Results for "Akiyoshi Tsuchiya"

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On the sign patterns of the coefficients of Hilbert polynomialsMar 21 2016Feb 10 2017We show that all sign patterns of the coefficients Hilbert polynomials of standard graded $k$-algebras are possible.
Best possible lower bounds on the coefficients of Ehrhart polynomialsJan 09 2015Jul 01 2015For an integral convex polytope $\mathcal{P} \subset \mathbb{R}^d$, we recall $L_\mathcal{P}(n)=|n\mathcal{P} \cap \mathbb{Z}^d|$ the Ehrhart polynomial of $\mathcal{P}$. Let $g_r(\mathcal{P})$ be the $r$th coefficients of $L_\mathcal{P}(n)$ for $r=0,\ldots,d$. ... More
Ehrhart polynomials of lattice polytopes with normalized volumes $5$Aug 07 2017May 28 2018A complete classification of the $\delta$-vectors of lattice polytopes whose normalized volumes are at most $4$ is known. In the present paper, we will classify all the $\delta$-vectors of lattice polytopes with normalized volumes $5$.
Gorenstein simplices and the associated finite abelian groupsFeb 09 2017Jul 25 2017It is known that a lattice simplex of dimension $d$ corresponds a finite abelian subgroup of $(\mathbb{R}/\mathbb{Z})^{d+1}$. Conversely, given a finite abelian subgroup of $(\mathbb{R}/\mathbb{Z})^{d+1}$ such that the sum of all entries of each element ... More
The $δ$-vectors of reflexive polytopes and of the dual polytopesNov 08 2014May 19 2016Let $\delta(\mathcal{P})$ be the $\delta$-vector of a reflexive polytope $\mathcal{P} \subset \mathbb{R}^d$ of dimension $d$ and $\delta(\mathcal{P} ^\vee)$ the $\delta$-vector of the dual polytope $\mathcal{P}^\vee \subset \mathbb{R}^d$. In general, ... More
Edge rings of bipartite graphs with linear resolutionsAug 15 2019Ohsugi and Hibi characterized the edge ring of a finite connected simple graph with a $2$-linear resolution. On the other hand, Hibi, Matsuda and the author conjectured that the edge ring of a finite connected simple graph with a $q$-linear resolution, ... More
Reflexive polytopes arising from edge polytopesDec 17 2017Aug 08 2018It is known that every lattice polytope is unimodularly equivalent to a face of some reflexive polytope. A stronger question is to ask whether every $(0,1)$-polytope is unimodularly equivalent to a facet of some reflexive polytope. A large family of $(0,1)$-polytopes ... More
Facets and volume of Gorenstein Fano polytopesJun 11 2016Feb 13 2017It is known that every integral convex polytope is unimodularly equivalent to a face of some Gorenstein Fano polytope. It is then reasonable to ask whether every normal polytope is unimodularly equivalent to a face of some normal Gorenstein Fano polytope. ... More
Enriched chain polytopesDec 05 2018Jun 17 2019Stanley introduced a lattice polytope $\mathcal{C}_P$ arising from a finite poset $P$, which is called the chain polytope of $P$. The geometric structure of $\mathcal{C}_P$ has good relations with the combinatorial structure of $P$. In particular, the ... More
Stanley's non-Ehrhart-positive order polytopesJun 21 2018We say a polytope is Ehrhart positive if all the coefficients in its Ehrhart polynomial are positive. Answering an Ehrhart positivity question posed on Mathoverflow, Stanley provided an example of a non-Ehrhart-positive order polytope of dimension $21$. ... More
Enriched order polytopes and Enriched Hibi ringsMar 03 2019Stanley introduced two classes of lattice polytopes associated to posets, which are called the order polytope ${\mathcal O}_P$ and the chain polytope ${\mathcal C}_P$ of a poset $P$. It is known that, given a poset $P$, the Ehrhart polynomials of ${\mathcal ... More
Levelness of Order PolytopesMay 08 2018Since their introduction by Stanley~\cite{StanleyOrderPoly} order polytopes have been intriguing mathematicians as their geometry can be used to examine (algebraic) properties of finite posets. In this paper, we follow this route to examine the levelness ... More
Nonincreasing depth functions of monomial idealsJul 25 2016Dec 01 2016Given a nonincreasing function $f : \mathbb{Z}_{\geq 0} \setminus \{ 0 \} \to \mathbb{Z}_{\geq 0}$ such that (i) $f(k) - f(k+1) \leq 1$ for all $k \geq 1$ and (ii) if $a = f(1)$ and $b = \lim_{k \to \infty} f(k)$, then $|f^{-1}(a)| \leq |f^{-1}(a-1)| ... More
On the sign patterns of the coefficients of Hilbert polynomialsMar 21 2016We show that all sign patterns of the coefficients Hilbert polynomials of standard graded $k$-algebras are possible.
