The Journal of the Indian Mathematical Society
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<div id="i-scholarabout">The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title 'the Journal of Indian Mathematical Society. The four numbers of the Journal constitute a single volume and it is published in two parts: numbers 1 and 2 (January to June) as one part and numbers 3 and 4 (July to December) as the second part. The four numbers of the Student are published as a single yearly volume. Only the research papers of high quality are published in the Journal.</div>Informatics Publishing Limited and The Indian Mathematical Societyen-USThe Journal of the Indian Mathematical Society0019-5839New Separation Axioms in Bitopological Spaces
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In this paper, new concepts of separation axioms are intro- duced in bitopological spaces. The implications of these new separation axioms among themselves as well as with other known separation ax- ioms are obtained. Fundamental properties of the suggested concepts are also investigated. Furthermore, we introduced the concept of R<sub>ij </sub>- neighborhoods and investigate some of their characterizations.M. Abo-ElhamayelZabidin Salleh2019-07-012019-07-0186An Introduction of Theory of Involutions in Ordered Semihypergroups and their Weakly Prime Hyperideals
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In this paper, we introduce ordered semihypergroups with involution and weakly prime semihyperideal, then we investigate some properties of prime, semiprime and weakly prime hyperideals in ordered semihypergroup with involution. Also, we study intra-regular ordered semihypergroups with involution. We prove that in ordered semihypergroup <em>S</em> with involution such that the involution preserves the order, a semihyperideal of <em>S</em> is prime if and only if it is both weakly prime and semiprime and if <em>S</em> is commutative, then the prime and weakly prime hyperideals of <em>S</em> coincide. Finally, we show that if <em>S</em> is an ordered semi- hypergroup with order preserving involution, then the semihyperideals of <em>S</em> are prime if and only if it is intra-regular.Abul BasarMohammad Yahya AbbasiSabahat Ali Khan2019-07-012019-07-0186Instability of MHD Fluid Flow through a Horizontal Porous Media in the Presence of Transverse Magnetic Field - A Linear Stability Analysis
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The study was to conduct a stability analysis of pressure driven ow of an electrically conducting fluid through a horizontal porous channel in the presence of a transverse magnetic field. We employed the Brinkman-extended Darcy model with fluid viscosity is different from effective viscosity. In deriving the equations governing the stability, a simplication is made using the fact that the magnetic Prandtl number Pr<sub>m</sub> for most of the electrically conducting fluids is assumed to be small. Using the Chebyshev collocation method, the critical Reynolds number Re<sub>c</sub>, the critical wave number α<sub>c</sub> and the critical wave speed c<sub>c</sub> are computed for various values of the parameters present in the problem. The neutral curves are drawn in the (Re, α)- plane for various values of the non-dimensional parameters present in the problem. This study also tells how the combined effect of the magnetic field strength and the porosity of the porous media to delay the onset of instability compare to their presence in isolation. In the absence of some parameters, the results obtained are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.M. S. Basavaraj2019-07-012019-07-0186Topological Vector Space Valued Measures on Topological Spaces
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If X is a compact Hausdorff space space, E is a complete Hausdorff topological vector space and μ : (C(X),ll.ll) → E a linear continuous exhaustive mapping, we rst give a different proof that there is then a unique reqular, L∞-bounded, exhaustive E-valued Borel measure μ on X such that μ(f) = ∫ fdμ, ∀f ∈ C(X). Then we consider X to be a completely regular Hausdorff space and prove the extension of Alexanderov's theorem: X is a completely regular Hausdorff space and μ : C<sub>b</sub>(X) → E a linear, continuos, exhaustive mapping and F is the algebra generated by zero-sets in X. Then there exist a unique nitely additive, exhaustive measure ν : F → E such that (i) ν is L∞-bounded i.e. the absolute convex hull of ν(F) (Γ(ν(F))) is bounded in E; (ii) ν is inner regular by zero-sets and outer regular by positive-sets; (iii) ∫ fdν = µ(f), ∀f ∈ C<sub>b</sub>(X).Surjit Singh Khurana2019-07-012019-07-0186Ideal Module Amenability of Triangular Banach Algebras
