• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.407-420
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• 2023

In this manuscript, we study the sufficient conditions for controllability of Volterra-Fredholm type fractional integro-differential systems in a Banach space. Fractional calculus and the fixed point theorem are used to derive the findings. Some examples are provided to illustrate the obtained results.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.195-205
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• 2003

For the boundary value problem (BVP) of second order functional differential equations for the one-dimensional $\rho$-Laplaclan: ($\Phi$$_{\rho}$(y'))'(t)+m(t)f(t, $y^{t}$ )=0 for t$\in$[0,1], y(t)=η(t) for t$\in$[-$\sigma$,0], y'(t)=ξ(t) for t$\in$[1,d], suitable conditions are imposed on f(t, $y^{t}$ ) which yield the existence of at least two positive solutions. Our result generalizes the main result of Avery, Chyan and Henderson.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• Korean Management Science Review
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• v.18 no.2
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• pp.25-38
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• 2001

The well-known back-propagation algorithm for multi-layered neural network has successfully been applied to pattern c1assification problems with remarkable flexibility. Recently. the multi-layered neural network is used as a powerful data mining tool. Nevertheless, in many cases with complex boundary of classification, the successful learning is not guaranteed and the problems of long learning time and local minimum attraction restrict the field application. In this paper, an Improved learning procedure of multi-layered neural network is proposed. The procedure is based on the generalized delta rule but it is particular in the point that the architecture of network is not fixed but enlarged during learning. That is, the number of hidden nodes or hidden layers are increased to help finding the classification boundary and such procedure is controlled by entropy evaluation. The learning speed and the pattern classification performance are analyzed and compared with the back-propagation algorithm.

• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.245-248
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• 2007

This paper provides some simple recursive formulas generation transition functions of finite cellular automata with triplet local transition functions under two states (0 and 1) and four different boundary conditions (0-0,0-1,1-0,1-1), and classify transition functions into several classes.

• Journal of the Korean Society of Industry Convergence
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• v.5 no.4
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• pp.303-307
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• 2002

We consider the problem y"=a(x,y)(y-b), (0$$y(0)=0,\;y^{\prime}(1)=g(y({\xi}),\;y^{\prime}({\xi})),\;{\xi}$$ fixed in (0,1). This is a model of steady-state heat conduction in a rod when the heat flux at the end x=1 is determined by observation of the temperature and heat flux at some interior point ${\xi}$. We establish conditions sufficient for existence, uniqueness, and positivity of solutions.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.639-663
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• 2011

Motivated by Agarwal and O'Regan ( Boundary value problems for general discrete systems on infinite intervals, Comput. Math. Appl. 33(1997)85-99), this article deals with the discrete type BVP of the infinite difference equations. The sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multi-fixed-point theorems can be extended to treat BVPs for infinite difference equations. The strong Caratheodory (S-Caratheodory) function is defined in this paper.

• The Transactions of the Korea Information Processing Society
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• v.6 no.11
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• pp.3140-3149
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• 1999

Skew correction for document images can be using a rotational transformation of pixel coordinates. In this paper we propose a method which corrects the document skew, by an amount of $\theta$ degrees, using block information, where the block is defined as a rectangular area containing adjacent black pixels. Processing speed of the proposed method is faster than that of the method using pixel transformation, since the number of floating-point operations can be reduced significantly. In the proposed method, we rotate only the four corner points of each block, and then identify the pixels inside the block. Two methods for inside pixel identification are proposed; the first method finds two points intersecting the boundary of the rotated block in each row, and determines the pixels between the two intersection points as the inside pixel. The second method finds boundary points based on Bresenham's line drawing algorithm, using fixed-point operation, and fills the region surrounded by these boundaries as black pixels. We have measured the performance of the proposed method by experimenting it with 2,016 images of various English and Korean documents. We have also proven the superiority of our algorithm through performance comparison with respect to existing methods based on pixel transformation.