• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.711-730
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• 1994

We consider Gibbs measures on $(R \times W_{0,0})^{Z^\nu}, W_{0,0} = {\omega \in C[0,1] : \omega(0) = \omega(1)}$, which are associated to an interaction between particles in lattice boson systems (quantum unbounded spin systems). In [4], the Gibbs measures were introduced in the study of equilibrium states of interacting lattice boson systems and were characterized by means of the equilibrium conditions. In this paper we utilize the techniques of the stochastic calculus of variations and the infinite dimensional Ito integral to derive stochastic equations which we call the equilibrium equations. We show that under appropriate conditions the equilibrium conditions and the equilibrium equations are equivalent. The lattice boson systems with superstable and regular interactions, which we studied in [4], are typical examples.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.663-677
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• 1999

This work is concerned mainly with the variational problem on an immersion x:M $\rightarrow$} $E^4$ . A new approach is introduced depends on the normal variation in any arbitrary normal direction in the normal bundle. The results of this work are considered as a continuation and an extension to that obtained in [1], [2] and [3], [4] respectively. The methods adapted here are based on Cartan's methods of moving frames and the calculus of variations.

• Journal of Pharmacopuncture
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• v.1 no.1
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• pp.35-52
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• 1997

In order to investigate experimentally that Bovis Calculus, Ursi Feli Aqua-acupuncture(BUA) have an effect on Adjuvant Arthritis in rats, the author inserted BUA at points corresponding with Chok-samni(ST36) and T'aegye(KI3), and observed an inhibitory rate of edema and pain, variations of White blood cell(WBC), Red blood cell(RBC), Hemoglobin(Hb) in blood. The author also observed the histological changes of joint tissue. The results were as follows : 1. The BUA group during the 6th and 9th were decreased with statistical significance in inhibitory rate of paw edema as compared with the control group. 2. The BUA group during the 3rd and 9th day were decreased with statistical significance in inhibitory rate of pain as compared with the control group. 3. The BUA group during the 3rd, 6th and 9th day were decreased with statistical significance in blood WBC as compared with the control group. The blood RBC and Hb didn't have statistical significance. 4. According to the histological studies, the synovial cells were necrotized at the 3rd, 6th and 9th day control group, but some synovial cells were necrotized at the 3rd day BUA group. The synovial cells of the the 6th and 9th day BUA group were recovered more than that of the 3th day group.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.737-748
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• 2018

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

• The Journal of Fisheries Business Administration
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• v.23 no.2
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• pp.53-67
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• 1992

It has been recognized, virtually from the time of its inception, that fisheries economics, like other aspects of resource economics, should ideally be cast in capital-theoretic terms. The fish population or biomass can be viewed as a capital stock in that, like conventional or man-made capital, it is capable of yielding a sustainable consumption flow through time. This study is to introduce the optimal control theory which was extended from the theory of calculus of variations into the study of former static theory of fisheries economics started by Gordon (1954). The optimal control theory eliminated the inadequacies of the classical techniques to a large extent. From this point of view, this study, on the base of Schaefer model, summerizes most of major results achieved so far, but does so in a manner such that the links with capital theory are made transparent. This study explores two sets of problems. The first concerns the optimal approach to the equilibrium stock, i.e. the optimal investment policy. The second set of problems arises from the relaxation of the highly restrictive assumption of autonomy (i.e. the assumption that the parameters are independent of time), then concludes the relaxation of linearity assumption together with the complexities caused by that.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.97-113
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• 2004

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.

• Bulletin of the Society of Naval Architects of Korea
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• v.20 no.2
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• pp.27-36
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• 1983

This paper presents numerical results of the added mass and damping coefficients of vertical axisymmetric bodies on or under the free surface. Also computed are the excitation forces on these bodies due to an incident regular wave system. The numerical scheme employs a localized finite-element method, which is based on the theory of the calculus of variations. The excitation forces and moments on a submerged half-spheroid lying on the bottom are computed and compared with the results obtained by others. he agreement is good. Several specific types of floating vertical axisymmetric platforms are considered for ten different wave lengths, in connection with the design of an ocean-thermal-energy converter platform. The added mass and damping coefficient, as well as the excitations, are presented. It is shown that simple strip theory gives a good approximation of the sway(and pitch) added mass for a disc platform having a long circular cylinder.

• Journal of Astronomy and Space Sciences
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• v.25 no.3
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• pp.255-266
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• 2008

The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.3
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• pp.6-15
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• 1992

This paper proposes a method for the global optimization of redundancy over the whole task period for a kinematically redundant robot. The necessary conditions based on the calculus of variations for an integral type cost criterion result in a second-order differential equation. For a cyclic task, the periodic boundary conditions due to conservativity requirements are discussed. We refine the two-point boundary value problem to an initial value adjustment problem and suggest a numerical search method for providing the conservative global optimal solution using the gradient projection method. Since the initial joint velocity is parameterized with the number of the redundancy, we only search the parameter value in the space of as many dimensions as the number of degrees of redundancy. We show through numerical examples that multiple nonhomotopic extremal solutions and the generality of the proposed method by considering the dynamics of a robot.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.121-130
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• 2018

This study deals with optimum geometry design of laterally loaded piles in a Winkler's medium through the Fully Stressed Design (FSD) method. A numerical algorithm distributing the mass by means of the FSD method and updating the moment by finite elements is implemented. The FSD method is implemented here using a simple procedure to optimise the beam length using an approach based on the calculus of variations. For this aim two conditions are imposed, one transversality condition at the bottom end, and a one sided constraint for moment and mass distribution in the lower part of the beam. With this approach we derive a simple condition to optimise the beam length. Some examples referred to different fields are reported. In particular, the case of laterally loaded piles in Geotechnics is faced.