• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1205-1211
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• 2010

In the present article, we investigate the possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor's K-group of the real numbers into the additive group of real numbers. Using this connection, it is shown that any such trace map must be trivial, but it is proposed that the target group of a nontrivial trace should be a linearized version of Milnor's K-theory as with the case of universal determinant for commuting tuples of matrices rather than just the field of constants.

• Journal of Environmental Impact Assessment
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• v.22 no.5
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• pp.491-511
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• 2013

In this study, three survey areas in Changnyeong, Miryang and Jinju of the confirmed the habitation of nutria and carried out the performance on the plant diet resource. From the habitat trace survey in the nutria habitat, a total of 336 trace points was shown. There were 181 trace points (54%) confirmed from St. 1 as the highest showing, followed by 52 trace points (15.4%) from St. 2, and 103 trace points (30.6)% from St. 3. The vascular plants distributed in the habitat area were a total of 182 taxonomic group with 57 families, 99 genus, 16 hybrids, and 1 race. The vascular plant living types in the habitat area are 1-year plant (Th, Th(w)) for 63class groups (34.6%), hemicryptophyte (H) for 42class groups(23.1%). plants, trees, crop plants were included. As a result of analyzing the overseas research cases on the diet plants of nutria, there are 195 taxonomic groups in a total of 39 families, 126 genus, 183 breeds, and 12 hybrids. In the study areas, feeding the plants was confirmed by the 7 taxonomic groups, aquatic plant, terrestrial From the total of 182 taxonomic groups discovered in the habitat area, 20 class groups, in 3 habitation region, 10 class groups of commonly appearing 49 class groups were shown to be the breed confirmed for diet in existing case studies, and assuming from it basis, the nutria habitating in the survey area is considered to have the supply of diverse diet resource to have flawless habitation. This is implication of having potential breeding possibility.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.113.2-113.2
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• 2014

Methanol masers are divided into two classes, I and II. Class II methanol masers trace the disk-outflow systems of massive young stellar objects (YSOs), while class I methanol masers appear to trace the interaction regions of outflows with the ambient molecular gas. Class II masers have been extensively studied by single dishes, connected arrays, and VLBIs. Meanwhile, class I masers have been much less studied. They have not been detected by any VLBI facility. Thus they have been believed to have more extended structures than class II masers. We made fringe surveys of 44GHz class I methanol maser emission towards more than 150 massive YSOs with flux densities >10 Jy using the Korean VLBI Network (KVN), and detected fringes in ~10% of the sources. We performed follow-up imaging observations of the detected maser sources with KVN and KVN+VERA (KaVA). The observations aim to investigate the distribution and kinematics of 44GHz methanol maser features in each source at milli-arcsecond resolutions, and to understand what they trace. In this talk we will present the fringe survey and imaging results and our plans for further studies. Additionally, we will also introduce the preliminary results of single-dish polarization observations of water and class I methanol masers.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.63-69
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• 2002

Given vectors x and y in a Hilbert space, an intepolating operator is a bounded operator T such that Tx=y. an interpolating operator for n vectors satisfies the equation Tx$_{i}$=y, for i=1, 2,…, n. In this article, we obtained the fellowing : Let x = (x$_{i}$) and y = (y$_{i}$) be two vectors in H such that x$_{i}$$\neq$0 for all i = 1, 2,…. Then the following statements are equivalent. (1) There exists an operator A in AlgＬ such that Ax = y, A is a trace-class operator and every E in Ｌ reduces A. (2) (equation omitted).mitted).

• Journal of KIISE:Computing Practices and Letters
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• v.14 no.9
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• pp.911-915
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• 2008

Software birthmark is the inherent characteristics that can identify a program. In this paper, we propose a Java class theft detection technique based on static API traces of class files. We utilize control flow analysis to increase resilience, and we apply the semi-global alignment trace comparison algorithm to increase credibility. The credibility and resilience experiments for XML parsers show that our birthmark is more efficient than existing birthmarks.

• Kyungpook Mathematical Journal
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• v.63 no.3
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• pp.373-411
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• 2023

Gompf proposed a conjecture on Cappell-Shaneson matrices whose affirmative answer implies that all Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. We study Gompf conjecture on Cappell-Shaneson matrices using various algebraic number theoretic techniques. We find a hidden symmetry between trace n Cappell-Shaneson matrices and trace 5 - n Cappell-Shaneson matrices which was suggested by Gompf experimentally. Using this symmetry, we prove that Gompf conjecture for the trace n case is equivalent to the trace 5 - n case. We confirm Gompf conjecture for the special cases that -64 ≤ trace ≤ 69 and corresponding Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. We also give a new infinite family of Cappell-Shaneson spheres which are diffeomorphic to the standard 4-sphere.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.357-359
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• 2007

In order to protect copyrighted materials, codes may be embedded in the content -to trace the traitors. Traceability (TA) codes, as a kind of such codes, have been extensively studied in the intervening years for use as a piracy deterrent. In this correspondence, we proposed a method to construct a class of traceability codes and gave out some parameters results of such codes.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.313-329
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• 2008

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 $B(l_2)$ of bounded linear operators on $l_2$ involving the duality relation among the class of compact operators K, the trace class $C_1$ and $B(l_2)$. We also study the reflexivity in such the algebras.

• East Asian mathematical journal
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• v.14 no.1
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• pp.21-26
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• 1998

The Fulgede-Putnam theorem asserts as if A and Bare normal operators and X is an operator such that AX=XB, then A*X=XB*. In this paper, we show that if A is k-quasihyponormal and B* is invertible k-quasihyponormal such that AX=XB for a Hilbert-Schmidt operator X, then A*X=XB*.