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Kinematic structure of planar mechanisms addresses the study of attributes determined exclusively by the joining pattern among the links forming a mechanism. The system group classification is central to the kinematic structure and consists of determining a sequence of kinematically and statically independent-simple chains which represent a modular basis for the kinematics and force analysis of the mechanism. This article presents a novel graph-based algorithm for structural analysis of planar mechanisms with closed-loop kinematic structure which determines a sequence of modules (Assur groups) representing the topology of the mechanism. The computational complexity analysis and proof of correctness of the implemented algorithm are provided. A case study is presented to illustrate the results of the devised method. © 2016, Springer Science+Business Media Dordrecht.

We review second-order system of coupled heat-diffusion equations. The system under consideration contains several arbitrary elements the forms of which are specified via the method of group classification based on the use of low-dimensional Lie algebras. We collect and present several results.

The paper describes the methodology of group classification and prediction the academic performance of the first-year students during the first trimester of education by building a decision tree based on the passing of the Unified State Exam (USE), В работе описывается методика групповой классификации и прогнозирования успеваемости студентов-первокурсников в течение первого триместра обучения с помощью построения дерева принятия решений на основе результатов сдачи Единого Государственного Экзамена (ЕГЭ)

The paper discusses the influence of such factors as the results of the Unified State Examination on the academic performance of the first-year students throughout the school year. It uses the technique of grouping students according to their level of performance, В работе рассматривается вопрос о влиянии такого фактора как результаты единого государственного экзамена на успеваемость студентов-первокурсников в течение всего учебного года. При этом используется методика группировки студентов по уровню их успеваемости

A complete group classification for the Klein-Gordon equation is presented. Symmetry generators, up to equivalence transformations, are calculated for each f (u) when the principal Lie algebra extends. Further, considered equation is investigated by using Noether approach for the general case n  2. Conserved quantities are computed for each calculated Noether operator. At the end, a brief conclusion is presented.

We consider a family of equations with two free functional parameters containing the classical Black–Scholes model, Schönbucher–Wilmott model, Sircar–Papanicolaou equation for option pricing as partial cases. A five-dimensional group of equivalence transformations is calculated for that family. That group is applied to a search for specifications' parameters specifications corresponding to additional symmetries of the equation. Seven pairs of specifications are found.

In his extensive work of 1884 on the group classification of ordinary differential equations Lie performed, inter alia, the group classification of the particular type of the second-order equations y″ = F (x, y). In the present paper we extend Lie's classification to the third-order equations y‴ = F (x, y, y′).

We review second-order system of coupled heat-diffusion equations. The system under consideration contains several arbitrary elements the forms of which are specified via the method of group classification based on the use of low-dimensional Lie algebras. We collect and present several results.

We review second-order system of coupled heat-diffusion equations. The system under consideration contains several arbitrary elements the forms of which are specified via the method of group classification based on the use of low-dimensional Lie algebras. We collect and present several results.

The present paper solves completely the problem of the group classification of nonlinear heat-conductivity equations of the form u(t)=F(t,x,u,u(x))u(xx)+G(t,x,u,u(x)). We have proved, in particular, that the above class contains no nonlinear equations whose invariance algebra has dimension more than five. Furthermore, we have proved that there are two, thirty-four, thirty-five, and six inequivalent equations admitting one-, two-, three-, four- and five-dimensional Lie algebras, respectively. Since the procedure which we use relies heavily upon the theory of abstract Lie algebras of low dimension, we give a detailed account of the necessary facts. This material is dispersed in the literature and is not fully available in English. After this algebraic part we give a detailed description of the method and then we derive the forms of inequivalent invariant evolution equations, and compute the corresponding maximal symmetry algebras. The list of invariant equations obtained in this way contains (up to a local change of variables) all the previously-known invariant evolution equations belonging to the class of partial differential equations under study.