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Siberian Advances in Mathematics最新文献

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Generalizations of o-Minimality o-Minimality 的一般化
Siberian Advances in Mathematics Pub Date : 2024-09-18 DOI: 10.1134/s1055134424030052
K. Zh. Kudaibergenov
{"title":"Generalizations of o-Minimality","authors":"K. Zh. Kudaibergenov","doi":"10.1134/s1055134424030052","DOIUrl":"https://doi.org/10.1134/s1055134424030052","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We introduce generalizations of o-minimality (<span>(lambda )</span>-o-minimality and weak <span>(lambda )</span>-p.o.-lin-minimality) and study their properties.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269530","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
Necessary Conditions for Existence of Solutions of a Certain Pseudohyperbolic System of Equations 某伪双曲方程组解存在的必要条件
Siberian Advances in Mathematics Pub Date : 2024-09-18 DOI: 10.1134/s1055134424030027
L. N. Bondar, S. B. Mingnarov
{"title":"Necessary Conditions for Existence of Solutions of a Certain Pseudohyperbolic System of Equations","authors":"L. N. Bondar, S. B. Mingnarov","doi":"10.1134/s1055134424030027","DOIUrl":"https://doi.org/10.1134/s1055134424030027","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In the present article, we consider the Cauchy problem for a pseudohyperbolic system that\u0000arises in modeling flexural-torsional vibrations of an elastic rod. For the function on\u0000the right-hand side of the system, we suggest necessary conditions for existence of a solution of\u0000the Cauchy problem in the Sobolev space with exponential weight.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266717","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
Unique Reconstruction of a Lambertian Optical Surface from Images 从图像中重建朗伯光学表面的独特方法
Siberian Advances in Mathematics Pub Date : 2024-09-18 DOI: 10.1134/s1055134424030036
E. Yu. Derevtsov
{"title":"Unique Reconstruction of a Lambertian Optical Surface from Images","authors":"E. Yu. Derevtsov","doi":"10.1134/s1055134424030036","DOIUrl":"https://doi.org/10.1134/s1055134424030036","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Within the framework of inverse problems of photometry, we study questions on\u0000reconstruction of the spatial location and luminosity of a Lambertian optical surface from its\u0000images obtained with the use of a small number of optical systems. We study causes of ambiguity\u0000in reconstruction of the location of such a surface. We suggest criteria for existence of a unique\u0000solution of the inverse problem on reconstruction of a luminous surface from three images for\u0000general weight functions and apply the results to specific classes of weight functions that model\u0000the degree of transparency of the medium (including its absorption or scattering).\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266720","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
Characterization of Holomorphic Functions by Zero Spherical Means 用零球面手段表征全形函数
Siberian Advances in Mathematics Pub Date : 2024-09-18 DOI: 10.1134/s1055134424030076
N. P. Volchkova, Vit. V. Volchkov
{"title":"Characterization of Holomorphic Functions by Zero Spherical Means","authors":"N. P. Volchkova, Vit. V. Volchkov","doi":"10.1134/s1055134424030076","DOIUrl":"https://doi.org/10.1134/s1055134424030076","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We continue to study the holomorphy problem for functions whose contour integrals over\u0000circles vanish. We consider the case in which a function <span>(f )</span> is defined on a deleted ball <span>(mathcal {D} )</span> in <span>(mathbb {C}^n)</span>\u0000(without its center) and integrate over all spheres of two fixed radii inside <span>(mathcal {D} )</span>. For <span>(fin C^{infty }(mathcal {D}) )</span>, we find conditions on the radii and size of\u0000<span>(mathcal {D} )</span> implying that <span>(f )</span> is a holomorphic function. We also show that these\u0000conditions cannot be weakened in the general case.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266721","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
The Structure of the Normalizers of Maximal Toruses in Lie-Type Groups 李型群中最大环的归一化结构
Siberian Advances in Mathematics Pub Date : 2024-09-18 DOI: 10.1134/s1055134424030040
A. A. Galt
{"title":"The Structure of the Normalizers of Maximal Toruses in Lie-Type Groups","authors":"A. A. Galt","doi":"10.1134/s1055134424030040","DOIUrl":"https://doi.org/10.1134/s1055134424030040","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The main aim of the present article is to survey results on the structure of the normalizers\u0000of maximal toruses in Lie-type groups. In particular, we present results on splitting of\u0000the normalizer of a maximal torus and, in the case of exceptional groups, on the minimal order of\u0000a lift in the corresponding normalizer for elements of the Weyl group.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266718","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
Identification of Difference Equations by Observations of Solutions with Perturbations from a Linear Manifold 通过观测具有线性湍流扰动的解来识别差分方程
Siberian Advances in Mathematics Pub Date : 2024-09-18 DOI: 10.1134/s1055134424030064
A. A. Lomov
{"title":"Identification of Difference Equations by Observations of Solutions with Perturbations from a Linear Manifold","authors":"A. A. Lomov","doi":"10.1134/s1055134424030064","DOIUrl":"https://doi.org/10.1134/s1055134424030064","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the Prony identification problem for coefficients of an autonomous difference\u0000equation by observations of noisy solutions with unknown additive perturbations from an arbitrary\u0000linear manifold. We establish a “projectivity” property of the variational objective function. For\u0000two main types of equations, we obtain criteria and sufficient conditions for identifiability.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266719","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
