Results for "Makoto Watanabe"

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Clustering of Emission-line Stars in the W5E HII regionFeb 19 2008We have made a new survey of emission-line stars in the W5E HII region to investigate the population of PMS stars near the OB stars by using the Wide Field Grism Spectrograph 2 (WFGS2). A total of 139 H-alpha emission stars were detected and their g'i'-photometry ... More
Buffering Time Strategies for Wireless Full-duplex Systems under Poisson TrafficNov 14 2016May 17 2018Full-duplex wireless communication has the potential to double the capacity of wireless networks by reducing the band occupancy of transmissions. However, a full-duplex capability cannot always reduce the band occupancy because the real traffic is not ... More
Buffering Time Strategies for Wireless Full-duplex Systems under Poisson TrafficNov 14 2016Full-duplex wireless communication has the potential to double the capacity of wireless networks by reducing the band occupancy of transmissions. However, a full-duplex capability cannot always reduce the band occupancy because the real traffic is not ... More
Evolution of the Relativistic Plasmoid-Chain in the Poynting-Dominated PlasmaJul 22 2013In this paper, we investigate the evolution of the plasmoid-chain in a Poynting-dominated plasma. We model the relativistic current sheet with cold background plasma using the relativistic resistive magnetohydrodynamic approximation, and solve its temporal ... More
Nonnegative solutions to stochastic heat equation with nonlinear driftJun 27 2013We consider one-dimensional stochastic heat equation with nonlinear drift, $\displaystyle \partial_t u=\frac{1}{2}\Delta u+b(u)u+\sigma(u)\dot{W}(t,x)$, where $b:\mathbb{R}_{+}\to \mathbb{R}$ is a continuous function and $\sigma:\mathbb{R}_{+}\to \mathbb{R}$ ... More
Clustering Analysis of Periodic Point Vortices with the $L$ FunctionAug 28 2006Mar 01 2007A motion of point vortices with periodic boundary conditions is studied by using Weierstrass zeta functions. Scattering and recoupling of a vortex pair by a third vortex becomes remarkable when the vortex density is large. Clustering of vortices with ... More
Bifurcations and Chaos in the Six-Dimensional Turbulence Model of GledzerMay 19 2006May 26 2006The cascade-shell model of turbulence with six real variables originated by Gledzer is studied numerically using Mathematica 5.1. Periodic, doubly-periodic and chaotic solutions and the routes to chaos via both frequency-locking and period-doubling are ... More
Determinantal Martingales and Interacting Particle SystemsJul 09 2013Determinantal process is a dynamical extension of a determinantal point process such that any spatio-temporal correlation function is given by a determinant specified by a single continuous function called the correlation kernel. Noncolliding diffusion ... More
Bessel process, Schramm-Loewner evolution, and Dyson modelMar 24 2011Bessel process is defined as the radial part of the Brownian motion (BM) in the $D$-dimensional space, and is considered as a one-parameter family of one-dimensional diffusion processes indexed by $D$, BES$^{(D)}$. It is well-known that $D_{\rm c}=2$ ... More
Survival probability of mutually killing Brownian motions and the O'Connell processDec 17 2011Mar 23 2012Recently O'Connell introduced an interacting diffusive particle system in order to study a directed polymer model in 1+1 dimensions. The infinitesimal generator of the process is a harmonic transform of the quantum Toda-lattice Hamiltonian by the Whittaker ... More
Closed incompressible surfaces of genus two in 3-bridge knot complementsFeb 28 2007In this paper, we characterize closed incompressible surfaces of genus two in the complements of 3-bridge knots and links. This characterization includes that of essential 2-string tangle decompositions for 3-bridge knots and links.
Edge number of knots and linksMay 30 2007We introduce a new numerical invariant of knots and links made from the partitioned diagrams. It measures the complexity of knots and links.
Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfacesDec 14 2007Feb 25 2015Some time ago, the chiral algebra theory of Beilinson-Drinfeld was expected to play a central role in the convergence of divergence in mathematical physics of superstring theory for quantization of gauge theory and gravity. Naively, this algebra plays ... More
Determinantal Martingales and Noncolliding Diffusion ProcessesMay 19 2013Jul 09 2014Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in the sense ... More
A remark on the bound for the free energy of directed polymers in random environment in 1+2 dimensionJun 18 2014We consider the behavior of the quantity $p(\beta)$; the free energy of directed polymers in random environment in $1+2$ dimension, where $\beta$ is inverse temperature. We know that the free energy is strictly negative when $\beta$ is not zero. In this ... More
Spectroscopy of Pentaquark BaryonsSep 07 2005A review is given to pentaquark mass predictions in quark models and QCD. It is pointed out that no successful quark model prediction is available for low-lying pentaquark states. Some new results of direct application of QCD, QCD sum rules and lattice ... More
On the derivation of several second order partial differential equations from a generalization of the Einstein equationMar 15 2016A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The nonrelativistic limits ... More
Double Periodicity and Frequency-Locking in the Langford EquationJul 05 2007The bifurcation structure of the Langford equation is studied numerically in detail. Periodic, doubly-periodic, and chaotic solutions and the routes to chaos via coexistence of double periodicity and period-doubling bifurcations are found by the Poincar\'e ... More
System of Complex Brownian Motions Associated with the O'Connell ProcessJun 11 2012Sep 15 2012The O'Connell process is a softened version (a geometric lifting with a parameter $a>0$) of the noncolliding Brownian motion such that neighboring particles can change the order of positions in one dimension within the characteristic length $a$. This ... More
Non-colliding system of Brownian particles as Pfaffian processJun 10 2005In the paper [7] we studied the temporally inhomogeneous system of non-colliding Brownian motions and proved that multi-time correlation functions are generally given by the quaternion determinants in the sense of Dyson and Mehta. In this report we give ... More
Knots and surfacesMar 30 2016This article is an English translation of Japanese article "Musubime to Kyokumen", Math. Soc. Japan, Sugaku Vol. 67, No. 4 (2015) 403--423. It surveys a specific area in Knot Theory concerning surfaces in knot exteriors.
Impossibility of obtaining split links from split links via twistingsApr 24 2001We show that if a split link is obtained from a split link $L$ in $S^3$ by $1/n$-Dehn surgery along a trivial knot $C$, then the link $L\cup C$ is splittable. That is to say, it is impossible to obtain a split link from a split link via a non-trivial ... More
Linear independence of values of logarithms revisitedApr 03 2019Let $m\ge 2$ be an integer, $K$ an algebraic number field and $\alpha\in K\setminus \{0,-1\}$ with sufficiently small absolute value. In this article, we provide a new lower bound for linear form in $1,{\rm{log}}(1+\alpha),\ldots,{\rm{log}}^{m-1}(1+\alpha)$ ... More
Branching random walks in random environment and super-Brownian motion in random environmentApr 23 2013Jun 27 2013We focus on the existence and characterization of the limit for a certain critical branching random walks in time-space random environment in one dimension which was introduced by M. Birnkenr Each particle performs simple random walk on $\mathbb{Z}$ ... More
AdS/CFT Duality User GuideSep 11 2014Aug 31 2016This is the draft/updated version of a textbook on "real-world" applications of the AdS/CFT duality for beginning graduate students in particle physics and for researchers in the other fields. The aim of this book is to provide background materials such ... More
Critical phenomena in the AdS/CFT dualityJun 25 2010We review black holes with second-order phase transition in string theory (R-charged black holes and holographic superconductors) and review their static and dynamic critical phenomena. Holographic superconductors have conventional mean-field values for ... More
Monodromy of Gauss-Manin connection for deformation by group cocyclesJul 28 2012We consider the 2-cocycle deformation of algebras graded by discrete groups. The action of the Maurer-Cartan form is shown to be cohomologous to the cup product action of the group cocycle. This allows us to compute the monodromy of the Gauss-Manin connection ... More