Volume, facets and dual polytopes of twinned chain polytopesDec 28 2015Let $P$ and $Q$ be finite partially ordered sets with $|P|=|Q|=d$, and $\mathcal{C}(P) \subset \mathbb{R}^d$ and $\mathcal{C}(Q) \subset \mathbb{R}^d$ their chain polytopes. The twinned chain polytope of $P$ and $Q$ is the normal Gorenstein Fano polytope ... More
Ehrhart polynomials with negative coefficientsDec 26 2013Dec 31 2013It is shown that, for each $d \geq 4$, there exists an integral convex polytope $\mathcal{P}$ of dimension $d$ such that each of the coefficients of $n, n^{2}, \ldots, n^{d-2}$ of its Ehrhart polynomial $i(\mathcal{P},n)$ is negative.
Cayley sums and Minkowski sums of $2$-convex-normal lattice polytopesApr 27 2018In the present paper, we consider the integer decomposition property for Minkowski sums and Cayley sums. In particular, we focus on these constructions arising from $2$-convex-normal lattice polytopes. Moreover, we discuss the level property of Minkowski ... More
Cayley sums and Minkowski sums of $2$-convex-normal lattice polytopesApr 27 2018Jul 30 2019In the present paper, we consider the integer decomposition property for Minkowski sums and Cayley sums. In particular, we focus on these constructions arising from $2$-convex-normal lattice polytopes. Moreover, we discuss the level property of Minkowski ... More
Volume, facets and dual polytopes of twinned chain polytopesDec 28 2015Feb 05 2018Let $(P,\leq_P)$ and $(Q,\leq_Q)$ be finite partially ordered sets with $|P|=|Q|=d$, and $\mathcal{C}(P) \subset \mathbb{R}^d$ and $\mathcal{C}(Q) \subset \mathbb{R}^d$ their chain polytopes. The twinned chain polytope of $P$ and $Q$ is the lattice polytope ... More
Dominating induced matchings of finite graphs and regularity of edge idealsDec 12 2014Aug 26 2015The regularity of an edge ideal of a finite simple graph $G$ is at least the induced matching number of $G$ and is at most the minimum matching number of $G$. If $G$ possesses a dominating inuduced matching, i.e., an induced matching which forms a maximal ... More
Reflexive polytopes arising from bipartite graphs with $γ$-positivity associated to interior polynomialsOct 29 2018Nov 01 2018In this paper, we introduce polytopes ${\mathcal B}_G$ arising from root systems $B_n$ and finite graphs $G$, and study their combinatorial and algebraic properties. In particular, it is shown that ${\mathcal B}_G$ is a reflexive polytope with a regular ... More
Enriched chain polytopesDec 05 2018Stanley introduced a lattice polytope $\mathcal{C}_P$ arising from a finite poset $P$, which is called the chain polytope of $P$. The geometric structure of $\mathcal{C}_P$ has good relations with the combinatorial structure of $P$. In particular, the ... More
Nef-partitions arising from unimodular configurationsAug 04 2019Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef-partition of a reflexive polytope $\mathcal{P}$ is a decomposition $\mathcal{P}=\mathcal{P}_1+\cdots+\mathcal{P}_r$ such that each ... More
The $h^*$-polynomials of locally anti-blocking lattice polytopes and their $γ$-positivityJun 11 2019A lattice polytope $\mathcal{P} \subset \mathbb{R}^d$ is called a locally anti-blocking polytope if for any closed orthant $\mathbb{R}^d_{\varepsilon}$ in $\mathbb{R}^d$, $\mathcal{P} \cap \mathbb{R}^d_{\varepsilon}$ is unimodularly equivalent to an anti-blocking ... More
The depth of a reflexive polytopeMay 31 2018Jan 16 2019Given arbitrary integers $d$ and $r$ with $d \geq 4$ and $1 \leq r \leq d + 1$, a reflexive polytope $\mathcal{P} \subset \mathbb{R}^d$ of dimension $d$ with ${\rm depth} K[\mathcal{P}] = r$ for which its dual polytope $\mathcal{P}^\vee$ is normal will ... More
