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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.

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

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

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

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

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

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.

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

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

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

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

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 $5$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 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

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

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

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.

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

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

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

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

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

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

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

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

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

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

Superconducting Quantum Annealing Architecture with LC ResonatorsMar 01 2019We propose a novel architecture for superconducting circuits to improve the efficiency of a quantum annealing system. To increase the capability of a circuit, it is desirable for a qubit to be coupled not only with adjacent qubits but also with other ... 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

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

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.

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

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

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

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

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

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

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

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

Supercurrent induced by tunneling Bogoliubov excitations in a Bose-Einstein condensateFeb 17 2009Jun 15 2009We study the tunneling of Bogoliubov excitations through a barrier in a Bose-Einstein condensate. We extend our previous work [Phys. Rev. A \textbf{78}, 013628 (2008)] to the case when condensate densities are different between the left and right of the ... More

Stability of Bose-Einstein condensates in a Kronig-Penney potentialOct 20 2006We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in ... More

An Extension of Chubanov's Polynomial-Time Linear Programming Algorithm to Second-Order Cone ProgrammingNov 07 2016Recently, Chubanov proposed an interesting new polynomial-time algorithm for linear program. In this paper, we extend his algorithm to second-order cone programming.

Approximating surface areas by interpolations on triangulationsOct 18 2016We consider surface area approximations by Lagrange and Crouzeix--Raviart interpolations on triangulations. For Lagrange interpolation, we give an alternative proof for Young's classical result that claims the areas of inscribed polygonal surfaces converge ... More

Convergence rate of stability problems of SDEs with (dis-)continuous coefficientsJan 18 2014Apr 02 2014We consider the stability problems of one dimensional SDEs when the diffusion coefficients satisfy the so called Nakao-Le Gall condition. The explicit rate of convergence of the stability problems are given by the Yamada-Watanabe method without the drifts. ... More

Finite element approximations of minimal surfaces: algorithms and mesh refinementJun 29 2017Jan 14 2018Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element approximations of ... More

A priori error estimates for Lagrange interpolation on trianglesAug 10 2014Jul 10 2015We present the error analysis of Lagrange interpolation on triangles. A new \textit{a priori} error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed ... More

Enhancement of critical current densities in (Ba,K)Fe2As2 wires and tapes using HIP techniqueSep 29 2016(Ba,K)Fe2As2 superconducting wires and tapes are fabricated by using hot isostatic pressing (HIP) technique, and their superconducting properties are studied. In the HIP round wire, transport critical current density (Jc) at 4.2 K has achieved record-high ... 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.

A Note on Hamilton-Jacobi Formalism and D-brane Effective ActionsOct 14 2003Jan 05 2004We first review the canonical formalism with general space-like hypersurfaces developed by Dirac by rederiving the Hamilton-Jacobi equations which are satisfied by on-shell actions defined on such hypersurfaces. We compare the case of gravitational systems ... More

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

Constructing of constraint preserving scheme for Einstein equationsOct 14 2016Oct 17 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

Double Precision Computation of the Logistic Map Depends on Computational Modes of the Floating-point Processing UnitMay 14 2013Today's most popular CPU can operate in two different computational modes for double precision computations. This fact is not very widely recognized among scientific computer users. The present paper reports the differences the modes bring about using ... More

Time scales of relaxation and Lyapunov instabilities in a one-dimensional gravitating sheet systemDec 09 1998The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional ... More

Landau damping of Bogoliubov excitations in optical lattices at finite temperatureJun 01 2005We study the damping of Bogoliubov excitations in an optical lattice at finite temperatures. For simplicity, we consider a Bose-Hubbard tight-binding model and limit our analysis to the lowest excitation band. We use the Popov approximation to calculate ... More

Damping of Bogoliubov Excitations in Optical LatticesNov 13 2003Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to coupling to a thermal cloud of such excitations. For simplicity, we consider a 1D Bose-Hubbard model and restrict ourselves ... More

What is the natural scale for a Lévy process in modelling term structure of interest rates?Dec 13 2006This paper gives examples of explicit arbitrage-free term structure models with L\'evy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a L\'evy process is a "natural" ... More

A Babuška-Aziz type proof of the circumradius conditionJun 10 2013Sep 18 2013In this paper the error of polynomial interpolation of degree 1 on triangles is considered. The circumradius condition, which is more general than the maximum angle condition, is explained and proved by the technique given by Babu\v{s}ka-Aziz.