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Linear preservers of spanning column rank of matrix sums over semirings
송석준 대한수학회 2008 대한수학회지 Vol.45 No.2
The spanning column rank of an m × n matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix pairs which satisfy additive properties with respect to spanning column rank of matrices over semirings. The spanning column rank of an m × n matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix pairs which satisfy additive properties with respect to spanning column rank of matrices over semirings.
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Sasakian twistor spinors and the first Dirac eigenvalue
김의철 대한수학회 2016 대한수학회지 Vol.53 No.6
On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1 \geq 5, \, m \, \equiv 0 \, \mbox{mod} \, 2,$ we prove a new eigenvalue estimate for the Dirac operator. In dimension 5, the estimate is valid without the eta-Einstein condition. Moreover, we show that the limiting case of the estimate is attained if and only if there exists such a pair $(\varphi_{\frac{m}{2} -1} , \, \varphi_{\frac{m}{2}} )$ of spinor fields (called {\it Sasakian duo}, see Definition 2.1) that solves a special system of two differential equations.
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A note on end properties of Marcinkiewicz Integral
Yong Ding 대한수학회 2005 대한수학회지 Vol.42 No.5
In this note we give the mapping properties of the Marcinkiewicz integral $\mu_\Omega$ at some end spaces.~More precisely, we first prove that $\mu_\Omega$ is a bounded operator from $H^{1,\infty}(\Bbb R^n)$ to $L^{1,\infty}$ $(\Bbb R^n)$.~As a corollary of the results above, we obtain again the weak type (1,1) boundedness of $\mu_\Omega,$ but the condition assumed on $\Omega$ is weaker than Stein's condition.~Finally, we show that $\mu_\Omega$ is bounded from BMO$(\Bbb R^n)$ to BMO$(\Bbb R^n)$.~The results in this note are the extensions of the results obtained by Lee and Rim recently.
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THE SYMMETRY OF spinC DIRAC SPECTRUMS ON RIEMANNIAN PRODUCT MANIFOLDS
홍규식,성찬영 대한수학회 2015 대한수학회지 Vol.52 No.5
It is well-known that the spectrum of a spinC Dirac operator on a closed Riemannian spinC manifold M2k of dimension 2k for k ∈ N is symmetric. In this article, we prove that over an odd-dimensional Riemannian product M2p/1 × M2q+1/2 with a product spinC structure for p ≥ 1, q ≥ 0, the spectrum of a spinC Dirac operator given by a product connection is symmetric if and only if either the spinC Dirac spectrum of M2q+1/2 is symmetric or (e 1/2 c1(L1)Aˆ(M1))[M1] = 0, where L1 is the associated line bundle for the given spinC structure of M1.
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The conditions for repelling the automorphism orbit from the boundary point
변지수 대한수학회 2003 대한수학회지 Vol.40 No.4
In this paper, we first prove that there are no automorphismorbits accumulating at a boundary point of the largest isolatedfinite type. We also present a generalization of the results ofIsaev and Krantz on the structure of the orbit accumulationpoints.
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Schatten's theorem on absolute Schur algebras
Jitti Rakbud,Pachara Chaisuriya 대한수학회 2008 대한수학회지 Vol.45 No.2
In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten’s Theorem on the Banach space B(l₂) of bounded linear operators on l₂ involving the duality relation among the class of compact operators K, the trace class C₁ and B(l₂). We also study the reflexivity in such the algebras. In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten’s Theorem on the Banach space B(l₂) of bounded linear operators on l₂ involving the duality relation among the class of compact operators K, the trace class C₁ and B(l₂). We also study the reflexivity in such the algebras.
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Complete moment convergence of moving average processes with dependent innovations
김태성,고미화,최용갑 대한수학회 2008 대한수학회지 Vol.45 No.2
Let {Yi;-∞<i<∞} be a doubly infinite sequence of identically distributed and Φ-mixing random variables with zero means and finite variances and {ai;-∞< i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of [수식] under some suitable conditions. Let {Yi;-∞<i<∞} be a doubly infinite sequence of identically distributed and Φ-mixing random variables with zero means and finite variances and {ai;-∞< i < ∞} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of [수식] under some suitable conditions.
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Aydin Gezer,Arif Salimov 대한수학회 2008 대한수학회지 Vol.45 No.2
The main purpose of this paper is to investigate diagonal lift of tensor fields of type (1, 1) from manifold to its tensor bundle of type (p, q) and to prove that when a manifold Mn admits a Kahlerian structure (p, g), its tensor bundle of type (p, q) admits an complex structure. The main purpose of this paper is to investigate diagonal lift of tensor fields of type (1, 1) from manifold to its tensor bundle of type (p, q) and to prove that when a manifold Mn admits a Kahlerian structure (p, g), its tensor bundle of type (p, q) admits an complex structure.
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정종수,Daya Ram Sahu 대한수학회 2008 대한수학회지 Vol.45 No.2
Let X be a real reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty closed convex subset of X, T : C → X a continuous pseudocontractive mapping, and A : C → C a continuous strongly pseudocontractive mapping. We show the existence of a path {xt} satisfying xt = tAxt+(1-t)Txt, t ∈ (0, 1) and prove that {xt} converges strongly to a fixed point of T, which solves the variational inequality involving the mapping A. As an application, we give strong convergence of the path {xt} defined by xt = tAxt +(1-t)(2I-T)xt to a fixed point of firmly pseudocontractive mapping T. Let X be a real reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty closed convex subset of X, T : C → X a continuous pseudocontractive mapping, and A : C → C a continuous strongly pseudocontractive mapping. We show the existence of a path {xt} satisfying xt = tAxt+(1-t)Txt, t ∈ (0, 1) and prove that {xt} converges strongly to a fixed point of T, which solves the variational inequality involving the mapping A. As an application, we give strong convergence of the path {xt} defined by xt = tAxt +(1-t)(2I-T)xt to a fixed point of firmly pseudocontractive mapping T.
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