The depth of a reflexive polytopeMay 31 2018Apr 15 2019Given arbitrary integers $d$ and $r$ with $d \geq 4$ and $1 \leq r \leq d + 1$, a reflexive polytope $\mathcal{P} \subset \mathbb{R}^d$ of dimension $d$ with ${\rm depth} K[\mathcal{P}] = r$ for which its dual polytope $\mathcal{P}^\vee$ is normal will ... More
Reflexive polytopes arising from partially ordered sets and perfect graphsApr 29 2017Feb 14 2018Reflexive polytopes which have the integer decomposition property are of interest. Recently, some large classes of reflexive polytopes with integer decomposition property coming from the order polytopes and the chain polytopes of finite partially ordered ... More
Flat $δ$-vectors and their Ehrhart polynomialsApr 09 2016Feb 08 2017We call the $\delta$-vector of an integral convex polytope of dimension $d$ flat if the $\delta$-vector is of the form $(1,0,\ldots,0,a,\ldots,a,0,\ldots,0)$, where $a \geq 1$. In this paper, we give the complete characterization of possible flat $\delta$-vectors. ... More
Classification of lattice polytopes with small volumesAug 01 2017Mar 27 2018Taking into consideration the fact that a complete characterization of the $\delta$-polynomials of lattice polytopes whose normalized volumes are at most $4$ is known, it is reasonable to classify, up to unimodular equivalence, the lattice polytopes whose ... More
Classification of lattice polytopes with small volumesAug 01 2017May 16 2019In the frame of a classification of general square systems of polynomial equations solvable by radicals, Esterov and Gusev succeeded in classifying all spanning lattice polytopes whose normalized volumes are at most $4$. In the present paper, we complete ... More
Reflexive polytopes arising from bipartite graphs with $γ$-positivity associated to interior polynomialsOct 29 2018Apr 27 2019In this paper, we introduce polytopes ${\mathcal B}_G$ arising from root systems $B_n$ and finite graphs $G$, and study their combinatorial and algebraic properties. In particular, it is shown that ${\mathcal B}_G$ is a reflexive polytope with a regular ... More
Facets and volume of Gorenstein Fano polytopesJun 11 2016It is known that every integral convex polytope is unimodularly equivalent to a face of some Gorenstein Fano polytope. In this paper, we discuss whether every normal polytope is unimodularly equivalent to a face of some normal Gorenstein Fano polytope. ... More
Reflexive polytopes arising from perfect graphsMar 13 2017Feb 26 2018Reflexive polytopes form one of the distinguished classes of lattice polytopes. Especially reflexive polytopes which possess the integer decomposition property are of interest. In the present paper, by virtue of the algebraic technique on Gr\"onbner bases, ... More
Depth of an initial idealJul 30 2019Aug 01 2019Given an arbitrary integer $d>0$, we construct a homogeneous ideal $I$ of the polynomial ring $S = K[x_1, \ldots, x_{3d}]$ in $3d$ variables over a filed $K$ for which $S/I$ is a Cohen--Macaulay ring of dimension $d$ with the property that, for each of ... More
Flat $δ$-vectors and their Ehrhart polynomialsApr 09 2016We call the $\delta$-vector of an integral convex polytope of dimension $d$ flat if the $\delta$-vector forms $(1,0,\ldots,0,a,\ldots,a,0,\ldots,0)$, where $a \geq 1$. In this paper, we give the complete characterization of possible flat $\delta$-vectors. ... More
Depth of an initial idealJul 30 2019Given an arbitrary integer $d>0$, we construct a homogeneous ideal $I$ of the polynomial ring $S = K[x_1, \ldots, x_{3d}]$ in $3d$ variables over a filed $K$ for which $S/I$ is a Cohen--Macaulay ring of dimension $d$ with the property that, for each of ... More
Self dual reflexive simplices with Eulerian $δ$-polynomialsJul 17 2016Given $n = 2, 3, \ldots$ , we construct a self dual reflexive simplex $\mathcal{Q}_n$ of dimension $n - 1$ such that (i) the normalized volume of $\mathcal{Q}_n$ is $n!$, (ii) the $\delta$-polynomial of $\mathcal{Q}_n$ is the Eulerian polynomial of degree ... More
