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ABSOLUTE EXTENSORS AND THE GEOMETRY OF MULTIPLICATION OF MONADS IN THE CATEGORY OF COMPACTA 紧类中绝对伸展量与单元的乘法几何
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003331
M. Zarichnyǐ
{"title":"ABSOLUTE EXTENSORS AND THE GEOMETRY OF MULTIPLICATION OF MONADS IN THE CATEGORY OF COMPACTA","authors":"M. Zarichnyǐ","doi":"10.1070/SM1993V074N01ABEH003331","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003331","url":null,"abstract":"An investigation is made of the geometry of the multiplication mappings for monads whose functorial parts are (weakly) normal (in the sense of Shchepin) functors acting in the category of compacta. A characterization is obtained for a power monad as the only normal monad such that the multiplication mapping is soft for some omega_1$ SRC=http://ej.iop.org/images/0025-5734/74/1/A02/tex_sm_3331_img4.gif/>. It is proved that the multiplication mappings and of the inclusion hyperspace monad and the monad of complete chained systems are homeomorphic to trivial Tychonoff fibrations for openly generated continua that are homogeneous with respect to character.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134033262","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
INTERPOLATION OF CONTINUOUS FUNCTIONS BY BERNSTEIN POLYNOMIALS ON TRIANGULABLE DOMAINS 可三角域上连续函数的Bernstein多项式插值
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003334
A. S. Loginov
{"title":"INTERPOLATION OF CONTINUOUS FUNCTIONS BY BERNSTEIN POLYNOMIALS ON TRIANGULABLE DOMAINS","authors":"A. S. Loginov","doi":"10.1070/SM1993V074N01ABEH003334","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003334","url":null,"abstract":"A refinement is given for a result of M. S. Bazelkov on the exact constant of interpolation of the class of continuous functions with a given convex majorant of the modulus of continuity by Bernstein polynomials.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132401552","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
ASYMPTOTICS OF THE COEFFICIENT OF QUASICONFORMALITY, AND THE BOUNDARY BEHAVIOR OF A MAPPING OF A BALL 拟共形系数的渐近性，以及球的映射的边界行为
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N02ABEH003363
M. N. Pantyukhina
{"title":"ASYMPTOTICS OF THE COEFFICIENT OF QUASICONFORMALITY, AND THE BOUNDARY BEHAVIOR OF A MAPPING OF A BALL","authors":"M. N. Pantyukhina","doi":"10.1070/SM1993V074N02ABEH003363","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003363","url":null,"abstract":"It is shown that if a quasiconformal automorphism of the unit ball in () has coefficient of quasiconformality in the ball of radius with asymptotic growth such that , then it has a radial limit at almost every point of the boundary. This asymptotic growth of is sharp in a certain sense.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115151846","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
FRACTIONAL ITERATES OF FUNCTIONS ANALYTIC IN THE UNIT DISK, WITH GIVEN FIXED POINTS 具有给定不动点的单位圆盘上解析函数的分数阶迭代
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003332
V. Goryainov
{"title":"FRACTIONAL ITERATES OF FUNCTIONS ANALYTIC IN THE UNIT DISK, WITH GIVEN FIXED POINTS","authors":"V. Goryainov","doi":"10.1070/SM1993V074N01ABEH003332","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003332","url":null,"abstract":"An infinitesimal description is obtained for fractional iterates of analytic functions on the unit disk under the condition that the functions and their iterates do not move fixed points on the unit circle at which they have finite angular derivatives.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123722189","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: 20
THE STEINER PROBLEM IN THE PLANE OR IN PLANE MINIMAL NETS 平面或平面极小网中的斯坦纳问题
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N02ABEH003362
A. Ivanov, A. Tuzhilin
{"title":"THE STEINER PROBLEM IN THE PLANE OR IN PLANE MINIMAL NETS","authors":"A. Ivanov, A. Tuzhilin","doi":"10.1070/SM1993V074N02ABEH003362","DOIUrl":"https://doi.org/10.1070/SM1993V074N02ABEH003362","url":null,"abstract":"The famous Steiner problem in the Euclidean plane, which is that of investigating minimal nets spanning fixed finite subsets M of points in the plane, is solved when M is extremal, i.e. when M lies on the boundary of its convex hull, and the nets are nondegenerate, i.e. have no vertices of degree 2.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129452462","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: 11
ON A SPECIAL LOOP, THE DICKSON FORM, AND THE LATTICE CONNECTED WITH $ O_7(3)$ 在一个特殊的循环上，dickson形式，以及与$ o_7(3)$相连的格
