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SYMMETRIC FINITE REPRESENTABILITY OF ℓp IN ORLICZ SPACES ORLICZ空间中p的对称有限可表示性
Vestnik of Samara University. Natural Science Series Pub Date : 2021-08-17 DOI: 10.18287/2541-7525-2020-26-4-15-24
S. V. Astashkin
{"title":"SYMMETRIC FINITE REPRESENTABILITY OF ℓp IN ORLICZ SPACES","authors":"S. V. Astashkin","doi":"10.18287/2541-7525-2020-26-4-15-24","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-4-15-24","url":null,"abstract":"It is well known that a Banach space need not contain any subspace isomorphic to a space ℓp (1 6 p ) or c0 (it was shown by Tsirelson in 1974). At the same time, by the famous Krivines theorem, every Banach space X always contains at least one of these spaces locally, i.e., there exist finite-dimensional subspaces of X of arbitrarily large dimension n which are isomorphic (uniformly) to ℓnp for some 1 6 p or cn0 . In thiscase one says that ℓp (resp. c0) is finitely representable in X. The main purpose of this paper is to give a characterization (with a complete proof) of the set of p such that ℓp is symmetrically finitely representable in a separable Orlicz space.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125032638","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 EFFECT OF METAL ALLOY MICROSTRUCTURE ON THE THICKNESS DISTRIBUTION IN THE CIRCULAR PLATE UNDER THE SUPERPLASTIC BLOW-FORMING 研究了金属合金组织对超塑性吹塑圆板厚度分布的影响
Vestnik of Samara University. Natural Science Series Pub Date : 2021-02-01 DOI: 10.18287/2541-7525-2020-26-2-50-62
T. Beliakova, I. Goncharov
{"title":"THE EFFECT OF METAL ALLOY MICROSTRUCTURE \u0000ON THE THICKNESS DISTRIBUTION IN THE CIRCULAR PLATE UNDER THE SUPERPLASTIC BLOW-FORMING","authors":"T. Beliakova, I. Goncharov","doi":"10.18287/2541-7525-2020-26-2-50-62","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-2-50-62","url":null,"abstract":"The gas-blow forming of sheet specimens under the superplastic conditions is the widespread and intensive developing technological method for metal-forming of modern alloys (mainly on the aluminium and titanium base). The investigation of evolution of the microstructure parameters in the deformation process is necessary to obtain the defect-free constructions with required mechanical properties. In thepresent paper the blow-forming process of the thin circular plate to the hemispherical form is modelled. The stress-strain relations used include the parameters of the grain size and of the hardening depending on theaccumulated plastic strain. It is shown that taking into account the evolution of the microstructure parameters in the superplastic deformation can significantly improve the estimation of the optimal characteristics of the manufacturing process and eventually can provide the most thickness-uniform engineering product.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132722090","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
SEMIGROUPS OF BINARY OPERATIONS AND MAGMA-BASED CRYPTOGRAPHY 二进制运算的半群和基于岩浆的密码
Vestnik of Samara University. Natural Science Series Pub Date : 2020-12-28 DOI: 10.18287/2541-7525-2020-26-1-23-51
V. Tsvetov
{"title":"SEMIGROUPS OF BINARY OPERATIONS AND MAGMA-BASED CRYPTOGRAPHY","authors":"V. Tsvetov","doi":"10.18287/2541-7525-2020-26-1-23-51","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-1-23-51","url":null,"abstract":"In this article, algebras of binary operations as a special case of finitary homogeneous relations algebrasare investigated. The tools of our study are based on unary and associative binary operations acting on theset of ternary relations. These operations are generated by the converse operation and the left-composition ofbinary relations. Using these tools, we are going to define special kinds of ternary relations that correspondto functions, injections, right- and left-total binary relations. Then we obtain criteria for these properties interms of ordered semigroups. Note, that there is an embedding of the semigroup of quasigroups operationsin the semigroup of magmas operation and further in the semigroup of ternary relations. This is similar toembedding the semigroup of bijections in the semigroup of functions and then in the semigroup of binaryrelations. Taking a binary operation as the generator of a cyclic semigroup, we can apply an exponentialsquaring method for the fast computation of its positive integer powers. Given that this is the main methodof public key cryptography, we are adapting the Diffie-Hellman-Merkle key exchange algorithm for magmasas a result.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126840766","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