Integer decomposition property for Cayley sums of order and stable set polytopesJul 16 2018Lattice polytopes which possess the integer decomposition property (IDP for short) turn up in many fields of mathematics. It is known that if the Cayley sum of lattice polytopes possesses IDP, then so does their Minkowski sum. In this paper, the Cayley ... More
Self dual reflexive simplices with Eulerian polynomialsJul 17 2016Mar 03 2017A lattice polytope $\mathcal{P}$ is called reflexive if its dual $\mathcal{P}^\vee$ is a lattice polytope. The property that $\mathcal{P}$ is unimodularly equivalent to $\mathcal{P}^\vee$ does not hold in general, and in fact there are few examples of ... More
Gorenstein properties and integer decomposition properties of lecture hall polytopesAug 13 2016Sep 08 2016Though much is known about ${\bf s}$-lecture hall polytopes, there are still many unanswered questions. In this paper, we show that ${\bf s}$-lecture hall polytopes satisfy the integer decomposition property (IDP) in the case of monotonic ${\bf s}$-sequences. ... More
Edge rings with $3$-linear resolutionsDec 10 2017Sep 11 2018It is shown that the edge ring of a finite connected simple graph with a $3$-linear resolution is a hypersurface.
Integer decomposition property for Cayley sums of order and stable set polytopesJul 16 2018Apr 03 2019Lattice polytopes which possess the integer decomposition property (IDP for short) turn up in many fields of mathematics. It is known that if the Cayley sum of lattice polytopes possesses IDP, then so does their Minkowski sum. In this paper, the Cayley ... More
Gorenstein simplices with a given $δ$-polynomialMay 15 2017Jul 22 2019To classify the lattice polytopes with a given $\delta$-polynomial is an important open problem in Ehrhart theory. A complete classification of the Gorenstein simplices whose normalized volumes are prime integers is known. In particular, their $\delta$-polynomials ... More
Quadratic Gröbner bases arising from partially ordered setsJun 02 2015Oct 07 2015The order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ associated to a partially ordered set $P$ are studied. In this paper, we introduce the convex polytope $\Gamma(\mathcal{O}(P), -\mathcal{C}(Q))$ which is the convex hull of $\mathcal{O}(P) ... More
Gorenstein polytopes with trinomial $h^*$-polynomialsMar 19 2015The characterization of lattice polytopes based upon information about their Ehrhart $h^*$-polynomials is a difficult open problem. In this paper, we finish the classification of lattice polytopes whose $h^*$-polynomials satisfy two properties: they are ... More
Gorenstein Fano polytopes arising from order polytopes and chain polytopesJul 12 2015Richard Stanley introduced the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ arising from a finite partially ordered set $P$, and showed that the Ehrhart polynomial of $\mathcal{O}(P)$ is equal to that of $\mathcal{C}(P)$. In ... More
Gorenstein simplices with a given $δ$-polynomialMay 15 2017It is fashionable among the study on convex polytopes to classify the lattice polytopes with a given $\delta$-polynomial. As a basic challenges toward the classification problem, we achieve the study on classifying lattice simplices with a given $\delta$-polynomial ... More
Laplacian Simplices Associated to DigraphsSep 30 2017We associate to a finite digraph $D$ a lattice polytope $P_D$ whose vertices are the rows of the Laplacian matrix of $D$. This generalizes a construction introduced by Braun and the third author. As a consequence of the Matrix-Tree Theorem, we show that ... More