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003341
V. Burichenko
{"title":"ON A SPECIAL LOOP, THE DICKSON FORM, AND THE LATTICE CONNECTED WITH $ O_7(3)$","authors":"V. Burichenko","doi":"10.1070/SM1993V074N01ABEH003341","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003341","url":null,"abstract":"A special commutative Moufang loop of order is described. With the help of this loop, a trilinear Dickson form is constructed whose automorphism group is a Chevalley group of type . Next, with the help of , a 27-dimensional representation is constructed for over , . This makes it possible to prove anew the embedding . A similar construction concerning the embedding is described.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129733574","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: 5
ON THE RELATIVE ROTATION OF MULTIVALUED POTENTIAL VECTOR FIELDS 关于多值势向量场的相对旋转
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003340
V. S. Klimov, N. V. Senchakova
{"title":"ON THE RELATIVE ROTATION OF MULTIVALUED POTENTIAL VECTOR FIELDS","authors":"V. S. Klimov, N. V. Senchakova","doi":"10.1070/SM1993V074N01ABEH003340","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003340","url":null,"abstract":"Conditions are presented under which the relative index of a critical set realizing a local minimum of a nonsmooth functional coincides with the Euler-Poincare characteristic of this set. An analogous result is obtained for the index of a functional increasing at .","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132951274","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: 17
ON A PROPERTY OF THE SUBDIFFERENTIAL 关于次微分的一个性质
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003335
A. I. Subbotin
{"title":"ON A PROPERTY OF THE SUBDIFFERENTIAL","authors":"A. I. Subbotin","doi":"10.1070/SM1993V074N01ABEH003335","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003335","url":null,"abstract":"Semicontinuous real functions are considered. The following property is established for the Dini directional semiderivative and the Dini semidifferential (the subdifferential). If at some point the semiderivative is positive in a convex cone of directions, then arbitrarily close to the point under consideration there exists a point at which the function is subdifferentiable and has a subgradient belonging to the positively dual cone. This result is used in the theory of the Hamilton-Jacobi equations to prove the equivalence of various types of definitions of generalized solutions.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114208090","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: 14
ON A PROBLEM WITH NONLOCAL BOUNDARY CONDITION FOR A PARABOLIC EQUATION 一类抛物型方程的非局部边界条件问题
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003345
L. A. Muravei, A. V. Filinovskii
{"title":"ON A PROBLEM WITH NONLOCAL BOUNDARY CONDITION FOR A PARABOLIC EQUATION","authors":"L. A. Muravei, A. V. Filinovskii","doi":"10.1070/SM1993V074N01ABEH003345","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003345","url":null,"abstract":"Well-posed solvability is proved in an appropriate energy space of a boundary value problem with a nonlocal boundary condition for a one-dimensional parabolic equation; two-sided uniform estimates of the solution are obtained, which replace the maximum principle. The existence of an optimal control of the diffusion coefficient in the problem of minimizing the quality functional is established in the class of functions of bounded variation.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128487047","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: 16
On the Representation of Functions as a Sum of Several Compositions 关于函数作为若干组合的和的表示
Mathematics of The Ussr-sbornik Pub Date : 1993-02-28 DOI: 10.1070/SM1993V074N01ABEH003339
V. Medvedev
{"title":"On the Representation of Functions as a Sum of Several Compositions","authors":"V. Medvedev","doi":"10.1070/SM1993V074N01ABEH003339","DOIUrl":"https://doi.org/10.1070/SM1993V074N01ABEH003339","url":null,"abstract":"Let be continuous mappings of a compactum onto compacta , . The following theorem is known for : if any bounded function on can be represented in the form , where and are bounded functions on and , then any continuous can be represented in the same form with continuous and . An example is constructed showing that the analogous theorem is false for .","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121125323","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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