pp 379-396
Semisimple Metacyclic Group Algebras
Gurmeet K Bakshi Shalini Gupta Inder Bir S Passi
Given a group 𝐺 of order $p_1p_2$, where $p_1,p_2$ are primes, and $\mathbb{F}_q$, a finite field of order 𝑞 coprime to $p_1p_2$, the object of this paper is to compute a complete set of primitive central idempotents of the semisimple group algebra $\mathbb{F}_q[G]$. As a consequence, we obtain the structure of $\mathbb{F}_q[G]$ and its group of automorphisms.
pp 397-404
On the Normal Subgroup with Coprime 𝐺-Conjugacy Class Sizes
Xianhe Zhao Guiyun Chen Jiaoyun Shi
Let 𝑁 be a normal subgroup of a group 𝐺. The positive integers 𝑚 and 𝑛 are the two longest sizes of the non-central 𝐺-conjugacy classes of 𝑁 with 𝑚>𝑛 and (𝑚,𝑛)=1. In this paper, the structure of 𝑁 is determined when 𝑛 divides $|N/N\cap Z(G)|$. Some known results are generalized.
pp 405-416
Fixed Points of 𝐼𝐴-Endomorphisms of a Free Metabelian Lie Algebra
Naime Ekici Demet Parlak Sönmez
Let 𝐿 be a free metabelian Lie algebra of finite rank at least 2. We show the existence of non-trivial fixed points of an 𝐼𝐴-endomorphism of 𝐿 and give an algorithm detecting them. In particular, we prove that the fixed point subalgebra Fix 𝜑 of an 𝐼𝐴-endomorphism 𝜑 of 𝐿 is not finitely generated.
pp 417-433
Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras
S J Bhatt P A Dabhi H V Dedania
Given a weighted discrete abelian semigroup $(S,𝜔)$, the semigroup $M_𝜔(S)$ of 𝜔-bounded multipliers as well as the Rees quotient $M_𝜔(S)/S$ together with their respective weights $\overline{𝜔}$ and $\overline{𝜔}_q$ induced by 𝜔 are studied; for a large class of weights 𝜔, the quotient $\ell^1(M_𝜔(S),\overline{𝜔})/\ell^1(S,𝜔)$ is realized as a Beurling algebra on the quotient semigroup $M_𝜔(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.
pp 435-446
On Hypersurfaces with two Distinct Principal Curvatures in Space Forms
We investigate the immersed hypersurfaces in space forms $\mathbb{N}^{n+1}(c),n≥ 4$ with two distinct non-simple principal curvatures without the assumption that the (high order) mean curvature is constant. We prove that any immersed hypersurface in space forms with two distinct non-simple principal curvatures is locally conformal to the Riemannian product of two constant curved manifolds. We also obtain some characterizations for the Clifford hypersurfaces in terms of the trace free part of the second fundamental form.
pp 447-455
On the 𝐿_{𝑝} Affine Isoperimetric Inequalities
We obtain an isoperimetric inequality which estimate the affine invariant 𝑝-surface area measure on convex bodies. We also establish the reverse version of 𝐿_{𝑝}-Petty projection inequality and an affine isoperimetric inequality of $𝛤_{-p}K$.
pp 457-468
Periodic and Subharmonic Solutions for Second Order 𝑝-Laplacian Difference Equations
Xia Liu Yuanbiao Zhang Bo Zheng Haiping Shi
In this paper, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to second order 𝑝-Laplacian difference equations are obtained by using the critical point theory. The proof is based on the Linking theorem in combination with variational technique.
pp 469-480
On the Uniqueness of the Solution of Dual Equation of a Singular Sturm–Liouville Problem
In this paper we consider differential systems having a singularity and one turning point. First, by a replacement, we transform the system to a linear second-order equation of Sturm–Liouville type with a singularity. Using the infinite product representation of solutions provided in [8], we obtain the dual equation, then we investigate the uniqueness of the solution for the dual equation of the inverse spectral problem of Sturm–Liouville equation. This result is necessary for expressing inverse problem of indefinite Sturm–Liouville equation.
pp 481-493
Mohamed Haiour Salah Boulaaras
In this paper we provide a maximum norm analysis of an overlapping Schwarz method on non-matching grids for quasi-variational inequalities related to impulse control problem with mixed boundary conditions. We provide that the discretization on every sub-domain converges in uniform norm. Furthermore, a result of approximation in uniform norm is given.
pp 495-501
We utilize the reformulated equations of the classical theory, as derived by Banerjee et al.(J. Math. Anal. Appl. 175 (1993) 458), to establish mathematically, the existence of hydrodynamic instability in single diffusive bottom heavy systems, when considered in the more general framework of the boundary conditions of the type specified by Beavers and Joseph (J. Fluid Mech. 30 (1967) 197), in the parameter regime $T_0𝛼_2>1$, where $T_0$ and 𝛼_{2} being some properly chosen mean temperature and coefficient of specific heat (at constant volume) variation due to temperature variation respectively.
pp 503-509 Subject Index
pp 510-512 Author Index
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Volume 127 | Issue 4
September 2017
© 2017 Indian Academy of Sciences, Bengaluru.