Ehrhart polynomials with negative coefficientsJun 01 2015May 02 2016It is shown that, for each $d \geq 4$, there exists an integral convex polytope $\mathcal{P}$ of dimension $d$ such that each of the coefficients of $n, n^{2}, \ldots, n^{d-2}$ of its Ehrhart polynomial $i(\mathcal{P},n)$ is negative. Moreover, it is ... More
Nonincreasing depth functions of monomial idealsJul 25 2016Jul 28 2016Given a nonincreasing function $f : \mathbb{Z}_{\geq 0} \setminus \{ 0 \} \to \mathbb{Z}_{\geq 0}$ such that (i) $f(k) - f(k+1) \leq 1$ for all $k \geq 1$ and (ii) if $a = f(1)$ and $b = \lim_{k \to \infty} f(k)$, then $|f^{-1}(a)| \leq |f^{-1}(a-1)| ... More
Regularity and $a$-invariant of Cameron--Walker graphsJan 06 2019Jan 31 2019Let $S$ be the polynomial ring over a field $K$ and $I \subset S$ a homogeneous ideal. Let $h(S/I,\lambda)$ be the $h$-polynomial of $S/I$ and $s = \mathrm{deg} h(S/I,\lambda)$ the degree of $h(S/I,\lambda)$. It follows that the inequality $s - r \leq ... More
Analysis and Extension of Omega-RuleApr 30 2009Mar 12 2011$\Omega$-rule was introduced by W. Buchholz to give an ordinal-free cut-elimination proof for a subsystem of analysis with $\Pi^{1}_{1}$-comprehension. His proof provides cut-free derivations by familiar rules only for arithmetical sequents. When second-order ... More
A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheafNov 19 2014Jan 12 2016For an ordinary abelian variety $X$, $F^e_*\mathcal{O}_X$ is decomposed into line bundles for every positive integer $e$. Conversely, if a smooth projective variety $X$ satisfies this property and its Kodaira dimension is non-negative, then $X$ is an ... More
On Equivalence of M$^\natural$-concavity of a Set Function and Submodularity of Its ConjugateJul 28 2017A fundamental theorem in discrete convex analysis states that a set function is M$^\natural$-concave if and only if its conjugate function is submodular. This paper gives a new proof to this fact.
Boundary S matrices for the open Hubbard chain with boundary fieldsJan 01 1997Jan 06 1997Using the method introduced by Grisaru et al., boundary S matrices for the physical excitations of the open Hubbard chain with boundary fields are studied. In contrast to the open supersymmetric t-J model, the boundary S matrix for the charge excitations ... More
Using binary decision diagrams for constraint handling in combinatorial interaction testingJul 03 2019Constraints among test parameters often have substantial effects on the performance of test case generation for combinatorial interaction testing. This paper investigates the effectiveness of the use of Binary Decision Diagrams (BDDs) for constraint handling. ... More
On homology 3-spheres defined by two knotsJan 29 2014Oct 28 2014We show that if each of $K_1$ and $K_2$ is a trefoil knot or figure eight knot, the homology 3-sphere defined by the Kirby diagram which is a simple link of $K_1$ and $K_2$ with framing (0, n) is represented by an n-twisted Whitehead double of $K_2$ . ... More
On the reduced grades of modules over commutative ringsMay 16 2016Let R be a commutative Noetherian ring. Recently, Dibaei and Sadeghi have studied the reduced grade of a horizontally linked R-module M of finite GC-dimension, where C is a semidualizing R-module. In this paper, we highly refine their results. In particular, ... More
Surrounding material effect on measurement of thunderstorm-related neutronsMar 29 2014Observations of strong flux of low-energy neutrons were made by $^{3}\mathrm{He}$ counters during thunderstorms [Gurevich et al (Phys. Rev. Lett. 108, 125001, 2012)]. How the unprecedented enhancements were produced remains elusive. To better elucidate ... More
Determinant formula for the six-vertex model with reflecting endApr 10 1998Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.
