• Journal of the Korean Mathematical Society
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• v.61 no.5
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• pp.975-995
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• 2024

In this paper, we utilize Nevanlinna theory to study the existence and forms of solutions for quadratic trinomial complex partial differential-difference equations of the form aF² + 2ωFG + bG² = exp(g), where ab ≠ 0, ω ∈ ℂ with ω² ≠ 0, ab and g is a polynomial in ℂⁿ. In order to achieve a comprehensive and thorough analysis, we study the characteristics of solutions in two specific cases: one when ω² ≠ 0, ab and the other when ω = 0. Because polynomials in several complex variables may exhibit periodic behavior, a property that differs from polynomials in single complex variables, our study of finding solutions of equations in ℂⁿ is significant. The main results of the paper improved several known results in ℂⁿ for n ≥ 2. Additionally, the corollaries generalize results of Xu et al. [Rocky Mountain J. Math. 52(6) (2022), 2169-2187] for trinomial equations with arbitrary coefficients in ℂⁿ. Finally, we provide examples that endorse the validity of the conclusions drawn from the main results and their related remarks.

• Journal of Pharmaceutical Investigation
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• v.32 no.2
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• pp.73-80
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• 2002

Cefuroxime axetil is a cephalosporin antibiotic having a high activity against a wide spectrum of Grampositive and Gram-negative microorganisms. It is a cephalosporin antibiotic which exist as 2 diastereoisomers: diastereoisomer A and B. It shows polymorphism of three forms: a crystalline form having a melting point of about $180^{\circ}C$, a substantially amorphous form having a high melting point of about $135^{\circ}C$ and a substantially amorphous form having a low melting point of about 70^{\circ}C$. The crystalline form of cefuroxime axetil is slightly soluble in water because diastereoisomer A has lower solubility than B in water. Substantially amorphous form of which there are no difference in solubility between diastereoisomer A and B has better solubility than crystalline form, but it forms a thicker gel than crystalline form upon contact with an aqueous medium. Based on this reason, cefuroxime axetil is not readily absorbable in the gastrointestinal tract, rendering its bioavailability on oral administration very low. The object of this study was to develop an improved non-crystalline cefuroxime axetil composition having a high physicochemical stability and bioavailability. A non-crystalline cefuroxime axetil solid dispersant showing no peak on a Differential Scanning Calorimetry (DSC) scan is prepared by dissolving cefuroxime axetil and a surfactant in an organic solvent; suspending a water-insoluble inorganic carrier in the resulting solution; and spray drying the resulting suspension to remove the organic solvent, said solid dispersant having an enhanced dissolution and stability of cefuroxime axetil and being useful for the preparation of a pharmaceutical composition for oral administration. Tablet was formulated with this cefuroxime axetil solid dispersant, disintegrants and other ingredients. It disintegrated and dissolved easily and dynamically in dissolution medium, so showed a good dissolution profile.

• ETRI Journal
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• v.40 no.3
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• pp.347-354
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• 2018

Using various offset times to separate differential services is the most common form of service differentiation in optical burst switching networks. In this approach, a larger offset time is given to a higher priority burst, but it causes this burst to have a longer delay. One solution to this problem is to adjust the burst assembly time so that the buffering delay of the higher priority burst is always shorter than that of the lower priority burst. However, this adjustment causes another problem, called delay unfairness, for bursts with differential priorities that share the same path to their destination. This article proposes a new solution for delay fairness using the burst assembly.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.34 no.5
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• pp.173-178
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• 1985

The control of a linear system with random coefficients is discussed here. The cost function is of a quadratic form and the random coefficients are assumed to be completely observable by the controller. Stochastic Process involved in the problem by the controller. Stochastic Process involved in the problem formulation is presented to be the unique strong solution to the corresponding stochastic differential equations. Condition for the optimal control is represented through the existence of solution to a Cauchy problem for the given nonlinear partial differential equation. The optimal control is shown to be a linear function of the states and a nonlinear function of random parameters.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.15-27
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• 2008

We present and discuss an algorithm for the numerical solution of initial value problems of the form $D_*^\alpha$y(t) = f(t, y(t)), y(0) = y0, where $D_*^\alpha$y is the derivative of y of order $\alpha$ in the sense of Caputo and 0<${\alpha}{\leq}1$. The algorithm is based on the fractional Euler's method which can be seen as a generalization of the classical Euler's method. Numerical examples are given and the results show that the present algorithm is very effective and convenient.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1113-1118
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• 2004

This paper presents the dynamic analysis method for an electromechanical system. The engineer has at his disposal a variety of software simulation tools. However, difficulties arise when the study of the behavior of complex electromechanical systems in combination with coupling element is required. Typical examples of such systems are machines for factory automation, home automation, and office automation. Dynamic systems analysis packages or electronic systems analysis packages offer the restrictive to simulate these mixed systems such electromechanical product. Electronic circuit analysis algorithm is easily incorporated into a multi-body dynamics analysis algorithm. The governing equation of electronic circuit is formulated as a differential algebraic equation form including both electrical and mechanical variables and is simultaneously solved in every time step. This analysis method clearly demonstrates the application potential for mixed electromechanical simulation.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.303-308
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• 2002

A governing differential equation (GDE) of PSC flexural member with constant eccentricity considering the long-term losses including concrete creep, shrinkage, and PS steel relaxation is derived based on the two approaches. The first approach utilizes the force and moment equilibrium equations derived based on the geometry of strains of the uniform and curvature strains while the second one utilizes the principle of minimum total potential energy formulation. The identity of the two GDE's is verified by comparing the coefficients consisting of the GDE's. The boundary conditions resulting from the functional analysis of the variational calculus are investigated. Rayleigh-Ritz method provides a way to get the explicit form of the continuous deflection function in which the total potential energy is minimized with respect to the unknown coefficients consisting of the trial functions. As a closure, the analytically calculated results are compared with the experiments and show good agreements.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.279-290
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• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• Journal of Korean Society for Atmospheric Environment
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• v.14 no.4
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• pp.303-312
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• 1998

To obtain the solution to the time-dependent particle size distribution of an aerosol undergoing gravitational coagulation, the moment method was used which converts the non linear integro-differential equation to a set of ordinary differential equations. A semi-numerical solution was obtained using this method. Subsequently, an analytic solution was given by approximating the collision kernel into a form suitable for the analysis. The results show that during gravitational coagulation, the geometric standard deviation increases and the geometric mean radius decreases as time increases.