On certain subclasses of multivalent functions with varying arguments of coefficients

In this paper we introduce and study new classes VM_{p,η}(λ,α,β) and VN_{p,η}(λ,α,β) of multivalent functions with varying arguments of coefficients. We obtain coefficients inequalities, distortion theorems and extreme points for functions in these classes. Also, we investigate several distortion inequalities involving fractional calculus. Finally, results on partial sums are considerd.

Attaining Fairness in Communication for Omniscience

This paper studies how to attain fairness in communication for omniscience that models the multi-terminal compress sensing problem and the coded cooperative data exchange problem where a set of users exchange their observations of a discrete multiple random source to attain omniscience—the state that all users recover the entire source. The optimal rate region containing all source coding rate vectors that achieve omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game. Two game-theoretic fairness solutions are studied: the Shapley value and the egalitarian solution. It is shown that the Shapley value assigns each user the source coding rate measured by their remaining information of the multiple source given the common randomness that is shared by all users, while the egalitarian solution simply distributes the rates as evenly as possible in the core. To avoid the exponentially growing complexity of obtaining the Shapley value, a polynomial-time approximation method is proposed which utilizes the fact that the Shapley value is the mean value over all extreme points in the core. In addition, a steepest descent algorithm is proposed that converges in polynomial time on the fractional egalitarian solution in the core, which can be implemented by network coding schemes. Finally, it is shown that the game can be decomposed into subgames so that both the Shapley value and the egalitarian solution can be obtained within each subgame in a distributed manner with reduced complexity.

OPTIMAL DESIGN OF CYLINDRICAL GEARS WITH CONVEX-CONCAVE CONTACT: OBJECTIVE FUNCTION AND VARIABLES PLANNING

Reducing the mass and dimensions of gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with a convex-concave contact of the teeth. Therefore, the study is devoted to the development of methods for the optimal design of cylindrical gears with convex-concave contact of the working surfaces. Optimality criteria: minimum contact stresses and (or) minimum relative sliding velocities, taking into account design, geometrical and technological constraints. C-C gearing was chosen as the object of research. It was proposed by the Slovak scientists M. Boshanski and M. Veresh. An objective function is constructed for the case of minimizing contact stresses. The optimality criterion is formulated as follows: contact stresses σH in the mesh must take the minimum possible value when all constraints are met. An objective function is also constructed for the case of minimizing the relative sliding velocities of profiles. The optimality criterion is formulated as follows: the relative sliding s velocities of profiles λ at the extreme points of mesh must take the minimum possible value when all the constraints are met. Variables planning are defined. These are pressure angle at the pole αС, the curvature radius at the upper part of contact path rkh, and the curvature radius at the lower part of contact path rkd. A method for solving the problem of optimal design is chosen. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. In further studies, it is planned to form a system of constraints on variables planning, to develop methods and algorithms for solving the problem. Also carry out test and verification calculations to confirm and evaluate the theoretical results. Keywords: gear, convex-concave contact, optimal design, objective function, variables planning

Why to build university spaces? How to discuss them? Appearance of a new lens

Since the 1990s, the university space has been the subject of many discussions due to the introduction of communication technologies to the learning process,which has become significantly visible after the effects of the COVID-19 pandemic nowadays. These debates focus on the two extreme points ofwhether university space is necessary or not. In this regard, this research claims that the arguments on this topic are based on subject-object duality. It aims to develop a ground covering the discussions that oscillate between the two extremes by referring to sociomateriality, which advocates the interwovenness of subject and object. Adopting a retrospective perspective, itrediscovers the debates from the 1960s at the onto-epistemological levelthrough a sociomaterial lens. Finally, it situates the discussion on university space within the past-present-future dialogue.

Discrete sizing, cross-sectional shape, topology optimization, and material selection of a framed automotive body

This study proposed a discrete structural optimization method for a framed automotive body. Up to four types of discrete design variables are considered simultaneously, that is, the sizing, cross-sectional shape, topology, and material variables. Firstly, to solve the nonconvex and nonlinear optimization problem, the original non-dominated sorting genetic algorithm, the third version (NSGA-III), is adapted. An improved extreme points identification scheme and a new mutation operator are proposed to stabilize the normalization of the population and accommodate the manufacturing constraints, respectively. Two test problems demonstrate that the modified NSGA-III can handle continuous and discontinuous multiple objective optimization. Subsequently, the classical 10-bar truss is used to illustrate the proposed method. A weight reduction of 4.5 kg is achieved as compared to previous optimal designs in the literature. Finally, a framed automotive body is optimized for maximizing the first order natural frequency and minimizing the total mass, the maximum stresses and the maximum displacements in different load cases and the manufacturing cost. The results obtained by different optimization procedures are presented and discussed. The results demonstrate the feasibility and effectiveness of the proposed method. A weight reduction of 17.59% is achieved while other structural performances satisfy the design requirements.

Estimating the Extreme Values in Gridding Data using Gauss Elimination Method: A New Approach in Potential Field Processing

The position of a maximum point of a function depends on its coefficients and order. The maximum horizontal gradient method is a popular method that greatly contributes to the detection of maximum points and approximation of geological structures edges. By adopting a mathematical logic, Blakely and Simpson established a quadratic function based on the characteristic of three points of a straight line in the fundamental directions. However, for potential field data like gravity and magnetic data, the coefficients of a quadratic function in each direction are not only dependent on the values of three points on a straight line, but also, they depend on the values of the surrounding points. This article proposes an algorithm which can detect maximum points more effectively in order to delineate geological structures boundaries from potential field data. The proposed algorithm uses a 3×3 neighborhood data grid to establish a two-variables function and to determine its coefficients by applying the Gaussian elimination method. After the two-variables function has been established, the algorithm estimates any extreme points and their positions from a set of four single-variable functions which correspond to the horizontal, vertical and the two diagonal directions by the cases x = 0, y = 0, y = -x and y = x of the main function. Finally, the conditions to detect the maximum point from the extreme points are defined. The validity of the algorithm was demonstrated on synthetic datasets generated by two different model structures. A real data application of the method has also been realized by estimating the geological boundaries by gravity data in the Vietnam’s continental shelf. The results obtained from the synthetic applications of the algorithm proved that it can determine more maximum points as compared to Blakely and Simpson method, and as a result, in all the test cases, it has drawn the real boundaries of the model structures more accurately. The application results of the method on real data revealed new boundary delineations in the research area, interpreted to be faults or fractures which lies between deep trench in the East Vietnam Sea.

The First Main Line in Russia

The article is dedicated to the 170th anniversary of the first Russian railway main line St. Petersburg–Moscow. The country’s railway transport, as the main type of transportation, has a rich history and remarkable patriotic, labour, scientific, and technical traditions. We must remember them. The emergence of railways in Russia, as in other countries of the world, was accompanied by many problems that needed to be solved: financing methods, types of ownership, track gauge, types of traction and signalling, traffic management and control, competition with other modes of transport, etc. The stage of emergence of railways in Russia is very instructive. What extreme points of view were expressed, and how long did it take to start building main lines? After the society realised the need for construction of railways, it became obvious that the costs required are not affordable neither for the state, nor for creditors, nor for private entrepreneurs. To better understand how construction of the first railway in Russia was conducted, the article offers many illustrations.