• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.719-728
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• 2012

In this paper, we develop a numerical method to solving an optimal control problem, which is governed by a parabolic partial differential equations(PDEs). Our approach is to approximate the PDE problem to initial value problem(IVP) in $\mathbb{R}$. Then, the homogeneous part of IVP is solved using semigroup theory. In the next step, the convergence of this approach is verified by properties of one-parameter semigroup theory. In the rest of paper, the original optimal control problem is solved by utilizing the solution of homogeneous part. Finally one numerical example is given.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.2
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• pp.131-144
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• 1992

Even though nonhomogeneous Markov Decision Processes subsume homogeneous Markov Decision Processes and are more practical in the real world, there are many results for them. In this paper we address the nonhomogeneous Markov Decision Process with objective to maximize average reward. By extending works of Ross [17] in the homogeneous case adopting the result of Bean and Smith [3] for the dicounted deterministic problem, we first transform the original problem into the discounted nonhomogeneous Markov Decision Process. Then, secondly, we transform into the discounted deterministic problem. This approach not only shows the interrelationships between various problems but also attacks the solution method of the undiscounted nohomogeneous Markov Decision Process.

• ETRI Journal
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• v.26 no.5
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• pp.423-431
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• 2004

In earlier works on transmitter power control in cellular radio systems, the problem of whether a signal-to-interference ratio (SIR) threshold is achievable is determined by apparently different rules for homogeneous and heterogeneous SIR systems. In this paper, we present a unified and more universal framework for both cases. We also highlight the conditions under which a given SIR threshold vector for the heterogeneous SIR system is achievable, although so far there is no general solution to this problem.

• Structural Engineering and Mechanics
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• v.53 no.1
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• pp.27-40
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• 2015

The rational analytical solutions are presented for functionally graded beams subjected to arbitrary tractions on the upper and lower surfaces. The Young's modulus is assumed to vary exponentially along the thickness direction while the Poisson's ratio keeps unaltered. Within the framework of symplectic elasticity, zero eigensolutions along with general eigensolutions are investigated to derive the homogeneous solutions of functionally graded beams with no body force and traction-free lateral surfaces. Zero eigensolutions are proved to compose the basic solutions of the Saint-Venant problem, while general eigensolutions which vary exponentially with the axial coordinate have a significant influence on the local behavior. The complete elasticity solutions presented here include homogeneous solutions and particular solutions which satisfy the loading conditions on the lateral surfaces. Numerical examples are considered and compared with established results, illustrating the effects of material inhomogeneity on the localized stress distributions.

• Geomechanics and Engineering
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• v.9 no.5
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• pp.631-644
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• 2015

This article considers the problems of cylindrical bending of functionally graded plates in which material properties vary through the thickness. The variation of the material properties follows two power-law distributions in terms of the volume fractions of constituents. In addition, this paper considers orthotropic materials rather than isotropic materials. The traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. Numerical results are presented to show the effect of the material distribution on the deflections and stresses. Results show that, all other parameters remaining the same, the studied quantities (stress, deflection) of P-FGM and E-FGM plates are always proportional to those of homogeneous isotropic plates. Therefore, one can predict the behaviour of P-FGM and E-FGM plates knowing that of similar homogeneous plates.

• Steel and Composite Structures
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• v.11 no.6
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• pp.489-504
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• 2011

This paper presents a theoretical investigation in free vibration of sigmoid functionally graded beams with variable cross-section by using Bernoulli-Euler beam theory. The mechanical properties are assumed to vary continuously through the thickness of the beam, and obey a two power law of the volume fraction of the constituents. Governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the vibration of the S-FGM beam are obtained for three different types of boundary conditions associated with simply supported, clamped and free ends. Results show that, all other parameters remaining the same, the natural frequencies of S-FGM beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of S-FGM beams knowing that of similar homogeneous beams.

• Advances in aircraft and spacecraft science
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• v.1 no.2
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• pp.219-232
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• 2014

This paper reports on an ongoing study investigating the feasibility of using an evolutionary method to develop the rules governing Self-Organised (SO) systems for use in swarms of unmanned aerial vehicles. In general, it is difficult to design swarm systems that follow explicit global behaviour. Unlike optimising a predefined objective function, the solution to the problem is the emergent behaviour in the SO systems which results from simultaneous interactions among agents and between agents and their environment. In this study, evolutionary algorithms are used to investigate their control and effectiveness in synthesising the weighting of different rules on SO emergent behaviour. Both homogeneous swarms and heterogeneous swarms were considered though the results provided are for a case study investigating the simplest problem a homogeneous swarm without mutation. Though simple this study does indicate the potential of the approach.

• Bulletin of the Korean Chemical Society
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• v.28 no.11
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• pp.2029-2033
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• 2007

Hydrotalcite, layered double hydroxides (LDH), with hexagonal morphology has been rapidly synthesized by microwave reaction within 1 hour by urea hydrolysis from homogeneous solution. Different synthesis parameters, Mg/Al molar ratio, microwave reaction temperature and microwave power were systematically investigated. Pure hydrotalcite phase was obtained for Mg/Al ratios of 2:1 and 3:1, and higher reaction temperature gave higher crystallinity. The hydrotalcite synthesized at 600W power shows the highest crystallinity and more homogeneous crystal size distribution. The hydrotalcite samples were characterized by powder X-ray diffraction (XRD), simultaneous thermogravimetric/differential thermal analysis (TG/DTA), Fourier Transform Infrared (FT-IR) and Scanning electron micrograph (SEM).

• Bulletin of the Korean Chemical Society
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• v.34 no.2
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• pp.595-599
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• 2013

The coordination of pyridyl-N to pentacyanoferrate for the detection of small organic antigens in solution is presented. The unique contribution of this paper is the direct conjugation of pyridyl-N in small organic antigens to pentacyanoferrate. Pentacyanoferrate is promising as an electrochemical label owing to its good electro-chemical properties, which can be utilized to generate an electrical signal in homogeneous electrochemical immunoassays. The facilely synthesized pyridyl-N to pentacyanoferrate was characterized by the electrochemical and spectroscopic methods. Hippuric acid (HA) has been detected competitively on the interaction of free HA and pentacyanoferrate-(4-aminomethylpyridine-hippuric acid) (Fe-HA) to its antibody, with the detection limit of 0.50 ${\mu}g\;mL^{-1}$. While pentacyanoferrate-based immunoassay is in its simplicity and infancy, the proposed immunoassay offers attractive opportunities for developing pyridyl-N-based the electrochemical detection of small organic antigens in the health care area.

• Geotechnical Engineering
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• v.13 no.1
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• pp.101-110
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• 1997

This paper presents a two dimensional p-version static infinite element for analyzing $1/r^n$ displacement decay type problems in unbounded media. The proposed element is developed by using shape functions based on approximate expressions of an analytical solution. Numerical results are presented for an opening in a homogeneous elastic infinite medium and a rigid footing rested on a homogeneous elastic half-space. The numerical results show the effectiveness of the proposed infinite element.