Search

For an involution near ring 𝒩 and its ideal ℐ, the text introduces an involution ideal-based zero- divisor graph Γℐ*(𝒩) which is an undirected graph with vertex set { x ∈ 𝒩 - ℐ: x𝒩y ⊂ ℐ (or y𝒩x ⊂ ℑ ) for some y ∈ 𝒩-ℐ}, where two distinct vertices x and y are adjacent if and only if y𝒩x* ⊂ ℐ or x𝒩y* ⊂ ℐ. The paper provides characterizations of Γℐ*(𝒩) when it forms a complete graph or a star graph. It also explores the structure of Γℐ*(𝒩), investigates its properties like connectedness with diam(Γℐ*(𝒩)) ≤ 3 and analyzes the connection of Γℐ*(𝒩) with Γℐ*(𝒩/ℐ). Furthermore, the paper discusses the chromatic number and clique number of the graph. It also characterizes all right permutable *-near-rings 𝒩 for which the graph Γℐ*(𝒩) can be with a finite chromatic number.

n the present paper, the authors introduce a new subclass namely; RL(φ4L, ν) of Kamali-type starlike functions defined in the open unit disk D connected with four-leaf shaped domain. We investigate the bounds of some initial coefficients, Fekete-Szegö inequality and other results of logarithmic coefficients for the function belonging to above class. Relevant connections of the results derived in this paper with those of earlier works are indicated.

The purpose of this paper is to establish necessary and sufficient optimality conditions and some duality results for weakly efficient solutions of a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. Using parametric approach, the problem (P) is first equivalently transformed into a parametric problem (P µ) with µ ∈ Rp, for which we construct then a dual problem. This is achieved in terms of conjugate duality theory. Under appropriate assumptions, the weak and strong duality results for (Pµ) are presented. These results permit us to give dual characterizations for the weakly efficient solutions of the problem (P).

The bicategory of Landau-Ginzburg models denoted by ℒ𝒢K possesses adjoints and this helps in explaining a certain duality that exists in the setting of Landau-Ginzburg models in terms of some specified relations. The construction of ℒ𝒢K is reminiscent of, but more complex than, the construction of the bicategory of associative algebras and bimodules. In this paper, we review this complex but very inspiring construction in order to expose it more to pure mathematicians. In particular, we spend some time explaining the intricate construction of unit morphisms in this bicategory from a new vantage point. Besides, we briefly discuss how this bicategory could be constructed in more than one way using the variants of the Yoshino tensor product. Furthermore, without resorting to Atiyah classes, we prove that the left and right unitors in this bicategory have direct right inverses but do not have direct left inverses.