Limit Theorems for Partial Sum Processes of Moving Averages Based on Heterogeneous Processes 基于异质过程的移动平均数偏和过程的极限定理
Siberian Advances in Mathematics Pub Date : 2024-09-18 DOI: 10.1134/s1055134424030015
N. S. Arkashov
{"title":"Limit Theorems for Partial Sum Processes of Moving Averages Based on Heterogeneous Processes","authors":"N. S. Arkashov","doi":"10.1134/s1055134424030015","DOIUrl":"https://doi.org/10.1134/s1055134424030015","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A class of partial sum processes based on a sequence of observations having the structure\u0000of finite-order moving averages is studied. The random component of this sequence is formed\u0000using a heterogeneous process in discrete time, while the non-random component is formed using a\u0000regularly varying function at infinity. The heterogeneous process with discrete time is defined as a\u0000power transform of partial sums of a certain stationary sequence. An approximation of the\u0000random processes from the above-mentioned class is studied by random processes defined as the\u0000convolution of a power transform of the fractional Brownian motion with a power function.\u0000Sufficient conditions for <span>(C)</span>-convergence in the\u0000Donsker invariance principle are obtained.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266716","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
Wormholes, Superfast Computations, and Selivanov’s Theorem 虫洞、超快计算和塞利瓦诺夫定理
Siberian Advances in Mathematics Pub Date : 2024-05-31 DOI: 10.1134/s1055134424020020
O. Kosheleva, V. Kreinovich
{"title":"Wormholes, Superfast Computations, and Selivanov’s Theorem","authors":"O. Kosheleva, V. Kreinovich","doi":"10.1134/s1055134424020020","DOIUrl":"https://doi.org/10.1134/s1055134424020020","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> While modern computers are fast, there are still many practical problems that require\u0000even faster computers. It turns out that on the fundamental level, one of the main factors limiting\u0000computation speed is the fact that, according to modern physics, the speed of all processes is\u0000limited by the speed of light. Good news is that while the corresponding limitation is very severe\u0000in Euclidean geometry, it can be more relaxed in (at least some) non-Euclidean spaces, and,\u0000according to modern physics, the physical space is not Euclidean. The differences from Euclidean\u0000character are especially large on micro-level, where quantum effects need to be taken into account.\u0000To analyze how we can speed up computations, it is desirable to reconstruct the actual distance\u0000values – corresponding to all possible paths – from the values that we actually measure – which\u0000correspond only to macro-paths and thus, provide only the upper bound for the distance. In our\u0000previous papers – including our joint paper with Victor Selivanov – we provided an explicit\u0000formula for such a reconstruction. But for this formula to be useful, we need to analyze how\u0000algorithmic is this reconstructions. In this paper, we show that while in general, no reconstruction\u0000algorithm is possible, an algorithm <i>is</i> possible if we\u0000impose a lower limit on the distances between steps in a path. So, hopefully, this can help to\u0000eventually come up with faster computations.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192963","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 Local Stability in the Complete Prony Problem 论完全普罗尼问题的局部稳定性
Siberian Advances in Mathematics Pub Date : 2024-05-31 DOI: 10.1134/s1055134424020044
A. A. Lomov
{"title":"On Local Stability in the Complete Prony Problem","authors":"A. A. Lomov","doi":"10.1134/s1055134424020044","DOIUrl":"https://doi.org/10.1134/s1055134424020044","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the variational Prony problem on approximating observations\u0000<span>(x )</span> by the sum of exponentials. We find critical points\u0000and the second derivatives of the implicit function <span>(theta )</span> that relates perturbation in <span>(x )</span> with the corresponding exponents. We suggest\u0000upper bounds for the second order increments and describe the domain, where the accuracy of\u0000a linear approximation of <span>(theta )</span> is acceptable.\u0000We deduce lower estimates of the norm of deviation of <span>(theta )</span> for small perturbations in <span>(x )</span>. We compare our estimates of this norm with\u0000upper bounds obtained with the use of Wilkinson’s inequality.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192941","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
Direct and Inverse Embedding Theorems for Different Dimensions for a Class of Multianisotropic Sobolev Spaces 一类多向异性索波列夫空间不同维度的直接和反嵌入定理
Siberian Advances in Mathematics Pub Date : 2024-05-31 DOI: 10.1134/s1055134424020019
M. A. Khachaturyan
{"title":"Direct and Inverse Embedding Theorems for Different Dimensions for a Class of Multianisotropic Sobolev Spaces","authors":"M. A. Khachaturyan","doi":"10.1134/s1055134424020019","DOIUrl":"https://doi.org/10.1134/s1055134424020019","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a class of completely regular polyhedrons <span>(mathfrak {N} )</span> and prove direct and inverse embedding theorems\u0000for different dimensions (i.e., theorems on the traces) for functions in the Sobolev multianisotropic\u0000space <span>( W^{mathfrak {N}}_2(mathbb {R}^3))</span>.\u0000</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192903","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
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