Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.2.247
N. Das, Satyajit Sahoo
In this paper, we consider little Hankel operators Γφ defined on the Bergman space L2 a(D) with symbol φ ∈ H∞(D) that are contractions. Necessary and sufficient conditions are obtained for the existence of a nontrivial unitary part of these little Hankel
{"title":"UNITARY PARTS OF CONTRACTIVE LITTLE HANKEL OPERATORS ON THE BERGMAN SPACE","authors":"N. Das, Satyajit Sahoo","doi":"10.59277/mrar.2023.25.75.2.247","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.247","url":null,"abstract":"In this paper, we consider little Hankel operators Γφ defined on the Bergman space L2 a(D) with symbol φ ∈ H∞(D) that are contractions. Necessary and sufficient conditions are obtained for the existence of a nontrivial unitary part of these little Hankel","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"9 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87743033","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}
Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.3.451
MEHDI REZAEI, MEHDI ALAEIYAN, ZEINAB FORUZANFAR
In this note, we point out a mistake in part (II) of Theorem 1.1 of [1] and correct it here. In [1], the authors investigated the structure of intransitive permutation groups with bounded movement having maximum degree.
{"title":"CORRIGENDUM TO “INTRANSITIVE PERMUTATION GROUPS","authors":"MEHDI REZAEI, MEHDI ALAEIYAN, ZEINAB FORUZANFAR","doi":"10.59277/mrar.2023.25.75.3.451","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.451","url":null,"abstract":"In this note, we point out a mistake in part (II) of Theorem 1.1 of [1] and correct it here. In [1], the authors investigated the structure of intransitive permutation groups with bounded movement having maximum degree.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953230","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}
Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.3.465
ABDUL RAUF, TAHIR MUSHTAQ QURESHI, CONSTANTIN FETECAU
Oscillatory motions of incompressible viscous fluids with exponential dependence of viscosity on the pressure between infinite horizontal parallel plates are analytically and numerically studied. The fluid motion is generated by the lower plate that oscillates in its plane and exact expressions are established for the steady-state solutions. The convergence of starting solutions to the corresponding steady-state solutions is graphically proved. The steady solutions corresponding to the simple Couette flow of the same fluids are obtained as limiting cases of the previous solutions. As expected, the fluid velocity diminishes for increasing values of the pressure-viscosity coefficient and ordinary fluids flow faster. The time required to reach the steady-state is graphically approximated. The spatial profiles of the starting solutions are presented both for oscillatory motions and the simple Couette flow.
{"title":"ANALYTICAL AND NUMERICAL SOLUTIONS FOR SOME","authors":"ABDUL RAUF, TAHIR MUSHTAQ QURESHI, CONSTANTIN FETECAU","doi":"10.59277/mrar.2023.25.75.3.465","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.465","url":null,"abstract":"Oscillatory motions of incompressible viscous fluids with exponential dependence of viscosity on the pressure between infinite horizontal parallel plates are analytically and numerically studied. The fluid motion is generated by the lower plate that oscillates in its plane and exact expressions are established for the steady-state solutions. The convergence of starting solutions to the corresponding steady-state solutions is graphically proved. The steady solutions corresponding to the simple Couette flow of the same fluids are obtained as limiting cases of the previous solutions. As expected, the fluid velocity diminishes for increasing values of the pressure-viscosity coefficient and ordinary fluids flow faster. The time required to reach the steady-state is graphically approximated. The spatial profiles of the starting solutions are presented both for oscillatory motions and the simple Couette flow.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953457","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}
Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.3.365
Saïma KHENISSY, IBRAHIM ZOUHIR
We consider an overdetermined eigenvalue problem related to the MEMS operator given by Lτ := ∆2 − τ∆ on a smooth bounded domain Ω ⊂ R N , N ≥ 2. We give radial solutions on balls. Moreover, we establish a symmetry result with respect to operator Lτ , that is, under some hypotheses, we show that if a solution does exist to the overdetermined eigenvalue problem, then the domain Ω must be a ball.
