Past Status (before 2017) | Papers

43

Can the Brans-Dicke Gravity with Λ Possibly be a Theory of Dark Matter?

Hongsu Kim | Astrophysics (2007)

The pure Brans-Dicke (BD) gravity with or without the cosmological constant Lambda has been taken as a model theory for the dark matter. Indeed, there has been a consensus that unless one modifies either the standard theory of gravity, namely, general relativity, or the standard model for particle physics, or both, one can never achieve a satisfying understanding of the phenomena associated with dark matter and dark energy. Along this line, our dark matter model in this work can be thought of as an attempt to modify the gravity side alone in the simplest fashion to achieve the goal. Among others, it is demonstrated that our model theory can successfully predict the emergence of dark matter halo-like configuration in terms of a self-gravitating spacetime solution to the BD field equations and reproduce the flattened rotation curve in this dark halo-like object in terms of the non-trivial energy density of the BD scalar field, which was absent in the context of general relativity where Newton's constant is strictly a ``constant'' having no dynamics. Our model theory, however, is not entirely without flaw, such as the prediction of relativistic jets in all types of galaxies which actually is not the case.

초록

The pure Brans-Dicke (BD) gravity with or without the cosmological constant Lambda has been taken as a model theory for the dark matter. Indeed, there has been a consensus that unless one modifies either the standard theory of gravity, namely, general relativity, or the standard model for particle physics, or both, one can never achieve a satisfying understanding of the phenomena associated with dark matter and dark energy. Along this line, our dark matter model in this work can be thought of as an attempt to modify the gravity side alone in the simplest fashion to achieve the goal. Among others, it is demonstrated that our model theory can successfully predict the emergence of dark matter halo-like configuration in terms of a self-gravitating spacetime solution to the BD field equations and reproduce the flattened rotation curve in this dark halo-like object in terms of the non-trivial energy density of the BD scalar field, which was absent in the context of general relativity where Newton's constant is strictly a ``constant'' having no dynamics. Our model theory, however, is not entirely without flaw, such as the prediction of relativistic jets in all types of galaxies which actually is not the case.

초록

The pure Brans-Dicke (BD) gravity with or without the cosmological constant Lambda has been taken as a model theory for the dark matter. Indeed, there has been a consensus that unless one modifies either the standard theory of gravity, namely, general relativity, or the standard model for particle physics, or both, one can never achieve a satisfying understanding of the phenomena associated with dark matter and dark energy. Along this line, our dark matter model in this work can be thought of as an attempt to modify the gravity side alone in the simplest fashion to achieve the goal. Among others, it is demonstrated that our model theory can successfully predict the emergence of dark matter halo-like configuration in terms of a self-gravitating spacetime solution to the BD field equations and reproduce the flattened rotation curve in this dark halo-like object in terms of the non-trivial energy density of the BD scalar field, which was absent in the context of general relativity where Newton's constant is strictly a ``constant'' having no dynamics. Our model theory, however, is not entirely without flaw, such as the prediction of relativistic jets in all types of galaxies which actually is not the case.

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42

Thermodynamics and evaporation of the noncommutive black hole

Yun Soo Myung, Yong-Wan Kim, Young-Jai Park | Journal of High Energy Physics 2007 (2007)

We investigate the thermodynamics of the noncommutative black hole whose static picture is similar to that of the nonsingular black hole known as the de Sitter-Schwarzschild black hole. It turns out that the final remnant of extremal black hole is a thermodynamically stable object. We describe the evaporation process of this black hole by using the noncommutativity-corrected Vaidya metric. It is found that there exists a close relationship between thermodynamic approach and evaporation process.

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41

ISOSPIN PARTICLE ON S2 WITH ARBITRARY NUMBER OF SUPERSYMMETRIES

SOON-TAE HONG, JOOHAN LEE, TAE HOON LEE and PHILLIAL OH | Modern Physics Letters A 22/20 (2007)

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40

Stringy Jacobi fields in Morse theory

Yong Seung Cho and Soon-Tae Hong | Physical Review D 75/12 (2007)

We consider the variation of the surface spanned by closed strings in a spacetime manifold. Using the Nambu-Goto string action, we induce the geodesic surface equation and the geodesic surface deviation equation which yields a Jacobi field, and we define the index form of a geodesic surface as in the case of point particles to discuss conjugate strings on the geodesic surface.