REFINED ANALYSIS OF STEADY STATE CREEP OF A ROTATING DISK AND A PLATE WITH A CENTRAL HOLE UNDER UNIFORM TENSILE LOAD BY THE QUAZILINEARIZATION METHOD 用准线性化方法对均匀拉伸载荷作用下旋转盘和带孔板的稳态蠕变进行了精细化分析
Vestnik of Samara University. Natural Science Series Pub Date : 2020-12-28 DOI: 10.18287/2541-7525-2020-26-1-78-94
L. Stepanova, R. M. Zhabbarov
{"title":"REFINED ANALYSIS OF STEADY STATE CREEP OF A ROTATING DISK AND A PLATE WITH A CENTRAL HOLE UNDER UNIFORM TENSILE LOAD BY THE QUAZILINEARIZATION METHOD","authors":"L. Stepanova, R. M. Zhabbarov","doi":"10.18287/2541-7525-2020-26-1-78-94","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-1-78-94","url":null,"abstract":"Refined analysis of the steady state creep of a rotating disk and a plate with a central hole under uniformtensile load by the quasilinearization method is presented. It is shown that the high values of the creepexponent in power law constitutive equations require more iterations in the framework of the quasilinearizationmethod in each problem. The approximation solution of the problem for an infinite plate with the circularhole under creep regime is obtained by the quazilinearization method. Four approximations of the solution ofthe nonlinear problems are found. It is shown that with increasing the number of approximations the solutionconverges to the limit numerical solution. It is worth to note that the tangential stress reaches its maximumvalue not at the circular hole but at the internal point of the plate. It is also shown that quazilinearizationmethod is an effective method for nonlinear problems.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"343 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127985231","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
EXTRACTION OF FRACTURE MECHANICS PARAMETERS FROM FEM ANALYSIS: ALGORITHMS AND PROCEDURES 从有限元分析中提取断裂力学参数:算法和程序
Vestnik of Samara University. Natural Science Series Pub Date : 2020-12-28 DOI: 10.18287/2541-7525-2020-26-1-69-77
Y. Bakhareva, A. Mironov, D. Petrova
{"title":"EXTRACTION OF FRACTURE MECHANICS PARAMETERS FROM FEM ANALYSIS: ALGORITHMS AND PROCEDURES","authors":"Y. Bakhareva, A. Mironov, D. Petrova","doi":"10.18287/2541-7525-2020-26-1-69-77","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-1-69-77","url":null,"abstract":"The paper describes new algorithms and procedures proposed for determining fracture mechanicsparameters from finite element analysis using the over deterministic method. The multi-parameter cracktip stress field description is used. The algorithms and procedures based on multi-parameter stress fieldrepresentations in series form are shown to be a powerful tool for reliable and accurate parameterdetermination. The technique is aimed at the determination of coefficients of the Williams series expansionfrom finite element analysis and is based on the over deterministic approach. The methodology is illustratedand applied to several cases of cracked specimens. Examples are presented for crack-tip fields recorded usingdigital photoelasticity. The results of finite element analysis are compared with the digital photoelasticityexperiments. The results are in good agreement. The principal stresses obtained from finite element methodare in good agreement with the isochromatic fringe patterns obtained by the photoelasticity method.Explanation has been made for giving guidance to a user on how best to approach implementation of themethod from a practical standpoint.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128223954","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
