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QUADRATIC FORMS ON THE $\mathcal{l}^2$ SPACES
Chung, Phil-Ung 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
In this article we shall introduce several operators on the reproducing kernel spaces and investigate quadratic forms on the $\mathcal{l}^2$ space. Using these operators we shall obtain a particular solution of a system of quadratic equations(1.5). Finally we can find an approximate solution of(1.5) by optimization of a nonnegative biquadratic polynomial.
Chung, Kyung-Tae,Chung, Phil-Ung,Hwang, In-Ho Korean Mathematical Society 1998 대한수학회보 Vol.35 No.4
Chung and et al. ([2].1991) introduced a new concept of a manifold, denoted by $^{\ast}g-SEX_n$, in Einstein's n-dimensional $^{\ast}g$-unified field theory. The manifold $^{\ast}g-SEX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{\lambda \nu}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor $^{\ast}g^{\lambda \nu}$. Recently, Chung and et al.([3],1998) obtained a concise tensorial representation of SE-curvature tensor defined by the SE-connection of $^{\ast}g-SEX_n$ and proved deveral identities involving it. This paper is a direct continuations of [3]. In this paper we derive surveyable tensorial representations of constracted curvature tensors of $^{\ast}g-SEX_n$ and prove several generalized identities involving them. In particular, the first variation of the generalized Bianchi's identity in $^{\ast}g-SEX_n$, proved in theorem (2.10a), has a great deal of useful physical applications.
Chung, Kyung-Tae,Chung, Phil-Ung,Hwang, In-Ho Korean Mathematical Society 1998 대한수학회지 Vol.35 No.4
Recently, Chung and et al. ([11], 1991c) introduced a new concept of a manifold, denoted by *g-SE $X_{n}$ , in Einstein's n-dimensional *g-unified field theory. The manifold *g-SE $X_{n}$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor * $g^{λν}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor * $g^{λν}$. This paper is the first part of the following series of two papers: I. The SE-curvature tensor of *g-SE $X_{n}$ II. The contracted SE-curvature tensors of *g-SE $X_{n}$ In the present paper we investigate the properties of SE-curvature tensor of *g-SE $X_{n}$ , with main emphasis on the derivation of several useful generalized identities involving it. In our subsequent paper, we are concerned with contracted curvature tensors of *g-SE $X_{n}$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in *g-SE $X_{n}$ , which has a great deal of useful physical applications.tions.
ON THE RELATION BETWEEN THE TIMEWIDTHS ?<sub>f</sub> AND ?<sub>f*h</sub>
Chung, Phil-Ung,Han, Song-Ho The Kangwon-Kyungki Mathematical Society 2000 한국수학논문집 Vol.8 No.2
In the present paper we shall first introduce the timewidth of a signal, and then we shall investigate the relation between the timewidths of a signal $f$ and of the convolution $f*h$ for some other signal $h$.
HOW TO SOLVE AN INFINITE SIMULTANEOUS SYSTEM OF QUADRATIC EQUATIONS
Chung, Phil Ung,Lin, Ying Zhen The Kangwon-Kyungki Mathematical Society 2005 한국수학논문집 Vol.13 No.2
In the present paper we shall introduce several operators on the reproducing kernel spaces. And using them we shall find a solution of an infinite system of quadratic equations (1.1). In particular we shall convert problem for finding an approximate solution of infinite system of quadratic equations into problem for minimizing nonnegative biquadratic polynomial.