• East Asian mathematical journal
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• v.27 no.3
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• pp.339-348
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• 2011

B. C. Berndt [6] has evaluated the transformation formula for a large class of functions that includes and generalizes the classical Dedekind eta-function. In this paper, we consider a twisted version of his formula. Using this transformation formula, we derive modular trans-formation formulas for the generating functions for cranks which were central to deduce K. Mahlburg's results in [11].

• East Asian mathematical journal
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• v.30 no.3
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• pp.335-353
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• 2014

We establish multiple extence of positive solutions for parameterized nonhomogeneous elliptic equations involving critical Sobolev exponent. The approach to the problem is variational method.

• East Asian mathematical journal
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• v.30 no.3
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• pp.311-319
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• 2014

It is shown that, for an even positive integer m with $m{\geq}4$ and arbitrary positive integer k and t, the complete multipartite graph $K_{km+1(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles in such a way that the decomposition is circulant.

• East Asian mathematical journal
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• v.29 no.1
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• pp.69-82
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• 2013

In this paper we consider a doubly nonlinear Volterra equation related to the Leray-Lions with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

• East Asian mathematical journal
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• v.35 no.5
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• pp.535-545
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• 2019

This paper is concerned with the optimal control problem associated to strong solution of Belousov-Zhabotinskii reaction model in 2D domain. That is, we otain the global existence of strong solution and show the existence of optimal control.

• East Asian mathematical journal
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• v.35 no.5
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• pp.547-557
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• 2019

This paper is concerned with the necessary conditions for optimal control problem governed by some ODE-PDE systems. That is, we obtain the necessary conditions for optimal control by showing the differentiability of the solution with respect to the control.

• East Asian mathematical journal
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• v.35 no.5
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• pp.589-595
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• 2019

In this paper, we prove that a special supersingular K3 surface of Artin invariant ${\sigma}$ over a field of odd characteristic p has a model over a finite field of $p^{2{\sigma}}$ elements.

• East Asian mathematical journal
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• v.35 no.3
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• pp.297-303
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• 2019

In this paper, the author introduces the class $L^p$-BV of functions which are of bounded variation in the sense of $L^p$-norm and investigates the degree of convergence for Fourier series of functions belonging to this class.

• East Asian mathematical journal
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• v.35 no.3
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• pp.331-340
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• 2019

In this paper, we investigate the stability for the functional equation $f(x+ky)-kf(x+y)+kf(x-y)-f(x-ky)-(k^3-k)f(y)+(k^3-k)f(-y)=0$ in the sense of M. S. Moslehian and Th. M. Rassias.

• East Asian mathematical journal
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• v.35 no.3
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• pp.351-356
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• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the general quartic functional equation f(5x + y) - 5f(4x + y) + 10f(3x + y) - 10f(2x + y) + 5f(x + y) - f(y) = 0.