• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.395-404
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• 2005

Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination

• 약학회지
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• 제27권1호
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• pp.1-10
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• 1983

Voltammetric deposition and differential pulse anodic stripping (DPASV) of Ge(IV)at a gold electrode was investigated. Germanium (IV) exhibits two stripping peaks by DPASV in sodium borate solution, the first peak at about -1.1v. vs SCE and the second one, in the range of -0.6 to -0.2v. vs SCE. Factors affecting the sensitivity and precision included the nature of working electrode, supporting electrolytes, deposition potential, deposition time, pH, pulse height, voltage scan rate. The relative standard deviation of the measurements of the peak currents, for 100ng/ml Ge(IV), was less than ${\pm}3%$. The detection limit of Ge(IV) was 0.01ng/ml. Percent recovery in the extraction procedure of Ge(IV) from matrices by benzene in c-HCl, followed by back extraction with saturated borax solution, ranged from 96 to 104%.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.559-581
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• 2021

In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral differential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Current Optics and Photonics
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• 제7권5호
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• pp.537-544
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• 2023

Differential phase contrast (DPC) microscopy, a central quantitative phase imaging (QPI) technique in cell biology, facilitates label-free, real-time monitoring of intrinsic optical phase variations in biological samples. The existing DPC imaging theory, while important for QPI, is grounded in paraxial diffraction theory. However, this theory lacks accuracy when applied to high numerical aperture (NA) systems that are vital for high-resolution cellular studies. To tackle this limitation, we have, for the first time, formulated a nonparaxial DPC imaging equation with a transmission cross-coefficient (TCC) for high NA DPC microscopy. Our theoretical framework incorporates the apodization of the high NA objective lens, nonparaxial light propagation, and the angular distribution of source intensity or detector sensitivity. Thus, our TCC model deviates significantly from traditional paraxial TCCs, influenced by both NA and the angular variation of illumination or detection. Our nonparaxial imaging theory could enhance phase retrieval accuracy in QPI based on high NA DPC imaging.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권1호
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• pp.33-58
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• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• Computers and Concrete
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• 제34권3호
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• pp.347-353
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• 2024

This paper investigates the second-grade fluid between two parallel plates. Fluid is produced due to stretching. Convective heat and mass transfer features are elaborated with thermal and solutal stratification. Thermal radiation and chemical reactions are also assumed in heat and mass transport processes partial differential. Formulated non-linear partial differential equations are transformed into non-linear ordinary differential equations by utilizing the suitable transformation. Convergent series solutions are computed via Homotopy Analysis Method (HAM). Effects of Hartman number, temperature field, velocity distribution and Prandtl number are sketched and analyzed through graphs. It is noticed that velocity field first decreases and after some distance it shows increasing behavior by the increment.

• Structural Engineering and Mechanics
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• 제90권3호
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• pp.219-232
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• 2024

In current study, for the first time, Nonlinear Bending of a skew microplate made of a laminated composite strengthened with graphene nanosheets is investigated. A mixture of mechanical and thermal stresses is applied to the plate, and the reaction is analyzed using the First Shear Deformation Theory (FSDT). Since different percentages of graphene sheets are included in the multilayer structure of the composite, the characteristics of the composite are functionally graded throughout its thickness. Halpin-Tsai models are used to characterize mechanical qualities, whereas Schapery models are used to characterize thermal properties. The microplate's non-linear strain is first calculated by calculating the plate shear deformation and using the Green-Lagrange tensor and von Karman assumptions. Then the elements of the Couple and Cauchy stress tensors using the Modified Coupled Stress Theory (MCST) are derived. Next, using the Hamilton Principle, the microplate's governing equations and associated boundary conditions are calculated. The nonlinear differential equations are linearized by utilizing auxiliary variables in the nonlinear solution by applying the Frechet approach. The linearized equations are rectified via an iterative loop to precisely solve the problem. For this, the Differential Quadrature Method (DQM) is utilized, and the outcomes are shown for the basic support boundary condition. To ascertain the maximum values of microplate deflection for a range of circumstances-such as skew angles, volume fractions, configurations, temperatures, and length scales-a parametric analysis is carried out. To shed light on how the microplate behaves in these various circumstances, the resulting results are analyzed.

• 패션비즈니스
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• 제13권1호
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• pp.91-101
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• 2009

The purpose of this study is to develop semantic differential scales which are necessary to evaluate visual image and effect of flare skirt. As a result of the first survey of 362 female college students, the most effective factors for shape of flare skirt are silhouette, volume of flare, and skirt length. Based on this result, we made flare skirt simulation for visual evaluation with using I-Designer program. 4 kinds of volume of flare($90^{\circ},\;180^{\circ},\;270^{\circ},\;360^{\circ}$) and 3 kinds of skirt length(48cm, 58cm, 68cm) are combined as variables for flare skirt of visual evaluation. For the second survey of 362 female college students, we asked to write suggested adjectives freely. As a result, we could draw out 210 adjectives. 'Feminine' was most frequently used word for flare skirt, and then, 'vivid', 'rhythmic', 'cute', 'soft', 'fat', and 'comfortable' in this order. With considering frequently used words in the preceding study, we selected 41 adjectives. Antonyms were selected from the resulted frequency of this study and preceding study, and the rest of words were found from dictionary. From these process, we developed semantic differential scales for visual image and effect of flare skirt.

• 전기학회논문지
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• 제59권8호
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• pp.1489-1496
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• 2010

A feed forward differential architecture of analog PRML decoder is investigated to implement on analog parallel processing circuits. The conventional PRML decoder performs the trellis processing with the implementation of single stage in digital and its repeated use. The analog parallel processing-based PRML comes from the idea that the decoding of PRML is done mainly with the information of the first several number of stages. Shortening the trellis processing stages but implementing it with analog parallel circuits, several benefits including higher speed, no memory requirement and no A/D converter requirement are obtained. Most of the conventional analog parallel processing-based PRML decoders are differential architecture with the feedback of the previous decoded data. The architecture used in this paper is without feedback, where error metric accumulation is allowed to start from all the states of the decoding stage, which enables to be decoded without feedback. The circuit of the proposed architecture is simpler than that of the conventional analog parallel processing structure with the similar decoding performance. Characteristics of the feed forward differential architecture are investigated through various simulation studies.