Contribution of the Large Magellanic Cloud to the Galactic WarpMar 28 2002Aug 13 2002Multi-scale interaction between the LMC, Galactic halo, and the disk is examined with N-body simulations, and precise amplitudes of the Galactic warp excitation are obtained. The Galactic models are constructed most realistically to satisfy available ... More
Survival and disruption of subsystems during a cold collapseDec 11 1997Dec 09 1998Cold collapse of a cluster composed of small identical clumps, each of which is in virial equilibrium, is considered. Since the clumps have no relative motion with respect to each other initially, the cluster collapses by its gravity. At the first collapse ... More
On homotopy $K3$ surfaces constructed by two knots and their applicationsJan 20 2015Let $LHT$ be a left handed trefoil knot and $K$ be any knot. We define $M_n(K)$ to be the homology $3$-sphere which is represented by a simple link of $LHT$ and $LHT \sharp K$ with framings $0$ and $n$ respectively. Starting with this link, we construct ... More
Synchronous Spatial Oscillation of Electron- and Mn-Spin Polarizations in Dilute-Magnetic-Semiconductor Quantum Wells under Spin-Orbit Effective Magnetic FieldsJun 16 2011Aug 02 2012In semiconductors, spin-orbit effective magnetic fields, i.e., the Rashba and Dresselhaus fields, are used to control electron-spin polarization. This operation, however, destroys the electron-spin coherence, and the spin polarization is limited to the ... More
Galois extensions, plus closure, and maps on local cohomologyApr 03 2011Given a local domain $(R,m)$ of prime characteristic that is a homomorphic image of a Gorenstein ring, Huneke and Lyubeznik proved that there exists a module-finite extension domain $S$ such that the induced map on local cohomology modules $H^i_m(R)\to ... More
Order-Chain PolytopesApr 07 2015Aug 22 2016Given two families $X$ and $Y$ of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate new class of polytopes is to take the intersection $\mathcal{P}=\mathcal{P}_1\cap\mathcal{P}_2$, where $\mathcal{P}_1\in X$, ... More
Critical behavior in $c=1$ matrix model with branching interactionsMar 16 1994Apr 22 1994Motivated by understanding the phase structure of $d >1$ strings we investigate the $c=1$ matrix model with $g' (\tr M(t)^{2})^{2}$ interaction which is the simplest approximation of the model expected to describe the critical phenomena of the large-$N$ ... More
Boundary bound states for the open Hubbard chain with boundary fieldsFeb 28 1997Mar 10 1997The boundary effects in the open Hubbard chain with boundary fields are studied. The boundary string solutions of the Bethe ansatz equations that give rise to a wave functions localized at the boundary and exponentially decreasing away from the boundary ... More
Landau and dynamical instabilities of Bose-Einstein condensates with superfluid flow in a Kronig-Penney potentialJul 07 2006We study the elementary excitations of Bose-Einstein condensates in a one-dimensional periodic potential and discuss the stability of superfluid flow based on the Kronig-Penney model. We analytically solve the Bogoliubov equations and calculate the excitation ... More
Superconducting networks with the proximity effectNov 06 2009May 20 2011We report on the first observation of a novel type of superconducting proximity network using a superconductor-normal metal bilayer. Little-Parks oscillation measurements show that the superconducting current flows through a path enclosed by the edge ... More
Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix modelApr 11 2019Apr 15 2019The Lorentzian type IIB matrix model has been studied as a promising candidate for a nonperturbative formulation of superstring theory. In particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. It has ... More
Perfect transmission of Higgs modes via anti-bound statesJun 26 2019We study tunneling properties of Higgs modes in superfluid Bose gases in optical lattices in the presence of a potential barrier introduced by local modulation of hopping amplitude. Solving the time-dependent Ginzburg-Landau equation, Higgs modes are ... More
Hamilton-Jacobi Method and Effective Actions of D-brane and M-brane in SupergravityMay 12 2003Oct 07 2003We show that the effective actions of D-brane and M-brane are solutions to the Hamilton-Jacobi (H-J) equations in supergravities. This fact means that these effective actions are on-shell actions in supergravities. These solutions to the H-J equations ... More
Comment on "ADM reduction of IIB on $H^{p,q}$ to dS braneworld"Oct 24 2012We make a comment on "ADM reduction of IIB on $H^{p,q}$ to dS braneworld" by E. Hatefi, A. J. Nurmagambetov and I. Y. Park, arXiv:1210.3825.