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Let A and B be unital Banach algebras and M be an unital Banach A,B-module. In this paper we define the concept of the (n)-ideal module amenability of Banach algebras and investigate the relation between the (2n-1)-ideal module amenability of triangular Banach algebra Τ = [A M <sub>B</sub>] (as a Τ = {[α α] : α ∈u}-module) and (2n - 1)-ideal module amenability of A and B (as an u-module), where u is a (not necessarily unital) Banach algebra such that A, B and M are commutative Banach u-bimodules. Finally, in the case that A = B = M = l<sup>1</sup>(S) and u = l<sup>1</sup>(E), for unital and commutative inverse semigroup S with idempotent set E, we show that <em>T</em> as an u-module is (2n - 1)- ideal module amenable while is not module amenable.Ebrahim Nasrabadi2019-07-012019-07-0186Solving Uncertain Differential Equation with Fuzzy Boundary Conditions
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In this paper, a novel technique has been developed for solving a general linear dierential equation with fuzzy boundary conditions. The target has been to use the developed technique to solve in particular the radon transport (subsurface soil to buildings) equation with uncertain (fuzzy) boundary conditions. The fuzzy boundary condition has been described by a triangular fuzzy number (TFN). Corresponding results are presented in term of plots and are also compared with crisp ones.T. D. RaoS. Chakraverty2019-07-012019-07-0186A General Inversion Pair and ρ-deformation of Askey Scheme
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The present work incorporates the general inverse series relations involving <em>p</em>-Pochhammer symbol and <em>p</em>-Gamma function. A general class of ρ-polynomials is introduced by means of this general inverse pair which is used to derive the generating function relations and summation formulas for certain <em>p</em>-polynomials belonging to this general class. This includes the<em> p</em>-deformation of Jacobi polynomials, the Brafman polynomials and Konhauser polynomials. Moreover, the orthogonal polynomials of Racah and those of Wilson are also provided ρ-deformation by means of the general inversion pair. The generating function relations and summation formulas for these polynomials are also derived. We then emphasize on the combinatorial identities and obtain their ρ-deformed versions.Rajesh V. SavaliaB. I. Dave2019-07-012019-07-0186Oscillation Theory of First Order Differential Equations with Delay
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In this paper we try to improve the conditions of [4]. Consequently, we introduce that<p>L>e-1/e-2(k + 1/λ<sub>1</sub>) - 1/e-2</p><p>is a sufficient condition for the oscillation of all solutions of first order delay differential equation</p><p>x′(t) + p(t)x(σ(t)) = 0</p><p>under the conditions</p><p>L < 1 and 0 < k </1/e,</p>where k=liminf<sub>t→∞</sub>∫<sup>t</sup><sub>σ(t)</sub> p(s)ds, L=limsup<sub>t→∞</sub>∫<sup>t</sup><sub>σ(t)</sub>p(s)ds<p>and λ<sub>1</sub>is the smaller root of the equation λ=e<sup>kλ</sup></p>Yutaka Shoukaku2019-07-012019-07-0186Core Rough Algebras and its Connection with Core Regular Double Stone Algebra
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In this paper a special sub class of rough set algebra (RSA) is identied and coined as core rough set algebra(CRSA). Further we studied the relationship between CRSA and core regular double Stone algebra (CRDSA) introduced in [10]. In fact, a representation theorem for CRDSA in terms of rough sets is established.A. R. J. SrikanthR. V. G. Ravi KumarG. V. S. R. Deekshitulu2019-07-012019-07-0186Numerical Study on the Effect of Angle of Inclination on Magnetoconvection Inside Enclosure with Heat Generating Solid Body
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Convective ow and heat transfer of uid inside a square en- closure having heat generating solid body, with various thermal boundary conditions is investigated numerically. The top wall of the enclosure is adiabatic, both the bottom and right walls are kept at constant temper- ature, while the left wall is heated using sin function. Numerical simu- lations is carried out by solving the governing equations using SIMPLE algorithm by means of the nite-volume method with power-law scheme. The important parameters focused are angle of inclination of the enclo- sure, area ratio of solid-enclosure, Hartmann number and temperature dierence ratio of solid- uid, which are ranges 0<sup>o</sup> - 90<sup>o</sup>, 0:0625 - 0:5625, 0 - 100 and 0 - 50, respectively. Thermal conductivity ratio of solid- uid is xed as 5 and Rayleigh number as 10<sup>5</sup>.P. UmadeviN. NithyadeviH. F. Oztop2019-07-012019-07-0186