Decomposition Rules Research Articles

Martensitic transformation of an austenitic stainless steel under non-proportional cyclic loading

In this study, a series of cyclic tests on a 304L stainless steel with different loading paths were conducted. It revealed that as the non-proportionality of loading path increased, the growth rate of martensitic content became higher and its distribution among the austenitic matrix appeared more uniform. A phase transformation kinetics equation was modified to describe the effect of cumulative plastic strain, loading amplitude and loading path on martensitic transformation. A stress decomposition rule was proposed to incorporate both the non-proportional hardening and martensitic transformation hardening to describe the hardening mechanism.

Decomposition Rules for the Ring of Representations of Non-Archimedean GLn

Abstract Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the sequence of p-adic groups $\{GL_n(F)\}_{n=0}^\infty $, with multiplication defined through parabolic induction. We study the problem of the decomposition of products of irreducible representations in $\mathcal{R}$. We obtain a necessary condition on irreducible factors of a given product by introducing a width invariant. Width $1$ representations form the previously studied class of ladder representations. We later focus on the case of a product of two ladder representations, for which we establish that all irreducible factors appear with multiplicity one. Finally, we propose a general rule for the composition series of a product of two ladder representations and prove its validity for cases in which the irreducible factors correspond to smooth Schubert varieties.

Структурное программирование как средство совершенствования компьютерной подготовки бакалавров

The article addresses the problems associated with computer training of engineers at higher schools, which are stemming from insufficiently clear understanding of the main training goal. If this training is seen as a part of the overall mathematical education with defining its goal as educating a student to solve problems on a computer, this goal is achieved by teaching to structured programming, which is a modern method of solving problems on a computer. Conceptually computer programming has presently been fully shaped as a science, a circumstance that fundamentally changes the very approach to education for programming. The structured programming philosophy forms the basis for understanding the programming process as a formalized problem solution process. Structured programing is based on the basic programming language PASCAL which was developed for teaching to computer programming. This language clearly reflects the capabilities of a computer as a tool; they are necessary and sufficient for solving problems of any complexity because the PASCAL language strictly defines the set of data types supporting the problem solving process. Education for structured programming is learning the technology of solving problems on a computer which is the basis of computer literacy of any higher school graduate. The top-down program development method, which includes the rules for aggregation and decomposition of sub-problems, has been laid at the heart of this technology. In learning computer programming as a technological process for solving problems, a student should gain skills of solving problems on a computer and develop an algorithmic way of thinking already at the initial stage of his or her education. This experience will be useful for the future engineer, a specialist on technologies in his or her profession.

The Generation of 3D Trimmed Elements for NURBS-Based Isogeometric Analysis

In conventional 3D NURBS-based isogeometric analysis (IGA), it is required to generate a discretized 3D model from the imported CAD model. Since a CAD file only contains surface information of the 3D object, generation of 3D mesh and trivariate basis functions are required for the IGA. In CAD system, the Boolean difference operation, so-called “trimming” is frequently employed for creating complex objects. To directly utilize the trimming information into analysis, trimmed elements need to be defined and their integration schemes are also needed. In this paper, trimmed elements searching, classification, decomposition and integration rules are presented. In the process, seven types of generalized trimmed elements are defined. Since covering all possible 3D geometries is not possible, three out of seven types of trimmed elements formed by extrusion are treated. The decomposition rule of trimmed elements is introduced and curved tetrahedral cells are adopted to integrate the trimmed elements. For numerical integration of curved tetrahedral cells, 3D NEFEM-like integration scheme has been developed. For the demonstration of the usage of the developed elements, two numerical examples of trimmed volume are treated.

