• Journal of Korean Institute of Industrial Engineers
• /
• v.8 no.2
• /
• pp.15-21
• /
• 1982

This paper offers an alternative to the common probability generating function approach to the solution of steady state equations when a Markovian queue has a multivariate state space. Identifying states and substates and grouping them into vectors appropriately, we formulate a two - dimensional Markovian queue as a Markov chain. Solving the resulting matrix equations the transition point steady state probabilities (SSPs) are obtained. These are then converted into arbitrary time SSPs. The procedure uses only probabilistic arguments and thus avoids a large and cumbersome state space which often poses difficulties in the solution of steady state equations. For the purpose of numerical illustration of the approach we solve a Markovian queue with one server and two classes of customers.

• Korean Journal of Mathematics
• /
• v.28 no.2
• /
• pp.205-221
• /
• 2020

Paranormed spaces are important as a generalization of the normed spaces in terms of having more general properties. The aim of this study is to introduce a new paranormed space |𝜙_z|(p) over the paranormed space ℓ(p) using Euler totient means, where p = (p_k) is a bounded sequence of positive real numbers. Besides this, we investigate topological properties and compute the α-, β-, and γ duals of this paranormed space. Finally, we characterize the classes of infinite matrices (|𝜙_z|(p), λ) and (λ, |𝜙_z|(p)), where λ is any given sequence space.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1351-1370
• /
• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.413-416
• /
• 1998

In this paper we first show that uniform PR systems and half independent PR systems have same dynamics, and then an important property of this two kinds of systems is derived. The most important property of uniform PR systems is that they have the ability of classifying m-dimensional problabilistic vector into in classes. The significance of studying the dynamics of uniform PR systems are tried from the beginning with a uniform PR system.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.235-258
• /
• 1998

We define a crossing of a link without referring to a specific projection of the link and describe a construction of a non-normalized Alexander polynomial associated to collections of such crossings of oriented links under an equivalence relation, called homology relation. The polynomial is computed from a special Seifert surface of the link. We prove that the polynomial is well-defined for the homology equivalence classes, investigate its relationship with the combinatorially defined Alexander polynomials and study some of its properties.

• Journal of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.805-818
• /
• 2010

We classify linear maps which preserve idempotents on $n{\times}n$ matrices over some classes of semirings. Our results include many known semirings like the semiring of all nonnegative integers, the semiring of all nonnegative reals, any unital commutative ring, which is zero divisor free and of characteristic not two (not necessarily a principal ideal domain), and the ring of integers modulo m, where m is a product of distinct odd primes.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.951-960
• /
• 2010

We provide the set of left-invariant minimal unit vector fields on the semi-direct product $\mathbb{R}^n\;{\rtimes}_p\mathbb{R}$, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form $\mathbb{R}^3\;{\rtimes}_p\mathbb{R}$ which are unimodular and of type (R).

• Journal of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1441-1456
• /
• 2017

We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.

• Communications for Statistical Applications and Methods
• /
• v.14 no.3
• /
• pp.687-698
• /
• 2007

A normal mixture model with which dependence between classes is incorporated is proposed in order to detect differentially expressed genes. Gene clustering approaches suffer from the high dimensional column of microarray expression data matrix which leads to the over-fit problem. Various methods are proposed to solve the problem. In this paper, use of simple averaging data within each class is proposed to overcome the various problems due to high dimensionality when the normal mixture model is fitted. Some experiments through simulated data set and real data set show its availability in actuality.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.7 no.1
• /
• pp.25-31
• /
• 2003

The concepts of stability of algorithms for solving the symmetric and generalized symmetric-definite eigenproblems are discussed. An algorithm for solving the symmetric eigenproblem $Ax={\lambda}x$ is stable if the computed solution z is the exact solution of some slightly perturbed system $(A+E)z={\lambda}z$. We use both normwise approach and componentwise way of measuring the size of the perturbations in data. If E preserves symmetry we say that an algorithm is strongly stable (in a normwise or componentwise sense, respectively). The relations between the stability and strong stability are investigated for some classes of matrices.