Spatial Structures of Fibrillar Proteins

The protein molecules are considerate in the space of the highest dimension with a change in dimension with demand at the conformation of the molecules. It was shown that the widespread quasi-plane model of the Pouling protein structure do not reflect and even contradict the spatial structures of the protein in various conformations. It was found that the linear structures and folded structures of the protein in space of the highest dimension have translational symmetry. The elementary elements of protein translational symmetry were determined, their dimensions were calculated (9 for the linear structures and 23 for folded structures).

Spline-approximation as the basis of computer technology design of linear structures routes

This article is a continuation of the article published in Journal of Applied Informatics nо.1 in 2019 [1]. In it, the problems of computer design of routes of various linear structures (new and reconstructed railways and highways, pipelines for various purposes, canals, etc.) are considered from a unified standpoint, as problems of approximating a sequence of points on plane of a smooth curve consisting of elements of a given type, i.e. spline. The fundamental difference from other approximation problems considered in the theory of splines and its applications is that the boundaries of the elements of the spline and even their number are unknown. Therefore, a two-stage scheme for finding a solution has been proposed. At the first stage, the number of spline elements and their parameters are determined using dynamic programming. For some tasks, this stage is the only one. In more complex cases, the result of the first stage is used as an initial approximation to optimize the spline parameters using nonlinear programming. Another complicating factor is the presence of numerous restrictions on the spline parameters, which take into account design standards and conditions for the construction and subsequent operation of the structure. The article discusses the features of mathematical models of the corresponding design problems. For a spline consisting of arcs of circles, mated by line segments, used in the design of the longitudinal profile of both new and reconstructed railways and highways and pipelines, a mathematical model is built and a new algorithm for solving a nonlinear programming problem is proposed, taking into account the structural features of the constraint system. In contrast to standard nonlinear programming algorithms, a basis is constructed in the zero-space of the matrix of active constraints and its modification is used when the set of active constraints changes. At the same time, to find the direction of descent at each iteration, no solution of auxiliary systems of equations is required at all. Two options for organizing the iterative optimization process are considered: descent through groups of variables in the presence of sections for independent construction of the descent direction and the traditional change of all variables in one iteration. Experimentally, no significant advantage of one of these options has been revealed.

Two-stage spline-approximation in linear structure routing

In the article, computer design of routes of linear structures is considered as a spline approximation problem. A fundamental feature of the corresponding design tasks is that the plan and longitudinal profile of the route consist of elements of a given type. Depending on the type of linear structure, line segments, arcs of circles, parabolas of the second degree, clothoids, etc. are used. In any case, the design result is a curve consisting of the required sequence of elements of a given type. At the points of conjugation, the elements have a common tangent, and in the most difficult case, a common curvature. Such curves are usually called splines. In contrast to other applications of splines in the design of routes of linear structures, it is necessary to take into account numerous restrictions on the parameters of spline elements arising from the need to comply with technical standards in order to ensure the normal operation of the future structure. Technical constraints are formalized as a system of inequalities. The main distinguishing feature of the considered design problems is that the number of elements of the required spline is usually unknown and must be determined in the process of solving the problem. This circumstance fundamentally complicates the problem and does not allow using mathematical models and nonlinear programming algorithms to solve it, since the dimension of the problem is unknown. The article proposes a two-stage scheme for spline approximation of a plane curve. The curve is given by a sequence of points, and the number of spline elements is unknown. At the first stage, the number of spline elements and an approximate solution to the approximation problem are determined. The method of dynamic programming with minimization of the sum of squares of deviations at the initial points is used. At the second stage, the parameters of the spline element are optimized. The algorithms of nonlinear programming are used. They were developed taking into account the peculiarities of the system of constraints. Moreover, at each iteration of the optimization process for the corresponding set of active constraints, a basis is constructed in the null space of the constraint matrix and in the subspace – its complement. This makes it possible to find the direction of descent and solve the problem of excluding constraints from the active set without solving systems of linear equations. As an objective function, along with the traditionally used sum of squares of the deviations of the initial points from the spline, the article proposes other functions taking into account the specificity of a particular project task.

What’s a term? An attempt to define the term within the theoretical framework of text linguistics

In texts for specific purposes, terms adopt a behaviour which is contrary to the prescriptive demands of traditional terminology. Indeed, they exhibit variability both on the level of their meaning content and on the level of their linear structure. Their meaning contents are not fixed, but may be changed by the language user’s verbal and non-verbal activities. Their linear structures are not fixed, but can be adjusted to the cha racteristics of their linguistic environment, specifically the sentence or sequence of sentences in which they are being used. Examined within the framework of text linguistics, it becomes clear that this variability con- tributes to two basic characteristics of any body of sentences which constitutes a text, namely text coherence and text cohesion. Consequently, the aim of this article is to propose a new definition of the term, a definition which underscores the role the term plays in bringing about texture in texts for specific purposes.

Response Spectrum with Uncertain Damping Using Artificial Neural Networks

It is evident that the response of linear structures under dynamic loads depends to two important dynamics parameters of structures, namely, the natural periods and structural damping. These parameters always characterize the oscillation and the energy dissipation of buildings. In fact, the values of these parameters differ significantly, before, during and after an earthquake from values selected during the design phase. This phenomenon, among other, introduces uncertainty into the building simulation process, which remarkably influences the structural response and associated performance of the structure under dynamic loads. This paper develops a new methodology to estimate the maximum absolute response for linear structures with uncertain damping using the Artificial Neural Networks (ANN) and the Monte Carlo method. The proposed method is illustrated using the target design response spectra corresponding to the EC8 for linear structures exposed to seismic loads. The numerical results revealed the practical applicability of the proposed methodology and the crucial influence of accounting the damping uncertainty in structural dynamics. Additionally, the method can be used in practice, mainly for important and special structures where uncertainty could lead to significant changes in structural response.