• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.161-166
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• 1986

Through the paper, we consider functions f analytic in the unit disk D={z:vertical bar z vertical bar <1} normalized by f(0)=0 and f'(0)=1. Following Rogosinski [5], we let T denote the class of all typically-real functions f which preserve half-plane in the following sense.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• Structural Engineering and Mechanics
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• v.23 no.5
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.145-155
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• 1997

• The Mathematical Education
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• v.13 no.2
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• pp.21-23
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• 1974

• Honam Mathematical Journal
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• v.43 no.3
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• pp.465-481
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• 2021

Let f be the function defined on the open unit disk, with f(0) = 0 = f'(0) - 1, satisfying Re (αf'(z) + (1 - α)zf'(z)/f(z)) > 0 or Re (αf'(z) + (1 - α)(1 + zf"(z)/f'(z)) > 0 respectively, where 0 ≤ α ≤ 1. Estimates for the Toeplitz determinants have been obtained when the elements are the coefficients of the functions belonging to these two subclasses.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.25-33
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• 2023

This paper's objectives are to present the $\mathcal{H}$ class of analytical functions and explore the many characteristics of the functions that belong to this class. Some inequalities regarding the angular derivative have been discovered for the functions in this class. In addition, the symmetry points on the unit disc are used for the obtained inequalities.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.15-25
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• 1983

The main purpose of the present paper is to generalize the results obtained by A. Hindmarsh in [7] to the holomorphic functions with non-negative real part defined on a complete circular domain D in certain class D in the complex euclidean space $C^{n}$. As described in .cint.2, D includes the bounded symmetric domains.s.

• Steel and Composite Structures
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• v.35 no.5
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• pp.671-685
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• 2020

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic-metal-ceramic (CMC) and metal-ceramic-metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton's principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.329-368
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• 1999

This paper surveys recent remarkable progress in the study of potential theory for symmetric stable processes. It also contains new results on the two-sided estimates for Green functions Poisson kernels and Martin kernels of discontinuous symmetric $alpha$ -stable process in bounded $C^{1,1}$ open sets. The new results give ex-plicit information on how the comparing constants depend on pa-rametrer $alpha$ and consequently recover the green function and Poisson kernel estimates for Brownian motion by passing $alpha{\uparrow}2$. In addition to these new estimates this paper surveys recent progress in the study of notions of harmonicity integral representation of harmonic func-tions boundary harnack inequality conditional gauge and intrinsic ultracontractivity for symmetric stable processes. Here is a table of contents.