Multiscale fuzzy entropy based on local mean decomposition and Fisher rule for EEG feature extraction in human motion analysis

Electroencephalogram (EEG) is a nonlinear, non-stationary, and random weak signal generated by a large number of neurons. It has great research value and practical significance in artificial intelligence, biomedical engineering and other fields. EEG feature extraction

Hysteretic behavior using the explicit material point method

The material point method (MPM) is an advancement of particle in cell method, in which Lagrangian bodies are discretized by a number of material points that hold all the properties and the state of the material. All internal variables, stress, strain, velocity, etc., which specify the current state, and are required to advance the solution, are stored in the material points. A background grid is employed to solve the governing equations by interpolating the material point data to the grid. The derived momentum conservation equations are solved at the grid nodes and information is transferred back to the material points and the background grid is reset, ready to handle the next iteration. In this work, the standard explicit MPM is extended to account for smooth elastoplastic material behavior with mixed isotropic and kinematic hardening and stiffness and strength degradation. The strains are decomposed into an elastic and an inelastic part according to the strain decomposition rule. To account for the different phases during elastic loading or unloading and smoothening the transition from the elastic to inelastic regime, two Heaviside-type functions are introduced. These act as switches and incorporate the yield function and the hardening laws to control the whole cyclic behavior. A single expression is thus established for the plastic multiplier for the whole range of stresses. This overpasses the need for a piecewise approach and a demanding bookkeeping mechanism especially when multilinear models are concerned that account for stiffness and strength degradation. The final form of the constitutive stress rate–strain rate relation incorporates the tangent modulus of elasticity, which now includes the Heaviside functions and gathers all the governing behavior, facilitating considerably the simulation of nonlinear response in the MPM framework. Numerical results are presented that validate the proposed formulation in the context of the MPM in comparison with finite element method and experimental results.

Knot polynomials for twist satellites

We begin the systematic study of knot polynomials for the twist satellites of a knot, when its strand is substituted by a 2-strand twist knot. This is a generalization of cabling (torus satellites), when the substitute of the strand was a torus knot. We describe a general decomposition of satellite's colored HOMFLY in those of the original knot, where contributing are adjoint and other representations from the “E8-sector”, what makes the story closely related to Vogel's universality. We also point out a problem with lifting the decomposition rule to the level of superpolynomials — it looks like such rule, if any, should be different for positive and negative twistings.

Performance Enhancement of Collaborative Filtering through the Fusion Algorithm of Singular Value Decomposition and Association Rule

Collaborative filtering (CF) is the leading algorithm as a recommendation system. However, the algorithm falls short due to the limitations of sparsity and scalability. Sparsity problem comes when the user has few items purchased or reviewed. Scalability problem occurs under too many users and items. In this study, the limitations of CF are enhanced through the usage of singular value decomposition (SVD) and association rule (AR). AR searches for relevance among items, and SVD decreases the dimensionality of the data to be applied on CF. This hybrid CF algorithm, which is combined with SVD and AR, is compared with other recommendation algorithms. Items which are included in computation were chosen through AR. SVD solved the short falls of data sparsity of CF. Both item-based CF and user-based CF are considered. The hybrid algorithm showed better performance than other recommendation systems under sparsity and scalability problem.

Identification and evaluation of wood price variability in Płock Forest District

The main aim of the research is to evaluate the variability of prices of selected wood assortments in the Płock Forest District. Prices of eight wood types were analysed according to the rules of time series decomposition using the CENSUS II X-11 method. The cycles length was also evaluated by means of Fourier spectral analysis. Data were obtained from the Płock Forest District and covered the years 2004—2014 on a monthly basis. On the basis of the conducted study, it was found that wood prices in the Płock Forest District are characterised by a clear share systematic variability which means that a trend and cyclicality can be distinguished. The results of this research have also shown considerable scale of seasonal and accidental fluctuations in wood prices. The analysis of wood prices showed a growing trend for all assortments, while the dynamics of seasonal fluctuations differed depending on the assortment. Significant intensity of random fluctuations was found, which were characterised by high amplitude of deviations.

Accelerating solutions of one-dimensional unsteady PDEs with GPU-based swept time–space decomposition

The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems require simulations with a level of resolution difficult to achieve in reasonable amounts of time—even in effectively parallelized solvers. Though the scale of the problem relative to available computing power is the greatest impediment to accelerating these applications, significant performance gains can be achieved through careful attention to the details of memory communication and access. The swept time–space decomposition rule reduces communication between sub-domains by exhausting the domain of influence before communicating boundary values. Here we present a GPU implementation of the swept rule, which modifies the algorithm for improved performance on this processing architecture by prioritizing use of private (shared) memory, avoiding interblock communication, and overwriting unnecessary values. It shows significant improvement in the execution time of finite-difference solvers for one-dimensional unsteady PDEs, producing speedups of 2–9× for a range of problem sizes, respectively, compared with simple GPU versions and 7–300× compared with parallel CPU versions. However, for a more sophisticated one-dimensional system of equations discretized with a second-order finite-volume scheme, the swept rule performs 1.2–1.9× worse than a standard implementation for all problem sizes.

