• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.141-151
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• 2006

We investigate the multiplicity of $2{\pi}$-periodic solutions of the nonlinear Hamiltonian system with almost polynomial and exponential potentials, $\dot{z}=J(G^{\prime}(z)+h(t))$, where $z:R{\rightarrow}R^{2n}$, $\dot{z}=\frac{dz}{dt}$, $J=\(\array{0&-I\\I&o}\)$, I is the identity matrix on $R^n$, $H:R^{2n}{\rightarrow}R$, and $H_z$ is the gradient of H. We look for the weak solutions $z=(p,q){\in}E$ of the nonlinear Hamiltonian system.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-709
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• 2006

Let X, Y be vector spaces. It is shown that if an even mapping $f:X{\rightarrow}Y$ satisfies f(0) = 0 and $$(0.1)\;f(\frac {x+y} 2+z)+f(\frac {x+y} 2-z)+f(\frac {x-y} 2+z)+f(\frac {x-y} 2-z)=f(x)+f(y)+4f(z)$$ for all x, y, z ${\in}$X, then the mapping $f:X{\rightarrow}Y$ is quadratic. Furthermore, we prove the Cauchy-Rassias stability of the functional equation (0.1) in Banach spaces.

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.59-73
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• 2019

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to $\mathcal{N}$(${\alpha}$) is investigated. For the function $f(z)=z+c_2z^2+C_3z^3+{\cdots}$ which is defined in the unit disc where $f(z){\in}\mathcal{N}({\alpha})$, we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with $f(b)={\frac{1}{b}}\int\limits_0^b$ f(t)dt. The sharpness of these inequalities is also proved.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.103-117
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• 2002

We consider the situation that ${\mathbb{Z}_p}\;=\;{\mathbb{Z}/p\mathbb{Z}}$ acts freely on a closed oriented 4-manifold X with ${b_2}^{+}\;{\geq}\;2$. In this situation, we study the relation between the Seiberg-Witten invariants of X and those of the quotient manifold $X/{\mathbb{Z}}_p$. We prove that the invariants of X are equal to those of $X/{\mathbb{Z}}_p$ modulo p.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.701-707
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• 1998

An operator $T{\in} {{\mathcal L}(H)}$ is generalized k-quasihyponormal if there exist a constant M>0 such that $T^{\ast k}[M^2(T-z)^{\ast}(T-z)-(T-z)(T-z)^{\ast}]T^k{\geq}0$ for some integer $k{\geq}0$ and all $Z{\in} {\mathbf C}$. In this paper, we show that it T is a generalized k-quasihyponormal operator with the property $0{\not\in}{\sigma}(T)$, then T is subscalar of order 2. As a corollary, we get that such a T has a nontrivial invariant subspace if its spectrum has interior in C.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.193-204
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• 2007

In this paper, we investigate some results concerning the stability of the following quadratic type functional equation: f(x + y) + f(x - y) + f(y + z) + f(y - z) + f(z + x) + f(z - x) = 4f(x) + 4f(y) + 4f(z).

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.53-68
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• 2017

The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.

• Honam Mathematical Journal
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• v.9 no.1
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• pp.71-76
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• 1987

Let M be a positive real number and c a complex numbcr such that $\left|c-1\right|<M{\leq}Re{c}$. Let $f,f(z)=z+a_{2}Z^{2}+...,$ be analytic and univalent in the unit disc. It is said to belong to the class S(c, M) if $\left|zf'(z)/f(z)-c\right|<M$ We find growth and rotation theorems for the class S(c, M).

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.269-278
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• 2021

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0, 𝜋). We find bounds for |f_z(z)|, ${\mid}f_{\bar{z}}(z){\mid}$ and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction.

• The Journal of the Acoustical Society of Korea
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• v.7 no.2
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• pp.65-73
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• 1988

In this paper, V(z) curve has been analyzed theoretically and compared with the experimental result, and the relation between the V(z) curve and the material characteristic has been studied. Angular spectrum and ray optics theory have been used for theoretical analysis and the acoustic microscope operating at a center frequency of 3 MHz has been used for experiment. In experiment, it has been shown that each material has a V(z) curve of a unique form and the interval of dips appearing in the V(z) curves have been used to determine the Rayleigh wave velocity.