Mathematical Notes最新文献_第3页

On One Type of Oscillatory Solutions of a Nonautonomous System with Relay Hysteresis 论带有中继滞后的非自主系统的一种振荡解

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050080

V. V. Yevstafyeva

{"title":"On One Type of Oscillatory Solutions of a Nonautonomous System with Relay Hysteresis","authors":"V. V. Yevstafyeva","doi":"10.1134/s0001434624050080","DOIUrl":"https://doi.org/10.1134/s0001434624050080","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3> We consider an (n)-dimensional system of first-order ordinary differential equations with a constant matrix having real, simple, and nonzero eigenvalues, with a discontinuous nonlinearity of two-position relay type with positive hysteresis and a continuous bounded perturbation function. We study continuous two-point oscillatory solutions with a certain period for the representative point to be returned to the switching hyperplane in the state space. When solving the Cauchy problem with initial condition at the switching point, we use the fitting method. We construct a system of transcendental equations for the switching instants and points. We prove a criterion for the existence and uniqueness of a solution with some fixed return period. For a system in the canonical form with diagonal matrix and with feedback vector of a special form, we obtain conditions for the solvability of a system of transcendental equations for the first switching instant for a given return period and formulas for the switching points. For a three-dimensional system, we give a numerical example to illustrate the theoretical results. ","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Yu. N. Subbotin’s Method in the Problem of Extremal Interpolation in the Mean in the Space $$L_p(mathbb R)$$ with Overlapping Averaging Intervals Yu.苏博廷方法在具有重叠平均区间的 $$L_p(mathbb R)$$ 空间中平均值的极值插值问题中的应用

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050365

V. T. Shevaldin

引用次数: 0

On the Existence of a Nonextendable Solution of the Cauchy problem for a $$(1+1)$$ -Dimensional Thermal-Electrical Model 论$$(1+1)$$-维热-电模型的考希问题非扩展解的存在性

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050018

M. V. Artem’eva, M. O. Korpusov

引用次数: 0

An Approach to Studying Leontief Type Stochastic Differential Equations 研究 Leontief 型随机微分方程的方法

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050110

E. Yu. Mashkov

{"title":"An Approach to Studying Leontief Type Stochastic Differential Equations","authors":"E. Yu. Mashkov","doi":"10.1134/s0001434624050110","DOIUrl":"https://doi.org/10.1134/s0001434624050110","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3> In a finite-dimensional space, we consider a linear stochastic differential equation in Itô form with a singular constant matrix on the left-hand side. Taking into account various economic applications of such equations, they are classified as Leontief type equations, since under some additional assumptions, a deterministic analog of the equation in question describes the famous Leontief input–output balance model taking into account reserves. In the literature, these systems are more often called differential–algebraic or descriptor systems. In general, to study this type of equations, one needs higher-order derivatives of the right-hand side. This means that one must consider derivatives of the Wiener process, which exist in the generalized sense. In the previous papers, these equations were studied using the technique of Nelson mean derivatives of random processes, whose description does not require generalized functions. It is well known that mean derivatives depend on the (sigma)-algebra used to find them. In the present paper, the study of this equation is carried out using mean derivatives with respect to a new (sigma)-algebra that was not considered in the previous papers. ","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Study on Strongly Lacunary Ward Continuity in 2-Normed Spaces 关于 2 规范空间中强空白区连续性的研究

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050262

Sibel Ersan

引用次数: 0

Stechkin’s Problem on Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line 斯泰奇金关于半线上均匀规范微分算子的逼近问题

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050225

R. R. Akopyan, V. V. Arestov, V. G. Timofeev

引用次数: 0

On a Property of Quasi-Kähler Manifolds 关于准凯勒流形的一个性质

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s000143462405002x

G. A. Banaru, M. B. Banaru

引用次数: 0

The Stationary Navier–Stokes–Boussinesq System with a Regularized Dissipation Function 具有正则耗散函数的静态 Navier-Stokes-Boussinesq 系统

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050031

E. S. Baranovskii

引用次数: 0

On Shemetkov’s Question about the $$mathfrak{F}$$ -Hypercenter 关于谢梅特科夫提出的 $$mathfrak{F}$ - 超中心问题

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050134

V. I. Murashka

引用次数: 0

Unique Response Roman Domination Versus 2-Packing Differential in Complementary Prisms 互补棱镜中的独特响应罗马统治与 2-Packing 差异

IF 0.6 4区数学

Mathematical Notes Pub Date : 2024-07-15 DOI: 10.1134/s0001434624050237

Z. N. Berberler, M. Çerezci

{"title":"Unique Response Roman Domination Versus 2-Packing Differential in Complementary Prisms","authors":"Z. N. Berberler, M. Çerezci","doi":"10.1134/s0001434624050237","DOIUrl":"https://doi.org/10.1134/s0001434624050237","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3> Let (G = (V,E)) be a graph of order (n). For (S subseteq V(G)), the set (N_e(S)) is defined as the external neighborhood of (S) such that all vertices in (V(G)backslash S) have at least one neighbor in (S). The differential of (S) is defined to be (partial(S)=|N_e(S)|-|S|), and the 2-packing differential of a graph is defined as $$partial_{2p}(G) =max{partial(S)colon S subseteq V(G) text{ is a 2-packing}}.$$ A function (fcolon V(G) to {0,1,2}) with the sets (V_0,V_1,V_2), where $$V_i ={vin V(G)colon f(v) = i},qquad i in {0,1,2},$$ is a unique response Roman dominating function if (x in V_0 ) implies that (| N( x ) cap V_2 | = 1) and (x in V_1 cup V_2 ) implies that (N( x ) cap V_2 = emptyset). The unique response Roman domination number of (G), denoted by (mu_R(G)), is the minimum weight among all unique response Roman dominating functions on (G). Let (bar{G}) be the complement of a graph (G). The complementary prism (Gbar {G}) of (G) is the graph formed from the disjoint union of (G) and (bar {G}) by adding the edges of a perfect matching between the respective vertices of (G) and (bar {G}). The present paper deals with the computation of the 2-packing differential and the unique response Roman domination of the complementary prisms (Gbar {G}) by the use of a proven Gallai-type theorem. Particular attention is given to the complementary prims of special types of graphs. Furthermore, the graphs (G) such that (partial_{2p} ( Gbar G)) and (mu _R(Gbar G)) are small are characterized. ","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":"48 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0