Conceptual design of the hybrid hydraulic system based on adjacency matrices operations

This paper presents a new method to describe the selection design of directional control valves in the form of matrix. The directional control valves in hybrid are the basic units to implement the distribution of flow in the hydraulic system. Both the design requirements of the hybrid hydraulic system and the basic units are expressed by the adjacency matrices. Therefore, the selection design of directional control valves is the process to decompose the adjacency matrix of the system into a series of sub-matrices according to the decomposition rules. The defined rules of adjacency matrices are obtained according with the composite physical model of several valves. For obtaining easily the selection design of directional control valves, the library of basic units is established. The style of directional control valves is obtained by matching the sub-matrices with the matrices of basic units. Through configuring the others components, a thorough conceptual design process of the hydraulic system is established. Example is given to illustrate the whole design process in detail.

Tensor product decomposition rules for weight modules over the Hopf–Ore extensions of group algebras

ABSTRACTIn this paper, we investigate the tensor structure of the category of finite- dimensional weight modules over the Hopf–Ore extensions kG(χ−1,a,0) of group algebras kG. The tensor product decomposition rules for all indecomposable weight modules are explicitly given under the assumptions that k is an algebraically closed field of characteristic zero, and the orders of χ and χ(a) are the same.

Relevance via decomposition

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition.

An embedding of the universal Askey–Wilson algebra into [formula omitted

The Askey–Wilson algebras were used to interpret the algebraic structure hidden in the Racah–Wigner coefficients of the quantum algebra Uq(sl2). In this paper, we display an injection of a universal analog △q of Askey–Wilson algebras into Uq(sl2)⊗Uq(sl2)⊗Uq(sl2) behind the application. Moreover we establish the decomposition rules for 3-fold tensor products of irreducible Verma Uq(sl2)-modules and of finite-dimensional irreducible Uq(sl2)-modules into the direct sums of finite-dimensional irreducible △q-modules. As an application, we derive a formula for the Racah–Wigner coefficients of Uq(sl2).

Idiosyncratic (Dis)agreement Patterns: The Structure and Diachrony of Russian Paucal Subjects

ABSTRACTPaucal constructions are unanimously considered one of the most puzzling areas of Russian grammar. The expressions containing lower numerals (dva/dve ‘two’, tri ‘three’, četyre ‘four’, as well as oba/obe ‘both’) display special morphosyntactic properties that have attracted the attention of many scholars. In this paper, we contribute to the debate on Russian paucal expressions in subject function by arguing that their historical development can clarify certain aspects of their synchronic pattern in the modern language. We review the diachronic process leading to the rise of paucal morphology in Russian and account for the morphologically heterogeneous nature of these expressions, coined in the language as a result of a series of historical accidents and adapted later to the language with relative success. In order to account for the synchronic disagreement patterns triggered by lower numerals in subject position (affecting unequally modifiers and verbs), we adopt an approach of featural decomposition and underspecification rules that renders the actual forms obtained in these paucal constructions. As a necessary part of the account, we also give some typological parallels, mainly from other unrelated languages.

A dual-system cooperative co-evolutionary algorithm for satellite equipment layout optimization

This paper develops a new dual-system cooperative co-evolutionary algorithm for multi-modules (or multi-bearing plate) satellite equipment layout optimization problem, based upon the Potter’s cooperative co-evolutionary framework. Firstly, a new dual-system framework based on the Potter’s cooperative co-evolutionary is constructed and then, corresponding system decomposition rule, matrix analysis method and coordination mechanism are presented. Finally, the way of matching algorithms (e.g. evolutionary algorithms and swarm intelligence algorithms) with systems A and B in the dual system is presented. The purpose is to enhance the computational accuracy and robustness of the developed algorithm for satellite equipment layout optimization problem. The experimental results show that the developed algorithm has better computational accuracy and robustness (computational success ratio and standard deviation) as compared with four dual-system algorithms and two single-system algorithms based upon Potter’s cooperative co-evolutionary.

