• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.179-186
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• 2009

Generalizing the approximately convex function which is introduced by D.H. Hyers and S.M. Ulam we establish an approximately convex Schwartz distribution and prove that every approximately convex Schwartz distribution is an approximately convex function.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.609-615
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• 2022

We give a formula for the sizes of the dual groups. It is obtained by generalizing a size estimation of certain algebraic structure that lies in the heart of the proof of the celebrated primality test by Agrawal, Kayal and Saxena. In turn, by using our formula, we are able to give a streamlined survey of the AKS test.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.89-96
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• 2023

Edgar obtained an identity between Fibonacci and Lucas numbers which generalizes previous identities of Benjamin-Quinn and Marques. Recently, Dafnis provided an identity similar to Edgar's. In the present article we give some generalizations of Edgar's and Dafnis's identities.

• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.217-238
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• 2019

With the advent of so-called "default" Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise, requiring the analyst to accept a one-size-fits-all approach to hypothesis testing. Further, such tests may not have the flexibility to test problems the scientist really cares about. In this tutorial, I demonstrate a flexible approach to generalizing one specific default test (the JZS t-test) (Rouder et al., Psychonomic Bulletin & Review, 16, 225-237, 2009) that is becoming increasingly popular in the social and behavioral sciences. The approach uses two results, the Savage-Dickey density ratio (Dickey and Lientz, 1980) and the technique of encompassing priors (Klugkist et al., Statistica Neerlandica, 59, 57-69, 2005) in combination with MCMC sampling via an easy-to-use probabilistic modeling package for R called Greta. Through a comprehensive mathematical description of the techniques as well as illustrative examples, the reader is presented with a general, flexible workflow that can be extended to solve problems relevant to his or her own work.

• KIPS Transactions on Computer and Communication Systems
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• v.10 no.8
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• pp.215-222
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• 2021

In order to alleviate the limited resource problem and interference problem in cellular networks, the dual connectivity technology has been introduced with the cooperation of small cell base stations. In this paper, we design a new efficient and fair resource allocation scheme for the dual connectivity technology. Based on two different bargaining solutions - Generalizing Tempered Aspiration bargaining solution and Gupta and Livne bargaining solution, we develop a two-stage radio resource allocation method. At the first stage, radio resource is divided into two groups, such as real-time and non-real-time data services, by using the Generalizing Tempered Aspiration bargaining solution. At the second stage, the minimum request processing speeds for users in both groups are guaranteed by using the Gupta and Livne bargaining solution. These two-step approach can allocate the 5G radio resource sequentially while maximizing the network system performance. Finally, the performance evaluation confirms that the proposed scheme can get a better performance than other existing protocols in terms of overall system throughput, fairness, and communication failure rate according to an increase in service requests.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.265-275
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• 1993

In this paper, we study the monotonicity of the Dittert function (abb. MD) on the line segment from A .mem. $K_{n}$ to J$_{n}$ generalizing both the Dittert conjecture and the Monotonicity conjecture for permanent, and obtain a sufficient condition on A .mem. $K_{n}$ for which the MD holds. It is also proved that if A .mem. $K_{n}$ satisfies the Dokovic inequality (1.2) then MD holds for A, and a subclass of $K_{n}$ for which MD holds is found. is found.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.529-539
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• 2001

This paper deals with the distributions of certain characteristics related to a symmetric random walk of an steps ending at an unspecified position, thus generalizing and extending the earlier work.

• Honam Mathematical Journal
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• v.26 no.1
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• pp.77-83
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• 2004

A class of topological algebras, which we call it a fundamental one, has already been introduced generalizing the famous Cohen factorization theorem to more general topological algebras. To prove the generalized versions of Cohen's theorem to locally multilplicatively convex algebras, and finally to fundamental topological algebras, the completness of the background spaces is one of the main conditions. The local convexity of the completion of a locally convex space is a well known fact and here we have a discussion on the completness of fundamental metrizable topological vector spaces.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.689-699
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• 2010

We discuss in this paper the notions of extended negative quadrant dependence and its properties. We study a class of bivariate uniform distributions having extended negative quadrant dependence, which is derived by generalizing the uniform representation of a well-known Farlie-Gumbel-Morgenstern distribution. Finally, we also study the limit behavior on the extended negative quadrant dependence.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.41-52
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• 2016

In the present paper, by generalizing the definition of the zero-difference balanced (ZDB) function to be the G-ZDB function, several classes of G-ZDB functions are constructed based on properties of cyclotomic numbers. Furthermore, some special constant composition codes are obtained directly from G-ZDB functions.