• Structural Engineering and Mechanics
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• v.38 no.5
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• pp.593-618
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• 2011

This paper deals with the problem of the determination of the response of a viscoelastic Bernoulli-Navier beam, which is resting on an elastic medium. Assuming uniaxial bending, the displacement of the beam axis is governed by an integro-differential equation. The compatibility of the displacements between the beam and the elastic medium is imposed through an integral equation. In general and in particular in the case of a Boussinesq medium, the solution has to be pursued numerically. On the contrary, in the case of a Winkler's medium the compatibility equation becomes a linear finite relationship, which allows finding an original analytical solution of the problem for both hereditary and aging behavior of the beam. Some numerical examples complete the paper, in which a comparison is made between the hereditary and the aging model for the creep of the beam.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.53-69
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• 2017

This paper demonstrates how a nineteenth century Japanese votive temple problem known as sangaku from Okayama prefecture can be solved using traditional mathematical methods of the Japanese Edo (1603-1868 CE). We compare a modern solution to a sangaku problem from Sacred Geometry: Japanese Temple Problems of Tony Rothman and Hidetoshi Fukagawa with a traditional solution of ${\bar{O}}hara$ Toshiaki (?-1828). Our investigation into the solution of ${\bar{O}}hara$ provides an example of traditional Edo period mathematics using the tenzan jutsu symbolic manipulation method, as well as producing new insights regarding the contextual nature of the rules of this technique.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.601-612
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• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• Journal of the Korea Society of Computer and Information
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• v.22 no.9
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• pp.9-16
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• 2017

The course timetabling problem is a problem assigning a set of subjects to the given classrooms and different timeslots, while satisfying various hard constraints and soft constraints. This problem is defined as a constraint satisfaction optimization problem and is known as an NP-complete problem. Various methods has been proposed such as integer programming, constraint programming and local search methods to solve a variety of course timetabling problems. In this paper, we propose an iterative improvement search method to solve the problem based on constraint programming. First, an initial solution satisfying all the hard constraints is obtained by constraint programming, and then the solution is repeatedly improved using constraint programming again by adding new constraints to improve the quality of the soft constraints. Through experimental results, we confirmed that the proposed method can find far better solutions in a shorter time than the manual method.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.501-505
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• 1998

In this paper, an LP problem with convex polyhedral objective coefficients is treated. In the problem, the interactivities of the uncertain objective coefficients are represented by a bounded convex polyhedron (a convex polytope). We develop a computation algorithm of a maxmin achievement rate solution. To solve the problem, first, we introduce the relaxation procedure. In the algorithm, a sub-problem, a bilevel programing problem, should be solved. To solve the sub-problem, we develop a solution method based on a branch and bound method. As a result, it is shown that the problem can be solved by the repetitional use of the simplex method.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.695-703
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• 2002

The fractional order evolutionary integral equations have been considered by first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application.

• Journal of the Korea Society of Computer and Information
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• v.24 no.9
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• pp.9-20
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• 2019

In this paper, we study the university timetabling problem, which consists of two subproblems, the university course timetabling problem and the examination timetabling problem. Given a set of classrooms, students, teachers, and lectures, the problem is to assign a number of courses (and examinations) to suitable timeslots and classrooms while satisfying the given set of constraints. We discuss the modeling and solution approaches to construct course and examination timetables for one of the largest Korean university. By using binary integer programming formulations, we describe these two complex real-world problems. Then, we propose a solution method, called NOGOOD, to solve the examination timetabling model. The computation results show that NOGOOD finds the optimal examination schedule for the given instance. Although we consider a specific instance of the university timetabling problem, the methods we use can be applicable to modeling and solving other timetabling problems.

• ETRI Journal
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• v.24 no.4
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• pp.280-289
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• 2002

In this work, we present a novel approach to the bit allocation problem that aims to minimize overall distortion subject to a bit rate constraint. The optimal solution can be found by the Lagrangian method with dynamic programming. However, the optimal bit allocation for block-based interframe coding is practically unattainable because of the interframe dependency of macroblocks caused by motion compensation. To reduce the computational burden while maintaining a result close to the optimum, i.e., near optimum, we propose an alternative method. First, we present a partitioned form of the bit allocation problem: a "frame-level problem" and "one-frame macroblock-level problems." We show that the solution to this new form is also the solution to the conventional bit allocation problem. Further, we propose a bit allocation algorithm using a "two-phase optimization technique" with an interframe dependency model and a rate-distortion model.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.75-79
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• 1998

It is well known that traveling salesman problem (for short, TSP) is one of mot important problems for optimization, and almost all optimization problems result in TSP. This paper describes on an effective solution of TSP using genetic algorithm. The features of our method are summarized as follows : (1) By using division and unification method, a large problem is replaced with some small ones. (2) Smoothing method proposed in this paper enables us to obtain a fine approximate solution globally. Accordingly, demerits caused by division and unification method are decreased. (3) Parallel operation is available because all divided problems are independent of each other.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.4
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• pp.201-208
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• 2010

This research is about developing an efficient solution procedure for the vehicle routing problem under varying vehicle moving speeds for hour-based time interval. Different moving speeds for every hour is too difficult condition to solve for this type of combinatorial optimization problem. A methodology to divide the 12 hour based time interval offered by government into 5 different time intervals and then divide delivery area into 12 small divisions first and then re-organizing them into 5 groups. Then vehicle moving speeds are no longer varying in each of the 5 divisions. Therefore, a typical TSP solution procedure may be applied to find the shortest path for all 5 divisions and then connect the local shortest paths to form a delivery path for whole area. Developed solution procedures are explained in detail with 60 points example.