• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.95-106
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• 2016

In this paper, according to the classical LSQR algorithm forsolving least squares (LS) problem, an iterative method is proposed for finding the minimum-norm pure imaginary solution of the quaternionic least squares (QLS) problem. By means of real representation of quaternion matrix, the QLS's correspongding vector algorithm is rewrited back to the matrix-form algorthm without Kronecker product and long vectors. Finally, numerical examples are reported that show the favorable numerical properties of the method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1541-1547
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• 2011

In this paper, using B.Ricceri's three critical points theorem, we prove the existence of at least three classical solutions for the problem $$\{u^{(4)}(t)={\lambda}f(t,\;u(t)),\;t{\in}(0,\;1),\\u(0)=u(1)=u^{\prime}(0)=u^{\prime}(1)=0,$$ under appropriate hypotheses.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.445-454
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• 2011

In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1727-1748
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• 2018

In this paper, we characterize the graded post-Lie algebra structures on the W-algebra W(2, 2). Furthermore, as applications, the homogeneous Rota-Baxter operators on W(2, 2) and solutions of the formal classical Yang-Baxter equation on $W(2,2){\ltimes}_{ad^*} W(2,2)^*$ are studied.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.947-953
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• 2015

Vecer derived a degenerate parabolic equation characterizing the price of Asian options with generally sampled average. It is well understood that there exists a unique probabilistic solution to Vecer's PDE but it remained unclear whether the probabilistic solution is a classical solution. We prove that the probabilistic solution to Vecer's PDE is indeed regular.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1247-1256
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• 2009

Finite difference schemes are considered for a nonlinear $Ca^{2+}$ diffusion equations with stationary and mobile buffers. The scheme inherits mass conservation as for the classical solution. Stability and $L^{\infty}$ error estimates of approximate solutions for the corresponding schemes are obtained. using the extended Lax-Richtmyer equivalence theorem.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.43-46
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• 2018

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the Hardy-Littlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from $L^p({\mathbb{R}}^n)$ to $L^q({\mathbb{R}}^n)$ for 1 ${\leq}$ q < p < ${\infty}$.

• East Asian mathematical journal
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• v.27 no.3
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• pp.289-297
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• 2011

The introduction of fuzzy differential equation is to deal wit fuzzy dynamic systems. As classical differential equations, it is difficult to find the solutions to all fuzzy differential equations. In this paper an existence and uniqueness theorem for linear fuzzy differential equations is obtained. Moreover, the exact solution to linear fuzzy differential equation is given.

• Journal of Aerospace System Engineering
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• v.1 no.4
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• pp.28-36
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• 2007

This paper presents critical buckling loads of laminated composites under cylindrical bending. In-plane displacements are assumed to vary exponentially through plate thickness. The accuracy of this theory is examined for symmetric/antisymmetric cross-ply, angle-ply and unsymmetric laminates under cylindrical bending. Analytical solutions are provided to investigate the effect of transverse shear deformation on critical buckling loads of the laminated plates, and the results are compared with those obtained from the first-order shear deformation plate theory and the classical laminated plate theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.224-243
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• 2022

In this paper, we prove the global existence of classical solutions to the 2D incompressible Boussinesq equations for the micropolar fluid. Furthermore, applying the Fourier splitting methods, we obtain the lager time decay properties.