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39

Analysis of conforming and nonconforming quadrilateral finite element methods for the Helmholtz equation

Ki-tak LEE, Taeyoung HA, Dongwoo SHEEN | Hokkaido Mathematical Journal 36/4 (2007)

In this paper we analyze numerical dispersion relation of some conforming and nonconforming quadrilateral finite elements. The elements employed in this analysis are the standard Q1 conforming finite element, the DSSY nonconforming element [5] and the P1-nonconforming quadrilateral finite element [14]. Several aspects of comparative analyses of the above three elements for two or three dimensional problems are shown.

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38

A FETI-DP preconditioner for mortar methods in three dimensions

Hyea Hyun Kim | Electronic Transactions on Numerical Analysis 26 (2007)

A FETI-DP method is developed for three dimensional elliptic problems with mortar discretization. Mortar matching conditions are considered as the continuity constraints in the FETI-DP formulation. Among them, face average constraints are selected as primal constraints in our FETI-DP formulation to achieve an algorithm as scalable as two dimensional problems. A Neumann-Dirichlet preconditioner is used in the FETI-DP formulation and it gives the condition number bound

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37

Ensemble learning of genetic networks from time-series expression data

Dougu Nam, Sung Ho Yoon, Jihyun F. Kim | Bioinformatics 23/23 (2007)

Motivation: Inferring genetic networks from time-series expression data has been a great deal of interest. In most cases, however, the number of genes exceeds that of data points which, in principle, makes it impossible to recover the underlying networks. To address the dimensionality problem, we apply the subset selection method to a linear system of difference equations. Previous approaches assign the single most likely combination of regulators to each target gene, which often causes over-fitting of the small number of data. Results: Here, we propose a new algorithm, named LEARNe, which merges the predictions from all the combinations of regulators that have a certain level of likelihood. LEARNe provides more accurate and robust predictions than previous methods for the structure of genetic networks under the linear system model. We tested LEARNe for reconstructing the SOS regulatory network of Escherichia coli and the cell cycle regulatory network of yeast from real experimental data, where LEARNe also exhibited better performances than previous methods. Availability: The MATLAB codes are available upon request from the authors.

초록

Motivation: Inferring genetic networks from time-series expression data has been a great deal of interest. In most cases, however, the number of genes exceeds that of data points which, in principle, makes it impossible to recover the underlying networks. To address the dimensionality problem, we apply the subset selection method to a linear system of difference equations. Previous approaches assign the single most likely combination of regulators to each target gene, which often causes over-fitting of the small number of data.

Results: Here, we propose a new algorithm, named LEARNe, which merges the predictions from all the combinations of regulators that have a certain level of likelihood. LEARNe provides more accurate and robust predictions than previous methods for the structure of genetic networks under the linear system model. We tested LEARNe for reconstructing the SOS regulatory network of Escherichia coli and the cell cycle regulatory network of yeast from real experimental data, where LEARNe also exhibited better performances than previous methods.

Availability: The MATLAB codes are available upon request from the authors.

초록

Motivation: Inferring genetic networks from time-series expression data has been a great deal of interest. In most cases, however, the number of genes exceeds that of data points which, in principle, makes it impossible to recover the underlying networks. To address the dimensionality problem, we apply the subset selection method to a linear system of difference equations. Previous approaches assign the single most likely combination of regulators to each target gene, which often causes over-fitting of the small number of data.

Results: Here, we propose a new algorithm, named LEARNe, which merges the predictions from all the combinations of regulators that have a certain level of likelihood. LEARNe provides more accurate and robust predictions than previous methods for the structure of genetic networks under the linear system model. We tested LEARNe for reconstructing the SOS regulatory network of Escherichia coli and the cell cycle regulatory network of yeast from real experimental data, where LEARNe also exhibited better performances than previous methods.

Availability: The MATLAB codes are available upon request from the authors.

