Pure Mathematics

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

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Arab Journal of Mathematical Sciences

Almost Kenmotsu 3-h-metric as a cotton soliton

In the present paper, we introduce the notion of ∗ -gradient ρ-Einstein soliton on a class of almost Kenmotsu manifolds. It is shown that if a (2 n+ 1) -dimensional (k, μ) ′-almost Kenmotsu manifold M admits ∗ -gradient ρ-Einstein soliton with Einstein potential f, then (1) the manifold M is locally isometric to Hn+1(- 4) × Rn, (2) the manifold M is ∗ -Ricci flat and (3) the Einstein potential f is harmonic or satisfies a physical Poisson’s equation. Finally, an illustrative example is presented. © 2021, Instituto de Matemática e Estatística da Universidade de São Paulo.

Sao Paulo Journal of Mathematical Sciences

On a class of almost Kenmotsu manifolds admitting an Einstein like structure

In [11], the author introduced inverse semimodules. Recently, in [8], we further studied properties of inverse semimodules and Clifford semimodules. In this paper, we consider inverse semimodules over a semiring R such that R is a distributive lattice of rings. In [3], the authors introduced von Neumann regular module and studied its properties. In this paper, we introduce von Neumann regular semimodule and study its different interesting properties. © 2021 Sciendo. All rights reserved.

Fulltext

Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica

Von Neumann regular semimodule

In the present paper, we first investigate a Sasakian 3-metric as a quasi-Yamabe gradient soliton. In the sequel, extending the notions of quasi-Yamabe soliton and Ricci-Yamabe soliton, the notion of generalized Ricci-Yamabe soliton is introduced. It is shown that if (g, V, λ, α, β, γ) is a generalized gradient Ricci-Yamabe soliton on a complete Sasakian 3-manifold M with potential function f, then M is compact Einstein and locally isometric to a unit sphere. Moreover, the potential vector field V is an infinitesimal contact transformation and pointwise collinear with the characteristic vector field ξ. Further, if h is the Hodge-de Rham potential for V, then, upto a constant, f = h. © 2021 NISC (Pty) Ltd.

Quaestiones Mathematicae

Sasakian 3-Metric as a Generalized Ricci-Yamabe soliton

The Pure and Applied Mathematics

SASAKIAN 3-MANIFOLDS SATISFYING SOME CURVATURE CONDITIONS ASSOCIATED TO Ƶ-TENSOR

For a Hausdorff zero-dimensional topological space X and a totally ordered field F with interval topology, let Cc(X, F) be the ring of all F-valued continuous functions on X with countable range. It is proved that if F is either an uncountable field or countable subfield of R, then the structure space of Cc(X, F) is βX, the Banaschewski Compactification of X. The ideals {Ocp,F:p∈β0X} in Cc(X, F) are introduced as modified countable analogue of the ideals { Op: p∈ βX} in C(X). It is realized that Cc(X,F)∩CK(X,F)=⋂p∈β0X\XOcp,F, and this may be called a countable analogue of the well-known formula CK(X) = ⋂ p∈βX\XOp in C(X). Furthermore, it is shown that the hypothesis Cc(X, F) is a Von-Neumann regular ring is equivalent to amongst others the condition that X is a P-space. © 2021, Iranian Mathematical Society.

Bulletin of the Iranian Mathematical Society

Ordered Field Valued Continuous Functions with Countable Range

Intermediate rings of the functionally countable subalgebra of C(X) (i.e., the rings Ac (X) lying between Cc∗ (X) and Cc (X)), where X is a Hausdorﬀ zero-dimensional space, are studied in this article. It is shown that the structure space of each Ac (X) is homeomorphic to β 0 X, the Banaschewski compactification of X. From this a main result of [A. Veisi, ec -filters and ec -ideals in the function-ally countable subalgebra C∗ (X), Appl. Gen. Topol.20(2) (2019), 395–405] easily follows. The countable counterpart of the m-topology and U -topology on C(X), namely mc -topology and Uc -topology, respectively, are introduced and using these, new characterizations of P -spaces and pseudocompact spaces are found out. Moreover, X is realized to be an almost P -space when and only when each maximal ideal/z-ideal in Cm(X) become a z 0-ideal. This leads to a characterization of Cc (X) among its intermediate rings for the case that X is an almost P -space. Noetherianness/Artinianness of Cc (X) and a few chosen subrings of Cc (X) are examined and finally, a complete description of z 0-ideals in a typical ring Ac (X) via z 0-ideals in Cc (X) is established. © 2020 NISC (Pty) Ltd.

Rings and subrings of continuous functions with countable range

The author [S. M. Yusuf, Inverse semimodules, J. Natur. Sci. Math. 6 (1966) 111-117.] introduced inverse semimodules. In this paper, we introduce Clifford semimodules. The Clifford semimodules have been characterized here as a strong R-semilattice of R-modules. The congruences on inverse semimodules, specially, the R-module congruences, have been characterized here completely. © 2021 World Scientific Publishing Company.

Asian-European Journal of Mathematics

Inverse semimodules

In this paper, we have discussed various topological properties of (Hausdörff) topological ternary semigroup and topological ternary group. We have proved that the Cartesian product of an arbitrary family of topological ternary semigroups is again a topological ternary semigroup. We have investigated the existence of identity and idempotent in a topological ternary semigroup and discussed a method to topologize a ternary semigroup (group) with a compatible topology using some family of pseudometrics. Finally, we have proved that a compact topological ternary semigroup contains a ternary subgroup. © 2021 World Scientific Publishing Company.