Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta最新文献_第3页

Existence of weak solutions for a $p(x)$-Laplacian equation via topological degree p(x) -拉普拉斯方程的拓扑度弱解的存在性

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-02

M. Ait Hammou, E. Rami

引用次数: 0

The Savage principle and accounting for outcome in single-criterion nonlinear problem under uncertainty 不确定单准则非线性问题的Savage原理及结果的计算

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2022-05-01 DOI: 10.35634/2226-3594-2022-59-03

V. Zhukovskiĭ, L. Zhukovskaya, S. P. Samsonov, L. Smirnova

{"title":"The Savage principle and accounting for outcome in single-criterion nonlinear problem under uncertainty","authors":"V. Zhukovskiĭ, L. Zhukovskaya, S. P. Samsonov, L. Smirnova","doi":"10.35634/2226-3594-2022-59-03","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-59-03","url":null,"abstract":"In the middle of the last century the American mathematician and statistician professor of Michigan University Leonard Savage (1917-1971) and the well-known economist, professor of Zurich University (Switzerland) Jurg Niehans (1919-2007) independently from each other suggested the approach to decision-making in one-criterion problem under uncertainty (OPU), called the principle of minimax regret. This principle along with Wald principle of guaranteed result (maximin) is playing the most important role in guaranteed under uncertainty decision-making in OPU. The main role in the principle of minimax regret is carrying out the regret function, which determines the Niehans-Savage risk in OPU. Such risk has received the broad extension in practical problems during last years. In the present article we suggest one of possible approaches to finding decision in OPU from the position of a decision-maker, which simultaneously tries to increase the payoff (outcome) and to reduce the risk (i.e., “to kill two birds with one stone in one throw”). As an application, an explicit form of such a solution was immediately found for a linear-quadratic variant of the OPU of a fairly general form.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91217652","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}

引用次数: 0

One task of routing jobs in high radiation conditions 在高辐射条件下布线作业的一个任务

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2021-11-01 DOI: 10.35634/2226-3594-2021-58-06

A. G. Chentsov, A. Chentsov, A. Sesekin

引用次数: 0

On a discrete game problem with non-convex control vectograms 一类具有非凸控制向量的离散博弈问题

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2021-11-01 DOI: 10.35634/2226-3594-2021-58-03

I. V. Izmestyev, V. I. Ukhobotov

引用次数: 0

On the construction of resolving control in the problem of getting close at a fixed time moment 论在固定时刻接近问题中解决控制的构建

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2021-11-01 DOI: 10.35634/2226-3594-2021-58-05

V. Ushakov, A. Ushakov, O. Kuvshinov

引用次数: 0

On the route construction in changing environments using solutions of the eikonal equation 利用eikonal方程解研究变化环境下的路线建设

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2021-11-01 DOI: 10.35634/2226-3594-2021-58-04

A. Kazakov, A. Lempert

引用次数: 0

A method for estimating the statistical error of the solution in the inverse spectroscopy problem 反演光谱问题解的统计误差估计方法

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2021-11-01 DOI: 10.35634/2226-3594-2021-58-01

T. M. Bannikova, V. Nemtsov, N. Baranova, G. Konygin, O. Nemtsova

{"title":"A method for estimating the statistical error of the solution in the inverse spectroscopy problem","authors":"T. M. Bannikova, V. Nemtsov, N. Baranova, G. Konygin, O. Nemtsova","doi":"10.35634/2226-3594-2021-58-01","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-01","url":null,"abstract":"A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81208954","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}

引用次数: 0

On the spectrum of a multidimensional periodic magnetic Shrödinger operator with a singular electric potential 具有奇异电位的多维周期磁Shrödinger算子的谱

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2021-11-01 DOI: 10.35634/2226-3594-2021-58-02

L. I. Danilov

{"title":"On the spectrum of a multidimensional periodic magnetic Shrödinger operator with a singular electric potential","authors":"L. I. Danilov","doi":"10.35634/2226-3594-2021-58-02","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-02","url":null,"abstract":"We prove absolute continuity of the spectrum of a periodic $n$-dimensional Schrödinger operator for $ngeqslant 4$. Certain conditions on the magnetic potential $A$ and the electric potential $V+sum f_jdelta_{S_j}$ are supposed to be fulfilled. In particular, we can assume that the following conditions are satisfied.\u0000(1) The magnetic potential $Acolon{mathbb{R}}^nto{mathbb{R}}^n$ either has an absolutely convergent Fourier series or belongs to the space $H^q_{mathrm{loc}}({mathbb{R}}^n;{mathbb{R}}^n)$, $2q>n-1$, or to the space $C({mathbb{R}}^n;{mathbb{R}}^n)cap H^q_{mathrm{loc}}({mathbb{R}}^n;{mathbb{R}}^n)$, $2q>n-2$.\u0000(2) The function $Vcolon{mathbb{R}}^ntomathbb{R}$ belongs to Morrey space ${mathfrak{L}}^{2,p}$, $pin big(frac{n-1}{2},frac{n}{2}big]$, of periodic functions (with a given period lattice), and\u0000$$limlimits_{tauto+0}suplimits_{00$ centered at a point $xin{mathbb{R}}^n$, $B^n_r=B^n_r(0)$, $v(B^n_r)$ is volume of the ball $B^n_r$, $C=C(n,p;A)>0$.\u0000(3) $delta_{S_j}$ are $delta$-functions concentrated on (piecewise) $C^1$-smooth periodic hypersurfaces $S_j$, $f_jin L^p_{mathrm{loc}}(S_j)$, $j=1,ldots,m$. Some additional geometric conditions are imposed on the hypersurfaces $S_j$, and these conditions determine the choice of numbers $pgeqslant n-1$. In particular, let hypersurfaces $S_j$ be $C^2$-smooth, the unit vector $e$ be arbitrarily taken from some dense set of the unit sphere $S^{n-1}$ dependent on the magnetic potential $A$, and the normal curvature of the hypersurfaces $S_j$ in the direction of the unit vector $e$ be nonzero at all points of tangency of the hypersurfaces $S_j$ and the lines ${x_0+tecolon tinmathbb{R}}$, $x_0in{mathbb{R}}^n$. Then we can choose the number $p>frac{3n}{2}-3$, $ngeqslant 4$.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82204150","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}

引用次数: 1

Numerical method for fractional diffusion-wave equations with functional delay 具有泛函时滞的分数阶扩散波方程的数值方法

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2021-05-01 DOI: 10.35634/2226-3594-2021-57-07

V. Pimenov, E. Tashirova

引用次数: 0

Spectrum assignment in linear systems with several commensurate lumped and distributed delays in state by means of static output feedback 基于静态输出反馈的具有若干相应集中和分布状态延迟的线性系统的频谱分配

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Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2020-11-01 DOI: 10.35634/2226-3594-2020-56-01

V. Zaitsev, I. G. Kim

引用次数: 2