• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.757-770
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• 1999

We analyse in this paper the possibility of using preconditioning techniques as for square non-singular systems, also in the case of inconsistent least-squares problems. We find conditions in which the minimal norm solution of the preconditioned least-wquares problem equals that of the original prblem. We also find conditions such that thd Kaczmarz-Extendid algorithm with relaxation parameters (analysed by the author in [4]), cna be adapted to the preconditioned least-squares problem. In the last section of the paper we present numerical experiments, with two variants of preconditioning, applied to an inconsistent linear least-squares model probelm.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.461-470
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• 2007

Parameter identification is studied in viscoelastic rods by solving an inverse problem numerically. The material properties of the rod, which appear in the constitutive relations, are recovered by optimizing an objective function constructed from reference strain data. The resulting inverse algorithm consists of an optimization algorithm coupled with a corresponding direct algorithm that computes the strain fields given a set of material properties. Numerical results are presented for two model inverse problems; (i)the effect of noise in the reference strain fields (ii) the effect of minimal reference data in space and/or time data.

• Nuclear Engineering and Technology
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• 제55권6호
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• pp.2263-2275
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• 2023

In general, an internal fire events probabilistic safety assessment (PSA) model is quantified by modifying the pre-existing internal event PSA model. Because many pieces of equipment or cables can be damaged by a fire, a single fire event can lead to multiple internal events PSA initiating events (IEs). Consequently, when the fire events PSA model is quantified, inappropriate minimal cut sets (MCSs), such as duplicate MCSs, may be generated. This paper shows that single quantification of a hypothetical single-top fire event PSA model may generate the following four types of inappropriate MCSs: duplicate MCSs, MCSs subsumed by other MCSs, nonsense MCSs, and MCSs with over-counted fire frequencies. Among the inappropriate MCSs, the nonsense MCSs should be addressed first because they can interfere with the right interpretation of the other MCSs and prevent the resolution of the issues related to the other inappropriate MCSs. In addition, we propose a resolution process for each of the issues caused by these inappropriate MCSs and suggest an overall procedure for resolving them. The results of this study will contribute to the understanding and resolution of the inappropriate MCSs that may appear in the quantification of fire events PSA models.

• 한국국방경영분석학회지
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• 제25권2호
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• pp.144-157
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• 1999

In this paper, we consider a new preventive replacement policy for the system which deteriorates while it is in operation with an increasing failure rate. The system is subject to two types of failure. A type 1 failure is repairable while a type 2 failure is not repairable. In the new policy, a system is replaced at the age of $t_p$ or at the instant the$\textsc{k}^{th}$ type 1 failure occurs, whichever comes first. However, if a type 2 failure occurs before a preventive replacement is performed, a failure replacement should be made. We assume that a type 1 failure can be rectified with a minimal repair. We also assume that a replacement takes a non-negligible amount of time while a minimal repair takes a negligible amount of time. Under a cost structure which includes a preventive replacement cost, a failure replacement cost and a minimal repair cost, we develop a model to find the optimal ($\textsc{k},t_p$) policy which minimizes the expected cost per unit time in the long run while satisfying a system availability constraint.

• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.235-244
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• 2003

In unreplicated factorial or fractional factorial experiments, the presence of one or more outliers can seriously affect the analysis of variance. Using the normal plot of t residuals to identify outliers in factorial or fractional factorial is an easy method to find these dubious points. In some cases, the t residuals form the identical pairs. One can not tell from the plot which is doubtful. This phenomenon occurs for all minimal designs of resolution IV, which fits the model containing all main effects and some two-factor interactions, whether it is orthogonal or not. In these kinds of models, when we drop one point or two points (not foldover pair) from the fraction, the phenomenon of identical pairs of t residuals may still occur. In this paper, the theoretical background of the phenomenon and its sequences will be investigated in detail.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2005년도 학술발표대회 논문집
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• pp.115-120
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• 2005