НАУЧНО-МЕТОДИЧЕСКИЕ ВОПРОСЫ ПОДГОТОВКИ СТУДЕНТОВ К ОЛИМПИАДАМ ПО НАЧЕРТАТЕЛЬНОЙ ГЕОМЕТРИИ

Academic Olympics on descriptive geometry are an important form of educational process in conditions when the discipline study’s teaching hours are reduced. The Academic Olympics allow identify talented students and motivate them to find possibilities on solutions for non-standard situations, to promote the formation of such qualities as persistence, endurance, accuracy. The Academic Olympics carrying requires not only organizational measures. Due to a low level of the geometrical knowledge gained at school, students need an additional theoretical training. Without it realizing of young people’s creative potential is impossible. The experience on carrying of the Academic Olympics on descriptive geometry at Bauman Moscow State Technical University and in other higher education institutions of this country allowed develop a technique of students training for such activities. In this paper scientific and methodical questions related to solution for tasks of increased complexity are considered. Simplification of solution algorithm and increase of its visualization can be reached by reduction of metric conditions to affine ones, and them, in turn — to projective ones. The attention in training for the Academic Olympics should be paid to the method of loci. School leavers know only about limited quantity of loci on a plane and have practically no ideas on the elementary loci in space. Therefore studying of loci on a plane and in space is necessary. For the method of loci the essence of simplification, decomposition and increments rules is revealed. If a return problem is solved more simply than a straight one, it is reasonable to use reverse ability method. Often the problem solution becomes simpler when using transformations, in particular, homothety and stretching (compression) transformations. The considered methods are illustrated by specific examples. Assimilation of the methods described in this publication isn't a complete guarantee of students’ success at the Academic Olympics, but, undoubtedly, it will be useful for them as will allow expand knowledge of the subject matter.

Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras

In this paper, we study the tensor product structure of the category of finite dimensional modules over Drinfeld doubles of Taft Hopf algebras. Tensor product decomposition rules for all finite dimensional indecomposable modules are explicitly given.

Finite bending of a multilayered cylindrical nanosector with residual deformations

This paper deals with the universal model describing plane strain bending of a multilayered sector of a cylindrical tube which can have residual deformations as well as nano-scale effects. In order to model the response of the sector at the nano-scale, the Gurtin–Murdoch theory is employed. Residual deformations of the layers, such as prestretch or precompression, are introduced into the model of finite bending using the multiplicative decomposition rule for corresponding deformation gradients. Numerous coupled nonlinear effects exhibited by the sector are discussed.

Partitioning prediction uncertainty in climate-dependent population models.

The science of complex systems is increasingly asked to forecast the consequences of climate change. As a result, scientists are now engaged in making predictions about an uncertain future, which entails the efficient communication of this uncertainty. Here we show the benefits of hierarchically decomposing the uncertainty in predicted changes in animal population size into its components due to structural uncertainty in climate scenarios (greenhouse gas emissions and global circulation models), structural uncertainty in the demographic model, climatic stochasticity, environmental stochasticity unexplained by climate-demographic trait relationships, and sampling variance in demographic parameter estimates. We quantify components of uncertainty surrounding the future abundance of a migratory bird, the greater snow goose (Chen caeruslescens atlantica), using a process-based demographic model covering their full annual cycle. Our model predicts a slow population increase but with a large prediction uncertainty. As expected from theoretical variance decomposition rules, the contribution of sampling variance to prediction uncertainty rapidly overcomes that of process variance and dominates. Among the sources of process variance, uncertainty in the climate scenarios contributed less than 3% of the total prediction variance over a 40-year period, much less than environmental stochasticity. Our study exemplifies opportunities to improve the forecasting of complex systems using long-term studies and the challenges inherent to predicting the future of stochastic systems.