• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.10
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• pp.1854-1860
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• 2008

In this paper, we deal with the problem of delay-dependent robust and non-fragile stabilization for descriptor systems with parameter uncertainties and time-varying delays on the basis of strict LMI(linear matrix inequality) technique. Also, the considering controller is composed of multiplicative uncertainty. The delay-dependent robust and non-fragile stability criterion without semi-definite condition and decomposition of system matrices is obtained. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free and stable in spite of all admissible parameter uncertainties, time-varying delays, and controller fragility. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.2
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• pp.168-174
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• 1983

The study is concerned with an analysis on the hydrofilm extrusion through conical dies. The upper bound method is adopted for the analysis of metal deformation in connection with hydrodynamic lubrication theory for the lubricant in order to determine the extrusion pressure for some variables such as reduction of area, die cone angle. In the upper bound method, a kinematically admissible velocity field is found by assuming proper streamlines and applying the flow function concept to the region of plastic deformation. The effect of work hardening is incorporated approximately by calculating the strains at the exit of the die. The experiments are carried out with the commercially pure aluminium for some chosen variables at room temperature. It is shown that the theoretical predictions are in good agreement with the experimental observations.

• Journal of KSNVE
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• v.5 no.3
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• pp.345-352
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• 1995

A very simple and computationally efficient numerical method is developed for the free vibration of arbitrary shape plates. A set of two- dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies for the arbitrary shape plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series function are constructed with adding order of polynomial. Natural frequencies are obtained for the arbitrary shape plates, with combinational boundary conditions. The obtained numerical results are presented, some cases are verified with other numerical methods in the literature.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.939-949
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• 2011

In this paper we give two matching theorems of Ky Fan type concerning open or closed coverings of nonempty convex sets in a topological vector space. One of them will permit us to put in evidence, when X and Y are convex sets in topological vector spaces, a new subclass of KKM(X, Y) different by any admissible class $\mathfrak{u}_c$(X, Y). For this class of set-valued mappings we establish a KKM-type theorem which will be then used for obtaining existence theorems for the solutions of two types of simultaneous relation problems.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.445-458
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• 2018

In this article we study the inclusion properties of the Bessel-Struve kernel functions in the Janowski class. In particular, we find the conditions for which the Bessel-Struve kernel functions maps the unit disk to right half plane. Some open problems with this aspect are also given. The third order differential subordination involving the Bessel-Struve kernel is also considered. The results are derived by defining suitable classes of admissible functions. One of the recurrence relation of the Bessel-Struve kernel play an important role to derive the main results.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1299-1322
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• 2020

We consider closed, star-shaped, admissible hypersurfaces in ℝⁿ⁺¹ expanding along the flow Ẋ = |X|^α-1 F^-β, α ≤ 1, β > 0, and prove that for the case α ≤ 1, β > 0, α + β ≤ 2, this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a round sphere after rescaling. Besides, for the case α ≤ 1, α + β > 2, if furthermore the initial closed hypersurface is strictly convex, then the strict convexity is preserved during the evolution process and the flow blows up at finite time.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.1-20
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• 2004

The paper presents a numerical method for the limit analysis of structures made of a rigid no-tension material. Firstly, we formulate the constrained minimum problem resulting from the application of the kinematic theorem, which characterizes the collapse multiplier as the minimum of all kinematically admissible multipliers. Subsequently, by using the finite element method, we derive the corresponding discrete minimum problem in which the objective function is linear and the inequality constraints are linear as well as quadratic. The method is then applied to some examples for which the collapse multiplier and a collapse mechanism are explicitly known. Lastly, the solution to the minimum problem calculated via numerical codes for quadratic programming problems, is compared to the exact solution.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1174-1177
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• 1987

The design of flow control protocols for integrared networks with complete voice traffic on the data link level is investigated. The class of admissible flow control policies analyzed maximized the average data link throughput subject to an average system time delay constraints a finite intervals (O,s). In particular, it is shown that the optimum control law is bang-bang (window flow mechanism). The window size L can be analytically derived from maximum tolerated time delay T, the input arrival C of the queueing system, the duration of the time interval S, the initial number of packets in the queue.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.6
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• pp.971-981
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• 1994

In this paper, we consider feedback-linearizing control of VR (Variable Reluctance) motors which have been increasingly used in high performance direct-drive applications. We characterize all torque controllers that can make the generated torque of a VR motor linear to torque command but without torque ripple. The torque controlles maximize the range of torque commands which are admissible under the physical limitation in stator currents. The whole class of all such torque controllers is parameterized in the explicit form which contains a function to be chosen freely. This free function can be used to achieve other control objectives as well as linear dynamic characteristics. As the examples for optimal choices of the free function, we actually determine two optimal free functions, one for minimal rate of change in current commands and the other for minimal power loss due to stator resistance. To illuminate further the practical use of torque controllers proposed in this paper, we present some experimental results for the case of a commercially available VR motor.