• Steel and Composite Structures
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• 제45권6호
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• pp.851-863
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• 2022

This research deals with the study of the Thomson heating effect in magneto-thermoelastic homogeneous isotropic rotating medium, influenced by linearly distributed load and as a result of modified couple stress theory. The charge density is taken as a function of the time of the induced electric current. The heat conduction equation with energy dissipation and with hyperbolic two-temperature (H2T) is used to formulate the model of the problem. Laplace and Fourier transforms are used to solve this mathematical model. Various components of displacement, temperature change, and axial stress as well as couple stress are obtained from the transformed domain. To get the solution in physical domain, numerical inversion techniques have been employed. The Thomson effect with GN (Green-Nagdhi) -III theory and Modified Couple Stress Theory (MCST) is shown graphically on the physical quantities.

• Advances in materials Research
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• 제11권1호
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• pp.23-39
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• 2022

This work deals with the two-dimensional deformation in a homogeneous isotropic nonlocal magneto-thermoelastic solid with two temperatures under the effects of inclined load at different inclinations. The mathematical model has been formulated by subjecting the bounding surface to a concentrated load. The Laplace and Fourier transform techniques have been used for obtaining the solution to the problem in transformed domain. The expressions for nonlocal thermal stresses, displacements and temperature are obtained in the physical domain using a numerical inversion technique. The effects of nonlocal parameter, rotation and inclined load in the physical domain are depicted and illustrated graphically. The results obtained in this paper can be useful for the people who are working in the field of nonlocal thermoelasticity, nonlocal material science, physicists and new material designers. It is found that there is a significant difference due to presence and absence of nonlocal parameter.

• Journal of the Korean School Mathematics Society
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• 제9권1호
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• pp.57-76
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• 2006

In this paper, we generalized number partion problems in elementary situations to number partition models that provide some mathematical problem situations for experiencing mathematising of secondary pre-service teachers. We designed substantial teaching units entitled 'the inquiry intof number partition models' through 4 steps: (1) key problems, (2) integration from the view of partition, (3) defining partition (4) a real practice of inquiry into models. This teaching unit can contribute to secondary pre-service teacher education as follows: first, This teaching unit have pre-service teachers experience mathemtising. second, This teaching unit have pre-service teachers see the connection between school mathematics and academic mathematics. third, This teaching unit have pre-service teachers foster their mathematical creativity.

• Journal of the Korean Mathematical Society
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• 제44권4호
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Journal of the Institute of Electronics Engineers of Korea SD
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• 제39권2호
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• pp.27-38
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• 2002

A new self-consistent mathematical model for semiconductor quantum well device was developed. The model was based on the direct solution of the Boltzmann transport equation, coupled to the Schrodinger and Poisson equations. The solution yielded the distribution function for a two-dimensional electron gas(2DEG) in quantum well devices. To solve the Boltzmann equation, it was transformed into a tractable form using a Legendre polynomial expansion. The Legendre expansion facilitated analytical evaluation of the collision integral, and allowed for a reduction of the dimensionality of the problem. The transformed Boltzmann equation was then discretized and solved using sparce matrix algebra. The overall system was solved by iteration between Poisson, Schrodinger and Boltzmann equations until convergence was attained.

• School Mathematics
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• 제15권4호
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• pp.957-973
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• 2013

This study analyzed Secondary Mathematically Gifted' mathematical thinking processes demonstrated from the activities. They configured regular triangle tessellations in the Non-Euclidean hyperbolic disk model. The students constructed the figure and transformation to construct the tessellation in the poincare disk. gsp file which is the dynamic geometric environmen, The students were to explore the characteristics of the hyperbolic segments, construct an equilateral triangle and inversion. In this process, a variety of strategic thinking process appeared and they recognized to the Non-Euclidean geometric system.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• 제12권5호
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• pp.694-704
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• 2001

In this work, We evaluate the performance of eigencanceller which can suppress directional interferences and noise effectively while maintaining specified beam pattern constraints. The constraints and optimal weight vector of eigencanceller vary by using interference and noise or desired signal, interference and noise as array input signal. From the analysis results in the steady state, We show that weight vectors in each case are simplified the form of projection equation that belongs to desired subspace orthogonal to interference subspace and eigencanceller has the better performance than DMI method through mathematical analysis and simulation.

