• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.837-844
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• 2010

In this paper, a class of initial value problem of hyperbolic equations for fourth order with multiple characteristics is considered and can be solved analytically by variable transforms. Also, similar to Goursat's problem we present a direct integration technique for finding a new solutions of an inhomogeneous hyperbolic equation of fourth order such that the attached conditions are given on its multiple characteristics.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.61-69
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• 2021

In this paper, we introduce a new three-step iterative scheme for three finite families of nonexpansive mappings in hyperbolic spaces. And, we establish a strong convergence and a ∆-convergence of a given iterative scheme to a common fixed point for three finite families of nonexpansive mappings in hyperbolic spaces. Our results generalize and unify the several main results of [1, 4, 5, 9].

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.309-322
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• 2021

A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.575-588
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• 2023

In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an n-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.407-420
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• 2024

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.1
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• pp.167-176
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• 1991

Finite element programs are developed, adopting the hyperbolic model and the Cam-clay model. In the hyperbolic model, a new model taking into account the volume change during shear is proposed and a new technique considering the density change underneath a footing is proposed. And a computing algorithm considered as more reasonable than existing one is presented. In the Cam-clay model, the deveoloped program is applied to sand, the case not recorded much, and then it is tried to analiza the behavior of sand from the viewpoint of the critical state concept. For this, the conventional CD triaxial compression tests and the footing model tests are carried out. The results are improved by 60 percent by using the modified hyperbolic model proposed. When the Cam-clay model is applied to sand, a model reflecting the overconsolidation effects and a computing algorithm accounting for the strain softening are needed. The results obtained by using the Cam-clay model are not much influenced by the value of the initial poisson's ratio, but those of the modified hyperbolic model are much influenced by that. So th values of the initial poisson's ratio must be selected deliberately in the numerical analysis.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.87-93
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• 1998

Mejia and Minda proved that if a hyperbolic simply connected region $\Omega$ is k-convex, then (equation omitted), $z \in \Omega$. We show that this inequality actually characterizes k-convex regions.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.149-157
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• 2015

We show that $C^1$-generically, the shadowable chain component of a $C^1$-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.191-202
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• 2005

A condition on forcing term insuring the multiplicity of Dirichlet-periodic solutions of nonlinear dissipative hyperbolic equations is discussed. The nonlinear term is assumed to have coercive growth.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.933-936
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• 1996

In this paper, we shall prove that the Kim-Kostrikin group is isomorphic to a hyperbolic orbifold group and so it is infinite.