Quantum Gravity and Black Hole Dynamics in 1+1 DimensionsNov 30 1992Dec 21 1992We study the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures are explicitly evaluated and the physical state conditions corresponding to the Hamiltonian and the momentum ... More
An Extension of Chubanov's Polynomial-Time Linear Programming Algorithm to Second-Order Cone ProgrammingNov 07 2016Jan 01 2017Recently, Chubanov proposed an interesting new polynomial-time algorithm for linear program. In this paper, we extend his algorithm to second-order cone programming.
Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methodsDec 18 2017Aug 30 2018We discuss the error analysis of the lowest degree Crouzeix-Raviart and Raviart-Thomas finite element methods applied to a two-dimensional Poisson equation. To obtain error estimations, we use the techniques developed by Babu\v{s}ka-Aziz and the authors. ... More
On the extended W-algebra of type sl_2 at positive rational levelFeb 26 2013Jul 15 2014The extended W-algebra of type sl_2 at positive rational level, denoted by M_{p_+,p_-}, is a vertex operator algebra that was originally proposed in [1]. This vertex operator algebra is an extension of the minimal model vertex operator algebra and plays ... More
Defaultable Bonds via HKAMar 23 2011To construct a no-arbitrage defaultable bond market, we work on the state price density framework. Using the heat kernel approach (HKA for short) with the killing of a Markov process, we construct a single defaultable bond market that enables an explicit ... More
Probabilistic representation of weak solutions to a parabolic boundary value problem on a non-smooth domainOct 14 2017The probabilistic representation of weak solutions to a parabolic boundary value problem is established in the following framework. The boundary value problem consists of a second order parabolic equation defined on a time-varying Lipschitz domain in ... More
Morphology of axisymmetric vesicles with encapsulated filaments and impuritiesJul 10 2002The shape deformation of a three-dimensional axisymmetric vesicle with encapsulated filaments or impurities is analyzed by integrating a dissipation dynamics. This method can incorporate systematically the constraint of a fixed surface area and/or a fixed ... More
Large Transport Critical Current Densities of Ag Sheathed (Ba,K)Fe2As2+Ag Superconducting Wires Fabricated by an ex-situ Powder-in-Tube (PIT) ProcessMar 09 2011We report large transport critical current densities observed in Ag-added (Ba,K)Fe2As2 superconducting wires prepared by an ex-situ powder-in-tube (PIT) process. The wire has a simple composite structure sheathed only by Ag. A precursor bulk material ... More
Constraint-Preserving Scheme for Maxwell's EquationsOct 14 2016We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical simulations showed that ... More
Integrable $1/r^2$ Spin Chain with Reflecting EndFeb 20 1996Feb 26 1996A new integrable spin chain of the Haldane-Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a {\it reflecting end}. The lattice points of this model consist of the square roots of the zeros of the Laguerre ... More
Long Period Sequences Generated by the Logistic Map over Finite Fields with Control Parameter FourOct 13 2015Recently, binary sequences generated by chaotic maps have been widely studied. In particular, the logistic map is used as one of the chaotic map. However, if the logistic map is implemented by using finite precision computer arithmetic, rounding is required. ... More
On the pole structures of the disconnected part of hyper elliptic g loop M point super string amplitudesSep 27 2012Apr 03 2015Structures of the disconnected part of higher genus superstring amplitudes restricted to the hyper elliptic cases are investigated in the NSR formalism, based on the DHoker Phong and recent results. A set of equations, which we can regard as a basic tool ... More
Complex Matrix Model and Fermion Phase Space for Bubbling AdS GeometriesJul 07 2005Nov 25 2005We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic ... More