• Journal of Biomedical Engineering Research
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• 제22권4호
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• pp.311-319
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• 2001

Statistical reconstruction methods in the context of a Bayesian framework have played an important role in emission tomography since they allow to incorporate a priori information into the reconstruction algorithm. Given the ill-posed nature of tomographic inversion and the poor quality of projection data, the Bayesian approach uses regularizers to stabilize solutions by incorporating suitable prior models. In this work we show that, while the quantitative performance of the standard filtered backprojection (FBP) algorithm is not as good as that of Bayesian methods, the application of spline-regularized smoothing to the sinogram space can make the FBP algorithm improve its performance by inheriting the advantages of using the spline priors in Bayesian methods. We first show how to implement the spline-regularized smoothing filter by deriving mathematical relationship between the regularization and the lowpass filtering. We then compare quantitative performance of our new FBP algorithms using the quantitation of bias/variance and the total squared error (TSE) measured over noise trials. Our numerical results show that the second-order spline filter applied to FBP yields the best results in terms of TSE among the three different spline orders considered in our experiments.

• Preventive Nutrition and Food Science
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• 제20권3호
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• pp.215-220
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• 2015

The moisture sorption isotherms of vacuum-dried edible green alga (Capsosiphon fulvescens) powders were determined at 25, 35, and $45^{\circ}C$ and water activity ($a_w$) in the range of 0.11~0.94. An inversion effect of temperature was found at high water activity (>0.75). Various mathematical models were fitted to the experimental data, and Brunauer, Emmett, and Teller model was found to be the most suitable model describing the relationship between equilibrium moisture content and water activity (<0.45). Henderson model could also provide excellent agreement between the experimental and predicted values despite of the intersection point. Net isosteric heat of adsorption decreased from 15.77 to 9.08 kJ/mol with an increase in equilibrium moisture content from 0.055 to $0.090kg\;H_2O/kg$ solids. The isokinetic temperature ($T_{\beta}$) was 434.79 K, at which all the adsorption reactions took place at the same rate. The enthalpy-entropy compensation suggested that the mechanism of the adsorption process was shown to be enthalpy-driven.

• Geophysics and Geophysical Exploration
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• 제27권3호
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• pp.181-195
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• 2024

This tutorial explains that the static effect in the magnetotelluric (MT) survey is a physical phenomenon caused by charges accumulated on the boundaries of subsurface inhomogeneities. To facilitate understanding of the physical phenomenon, differences between static induction and charge accumulation on the boundary are explained and analyzed with help of schematic illustrations. Subsequently, from the electromagnetic (EM) integral equation formulation, it is clearly shown that the secondary electric field due to charges accumulated on the interface in the presence of the primary field appears as the static effect. Therefore, except in the cases of the layered earth or a two-dimensional earth with transverse magnetic (TM) mode excitation, the static effect always exists in MT responses and further, it is not 'static' but rather frequency dependent. Despite the fact that the static effect is a secondary electric field due to inhomogeneity, inevitable under-sampling in the frequency and spatial domains prevent the effect from being handled properly in numerical inversion. Therefore, considering the practical aspects of the MT survey, which cannot be a continuous measurement covering the entire survey area over a wide frequency band, a three-dimensional (3-D) inversion incorporating the static shift as a constraint with the Gaussian distribution is introduced. To enhance understanding of the integral equation EM modeling, the formulation of the 3-D integral equation and mathematical analyses of the Green tensor and scattering current are described in detail in the Appendix.