Pub Date : 2019-11-01DOI: 10.20537/2226-3594-2019-54-05
T. Tinyukova, Y. Chuburin
{"title":"Andreev reflection in the p-wave superconductor–normal metal contact","authors":"T. Tinyukova, Y. Chuburin","doi":"10.20537/2226-3594-2019-54-05","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-54-05","url":null,"abstract":"","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73854524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-01DOI: 10.20537/2226-3594-2019-54-09
T. Yuldashev
{"title":"Spectral singularities of solutions to a boundary-value problem for the Fredholm integro-differential equation of the second order with reflection of argument","authors":"T. Yuldashev","doi":"10.20537/2226-3594-2019-54-09","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-54-09","url":null,"abstract":"","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79926000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-01DOI: 10.20537/2226-3594-2019-54-06
V. Ushakov, A. Ershov, M. Pershakov
{"title":"On one addition to evaluation by L. S. Pontryagin of the geometric difference of sets in a plane","authors":"V. Ushakov, A. Ershov, M. Pershakov","doi":"10.20537/2226-3594-2019-54-06","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-54-06","url":null,"abstract":"","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84076963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-01DOI: 10.20537/2226-3594-2019-54-02
E. Zhukovskiy, W. Merchela
{"title":"On the continuous dependence on the parameter of the set of solutions of the operator equation","authors":"E. Zhukovskiy, W. Merchela","doi":"10.20537/2226-3594-2019-54-02","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-54-02","url":null,"abstract":"","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73338945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-01DOI: 10.20537/2226-3594-2019-54-03
A. Lipin
{"title":"On a problem related to second-order Diophantine equations","authors":"A. Lipin","doi":"10.20537/2226-3594-2019-54-03","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-54-03","url":null,"abstract":"","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86134731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-05DOI: 10.20537/2226-3594-2019-53-07
A. Kolinichenko, L. Ryashko
In this paper, a distributed Brusselator model with diffusion is investigated. It is well known that this model undergoes both Andronov-Hopf and Turing bifurcations. It is shown that in the parametric zone of diffusion instability the model generates a variety of stable spatially nonhomogeneous structures (patterns). This system exhibits a phenomenon of the multistability with the diversity of stable spatial structures. At the same time, each pattern has its unique parametric range, on which it may be observed. The focus is on analysis of stochastic phenomena of pattern formation and transitions induced by small random perturbations. Stochastic effects are studied by the spatial modality analysis. It is shown that the structures possess different degrees of stochastic sensitivity.
{"title":"Modality analysis of patterns in reaction-diffusion systems with random perturbations","authors":"A. Kolinichenko, L. Ryashko","doi":"10.20537/2226-3594-2019-53-07","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-53-07","url":null,"abstract":"In this paper, a distributed Brusselator model with diffusion is investigated. It is well known that this model undergoes both Andronov-Hopf and Turing bifurcations. It is shown that in the parametric zone of diffusion instability the model generates a variety of stable spatially nonhomogeneous structures (patterns). This system exhibits a phenomenon of the multistability with the diversity of stable spatial structures. At the same time, each pattern has its unique parametric range, on which it may be observed. The focus is on analysis of stochastic phenomena of pattern formation and transitions induced by small random perturbations. Stochastic effects are studied by the spatial modality analysis. It is shown that the structures possess different degrees of stochastic sensitivity.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73268102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-05DOI: 10.20537/2226-3594-2019-53-11
Ли Лу
It is well known that the decomposition of injective modules over noetherian rings is one of the most aesthetic and important results in commutative algebra. Our aim is to prove similar results for graded noetherian rings. In this paper, we will study the structure theorem for $gr$-injective modules over $gr$-noetherian $G$-graded commutative rings, give a definition of the $gr$-Bass numbers, and study their properties. We will show that every $gr$-injective module has an indecomposable decomposition. Let $R$ be a $gr$-noetherian graded ring and $M$ be a $gr$-finitely generated $R$-module, we will give a formula for expressing the Bass numbers using the functor $Ext$. We will define the section functor $Gamma_{V}$ with support in a specialization-closed subset $V$ of $Spec^{gr}(R)$ and the abstract local cohomology functor. Finally, we will show that a left exact radical functor $F$ is of the form $Gamma_V$ for a specialization-closed subset $V$.
{"title":"Structural theorem for gr-injective modules over gr-noetherian G-graded commutative rings and local cohomology functors","authors":"Ли Лу","doi":"10.20537/2226-3594-2019-53-11","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-53-11","url":null,"abstract":"It is well known that the decomposition of injective modules over noetherian rings is one of the most aesthetic and important results in commutative algebra. Our aim is to prove similar results for graded noetherian rings. In this paper, we will study the structure theorem for $gr$-injective modules over $gr$-noetherian $G$-graded commutative rings, give a definition of the $gr$-Bass numbers, and study their properties. We will show that every $gr$-injective module has an indecomposable decomposition. Let $R$ be a $gr$-noetherian graded ring and $M$ be a $gr$-finitely generated $R$-module, we will give a formula for expressing the Bass numbers using the functor $Ext$. We will define the section functor $Gamma_{V}$ with support in a specialization-closed subset $V$ of $Spec^{gr}(R)$ and the abstract local cohomology functor. Finally, we will show that a left exact radical functor $F$ is of the form $Gamma_V$ for a specialization-closed subset $V$.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88290979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-01DOI: 10.20537/2226-3594-2019-53-06
I. Zykov
In this paper, we consider the problem of constructing external estimates of reachable sets as a level set of a certain differentiable Lyapunov-Bellman function (depending only on the state vector) for a control system with an integral control constraint. In particular, with its suitable choice, one can obtain ellipsoidal and rectangular estimates. The proposed constructions are based on integral estimates, the maximum solution, and the comparison principle for systems of differential inequalities. By using time in the arguments of the Lyapunov-Bellman function, it is possible to obtain more accurate estimates. In the linear nonstationary case, the latter can coincide with the set of reachability. A number of illustrative examples for nonlinear systems are given.
