• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.1-5
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• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.483-488
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• 2004

Results on the analytic behavior of the limiting spectral distribution of large dimensional random matrices, studied in Marcenko and Pastur [2], are derived. Using the Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic whenever it is positive [3]. In the present paper, it is derived that the behavior of it resembles the behavior of a square root function near the boundary of its support.

• East Asian mathematical journal
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• v.34 no.4
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• pp.359-369
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• 2018

This note, we first show that the famous Carleman's inequality can be improved if we find a positive sequence $\{c_n\}$ such that $c_n{\sum\limits_{j=n}^{\infty}}{\frac{1}{j\(\prod_{k=1}^{j}ck\)^{\frac{1}{j}}}}$ < e. Then we list a lot of known results in the literature improving Carleman's inequality by this method. These results can be a good source to a further research for interested students. We next consider about similar improvement of Polya-Knopp's inequality, which is a continuous version of Carleman's inequality. We show by a manner parallel to the case of Carleman's inequality that Polya-Knopp's inequality can be improved if we find a positive function c(x) such that $c(x){\int}_{x}^{\infty}\frac{1}{t\;{\exp}\(\frac{1}{t}{\int}_{0}^{t}{\ln}\;c(s)\;ds\)}dt$ < e. But there are no known results improving Polya-Knopp's inequality by this method. Suggesting to find a new method, we lastly show that there is no nice continuous function c(x) that satisfies the inequality.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.75-106
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• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.29-53
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• 2001

This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1561-1597
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• 2019

In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated function systems, they are given [32] by a sequence of collections of continuous maps on a compact topological space, where maps are allowed to vary between iterations. Several basic properties of topological pressure and topological entropy of NAIFSs are provided. Especially, we generalize the classical Bowen's result to NAIFSs ensures that the topological entropy is concentrated on the set of nonwandering points. Then, we define the notion of specification property, under which, the NAIFSs have positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the ${\ast}$-expansive property for NAIFSs is introduced. We will prove that the topological pressure of any continuous potential can be computed as a limit at a definite size scale whenever the NAIFS satisfies the ${\ast}$-expansive property. Finally, we study the NAIFSs induced by expanding maps. We prove that these NAIFSs having the specification and ${\ast}$-expansive properties.

• Steel and Composite Structures
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• v.21 no.6
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• pp.1307-1325
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• 2016

Nonlinear behavior of two-span, continuous composite steel-concrete girders strengthened with Carbon Fiber Reinforced Polymers (CFRP) bonded to the top of concrete slab over the negative moment region was evaluated using a non-linear Finite Element (FE) model in this paper. A three-dimensional FE model of continuous composite girder using commercial software ABAQUS simulated and validated with experimental results. The interfacial regions of the composite girder components were modeled using suitable interface elements. Validation of the proposed numerical model with experimental data confirmed the applicability of this model to predict the loading history, strain level for the different components and concrete-steel relative slip. The FE model captured the different modes of failure for the continuous composite girder either in the concrete slab or at the interfacial region between CFRP sheet and concrete slab. Through a parametric study, the thickness of CFRP sheet and shear connection required to develop full capacity of the continuous composite girder at negative moment zone have been investigated. The FE results showed that the proper thickness of CFRP sheet at negative moment region is a function of the adhesive strength and the positive moment capacity of the composite section. The shear connection required at the negative moment zone depends on CFRP sheet's tensile stress level at ultimate load.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.763-772
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• 2010

This paper deals with the existence of triple positive solutions for the nonlinear second-order three-point boundary value problem z"(t)+a(t)f(t, z(t), z'(t))=0, t $\in$ (0, 1), $z(0)={\nu}z(1)\;{\geq}\;0$, $z'(\eta)=0$, where 0 < $\nu$ < 1, 0 < $\eta$ < 1 are constants. f : [0, 1] $\times$ [0, $+{\infty}$) $\times$ R $\rightarrow$ [0, $+{\infty}$) and a : (0, 1) $\rightarrow$ [0, $+{\infty}$) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.

• Journal of Korean Society of Transportation
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• v.31 no.4
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• pp.85-94
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• 2013

The Continuous Risk Profile (CRP) has been well known to be the most accurate and efficient among existing network screening methods. However, the classical CRP uses safety performance functions (SPFs) which require a huge investment to construct a database system. This study aims to suggest a new CRP method using average crash frequencies of homogeneous groups, instead of SPFs, as rescaling factors. Hierarchical clustering analysis is performed to classify freeway segments into homogeneous groups based on the data of AADT and number of lanes. Using the data from I-880 in California, the proposed method is compared to other several network screening methods. The results show that the proposed method decrease false positive rates while it does not produce any false negatives. The method developed in this study can be easily applied to screen freeway networks without any additional complex database systems, and contribute to the improvement of freeway safety management systems.

• Archives of Craniofacial Surgery
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• v.11 no.2
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• pp.73-76
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• 2010

Purpose: There are several surgical methods for correcting a velopharyngeal insufficiency (VPI) but in some cases, it is not possible to achieve complete recovery of the velopharyngeal function. This paper introduces a new therapy for treating hypernasality without further surgery using continuous positive airway pressure (CPAP). Methods: CPAP therapy was applied to seven VPI patients for eight weeks from April of 2007 to September of 2009. All patients underwent palatoplasty for the cleft palate and six patients underwent palatal lengthening for VPI before CPAP therapy. A speech pathologist performed an auditory perceptual evaluation to evaluate the improvement in hypernasality after 8-week CPAP therapy. Results: Six patients showed an improvement in hypernasality after CPAP therapy according to the auditory perceptual evaluation. One patient with severe hypernasality responded to the early part of therapy but the hypernasality did not improve after therapy. Conclusion: CPAP therapy might be effective in reducing the hypernasality in patients with VPI by providing resistance training to strengthen the velopharyngeal closure muscles. In particular, CPAP therapy could be more effective for patients who show mild to moderate hypernasality after surgery.