我们考虑与光滑有界域上Lτ:=∆2−τ∆给出的MEMS算子相关的一个过定特征值问题Ω∧R N, N≥2。我们给出了球的径向解。此外，我们建立了一个关于Lτ算子的对称结果，即在某些假设下，我们证明了如果超定特征值问题的解存在，那么定义域Ω一定是一个球。
{"title":"On an overdetermined eigenvalue problem with mems operator","authors":"Saïma KHENISSY, IBRAHIM ZOUHIR","doi":"10.59277/mrar.2023.25.75.3.365","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.365","url":null,"abstract":"We consider an overdetermined eigenvalue problem related to the MEMS operator given by Lτ := ∆2 − τ∆ on a smooth bounded domain Ω ⊂ R N , N ≥ 2. We give radial solutions on balls. Moreover, we establish a symmetry result with respect to operator Lτ , that is, under some hypotheses, we show that if a solution does exist to the overdetermined eigenvalue problem, then the domain Ω must be a ball.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953775","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}
Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.3.413
SHINGO TAKI
We study cyclic quotient singularities given by automorphisms of maximum order on K3 surfaces. In particular, we describe fixed loci of such automorphisms, and provide types of these singularities
{"title":"SINGULARITIES OF QUOTIENT SURFACES OF K3 SURFACES","authors":"SHINGO TAKI","doi":"10.59277/mrar.2023.25.75.3.413","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.413","url":null,"abstract":"We study cyclic quotient singularities given by automorphisms of maximum order on K3 surfaces. In particular, we describe fixed loci of such automorphisms, and provide types of these singularities","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953476","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}
Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.2.231
W. Chu
By means of partial fraction decompositions, a shorter proof is presented for the important interpolation formula of trigonometric polynomials discovered by Riesz (1914).
{"title":"SHORTER PROOF OF THE RIESZ INTERPOLATION FORMULA FOR TRIGONOMETRIC POLYNOMIALS","authors":"W. Chu","doi":"10.59277/mrar.2023.25.75.2.231","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.231","url":null,"abstract":"By means of partial fraction decompositions, a shorter proof is presented for the important interpolation formula of trigonometric polynomials discovered by Riesz (1914).","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87188960","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}
Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.2.235
S. M. S. Nabavi Sales
We consider the orthogonality preserving property to study sesquilinear forms. We state some characterizations for Hermitian sesquilinear forms through this kind of approach. We, then, state a Wigner type equation and present some results in this regard.
{"title":"SESQUILINEAR FORMS AND THE ORTHOGONALITY PRESERVING PROPERTY","authors":"S. M. S. Nabavi Sales","doi":"10.59277/mrar.2023.25.75.2.235","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.235","url":null,"abstract":"We consider the orthogonality preserving property to study sesquilinear forms. We state some characterizations for Hermitian sesquilinear forms through this kind of approach. We, then, state a Wigner type equation and present some results in this regard.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"276 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75032479","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}
Pub Date : 2023-01-01DOI: 10.59277/mrar.2023.25.75.3.505
DORIN POPESCU
We describe the immediate extensions of a one dimensional valuation ring V which could be embedded in some separation of a ultrapower of V with respect to a certain ultrafilter. For such extensions, a kind of Artin’s approximation holds.
{"title":"IMMEDIATE EXTENSIONS OF VALUATION RINGS AND","authors":"DORIN POPESCU","doi":"10.59277/mrar.2023.25.75.3.505","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.3.505","url":null,"abstract":"We describe the immediate extensions of a one dimensional valuation ring V which could be embedded in some separation of a ultrapower of V with respect to a certain ultrafilter. For such extensions, a kind of Artin’s approximation holds.","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135954541","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}
Pub Date : 2022-12-08DOI: 10.59277/mrar.2023.25.75.2.221
Antal Jo'os
It is known that ∞P i=1 1/i2 = π2/6. Meir and Moser asked what is the smallest ϵ such that all the squares of sides of length 1, 1/2, 1/3, . . . can be packed into a rectangle of area π2/6 + ϵ. A packing into a rectangle of the right area is called perfec
{"title":"PERFECT PACKING OF SQUARES","authors":"Antal Jo'os","doi":"10.59277/mrar.2023.25.75.2.221","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.221","url":null,"abstract":"It is known that ∞P i=1 1/i2 = π2/6. Meir and Moser asked what is the smallest ϵ such that all the squares of sides of length 1, 1/2, 1/3, . . . can be packed into a rectangle of area π2/6 + ϵ. A packing into a rectangle of the right area is called perfec","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"189 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88112026","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}
Pub Date : 2022-02-26DOI: 10.59277/mrar.2023.25.75.2.199
Tooba Zahid, Zunaira Sajid, M. Ishaq
Let S be a ring of polynomials in finitely many variables over a field. In this paper, we give lower bounds for depth and Stanley depth of modules of the type S/It for t ≥ 1, where I is the edge ideal of some caterpillar and lobster trees. These new bound
{"title":"DEPTH AND STANLEY DEPTH OF POWERS OF THE EDGE Depth and Stanley depth of powers of the edge ideals of some caterpillar and lobster trees","authors":"Tooba Zahid, Zunaira Sajid, M. Ishaq","doi":"10.59277/mrar.2023.25.75.2.199","DOIUrl":"https://doi.org/10.59277/mrar.2023.25.75.2.199","url":null,"abstract":"Let S be a ring of polynomials in finitely many variables over a field. In this paper, we give lower bounds for depth and Stanley depth of modules of the type S/It for t ≥ 1, where I is the edge ideal of some caterpillar and lobster trees. These new bound","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"6 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80234334","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}
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