• Kyungpook Mathematical Journal
• /
• v.60 no.4
• /
• pp.683-710
• /
• 2020

Let ℕ be the set of nonnegative integers and 𝕬 be a 2-torsion free triangular algebra over a commutative ring ℛ. In the present paper, under some lenient assumptions on 𝕬, it is proved that if Δ = {𝛿_n}_n∈ℕ is a sequence of ℛ-linear mappings 𝛿_n : 𝕬 → 𝕬 satisfying ${\delta}_n([[x,\;y],\;z])\;=\;\displaystyle\sum_{i+j+k=n}\;[[{\delta}_i(x),\;{\delta}_j(y)],\;{\delta}_k(z)]$ for all x, y, z ∈ 𝕬 with xy = 0 (resp. xy = p, where p is a nontrivial idempotent of 𝕬), then for each n ∈ ℕ, 𝛿_n = d_n + 𝜏_n; where d_n : 𝕬 → 𝕬 is ℛ-linear mapping satisfying $d_n(xy)\;=\;\displaystyle\sum_{i+j=n}\;d_i(x)d_j(y)$ for all x, y ∈ 𝕬, i.e. 𝒟 = {d_n}_n∈ℕ is a higher derivation on 𝕬 and 𝜏_n : 𝕬 → Z(𝕬) (where Z(𝕬) is the center of 𝕬) is an ℛ-linear map vanishing at every second commutator [[x, y], z] with xy = 0 (resp. xy = p).

• Journal of the Korea Society for Simulation
• /
• v.17 no.4
• /
• pp.241-247
• /
• 2008

In this study we consider an M/D/1 queue with a finite buffer. Due to the finiteness of the buffer capacity arriving customers can not join the system and turn away without service when the buffer is full. Even though a computational method for blocking probabilities in an M/D/1/K queue is already known, it is very complex to use. The aim of this study is to propose a new way to compute blocking probability by using (max,+)-algebra. Our approach provide a totally different and easier way to compute blocking probabilities and it is, moreover, immediately applicable to more generous queueing systems.

• Honam Mathematical Journal
• /
• v.30 no.4
• /
• pp.645-658
• /
• 2008

In this paper, left-regular maps on d-algebras are defined. These mappings show behaviors reminiscent of homomorphisms on d-algebras which have been studied elsewhere. In particular for these mappings kernels, annihilators and co-annihilators are defined and some of their properties are investigated, especially in the setting of positive implicative d-algebras.

• Honam Mathematical Journal
• /
• v.40 no.3
• /
• pp.539-548
• /
• 2018

The notions of Smarandache (positive implicative, commutative, implicative) d-algebras, Smarandache subalgebras of Smarandache d-algebras and Smarandache BCK-ideals(d-ideals) of a Smarandache d-algebras are introduced. Examples are given, and several related properties are investigated.

• Journal of the Chungcheong Mathematical Society
• /
• v.3 no.1
• /
• pp.41-48
• /
• 1990

Let D' : $C^n$[0, 1] ${\rightarrow}$ M be a second order derivation from the Banach algebra of n times continuously differentiable functions on [0, 1] into a Banach $C^n$[0, 1]-module M and let D be the primitive of D'. If D' is continuous and D'(z) lies in the 1-differential subspace, then it is completely determined by D(z) and D'(z) where z(t)=t, $0{\leq}t{\leq}1$.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1219-1233
• /
• 2019

Let $E{\rightarrow}M$ be an arbitrary vector bundle of rank k over a Riemannian manifold M equipped with a fiber metric and a compatible connection $D^E$. R. Albuquerque constructed a general class of (two-weights) spherically symmetric metrics on E. In this paper, we give a characterization of locally symmetric spherically symmetric metrics on E in the case when $D^E$ is flat. We study also the Einstein property on E proving, among other results, that if $k{\geq}2$ and the base manifold is Einstein with positive constant scalar curvature, then there is a 1-parameter family of Einstein spherically symmetric metrics on E, which are not Ricci-flat.

• Communications of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.375-381
• /
• 2019

In this paper, we introduce an operation denoted by [$Br_e$], a bracket operation, which maps an arbitrary groupoid ($X,{\ast}$) on a set X to another groupoid $(X,{\bullet})=[Br_e](X,{\ast})$ which on groups corresponds to sending a pair of elements (x, y) of X to its commutator $xyx^{-1}y^{-1}$. When applied to classes such as d-algebras, BCK-algebras, a variety of results is obtained indicating that this construction is more generally useful than merely for groups where it is of fundamental importance.

• Kyungpook Mathematical Journal
• /
• v.63 no.3
• /
• pp.345-353
• /
• 2023

Reduced solutions of size 2 and degree n of the Tarry-Escott problem over M₂(ℚ) are determined. As an application, the diophantine equation αAⁿ + βBⁿ = αCⁿ + βDⁿ, where α, β are rational numbers satisfying α + β ≠ 0 and n ∈ {1, 2}, is completely solved for A, B, C, D ∈ M₂(ℚ).

• Journal of the Chungcheong Mathematical Society
• /
• v.7 no.1
• /
• pp.41-46
• /
• 1994

In this paper, we show that if A is a Banach algebra with radical R and D is a left derivation on A then $D(A){\subset}R$ if and only if $Q_RD^n$ is continuous for all $n{\geq}1$, where $Q_R$ is the canonical quotient map from A onto A/R.

• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.361-366
• /
• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.