• East Asian mathematical journal
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• v.31 no.3
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• pp.321-335
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• 2015

The existence of at least one solution to a system of multipoint boundary value problems on an infinite interval is investigated by using the Alternative of Leray-Schauder.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.349-356
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• 2005

In this paper, by using the Leray-Schauder continuation theorem and Wirtinger-type inequalities, we establish the existence and uniqueness theorems for two-point boundary value problems of a certain class of fourth-order nonlinear differential equations.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.823-824
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• 2018

• IEMEK Journal of Embedded Systems and Applications
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• v.18 no.4
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• pp.195-201
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• 2023

The degree of contribution each sensor makes towards the total information gathered by all sensors is not uniform in spatially correlated sensor fields. Considering bit allocation problem in such a spatially correlated sensor field, the number of bits to be allocated to each sensor should be proportional to the degree of contribution the sensor makes. In this paper, we deploy Shapley value, a representative solution concept in cooperative game theory, and utilize it in order to quantify the degree of contribution each sensor makes. Shapley value is a system that determines the contribution of an individual player when two or more players work in collaboration with each other. To this end, we cast the bit allocation problem into a cooperative game called bit allocation game where sensors are regarded as the players, and a payoff function is given in the criteria of mutual information. We show that the Shapley value fairly quantifies an individual sensor's contribution to the total payoff achieved by all sensors following its desirable properties. By numerical experiments, we confirm that sensor that needs more bits to cover its area has larger Shapley value in spatially correlated sensor fields.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.1
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• pp.157-162
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• 2023

To NP-complete 3-SAT problem, this paper proposes a O(nm) polynomial time algorithm, where n is the number of literals and m is the total frequency of all literals in equation f. The algorithm firstly decides a truth value of a literal in sequence of previously-set priority. The priority order is as follows: a literal whose occurrence in a clause is 1(k=1), a literal which is k≥2 and whose truth value is either 0 or 1, and a literal with the minimum frequency. Then, literals whose truth value is determined are then deleted from clause T and the remaining clauses. This process is repeated l times, the number of literals. As a result, the proposed algorithm has been successful in accurately determining the satisfiability of a given equation f and in deciding the truth value of all the literals. This paper, therefore, provides not only a linear-time algorithm as a viable solution to the SAT problem, but also a basis for solving the P versus NP problem.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• Journal of the Korean Institute of Navigation
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• v.24 no.5
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• pp.361-371
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• 2000

This paper treats a genetic algorithm for ship scheduling problem in set packing formulation. We newly devised a partition based representation of solution and compose initial population using a domain knowledge of problem which results in saving calculation cost. We established replacement strategy which makes each individual not to degenerate during evolutionary process and applied adaptive mutate operator to improve feasibility of individual. If offspring is feasible then an improve operator is applied to increase objective value without loss of feasibility. A computational experiment was carried out with real data and showed a useful result for a large size real world problem.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.249-265
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• 2017

Interface problem here refers to a second order elliptic problem with a discontinuous coefficient for the second order derivatives. For the corresponding boundary value problem, the maximum principle still holds but Hopf's boundary point lemma may fail. We will give an optimal power type estimate that replaces Hopf's lemma at those boundary points, where this coefficient jumps.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.6
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• pp.780-785
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• 1998

In this paper, it is shown that the conventional methods for dealing with the singularity problem of a manipulator can be generalized as a local minimization problem with differently weighted objective functions. A new damping method proposed in this article automatically determines the damping amounts for singular values, which are inversely proportional to the magnitude of the singular values. Furthermore, this can be done without explicitly computing the singular values. The proposed method can be applied to all the manipulators with revolute joints.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.183-198
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• 2003

We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.