{"title":"On external estimates of reachable sets of control systems with integral constraints","authors":"I. Zykov","doi":"10.20537/2226-3594-2019-53-06","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-53-06","url":null,"abstract":"In this paper, we consider the problem of constructing external estimates of reachable sets as a level set of a certain differentiable Lyapunov-Bellman function (depending only on the state vector) for a control system with an integral control constraint. In particular, with its suitable choice, one can obtain ellipsoidal and rectangular estimates. The proposed constructions are based on integral estimates, the maximum solution, and the comparison principle for systems of differential inequalities. By using time in the arguments of the Lyapunov-Bellman function, it is possible to obtain more accurate estimates. In the linear nonstationary case, the latter can coincide with the set of reachability. A number of illustrative examples for nonlinear systems are given.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85656363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-01DOI: 10.20537/2226-3594-2019-53-09
P. Lebedev, A. A. Uspenskii
For the development of analytical and numerical algorithms for constructing nonsmooth solutions of optimal control problems, procedures are proposed for constructing scattering curves for a single class of control velocity problems. We consider the reduction problems for a minimal time of solutions of a dynamical system with a circular velocity vectogram for the case where the target set is generally nonconvex, and its boundary has points at which the curvature smoothness is violated. These points are referred to as pseudovertices, the characteristic points of the target set, which are responsible for the occurrence of the singularity of the optimal result function. When forming a proper reparameterization (in this case, taking into account the geometry of the velocity vector diagram) of the arc of the boundary of the target set containing a pseudovertex, the scattering curve is constructed as an integral curve. Moreover, the initial conditions of the corresponding Cauchy problem are determined by the properties of the pseudovertex. One of the numerical characteristics of the pseudovertex, the pseudovertex marker, determines the initial velocity of the material point describing a smooth portion of the scattering curve. This approach to the identification and construction (in analytical or numerical form) of singular curves was previously substantiated for a number of cases of a target boundary that are different in the order of smoothness. It should be emphasized that the case considered in this paper is the most specific, in particular, because of the revealed connection between the dynamic problem and the problem of polynomial algebra. It is proved that the pseudovertex marker is the nonpositive root of some third-order polynomial whose coefficients are determined by the one-sided derivatives of curvatures of the pseudovertex of the target set. The effectiveness of the developed theoretical methods and numerical procedures is illustrated by specific examples.
{"title":"Construction of a solution to a velocity problem in the case of violation of the smoothness of the curvature of the target set boundary","authors":"P. Lebedev, A. A. Uspenskii","doi":"10.20537/2226-3594-2019-53-09","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-53-09","url":null,"abstract":"For the development of analytical and numerical algorithms for constructing nonsmooth solutions of optimal control problems, procedures are proposed for constructing scattering curves for a single class of control velocity problems. We consider the reduction problems for a minimal time of solutions of a dynamical system with a circular velocity vectogram for the case where the target set is generally nonconvex, and its boundary has points at which the curvature smoothness is violated. These points are referred to as pseudovertices, the characteristic points of the target set, which are responsible for the occurrence of the singularity of the optimal result function. When forming a proper reparameterization (in this case, taking into account the geometry of the velocity vector diagram) of the arc of the boundary of the target set containing a pseudovertex, the scattering curve is constructed as an integral curve. Moreover, the initial conditions of the corresponding Cauchy problem are determined by the properties of the pseudovertex. One of the numerical characteristics of the pseudovertex, the pseudovertex marker, determines the initial velocity of the material point describing a smooth portion of the scattering curve. This approach to the identification and construction (in analytical or numerical form) of singular curves was previously substantiated for a number of cases of a target boundary that are different in the order of smoothness. It should be emphasized that the case considered in this paper is the most specific, in particular, because of the revealed connection between the dynamic problem and the problem of polynomial algebra. It is proved that the pseudovertex marker is the nonpositive root of some third-order polynomial whose coefficients are determined by the one-sided derivatives of curvatures of the pseudovertex of the target set. The effectiveness of the developed theoretical methods and numerical procedures is illustrated by specific examples.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82192870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-01DOI: 10.20537/2226-3594-2019-53-08
S. Kopysov, I. Kadyrov, A. Novikov
{"title":"Resource efficient finite element computing on multicore architectures","authors":"S. Kopysov, I. Kadyrov, A. Novikov","doi":"10.20537/2226-3594-2019-53-08","DOIUrl":"https://doi.org/10.20537/2226-3594-2019-53-08","url":null,"abstract":"","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73780331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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