation for Dynamically-Loaded Journal Bearings

This paper describes a computationally efficient, finite element implementation of a generalized short bearing (GSB) formulation to account for mass conservation in cavitated bearing regions. The method is applied to a set of examples representing partial and full journal bearings under transient loads and kinematics. Bearing performance trends are captured well by the GSB formulation when compared with results obtained from complete two-dimensional formulations and from experiments. The computational speed of the GSB formulation is approximately 40 to 200 times faster than the complete formulation for the examples provided in the paper.

On the boundary conditions formulation in the problems of synthesis of woven 3d materials

В статье обсуждаются формулировки определяющих дифференциальных ограничений на поверхности наращивания на случай моделирования процессов формирования 3D материала, характеризующегося дополнительными характерными директорами (направлениями выкладки волокон в тканых материалах, арматуры в бетонных конструкциях). Выведена общая форма тензорного соотношения на поверхности наращивания, при учете дополнительных выделенных направлений. Определить набор совместных рациональных инвариантов тензора напряжений и характерных директоров. Дана инвариантно-полная формулировка определяющих соотношений на поверхности наращивания. Полученные результаты могут быть использованы для постановки и решения краевых задач, моделирующих процессы синтеза тканых 3D материалов. The article discusses the formulation of the defining differential constraints on the buildup surface in the case of modeling the processes of forming a 3D material characterized by additional characteristic directors (directions of laying fibers in woven materials, reinforcement in concrete structures). The general form of the tensor relation on the growing surface is derived, taking into account the additional selected directions. Determine the set of joint rational invariants of the stress tensor and characteristic directors. An invariant-complete formulation of the constitutive relations on the surface of the build-up is given. The results obtained can be used to formulate and solve boundary value problems that simulate the processes of synthesis of woven 3D materials.

ECONOMIC SECURITY OF THE INDIVIDUAL IN THE SYSTEM OF ECONOMIC SECURITY OF THE STATE

A more complete formulation of the economic security of the individual is its consideration in the form of personal capabilities and readiness to create an appropriate degree of self-protection and self-development in the circumstances of the formation by state institutions of such levers for the execution and protection of significant personal interests, according to which it is possible to implement a constant and balanced improvement of the state economy and the country as a whole as an independent modernizing system from the outside world.

A comprehensive study of a similarity criterion in cardiac computerized tomography images enhancement

This research focuses on the study of a particular filter based on a similarity criterion that has been applied to improve the information contained in images acquired using different cardiac imaging modalities. The primary attention of this study is to examine which component of the similarity criterion generates more relevant information useful to increase the medical image quality. In this sense, four case studies are established, first a complete formulation of the similarity criterion is considered, and then three additional cases, representing each component of the criterion; such cases are referred to as full, main, residual1, and residual2, respectively. A score function is used for quantifying and then assessing the impact of each component of the similarity criterion. Such measure is a relation between some full–reference and blind–reference image enhancement measures. A computer generated phantom and a representative clinical dataset (1270 three–dimensional images from 126 patients) are used in a thorough evaluation of the similarity criterion. In general terms of performance of the image enhancement technique, the results of the study reveal that the component residual1 outperforms than the other two components of similarity criterion or its complete formulation.

Quantum cosmology and the equation Schwinger - Tomonaga.

In this article we will use the recent approach to quantum cosmology based on the principle of uncertainty between the Hubble parameter and the volume of the space. In this article, we use the complete formulation of the equations for the wave function of the universe. For this purpose, the Schwinger equation for the evolution of the wave function along the hyper-surface of space-time.

Equation of quantum cosmology on the basis of the equation the Schwinger - Tomonaga

The modern formulation of cosmology has different approaches, one of which is quantum cosmology. For example, the equation Wheeler - DeWitt without a direct evolution. In this article we will use the recent approach to quantum cosmology based on the principle of uncertainty between the Hubble parameter and the volume of the space. In this article, we use the complete formulation of the equations for the wave function of the universe. For this purpose, the Schwinger equation for the evolution of the wave function along the Hyper-surface of space-time.

Living in a Gender-Binary World

Baker, Gentry, and Rittenburg’s (2005) model of consumer vulnerability outlines the personal, social, and structural characteristics that frame consumers’ experiences of vulnerability in the marketplace. Later applications and enhancements have expanded consumer vulnerability theory. While the theory has been applied in numerous settings, to date it has not been used to examine the ways that gender identity may intersect with market factors to produce vulnerability. Application in this setting also allows for the integration of various model enhancements, and the examination of vulnerability using a more complete formulation of the theory. Based on in-depth qualitative interviews and collages, along with examples from current marketing practice, our research shows consumer vulnerability to be a useful lens for understanding gender variant consumers’ experiences and the ways in which marketing systems can be engaged to reshape those experiences.