• Nuclear Engineering and Technology
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• 제54권1호
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• pp.275-282
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• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Steel and Composite Structures
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• 제43권3호
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• pp.293-309
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• 2022

Accurate design models for predicting the shear resistance of headed studs in solid concrete slabs are essential for obtaining economical and safe steel-concrete composite structures. In this study, symbolic regression with genetic programming (GPSR) was applied to experimental data to formulate new descriptive equations for predicting the shear resistance of studs in solid slabs using both normal and lightweight concrete. The obtained GPSR-based nominal resistance equations demonstrated good agreement with the test results. The equations indicate that the stud shear resistance is insensitive to the secant modulus of elasticity of concrete, which has been included in many international standards following the pioneering work of Ollgaard et al. In contrast, it increases when the stud height-to-diameter ratio increases, which is not reflected by the design models in the current international standards. The nominal resistance equations were subsequently refined for use in design from reliability analyses to ensure that the target reliability index required by the Eurocodes was achieved. Resistance factors for the developed equations were also determined following US design practice. The stud shear resistance predicted by the proposed models was compared with the predictions from 13 existing models. The accuracy of the developed models exceeds the accuracy of the existing equations. The proposed models produce predictions that can be used with confidence in design, while providing significantly higher stud resistances for certain combinations of variables than those computed with the existing equations given by many standards.

• Nuclear Engineering and Technology
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• 제55권1호
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• pp.131-143
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• 2023

Constitutive equations in a nuclear reactor safety analysis code are mostly empirical correlations developed from experiments, which always accompany uncertainties. The accuracy of the code can be improved by modifying the constitutive equations fitting wider range of data with less uncertainty. Thus, the sensitivity of the code with respect to the constitutive equations is evaluated quantitatively in the paper to understand the room for improvement of the code. A new methodology is proposed which first starts by dividing the thermal hydraulic conditions into multiple sub-regimes using self-organizing map (SOM) clustering method. The sensitivity analysis is then conducted by multiplying an arbitrary set of coefficients to the constitutive equations for each sub-divided thermal-hydraulic regime with SOM to observe how the code accuracy varies. The randomly chosen multiplier coefficient represents the uncertainty of the constitutive equations. Furthermore, the set with the smallest error with the selected experimental data can be obtained and can provide insight which direction should the constitutive equations be modified to improve the code accuracy. The newly proposed method is applied to a steady-state experiment and a transient experiment to illustrate how the method can provide insight to the code developer.

• International Journal of Air-Conditioning and Refrigeration
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• 제10권2호
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• pp.65-71
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• 2002

The objective of this study is to evaluate the design parameters and to develop the cooling and heating load prediction equations of office buildings. The building load calculation simulation was carried out using the DOE-2.1E program. The results of the simulation were used as data for multiple regression analysis which could develop the load prediction equations.

• 대한수학회보
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• 제50권1호
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• pp.143-159
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• 2013

This paper is concerned with the long time behavior for the solution semiflow of the coupled two-compartment Gray-Scott equations with the homogeneous Neumann boundary condition on a bounded domain of space dimension $n{\leq}3$. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the equations possesses a global attractor in $H^k({\Omega})^4$ ($k{\geq}0$) space.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권4호
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• pp.253-265
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• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

• 대한수학회논문집
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• 제32권2호
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• pp.333-352
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• 2017

In this research work, by using the random resolvent operator techniques associated with random ($A_t$, ${\eta}_t$, $m_t$)-monotone operators, is to established an existence and convergence theorems for a class of fuzzy system of random nonlinear equations with fuzzy mappings in Hilbert spaces. Our results improve and generalized the corresponding results of the recent works.

• 대한수학회지
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• 제54권3호
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• pp.909-943
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• 2017

This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.35-48
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• 2016

In this paper we deal with the expressions of solutions and the periodicity nature of some systems of nonlinear difference equations with order three with nonzero real numbers initial conditions.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.307-316
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• 2008

Real life problems can be expressed as a congruence modulus n and split into a system of congruence equations in modulus factors of n. A system of congruence equations can be combined into a congruence equation under certain conditions. This paper uniquely presents and critically reviews the generalized Chinese Remainder Theorem (CRT) for combining systems of congruence equations into single congruence equations. Sequential and parallel implementation strategies of the generic CRT are outlined. A variety of unique applications of the CRT are discussed.