• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.747-752
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• 2013

It's known that one could use a fixed loxodromic or parabolic element in $M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of a non-elementary M$\ddot{o}$bius group G. In this paper, we discuss the discreteness of G by using a fixed elliptic element.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.57-61
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• 2012

It is well known that one could use a fixed loxodromic or parabolic element of a non-elementary group $G{\subset}M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of G. In this paper, we show that a test map need not be in G. We also construct an example to show that the similar result using an elliptic element as a test map does not hold.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.249-255
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• 2021

The aim of this work is to study the discreteness of the spectrum of the Schrödinger operator on infinite quantum graphs in a magnetic field. The problem was solved on a set of quantum graphs of a special kind.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.275-288
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• 2010

A one-holed torus ${\Sigma}$(l, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus ${\Sigma}$(1, 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of ${\Sigma}$(1, 1).

• Asia Marketing Journal
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• v.18 no.4
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• pp.125-138
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• 2017

The goal of the study is to understand how consumers' constraint as opposed to utility structure gives rise to final decision when consumers purchase more than one variant of product at a time, i.e., horizontal variety seeking or multiple-discreteness. Purchase and consumption decision not only produces utility but also involves some sort of cognitive pressure. Past consumption or last purchase is likely to be linked to this burden we face such as concern for obesity, risk of harm, and guilt for mischief. In this research, the existence and the role of dynamic constraint are investigated through a microeconomic utility model with multiple dynamic constraint. The model is applied to the salty snacks data collected from field study where burden for spiciness serves as a constraint. The results are compared to the conventional multiple discreteness choice models of static constraints, and policy implications on price discounts is explored. The major findings are that first, one would underestimate the level of consumer preference for product offerings when ignoring the carry-over of the concern from the past consumption, and second, the impact of price promotion on demand would be properly evaluated when the model allows for the role of constraint as both multiple and dynamic. The current study is different from the existing studies in two ways. First, it captures the effect of 'mental constraint' on demand in formal economic model. Second, unlike the state dependence well documented in the literature, the study proposes the notion of state dependence in different way, via constraint rather than utility.

• The Mathematical Education
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• v.22 no.1
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• pp.67-68
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• 1983

In this note we consider properties for the discreteness of the spectrum of second-order differential operators. If we give some conditions, then the spectrum of any self-adjoint extension of $A_{0}$ , $A_{0}$ u=$\alpha$[u], D( $A_{0}$ )= $C_{0}$ $^{\infty}$(0.1) is discrete.1) is discrete.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.71-85
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• 2003

In the economic design of the process control procedure, where quality is measured at certain time intervals, its properties are difficult to derive due to the discreteness of the measurement intervals. In this paper a Markov chain representation of the process monitoring procedure is developed and used to derive its properties when the process follows an ARIMA(0,1,1) model, which is designed to describe the effect of the noise and the special cause in the process cycle. The properties of the Markov chain depend on the transition matrix, which is determined by the control procedure and the process distribution. The derived representation of the Markov chain can be adapted to most different types of control procedures and different kinds of process distributions by obtaining the corresponding transition matrix.

• Asia Marketing Journal
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• v.22 no.1
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• pp.41-60
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• 2020

The goal of the study is to understand the role of social norm in purchase decisions where demand is revealed in the form of multiple-discreteness. Consumers are socially engaged in various activities through the expectation from others in their community. Actions or decisions are likely to reflect this influence. This implicit or explicit social norm is revealed as the rules, regulations, and standards that are understood, shared, endorsed, and expected by group members. When consumers' decisions are in distance from the norm, they come to face discomfort such as shame, guilt, embarrassment, and anxiety. These pressure act as a constraint as opposed to utility in their decision making. In this study, the effect of social norms on consumer demand is captured via multiple constraint model where constraints are not only from budget equation but also from psychological burden induced by the deviation from the norm. The posterior distributions of model parameters were estimated via conjoint study allowing for heterogeneity via hierarchical Bayesian framework. Individual characteristics such as age, gender and work experience are also used as covariates for capturing the observed heterogeneity. The empirical results show the role of social norm as constraint in consumers' utility maximization. The proposed model accounting for social constraint outperforms the standard budget constraint-only model in terms of model fit. It is found that people with longer job experience tend to be more robust and resistant to the deviation from the norm. Incorporating social norm into the utility model allows for another means to disentangle the reason for no-purchase as 'not preferred' and 'not able to buy'.

• Journal of the Korean Operations Research and Management Science Society
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• v.11 no.2
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• pp.13-26
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• 1986

This paper considers the routing problem in session-based communication network, particularly where the pattern of message transmission is characterized by non-bifurcated traffic flows. Due to the discreteness property of its solution space, the problem is formulated as normalized mlticommodity network flows with integer restrictions and an effective penalty system is suggested to solve it. To show its effectiveness, a simple example and a preliminary computational experience are provided. Finally, numerous application areas of the algorithm are suggested.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.82-88
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• 1998

As a par of a project related to the development of the design algorithm of a compact heat exchanger for the application of the electronic home appliances, the effect of the discreteness of the airflow boundary generated on the cooling fin surface on the heat transfer and pressure drop characteristics of the heat exchanger was studied numerically. In general, there are two critical design parameters seriously considered in the design of the heat exchanger; heat transfer rate(Q) and pressure drop coefficient(C/sub p/). Even though the higher heat transfer rate with lower pressure drop characteristics is required in a design of the heat exchanger, it is not an easy job to satisfy both conditions at the same time because these two parameters are phenomenally inversely proportional. To control the boundary layer thickness and its length along the streamline, the surface of the flat fin was modified to accelerate the heat transfer rate on the fin surface. To understand the effect of the discreted fin size(S/sub w/) and its location(S/sub h/) on the performance of the heat exchanger in the airflow field, the flat fin was modified as shown in Fig. 1. From this study, it was found that the smaller and more number of slits on the fin surface showed the higher energy diffusion rate. It means that the discreteness of the boundary layer is quite important on the heat transfer rate of the heat exchanger. On the other hand, if the fin surface configuration is very complex than needed, higher static pressure drop occurs than required in a system and it may be a reason of the induced aerodynamic noise in the heat exchanger.