• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.153-176
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• 2003

From the equation of motion of a "bare" non-uniform beam (without any concentrated elements), an eigenfunction in term of four unknown integration constants can be obtained. When the last eigenfunction is substituted into the three compatible equations, one force-equilibrium equation, one governing equation for each attaching point of the concentrated element, and the boundary equations for the two ends of the beam, a matrix equation of the form [B]{C} = {0} is obtained. The solution of |B| = 0 (where ${\mid}{\cdot}{\mid}$ denotes a determinant) will give the "exact" natural frequencies of the "constrained" beam (carrying any number of point masses or/and concentrated springs) and the substitution of each corresponding values of {C} into the associated eigenfunction for each attaching point will determine the corresponding mode shapes. Since the order of [B] is 4n + 4, where n is the total number of point masses and concentrated springs, the "explicit" mathematical expression for the existing approach becomes lengthily intractable if n > 2. The "numerical assembly method"(NAM) introduced in this paper aims at improving the last drawback of the existing approach. The "exact"solutions in this paper refer to the numerical results obtained from the "continuum" models for the classical analytical approaches rather than from the "discretized" ones for the conventional finite element methods.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.299-308
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• 2009

It is very rare to conduct an experimental design with a single objective in mind. since we have uncertainties in model and its assumptions. Basically we have three approaches in literature to handle this problem, the mini-max, compound, constrained experimental design. Since Cook and Wong (1994) announced the equivalence between the compound and the constrained design, many constrained experimental design approaches have adopted the approximate design algorithm of compound experimental design. In this paper we attempt to modify the row-exchange algorithm under exact experimental design setting, not approximate experimental design one. This attempt will provide more realistic design setting for the field experiment. In this process we proposed another criterion on how to set the constrained experimental design. A graph to show the general issue of infeasibility, which occurs quite often in constrained experimental design, is suggested.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.1
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• pp.161-176
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• 2005

In a situation that ordinal preferences on multiattribute weights are captured, we present two solution approaches: an exact approach and an approximate method. The former, an exact solution approach via interaction with a decision-maker, pursues the progressive reduction of a set of non-dominated alternatives by narrowing down the feasible attribute weights region. Subsequent interactive questions and responses, however, sometimes may not guarantee the best alternative or a complete rank order of a set of alternatives that the decision-maker desires to have. Approximate solution approaches, on the other hand, can be divided into three categories including surrogate weights methods, dominance value-based decision rules, and three classical decision rules. Their efficacies are evaluated in terms of choice accuracy via a simulation analysis. The simulation results indicate that a proposed hybrid approach, intended to combine an exact solution approach through interaction and a dominance value-based approach, is recommendable for aiding a decision making in a case that a final choice is seldom made at single step under attribute weights that are imprecisely specified beyond ordinal descriptions.

• International Journal of Highway Engineering
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• v.18 no.2
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• pp.51-60
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• 2016

PURPOSES : The applicability of the mechanics-based similarity concept (suggested by Feng et al.) for determining scaled variables, including length and load, via laboratory-scale tests and discrete element analysis, was evaluated. METHODS: Several studies on the similarity concept were reviewed. The exact scaling approach, a similarity concept described by Feng, was applied in order to determine an analytical solution of a free-falling ball. This solution can be considered one of the simplest conditions for discrete element analysis. RESULTS : The results revealed that 1) the exact scaling approach can be used to determine the scale of variables in laboratory tests and numerical analysis, 2) applying only a scale factor, via the exact scaling approach, is inadequate for the error-free replacement of small particles by large ones during discrete element analysis, 3) the level of continuity of flowable materials such as SCC and cement mortar seems to be an important criterion for evaluating the applicability of the similarity concept, and 4) additional conditions, such as the kinetics of particle, contact model, and geometry, must be taken into consideration to achieve the maximum radius of replacement particles during discrete element analysis. CONCLUSIONS : The concept of similarity is a convenient tool to evaluate the correspondence of scaled laboratory test or numerical analysis to physical condition. However, to achieve excellent correspondence, additional factors, such as the kinetics of particles, contact model, and geometry, must be taken into consideration.

• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.229-234
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• 2008

A Cook-type distance is considered for investigating the influence of observations in constrained regression models. Its exact sampling distribution is derived, which is used for judging whether each observation is influential or not. A numerical example is provided for illustration.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.559-570
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• 1998

This paper introduces doubly Winsorized Poisson auto-model by truncating the support of a Poisson random variable both from above and below, and shows that this model has a same form of negpotential function as regular Poisson auto-model and one-way Winsorized Poisson auto-model. Strategies for maximum likelihood estimation of parameters are discussed. In addition to exact maximum likelihood estimation, Monte Carlo maximum likelihood estimation may be applied to this model.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1051-1068
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• 2015

We use methods of relative homological algebra on the category C(mod${\Lambda}$), of complexes of finitely generated modules over an artin algebra ${\Lambda}$, to give some characterizations of almost split sequences.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.555-563
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• 2002

This paper discusses cubic equations in general saddlepoint approximations. Exact roots are found for various cases by trigonometric identities, the root which is appropriate for the general saddlepoint approximations is selected and discussed, and the defective cases in which the general saddlepoint approximations cannot be used are found.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.197-204
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• 1996

We consider a two sample rank test for a bivariate mixture distribution based on Johnson's quantile score. The test statistic is simple to calculate and the exact distribution under the null hypothesis is obtained. A numerical example is given.

• Tunnel and Underground Space
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• v.3 no.2
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• pp.109-117
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• 1993

The existence and exact location of cavity is very important for the stability of the large underground storage house or building. Numerical method such as finite element method and finite diference methods are widely used because of model's complexity. Preliminary tests such as calculation step test, mesh size test and model size test were tried. Upper shadow zone and lower shadow zone can be calculated from 50% amplitude level of measuring data. From these statistical methods, the calculatied position of cavity coincided nearly with actual position of model testing cavity.