• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• Management Science and Financial Engineering
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• v.2 no.1
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• pp.147-176
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• 1996

The main objective of this study is to uncover the differences in the programming behavior between methodology creators and methodology users. We conducted an experiment with methodology creators who have invented one of the major object-oriented methodologies and with professional programmers who have used the same methodology for their software-development projects. In order to explain the difference between the two groups, we propose a theoretical framework that views programming as search in four problem spaces: representation, rule, instance and paradigm spaces. The main problem spaces in programming are the representation and rule spaces, while the paradigm and instance spaces are the supporting spaces. The results of the experiment showed that the methodology creators mostly adopted the paradigm space as their supporting space, while the methodology users chose the instance space as their supporting space. This difference in terms of the supporting space leads to different search behaviors in the main problem spaces, which in turn resulted in different final programs and performance.

• Journal of KIISE:Software and Applications
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• v.33 no.6
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• pp.574-579
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• 2006

The feature selection algorithms should broadly and efficiently explore the huge problem spaces to find a good solution. This paper attempts to gain insights on the fitness landscape of the spaces and to improve search capability of the algorithms. We investigate the solution spaces in terms of statistics on local maxima and minima. We also analyze behaviors of the existing algorithms and improve their solutions.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.595-619
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• 2022

The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.157-174
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• 2004

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.3
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• pp.156-165
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• 2005

A new heuristic algorithm for the heterogeneous single container loading problem is proposed in this paper, This algorithm fills empty spaces with the homogeneous load-blocks of identically oriented boxes and splits residual space into three sub spaces starting with an empty container. An initial loading pattern is built by applying this approach recursively until all boxes are exhausted or no empty spaces are left. In order to generate alternative loading patterns, the load-blocks of pattern determining spaces are replaced with the alternatives that were generated on determining the load-blocks. An improvement algorithm compares these alternatives with the initial pattern to find improved one. Numerical experiments with 715 test cases show the good performance of this new algorithm, above all for problems with strongly heterogeneous boxes.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.447-459
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• 1995

A fundamental problem is to construct linear systems with given transfer functions. This problem has a well known solution for unitary linear systems whose state spaces and coefficient spaces are Hilbert spaces. The solution is due independently to B. Sz.-Nagy and C. Foias [15] and to L. de Branges and J. Ball and N. Cohen [4]. Such a linear system is essentially uniquely determined by its transfer function. The de Branges-Rovnyak construction makes use of the theory of square summable power series with coefficients in a Hilbert space. The construction also applies when the coefficient space is a Krein space [7].

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1631-1637
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• 2013

This paper generalizes the Aleksandrov problem and Mazur Ulam theorem to the case of $n$-normed spaces. For real $n$-normed spaces X and Y, we will prove that $f$ is an affine isometry when the mapping satisfies the weaker assumptions that preserves unit distance, $n$-colinear and 2-colinear on same-order.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1347-1359
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• 2017

The purpose of this paper is to give some new iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces. We also give the applications of the obtained result for the convex feasibility problem and constrained convex optimization problem in Hilbert spaces.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.771-782
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• 2019

We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.