PROBLEMS OF DIFFERENTIAL AND TOPOLOGICAL DIAGNOSTICS. PART 4. THE CASE OF EXACT TRAJECTORIAL MEASUREMENTS 微分和拓扑诊断问题。第4部分。精确轨迹测量的例子
Vestnik of Samara University. Natural Science Series Pub Date : 2020-12-28 DOI: 10.18287/2541-7525-2020-26-1-52-68
Maxim V. Shamolin
{"title":"PROBLEMS OF DIFFERENTIAL AND TOPOLOGICAL DIAGNOSTICS. PART 4. THE CASE OF EXACT TRAJECTORIAL MEASUREMENTS","authors":"Maxim V. Shamolin","doi":"10.18287/2541-7525-2020-26-1-52-68","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-1-52-68","url":null,"abstract":"Proposed work is the fourth in the cycle, therefore, the diagnostic problem is formulated for the case ofexact trajectorial measurements, the diagnostic theorem is stated and proved, and two diagnostic algorithmsthat follow from this theorem are presented. Techniques for an a priori counting of constants, which shouldbe stored in a program for the computer-aided diagnostics whenever the first diagnostic algorithm is used,and other algorithmic parameters are considered. If the second algorithm is applied, the constants should notbe stored; this algorithm is based on the search for the minimum value of the diagnostic functional amongthe values of this functional that were obtained in the process of diagnostics for the a priori chosen set ofreference malfunctions. Various extensions of the diagnostic theorem are considered, namely, the problem ofwhether the diagnostic algorithms thus obtained are applicable when the dimension of the diagnostic vectorbeing used is lower than that of the state vector or when the uninterrupted express-diagnostics with nochecking surface is carried out, the problem of selecting the minimum diagnostic time, the diagnostics ofmalfunctions occurring in the neighborhoods of reference non-degenerate malfunctions and not envisaged inthe a priori list. We consider other functionals solving the diagnostic problem. Finally, we state the extendeddiagnostic problem that is solved by using the proposed algorithms.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129037669","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: 3
ON DECODING ALGORITHMS FOR GENERALIZED REED — SOLOMON CODES WITH ERRORS AND ERASURES 关于有误差和擦除的广义里德-所罗门码的解码算法
Vestnik of Samara University. Natural Science Series Pub Date : 2020-05-06 DOI: 10.18287/2541-7525-2020-26-3-17-29
S. M. Ratseev, O. Cherevatenko
{"title":"ON DECODING ALGORITHMS FOR GENERALIZED REED — SOLOMON CODES WITH ERRORS AND ERASURES","authors":"S. M. Ratseev, O. Cherevatenko","doi":"10.18287/2541-7525-2020-26-3-17-29","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-3-17-29","url":null,"abstract":"The article is devoted to the decoding algorithms for generalized Reed Solomon codes with errorsand erasures. These algorithms are based on Gao algorithm, Sugiyama algorithm, Berlekamp Massey algorithm (Peterson Gorenstein Zierler algorithm). The first of these algorithms belongs to syndrome-free decoding algorithms, the others to syndrome decoding algorithms. The relevance of these algorithms is that they are applicable for decoding Goppa codes, which are the basis of some promising post-quantum cryptosystems. These algorithms are applicable for Goppa codes over an arbitrary field, as opposed to the well-known Patterson decoding algorithm for binary Goppa codes.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"44 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141206104","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
ON THE SOLVABILITY OF SOME BOUNDARY VALUE PROBLEMS WITH INVOLUTION 若干边值问题的可解性
Vestnik of Samara University. Natural Science Series Pub Date : 2020-05-06 DOI: 10.18287/2541-7525-2020-26-3-7-16
K. Nazarova, B. Turmetov, K. Usmanov