This paper introduces models for preventive maintenance policies and considers periodic preventive maintenance policy with minimal repair when the failure of system occurs. It is assumed that minimal repairs do not change the failure rate of the system. The failure rate under prevention maintenance received an effect by a previously prevention maintenance and the slope of failure rate increases the model where it considered. Also the start point of failure rate under prevention maintenance considers the degradation of system and that it increases quotient, it assumed. Per unit time it bought an expectation cost from under this prevention maintenance policy. We obtain the optimal period time and the number for the periodic preventive maintenance by using Nakagawa's Algorithm, which minimizes the expected cost rate per unit time. Finally, it suppose that the failure time of a system has a Weibull distribution as an example and we obtain an expected cost rate per unit time the optimal period time and the number when cost of replacement and cost of minimal repair change.

• 대한수학회지
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• 제56권5호
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• pp.1173-1246
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• 2019

We find all P-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces (a corrected version of) Jan Steven's list [Manuscripta Math. 1993] of the numbers of P-resolutions of each singularities. We then compute the dimensions and Milnor numbers of the corresponding irreducible components of the reduced base spaces of versal deformations of each singularities. Furthermore we realize Milnor fibers as complements of certain divisors (depending only on the singularities) in rational surfaces via the semi-stable minimal model program for 3-folds. Then we compare Milnor fibers with minimal symplectic fillings, where the latter are classified by Bhupal and Ono [Nagoya Math. J. 2012]. As an application, we show that there are 6 pairs of entries in the list of Bhupal and Ono [Nagoya Math. J. 2012] such that two entries in each pairs represent diffeomorphic minimal symplectic fillings.

• 한국신뢰성학회지:신뢰성응용연구
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• 제13권4호
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• pp.229-239
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• 2013

This paper reports a manner to use a Bayesian approach to derive the optimal replacement policy. In order to produce a system with minimal repair warranty, a replacement model with the extended warranty is considered. Within the warranty period, the failed system is minimally repaired by the manufacturer at no cost to the end-user. The failure time is assumed to follow a Weibull distribution with unknown parameters. The expected cost rate per unit time, from the end-user's viewpoints, is induced by the Bayesian approach, and the optimal replacement policy to minimize the cost rate is proposed. Finally, a numerical example illustrating to derive the optimal replacement policy based on the Bayesian approach is described.

• 한국경영과학회지
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• 제14권2호
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• pp.53-66
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• 1989

The Public Vehicle Routing Problem (PVRP) is to find the minimum total cost routes of M or less Public-Vehicles to traverse the required arcs(streets) at least once, and return to their starting depot on a directed network. In this paper, first, a mathematical model is formulated as minimal cost flow model with illegal subtour elimination constraints, and with the fixed cost and routing cost as an objective function. Second, an efficient branch and bound algorithm is developed to obtain an exact solution. A subproblem in this method is a minimal cost flow problem relaxing illegal subtour elimination constraints. The branching strategy is a variable dichotomy method according to the entering nonrequired arcs which are candidates to eneter into an illegal subtour. To accelerate the fathoming process, a tighter lower bound of a candidate subproblem is calculated by using a minimum reduced coast of the entering nonrequired arcs. Computational results based on randomly generated networks report that the developed algorithm is efficient.

• 한국미생물생명공학회:학술대회논문집
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• 한국미생물생명공학회 2005년도 2005 Annual Meeting & International Symposium
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• pp.54-62
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• 2005

While genomics (the set of experimental and computational tools that allows the blueprints of life to be read) opens the doors to a more rational approach to the design and use of living cells to bring about desirable chemical transformations, genomics is, by itself, insufficient. We need tools that allow us to relate genomic and molecular information to cellular physiology and then to the response of a population of cells. We propose the development of hybrid computer cellular models. In such models genomics and chemical detail for a cellular subsystem (e.g. pathogenesis) is embedded in a coarse-grain cell model. Such a construct allows the quantitative and explicit linkage of genomic detail to cell physiology to the extracellular environment. To illustrate the principles involved we are constructing a model for a minimal cell. A minimal cell is a bacterial cell with the fewest number of genes necessary to sustain life as a free living microbe.