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36

Ising antiferromagnets in a nonzero uniform magnetic field

Chi-Ok Hwang, Seung-Yeon Kim, Daeseung Kang, Jin Min Kim | Journal of Statistical Mechanics: Theory and Experiment 2007 (2007)

We evaluate the density of states g(M,E) as a function of energy E and magnetization M of Ising models on square and triangular lattices, using the exact enumeration method for small systems and the Wang–Landau method for larger systems. From the density of states the average magnetization per spin, m(T,h), of the antiferromagnets has been obtained for any values of temperature T and uniform magnetic field h. Also, based on g(M,E), the behaviour of m(T,h) is understood microcanonically. The microcanonical approach reveals the differences between the unfrustrated model (on the square lattice) and the frustrated one (on the triangular lattice).

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35

Normal generation and Clifford index on algebraic curves

Youngook Choi; Seonja Kim; Young Rock Kim | Mathematische Zeitschrift 257/23 (2007)

For a smooth curve C it is known that a very ample line bundle L">LL on C is normally generated if Cliff(L">LL ) < Cliff(C) and there exist extremal line bundles L">LL (:non-normally generated very ample line bundle with Cliff(L">LL ) = Cliff(C)) with h1(L)≤1">h1(L)≤1h1(L)≤1 . However it has been unknown whether there exists an extremal line bundle L">LL with h1(L)≥2">h1(L)≥2h1(L)≥2 . In this paper, we prove that for any positive integers (g, c) with g =？ 2c +？ 5 and c≡0">c≡0c≡0 (mod 2) there exists a smooth curve of genus g and Clifford index c carrying an extremal line bundle L">LL with h1(L)=2">h1(L)=2h1(L)=2 . In fact, a smooth quadric hypersurface section C of a general projective K3 surface always has an extremal line bundle L">LL with h1(L)=2">h1(L)=2h1(L)=2 . More generally, if C has a line bundle M">MM computing the Clifford index c of C with (3c/2)+3<degM≤g−1">(3c/2)+3<degM≤g？1(3c/2)+3<degM≤g？1 , then C has such an extremal line bundle L">LL .

초록

For a smooth curve C it is known that a very ample line bundle $L$ on C is normally generated if Cliff( $L$ ) < Cliff(C) and there exist extremal line bundles $L$ (:non-normally generated very ample line bundle with Cliff( $L$ ) = Cliff(C)) with $h^{1} (L) \leq 1$ . However it has been unknown whether there exists an extremal line bundle $L$ with $h^{1} (L) \geq 2$ . In this paper, we prove that for any positive integers (g, c) with g =？ 2c +？ 5 and $c \equiv 0$ (mod 2) there exists a smooth curve of genus g and Clifford index c carrying an extremal line bundle $L$ with $h^{1} (L) = 2$ . In fact, a smooth quadric hypersurface section C of a general projective K3 surface always has an extremal line bundle $L$ with $h^{1} (L) = 2$ . More generally, if C has a line bundle $M$ computing the Clifford index c of C with $(3 c / 2) + 3 < \deg M \leq g ？ 1$ , then C has such an extremal line bundle $L$ .

초록

For a smooth curve C it is known that a very ample line bundle $L$ on C is normally generated if Cliff( $L$ ) < Cliff(C) and there exist extremal line bundles $L$ (:non-normally generated very ample line bundle with Cliff( $L$ ) = Cliff(C)) with $h^{1} (L) \leq 1$ . However it has been unknown whether there exists an extremal line bundle $L$ with $h^{1} (L) \geq 2$ . In this paper, we prove that for any positive integers (g, c) with g =？ 2c +？ 5 and $c \equiv 0$ (mod 2) there exists a smooth curve of genus g and Clifford index c carrying an extremal line bundle $L$ with $h^{1} (L) = 2$ . In fact, a smooth quadric hypersurface section C of a general projective K3 surface always has an extremal line bundle $L$ with $h^{1} (L) = 2$ . More generally, if C has a line bundle $M$ computing the Clifford index c of C with $(3 c / 2) + 3 < \deg M \leq g ？ 1$ , then C has such an extremal line bundle $L$ .

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34

ANTI-SYMPLECTIC INVOLUTIONS ON NON-KAHLER SYMPLECTIC 4-MANIFOLDS

Cho, Yong-Seung; Hong, Yoon-Hi | Journal of the Korean Mathematical Society (대한수학회지) 44/4 (2007)

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