{"title":"ON THE SOLVABILITY OF SOME BOUNDARY VALUE PROBLEMS \u0000WITH INVOLUTION","authors":"K. Nazarova, B. Turmetov, K. Usmanov","doi":"10.18287/2541-7525-2020-26-3-7-16","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-3-7-16","url":null,"abstract":"This article is devoted to the study of the solvability of some boundary value problems with involution.In the space Rn, the map Sx=x is introduced. Using this mapping, a nonlocal analogue of the Laplace operator is introduced, as well as a boundary operator with an inclined derivative. Boundary-value problems are studied that generalize the well-known problem with an inclined derivative. Theorems on the existence and uniqueness of the solution of the problems under study are proved. In the Helder class, the smoothness of the solution is also studied. Using well-known statements about solutions of a boundary value problem with an inclined derivative for the classical Poisson equation, exact orders of smoothness of a solution to the problem under study are found.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125467982","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
RESIDUAL STRESSES IN A THERMOELASTIC CYLINDER RESULTING FROM LAYER-BY-LAYER SURFACING 由逐层堆焊引起的热弹性圆柱体中的残余应力
Vestnik of Samara University. Natural Science Series Pub Date : 2020-05-06 DOI: 10.18287/2541-7525-2020-26-3-63-90
S. Lychev, M. Fekry
{"title":"RESIDUAL STRESSES IN A THERMOELASTIC CYLINDER RESULTING FROM LAYER-BY-LAYER SURFACING","authors":"S. Lychev, M. Fekry","doi":"10.18287/2541-7525-2020-26-3-63-90","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-3-63-90","url":null,"abstract":"The article investigates the residual stresses arising in a thermoelastic cylinder as a result of layer-by-layer deposition of material on its lateral surface. Residual stresses are defined as the limiting values of internal stresses developing during the technological process. Internal stresses are caused by incompatible deformations that accumulate in the body as a result of joining parts with different temperatures. For the analysis of internal stresses, an analytical solution of the axisymmetric quasi-static problem of thermoelasticity for a layer-by-layer growing cylinder is constructed. It is shown that the distribution of residual stresses dependson the scenario of the surfacing process. In this case, the supply of additional heat to the growing body can significantly reduce the unevenness of the temperature fields and reduce the intensity of residual stresses. The most effective is uneven heating, which can be realized, for example, by the action of an alternating current with a tunable excitation frequency. This is illustrated by the calculations performed using the constructedanalytical solution.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129228673","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
DETERMINATION OF THE COEFFICIENTS OF ASYMPTOTIC CRACK—TIP STRESS EXPANSION. MIXED MODE LOADING OF THE PLATE 渐近裂纹尖端应力扩展系数的确定。板的混合模式加载
Vestnik of Samara University. Natural Science Series Pub Date : 2020-05-06 DOI: 10.18287/2541-7525-2020-26-3-40-62
O. Belova, L. Stepanova
{"title":"DETERMINATION OF THE COEFFICIENTS OF ASYMPTOTIC CRACK—TIP STRESS EXPANSION. MIXED MODE LOADING OF THE PLATE","authors":"O. Belova, L. Stepanova","doi":"10.18287/2541-7525-2020-26-3-40-62","DOIUrl":"https://doi.org/10.18287/2541-7525-2020-26-3-40-62","url":null,"abstract":"The aim of the study is to calculate the coefficients of M. Williams asymptotic expansion of stress anddisplacement fields using the data of finite element modeling of a plate with an inclined central crack in a uniaxial tension field. In this work, we also simulated the loading of a half-disk with a vertical and oblique notch under conditions of three-point bending. The simulation was carried out in the multifunctional software SIMULIA Abaqus. The paper proposes an algorithm for calculating the coefficients. The program, written in the MAPLE computer algebra system, allows calculating any predetermined number of M. Williams expansioncoefficients (amplitude or scale factors) and uses the values of the stress tensor components at points in the vicinity of the crack and their coordinates as input. The analysis of the influence of the number of calculated coefficients on the accuracy of their determination is carried out. Recommendations on the choice of points for calculating the coefficients are given.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126030446","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
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