Perspective Chapter: Digital Business Model: The Present, Future, and the Vision

An imperative contemporary management dilemma in moments of rapidly evolving regarding the ongoing digital transformation of business and society in general is recognizing and trying to translate these adjustments into digital business model innovation (DBMI). Academia has plenty to show in exchange of assisting with this managerial problem, but studies in the field still seem to be hazy in terms of what DBMI is, the present, future, and vision. Therefore, this article aimed to review the present situation of DBMI, its future, and its vision in the general context. The secondary databases were used to collect the relevant articles, and the outcome of the study found that DBMI has attained prolonged growth in different businesses especially in COVID-19 period. This scenario would not be changed in future because of increasing digital impact on several businesses. Therefore, it is recommended for all types of businesses to adopt digital business model innovation to attain competitive advantage

Characterizations of *-Lie derivable mappings on prime *-rings

Let R be a *-ring containing a nontrivial self-adjoint idempotent. In this paper it is shown that under some mild conditions on R, if a mapping d : R → R satisfies d([U*, V]) = [d(U)*, V] + [U*, d(V)] for all U, V ∈ R, then there exists ZU,V ∈ Z(R) (depending on U and V), where Z(R) is the center of R, such that d(U + V) = d(U) + d(V) + ZU,V. Moreover, if R is a 2-torsion free prime *-ring additionally, then d = ψ + ξ, where ψ is an additive *-derivation of R into its central closure T and ξ is a mapping from R into its extended centroid C such that ξ(U + V) = ξ(U) + ξ(V) + ZU,V and ξ([U, V]) = 0 for all U, V ∈ R. Finally, the above ring theoretic results have been applied to some special classes of algebras such as nest algebras and von Neumann algebras

Nonlinear generalized Jordan (σ, Γ)-derivations on triangular algebras

Let R be a commutative ring with identity element, A and B be unital algebras over R and let M be (A,B)-bimodule which is faithful as a left A-module and also faithful as a right B-module. Suppose that A = Tri(A,M,B) is a triangular algebra which is 2-torsion free and σ, Γ be automorphisms of A. A map δ:A→A (not necessarily linear) is called a multiplicative generalized (σ, Γ)-derivation (resp. multiplicative generalized Jordan (σ, Γ)-derivation) on A associated with a (σ, Γ)-derivation (resp. Jordan (σ, Γ)-derivation) d on A if δ(xy) = δ(x)r(y) + σ(x)d(y) (resp. σ(x2) = δ(x)r(x) + δ(x)d(x)) holds for all x, y Є A. In the present paper it is shown that if δ:A→A is a multiplicative generalized Jordan (σ, Γ)-derivation on A, then δ is an additive generalized (σ, Γ)-derivation on A

Quantum Codes from Constacyclic Codes over the Ring Fq[u1,u2]/〈 u 1 2 -u1, u 2 2 -u2,u1u2-u2u1〉

In this paper, we study the structural properties of ( α + u 1 β + u 2 γ + u 1 u 2 δ ) -constacyclic codes over R = F q [ u 1 , u 2 ] / ⟨ u 1 2 − u 1 , u 2 2 − u 2 , u 1 u 2 − u 2 u 1 ⟩ where q = p m for odd prime p and m ≥ 1 . We derive the generators of constacyclic and dual constacyclic codes. We have shown that Gray image of a constacyclic code of length n is a quasi constacyclic code of length 4 n . Also we have classified all possible self dual linear codes over this ring R . We have given the applications by computing non-binary quantum codes over this ring R

A Study of the Inherent Inj-equitable Graphs

Let G be a graph. The inherent Inj-equitable graph of a graph G(IIE(G)) is the graph with the same vertices as G and any two vertices u and v are adjacent in IIE(G) if they are adjacent in G and jdegin(u