• Management Science and Financial Engineering
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• 제22권1호
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• pp.5-12
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• 2016

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

• 인지과학
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• 제1권2호
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• pp.317-346
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• 1989

물체의 외곽형태로부터 개념적 인식을 도출학기 위하여 사람의 직관과 부합하는 인지적 형태분할 방법을 제안하였다. 의미있는 부분과 그들의 관계로써 형태의 구조를 기술한느 표현은 인지능력을 포함하며 보다 인간적인 방법이다. 일반적으로 인고물은 많은 동직선들과 규칙성을 갖는다. 이러한 인공물의 인지적 분할을 위해서 인지실험에서 의거한 많은 규칙들을 동직선성과 규칙성의 맥락에서 적용하였다. 자연물에 관한 인지적 분할은 하나의 오목점에 대하여 선과 점들의 가능한 배치를 분석하여 이루어졌다. 분할선의 길이, 오목점에서 분할선의 수효, 오목점의 근접성, 오목점의 첨예성, 점들의 대응성과 같은 5가지의 평가기준을 가중합으로 하여 각 배치에 대한 비용함수를 계산한다. 이들 기준은 근접성, 대칭성, 단순성과 같은 사람의 지각속성을 반영한다. 가장 적합한 점은 비용함수를 계산하여 3가지 점들의 집합에서 선택된다. 상이한 종류의 형태에 대하여 수행된 실험은 사람의 직관과 호응하는 결과를 보여 주었다.

• Journal of the Korean Statistical Society
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• 제18권1호
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• pp.62-71
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• 1989

We consider a Markov proces ${X_n} on [0,\infty)^k$ which is generated by $X_{n+1} = f(X_n) + \varepsilon_{n+1}$ where f is a continuous, nondecreasing concave function. Sufficient conditions for the existence of a unique invariant probability measure for ${X_n}$ are obtained.

• 한국통신학회논문지
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• 제38A권8호
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• pp.724-732
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• 2013

본 논문은 다중 사용자 (multiuser) 다중 안테나 (MIMO, multiple-input and multiple-output) 시스템을 기반으로 거대 안테나 시스템 (massive MIMO system)에 대한 성능 분석을 진행한다. 하향 링크 프레임 구조를 고려한 평균 셀 용량을 도출하고, 해당 평균 셀 용량을 기지국 안테나 수 및 사용자 수에 대하여 분석한다. 평균 셀 용량은 기지국 안테나 수 및 사용자 수에 대해 오목 함수 (concave function)이며 이러한 특징을 통해 최적의 기지국 안테나 수 및 사용자 수를 도출한다. 실험 결과를 통해 수식적으로 도출한 최적 안테나 수 및 사용자 수는 실험을 통한 최적 값과 일치함을 확인하였으며 도출한 최적 값을 통해 최대 값의 평균 셀 용량을 얻을 수 있음을 확인할 수 있다.

• Journal of Communications and Networks
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• 제15권4호
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• pp.362-369
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• 2013

The optimal number of users achieving the maximum sum throughput is analyzed in zero-forcing (ZF) based multiuser multiple-input multiple-output (MIMO) systems with a large number of base station (BS) antennas. By utilizing deterministic ergodic sum rates for the ZF-beam forming (ZF-BF) and ZF-receiver (ZF-R) with a large number of BS antennas [1], [2], we can obtain the ergodic sum throughputs for the ZF-BF and ZF-R for the uplink and downlink frame structures, respectively. Then, we can also formulate and solve the optimization problems maximizing the ergodic sum throughputs with respect to the number of users. This paper shows that the approximate downlink sum throughput for the ZF-BF is a concave function and the approximate uplink sum throughput for the ZF-R is also a concave function in a feasible range with respect to the number of users. The simulation results verify the analyses and show that the derived numbers of users provide the maximum sum throughputs for the ZF-BF as well as ZF-R in multiuser MIMO systems with a large number of BS antennas.

• Current Optics and Photonics
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• 제5권3호
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• pp.220-228
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• 2021

To improve the measurement accuracy of a solar-radiation observer instrument, aiming at the problem of multiorder-stray-light interference caused by the diffraction of the flat-field concave grating in the spectroscopic system, straylight suppression methods for different forms of optical traps are studied. According to the grating surface-scattering distribution-function model, the bidirectional scattering distribution function (BSDF) of a dust-polluted surface and the flat-field concave grating's transition area of the spectroscopic system is calculated, and a Lyot stop with blade baffle is designed to suppress this kind of stray light. For diffraction multiorder stray light, based on the theory of light-energy transmission, a design for precise positioning of the trench optical trap is proposed. The superiority of the method is verified through simulation and actual measurement. The simulation results show that in a spectroscopic system approximately 160 mm × 140 mm × 80 mm in size, the energy of the stray light is reduced by one order of magnitude by means of the trench optical trap and Lyot stop, and the number of beams is reduced from 5664 to 1040. The actual measurements show that the stray-light-suppression efficiency is about 69.4%, which is effective reduction of the amount of stray light.

• 대한수학회보
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• 제51권5호
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• pp.1551-1559
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• 2014

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle ${\pi}{\alpha}$, ${\alpha}{\in}(1,2]$, at infinity. We derive the exact interval for the variability of the real Taylor coefficients of these functions and we prove that the corresponding complex Taylor coefficients of such functions are contained in certain discs lying in the right half plane. In addition, we also determine generalized central functions for the aforesaid class of functions.

• 경영과학
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• 제10권1호
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• pp.193-205
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• 1993

This paper presents a mathematical model for a class of vertical integration decisions. The problem structure of interest consists of raw material vendors, components suppliers, components processing plants, final product (assembly) plants and external components buyers. Economic feasibility of operating components plants instead of keeping outside suppliers is our major concern. The model also determines assignment of product lines and production volumes to each open plant considering the cost impacts of economies of scale and plant complexity. The problem formulation leads to a concave, mixed integer mathematical program. Given the state of the art of nonlinear programming techniques, it is often not possible to find global optima for reasonably sized such problems. We developed an optimization solution algorithm within the framework of Benders decomposition for the case of a piecewise linear concave cost function. It is shown that our algorithm generates optimal solutions efficiently.

• Steel and Composite Structures
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• 제27권6호
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• pp.777-788
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• 2018

An investigation on the thermal buckling resistance of simply supported FGM beams having parabolic-concave thickness variation and temperature dependent material properties is presented in this paper. An analytical formulation based on the first order beam theory is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. a function of thickness variation is introduced which controls the parabolic variation intensity of the beam thickness without changing its original material volume. The results showed the high importance of taking into account the temperature-dependent material properties in the thermal buckling analysis of such critical beam sections. Different Influencing parametric on the thermal stability are studied which may help in design guidelines of such complex structures.

• Steel and Composite Structures
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• 제29권5호
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• pp.591-602
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• 2018

This research presents an investigation on the thermal buckling resistance of FGM plates having parabolic-concave thickness variation exposed to uniform and gradient temperature change. An analytical formulation is derived and the governing differential equation of thermal stability is solved numerically using finite difference method. A specific function of thickness variation is introduced where it controls the parabolic variation intensity of the thickness without changing the original material volume. The results indicated that the loss ratio in buckling resistance is the same for any gradient temperature profile. Influencing geometrical and material parameters on the loss ratio in the thermal resistance buckling are investigated which may help in design guidelines of such complex structures.