Towards black hole scatteringJul 17 2003Oct 01 2003We study black holes in three-dimensional Chern-Simons gravity with a negative cosmological constant. In particular, we identify how the Chern-Simons interactions between a scattering particle and a black hole project the particle wavefunction onto a ... More
M5-brane Effective Action as an On-shell Action in SupergravityOct 27 2004Jan 05 2005We show that the covariant effective action for M5-brane is a solution to the Hamilton-Jacobi (H-J) equations of 11-dimensional supergravity. The solution to the H-J equations reproduces the supergravity solution that represents the M2-M5 bound states. ... More
Constructing of constraint preserving scheme for Einstein equationsOct 14 2016Jul 14 2017We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint preserves in the discrete ... More
Reorganizing topologies of Steiner trees to accelerate their eliminationNov 11 2015Mar 12 2018We describe a technique to reorganize topologies of Steiner trees by exchanging neighbors of adjacent Steiner points. We explain how to use the systematic way of building trees, and therefore topologies, to find the correct topology after nodes have been ... More
Constrained locating arrays for combinatorial interaction testingDec 06 2017May 31 2019This paper introduces the notion of Constrained Locating Arrays (CLAs), mathematical objects which can be used for fault localization in software testing. CLAs extend ordinary locating arrays to make them applicable to testing of systems that have constraints ... More
Newton-Kantorovitch method for decoupled forward-backward stochastic differential equationsJun 05 2018We present and prove a Newton-Kantorovitch method for solving decoupled forward-backward stochastic differential equations (FBSDEs) involving smooth coefficients with uniformly bounded derivatives. As Newton's method is required a suitable initial condition ... More
The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of UnityFeb 26 2009Jul 07 2009We prove the abelian category of the modules over triplet VOA W(p) is category equivalent to the abelian category of the modules over quantum algebra of type sl_2 at root of unity.
Local field theory from the expanding universe at late times in the IIB matrix modelAug 24 2012Nov 26 2012Recently we have shown that (3+1)-dimensional expanding universe appears dynamically and uniquely from the Lorentzian version of the IIB matrix model, which is considered as a nonperturbative formulation of superstring theory. Similarly, it is possible ... More
Conformal dynamics in gauge theories via non-perturbative renormalization groupApr 27 2007Oct 19 2007The dynamics at the IR fixed point realized in the $SU(N_c)$ gauge theories with massless Dirac fermions is studied by means of the non-perturbative renormalization group. The analysis includes the IR fixed points with non-trivial Yukawa couplings. The ... More
Supercurrent behavior of low-energy Bogoliubov phonon and anomalous tunneling effect in a Bose-Einstein condensateJun 03 2008We investigate tunneling properties of Bogoliubov mode in a Bose-Einstein condensate. Using an exactly solvable model with a delta-functional barrier, we show that each component in the two-component wavefunction (u,v) of low-energy Bogoliubov phonon ... More
Constructing of constraint preserving scheme for Einstein equationsOct 14 2016We propose a new numerical scheme of evolution for the Einstein equations using the discrete variational derivative method (DVDM). We derive the discrete evolution equation of the constraint using this scheme and show the constraint preserves in the discrete ... More
Stability problems for Cantor stochastic differential equationsApr 23 2016We consider driftless stochastic differential equations and the diffusions starting from the positive half line. It is shown that the Feller test for explosions gives a necessary and sufficient condition to hold pathwise uniqueness for diffusion coefficients ... More
A generalized volume law for entanglement entropy on the fuzzy sphereNov 19 2016We investigate entanglement entropy in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model. In our previous study, we confirmed that entanglement entropy in the free case is proportional to the square of the boundary area ... More