• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.53-69
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• 2022

In this paper, we are concerned with a class of mixed Hessian curvature equations with non-degeneration. By using the maximum principle and constructing an auxiliary function, we obtain the interior gradient estimate of (k - 1)-admissible solutions.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.491-511
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• 2006

The existence of the admissible solution for conservation laws of trilinear type occurring material sciences was proved by Abeyaratne and Knowles. LeFloch proved the existence of admissible solutions of conservation laws of this type via Glimm's method. In this paper we introduce a front tracking solution and prove the existence of the front tracking solution. We also investigate the admissibility of solutions via the Front Tracking Method.

• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.115-123
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• 2011

The present work deals with obtaining the critical buckling load and the natural frequencies of clamped, orthotropic, rectangular thin plates subjected to different linear distributed in-plane forces. An analytical solution is proposed. Using the Ritz method, the dependence between in-plane forces and natural frequencies are estimated for various plate sizes, and some results are compared with finite element solutions and where possible, comparison is made with previously published results. Beam functions are used as admissible functions in the Ritz method.

• Transactions of Materials Processing
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• v.3 no.1
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• pp.23-37
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• 1994

The upper bound element technique(UBET) is used to analyze the final stage of the axisymmetric forward extrusion. Kinematically admissible velocity field involving curved surface of velocity discontinuity is assumed. The required power to arise the piping defect is obtained and is compared with Aviture's solution a the same condition. Conditions for inception of the cavity and development of the pipe are predicted. The internal radius of the pipe and critical length of billet are also determined. Experiments are carried out for extrusion with lead specimens to investigate the piping phenomena. The theoretically predicted results showed reasonably good agreement with the experimental observation.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.61-76
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• 2002

The robust non-fragile guaranteed cost control problem is studied in this paper for class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-hounded arid time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound far all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost contrellers is 7iven in terms of the feasible solution to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.

• Journal of Electrical Engineering and Technology
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• v.4 no.1
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• pp.55-65
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• 2009

Due to the rapid increase of electricity demand, consideration of environmental constraints in optimal power flow (OPF) problems is increasingly important. In Algeria, up to 90% of electricity is produced by thermal generators (vapor, gas). In order to keep the emission of gaseous pollutants like sulfur dioxide (SO2) and Nitrogen (NO2) under the admissible ecological limits, many conventional and global optimization methods have been proposed to study the trade-off relation between fuel cost and emissions. This paper presents an efficient decomposed Parallel GA to solve the multi-objective environmental/economic dispatch problem. At the decomposed stage the length of the original chromosome is reduced successively and adapted to the topology of the new partition. Two subproblems are proposed: the first subproblem is related to the active power planning to minimize the total fuel cost, and the second subproblem is a reactive power planning design based in practical rules to make fine corrections to the voltage deviation and reactive power violation using a specified number of shunt dynamic compensators named Static Var Compensators (SVC). To validate the robustness of the proposed approach, the algorithm proposed was tested on the Algerian 59-bus network test and compared with conventional methods and with global optimization methods (GA, FGA, and ACO). The results show that the approach proposed can converge to the near solution and obtain a competitive solution at a critical situation and within a reasonable time.