• Interaction and multiscale mechanics
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• v.2 no.2
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• pp.129-151
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• 2009

This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.161-184
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• 2020

In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of [18,19]. We also prove the boundedness of the k-fractional integral operator on L_p[a, b].

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.118-127
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• 1991

In this paper, criteria and algorithms for the optimal service rate in a closed queueing network have been established. The objective is to minimize total cost. It is shown that system throughput is increasing concave over the service rate of a node and cycle time is increasing convex over the set of service times with a single calss of cubsomers. This enables developing an algorithm using a steepest descent method when the cost function for service rate is convex. The efficiency of the algorithm rests on the fact that the steepest descent direction is readily obtained at each iteration from the MVA algorithm. Several numerical examples are presented. The major application of this research is optimization of facility capacity in a manufacturing system.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.171-177
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• 1993

In this paper, we show that Greene-Krantz's conjecture is true for certain class of domains. In fact, we give a complete classification of automorphism groups of domains of the form (Fig.) where the function .phi. is a real valued $C^{\infty}$ function in a neighborhood of [0,1] which satisfies the following conditions; (1) .phi.(0)=.phi.'(0)=0 and .phi.(1)=1, (2) .phi.(t) is increasing and convex for t>0.vex for t>0.

• Journal of the Korea Safety Management & Science
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• v.16 no.2
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• pp.217-230
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• 2014

The purpose of this study is to develop the Generalized Depreciation Function (GDF) and Winfrey Depreciation Function (WDF) by reviewing methods for the depreciation accountings. The Depreciation Accounting Models (DAM), including straight-line model, declining-balance model, sum-of-the-year-digit model and sinking fund model presented in this paper, are reclassified into the charging pattern of increasing type, decreasing type and constant type. This paper also discusses the development of the GDFs based on convex type, concave type and constant type according to the demand pattern of product, frequency of plant usage, deterioration of time, relative inadequacy, Capital Expenditure (CAPEX) and Operating Expenditure (OPEX) of the Total Productive Maintenance (TPM). The WDFs presented in this paper depict a sudden degradation of plant performance by measuring the change of TPM activity at the midpoint of useful life of asset. The WDFs are classified into left-modal type, symmetrical type and right-modal type by varying the value of skewness and kurtosis. Moreover, three increasing patterns, such as convex, concave and linear types, are used in this paper to present the distinct identification of WFDs by using Instantaneous Depreciation Rate (IDR) in terms of Performance Depreciation Function (PDF) and Depreciation Density Function (DDF). In order to have better understanding of depreciation models, the numerical examples are used for evaluating the Net Operating Less Adjusted Tax (NOPLAT) and Economic Value Added (EVA). It is concluded that the depreciation models showing a large dispersion of EVA require the adjustment of NOPLAT and Invested Capital (IC) based on the objective cash basis and net operating activity for reducing the variation of EVA.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.4
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• pp.279-283
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• 2005

This paper deals with the design of a low-order H/sub ∞/ controller by using an iterative linear matrix inequality (LMI) method. The low-order H/sub ∞/ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, the recently developed penalty function method is applied. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. Numerical experiments showed the effectiveness of the proposed algorithm.

• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.1
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• pp.24-30
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• 1988

We study the optimal allocation of machines and pallets in a class of manufacturing systems. The FMS is modeled as a closed queueing network with balanced loading of the stations. An Algorithm is developed, which exploits the properties of the throughput function and solves the allocation problem for increasing concave profit and convex cost. We also study the more general case of allocating machines and pallets among a set of FMSs. A dynamic programming approach is developed, which solves the problem with O(M$^{3}$N$^{2}$) operations.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1105-1116
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• 1996

A partial ordering is developed among weakly positive quadrant dependent (WPQD) bivariate random vectors. This permits us to measure the degree of WPQD-ness and to compare pairs of WPQD random vectors. Some properties and closures under certain statistical operations are derived. An application is made to measures of dependence such as Kendall's $\tau$ and Spearman's $\rho$.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.3
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• pp.1-10
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• 1996

In this paper, the problem of simultaneously allocating servers and loadings of stations in a class of manufacturing systems modelled as network of queues is considered. The throughput function of the closed network of queues is demonstrated as a Schur convex function of server allocation, that is, increasing the server allocation vector under majorization increases the performance in the ship in terms of the throughput. It also reduces the congestion in the open network of queues in terms of reducing the total number of jobs in the sense of likelihood ratio ordering. These are the extentions of the numerical results of Green and Guha (1995) in the service system with independent M/M/c systems to the network of queues. The results can be used to support production planning in certain manufacturing systems.

• International Journal of Precision Engineering and Manufacturing
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• v.7 no.4
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• pp.51-56
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• 2006

This paper proposes a control algorithm, which is verified experimentally, for aspherical surface grinding and polishing. The algorithm provides simultaneous control of the position and interpolation of an aspheric curve. The nonlinear formula for the tool position was derived from the aspheric equation and the shape of the tool. The function was partitioned at specific intervals and the control parameters were calculated at each control section. The position, acceleration, and velocity at each interval were updated during the process. A position error feedback was introduced using a rotary encoder. The feedback algorithm corrected the position error by increasing or decreasing the feed speed. In the experimental verification, a two-axis machine was controlled to track an aspherical surface using the proposed algorithm. The effects of the control and process parameters were monitored. The results demonstrated that the maximum tracking error with tuned parameters was at the submicron level for concave and convex surfaces.