• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1011-1020
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• 2008

The problem of finding Cramer rule for solutions of some restricted linear equation Ax = b has been widely discussed. Recently Wang and Qiao consider the following more general problem AXB = D, $R(X){\subset}T$, $N(X){\supset}\tilde{S}$. They present the solution of above general restricted matrix equation by using generalized inverses and give an explicit expression for the elements of the solution matrix for the matrix equation. In this paper we re-consider the restricted matrix equation and give an equivalent matrix equation to it. Through the equivalent matrix equation, we derive condensed Cramer rule for above restricted matrix equation. As an application, condensed determinantal expressions for $A_{T,S}^{(2)}$ A and $AA_{T,S}^{(2)}$ are established. Based on above results, we present a method for computing the solution of a kind of restricted matrix equation.

• Journal of Mechanical Science and Technology
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• 제15권6호
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• pp.813-820
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• 2001

Solutions of inviscid rotational flows near the corners of an arbitrary angle and within a triangle of arbitrary shapes are presented. The corner-flow solutions has a rotational component as a particular solution. The addition of irrotatoinal components yields a general solution, which is indeterminate unless the far-field condition is imposed. When the corner angle is less than 90$^{\circ}$the flow asymptotically becomes rotational. For the corner angle larger than 90$^{\circ}$it tends to become irrotational. The general solution for the corner flow is then applied to rotational flows within a triangle (Method I). The error level depends on the geometry, and a parameter space is presented by which we can estimate the error level of solutions. On the other hand, Method II employing three separate coordinate systems is developed. The error level given by Method II is moderate but less dependent on the geometry.

• 응용통계연구
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• 제20권2호
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• pp.373-385
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• 2007

선형모형에서 최소자승법에 의한 정규방정식의 해는 유일하지 않은 경우도 있는데 문헌에 따르면 일반화 역행렬을 정의하여, 그 해를 SAS IML로 취급하고 있다. 본 논문에서는 이것에 대한 이론을 보다 체계화하여 교육 및 연구에 도움을 주고자 하는데 그 목적이 있다.

• Journal of Nutrition and Health
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• 제47권6호
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• pp.484-488
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• 2014

Purpose: This study investigated the question of whether the addition of natural ingredients (pear fermented solution, celery powder, vitamin C) in curing agents may influence antioxidant activities and nutritional characteristics of smoked duck. Methods: Smoked duck samples with general or natural curing agent containing three additive ingredients were examined to determine total polyphenol contents, antioxidant activities, pH, TBARS, and food additives residue (nitrite ion, antioxidant, sodium glutamate). Results: Smoked duck with natural curing agent showed a higher level of total polyphenol content and antioxidant activities than smoked duck using general curing agent (p < 0.05). The pH and TBARS of smoked duck were significantly decreased by the addition of natural curing ingredients compared to those of smoked duck using general curing agent (p < 0.05). The residues of food additives were not detected in smoked duck using natural curing agent. Conclusion: Findings suggest that the addition of pear fermented solution, celery powder, and vitamin C in natural duck curing agent may improve the antioxidant activities and nutritional characteristics of smoked duck and provides health benefits.

• 충청수학회지
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• 제27권3호
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• pp.475-477
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• 2014

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.

• 한국해양공학회지
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• 제24권1호
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• pp.34-38
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• 2010

An analytical solution procedure for the dynamic response of beams with variable properties is developed by using an asymptotic solution and the Green's function. This asymptotic closed form solution is derived for the transverse vibration of beams under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is still found to be very accurate even in the case of large variation, such as step change in cross-section, mass, and tension. Therefore, this derived asymptotic closed form solution and the Green's function can be easily applied to find dynamic responses for various kind of beam vibration problems.

• 충청수학회지
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• 제10권1호
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• pp.87-95
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• 1997

In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

• 대한수학회논문집
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• 제20권2호
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• pp.381-393
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• 2005

We consider a type of large deviation principle obtained by Freidlin and Wentzell for the solution of Stochastic differential equations in a conuclear space. We are using exponential tail estimates and exit probability of a Ito process. The nuclear structure of the state space is also used.

• 대한수학회지
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• 제59권6호
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• pp.1083-1101
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• 2022

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admit a unique solution which belongs to class 𝔻.

• 대한수학회보
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• 제52권6호
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• pp.1827-1838
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• 2015

We give some results on hyperstability for the general linear equation. Namely, we show that a function satisfying the linear equation approximately (in some sense) must be actually the solution of it.