Hyperon-Nucleon Interaction in a Quark ModelOct 13 1993A lecture given at the International School Seminar on {\sl Hadrons and Nuclei from QCD}, Tsuruga-Vladivostok-Sapporo, August-September, 1993. A realistic hyperon ($Y$)-nucleon ($N$) interaction based on the quark model and the one-boson-exchange potential ... More
On the nonrelativistic limit of a semilinear field equation in a uniform and isotropic spaceDec 26 2015The nonrelativistic limit of a semilinear field equation is considered in a uniform and isotropic space.The scale-function of the space is constructed based on the Einstein equation.The Cauchy problem of the limit-equation is considered,and global and ... More
Topological Aspects of an Antisymmetric Background Field on OrbifoldsJan 14 1993We study string theory on orbifolds in the presence of an antisymmetric constant background field in detail and discuss some of new aspects of the theory. It is pointed out that the term with the antisymmetric background field can be regarded as a topological ... More
Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processesMay 10 2016Sep 22 2016The Bessel process with parameter $D>1$ and the Dyson model of interacting Brownian motions with coupling constant $\beta >0$ are extended to the processes in which the drift term and the interaction terms are given by the logarithmic derivatives of Jacobi's ... More
Minuscule Schubert Varieties and Mirror SymmetryJan 31 2013Aug 23 2017We consider smooth complete intersection Calabi-Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi-Yau 3-folds of this type up ... More
Baryon-Baryon Interaction in the Quark Cluster ModelJun 19 2003The quark cluster model approach to the baryon-baryon interaction is reviewed and recent application to the charge symmetry breaking in nuclear force is discussed.
Summary of the YITP-RCNP Workshop on Chiral Restoration in Nuclear MediumJun 19 2003This is a personal summary of the workshop. I overview the topics of the workshop and itemize what we learned at the workshop.
Strong and Weak Interactions of Strange HadronsFeb 15 1995I review hadronic processes involving strange hadrons, especially hyperons from the quark structure point of view. The strong interaction of quarks expects several important new features when the strangeness is introduced upon the non-strange degrees ... More
Dynamics of Multiquark Systems: Mass, Width and ExoticsOct 27 2006Exotic multi-quark states are examined in the quark model and in QCD. Current status of theoretical studies of the pentaquark Theta^+ is reported. We show recent analyses of multi-quark components of baryons. A novel method to extract a compact excited ... More
Chiral Symmetry and Weak Decay of HypernucleiJun 15 1999The weak decays of hyperons and hypernuclei are studied from the chiral symmetry viewpoint. The soft pion relations are useful in understanding the isospin properties of the weak hyperon decays. Recent development on the short-range part of the $\Lam ... More
Unknotting submanifolds of the 3-sphere by twistingsSep 21 2016By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox's re-embedding can be replaced with twistings. In this paper, we will show that any closed ... More
Ground state property of Bose-Einstein gas for arbitrary power low interactionJan 16 2002We study Bose-Einstein gas for an arbitrary power low interaction $C_{\alpha}r^{-\alpha}$. This is done by the Hartree Fock Bogoliubov (HFB) approach at $T \le T_{c}$ and the mean field approach at $T>T_{c}$. Especially, we investigate the ground state ... More
On the Probability Distribution of Velocity Circulation in Three-Dimensional TurbulenceJul 23 1993The probability distribution functions of the circulation of velocity in three-dimensional decaying isotropic turbulence are examined by the database of the numerical simulation based on the pseudospectral method. It is shown that the standard deviation ... More
Reciprocal Time Relation of Noncolliding Brownian Motion with DriftApr 25 2012Jun 15 2012We consider an $N$-particle system of noncolliding Brownian motion starting from $x_1 \leq x_2 \leq ... \leq x_N$ with drift coefficients $\nu_j, 1 \leq j \leq N$ satisfying $\nu_1 \leq \nu_2 \leq ... \leq \nu_N$. When all of the initial points are degenerated ... More
Elliptic Determinantal Process of Type ANov 17 2013Sep 29 2014We introduce an elliptic extension of Dyson's Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant evaluations related to the reduced affine root system ... More
Coexistence of coiled surfaces and spanning surfaces for knots and linksNov 26 2012It is a well-known procedure for constructing a torus knot or link that first we prepare an unknotted torus and meridian disks in the complementary solid tori of it, and second smooth the intersections of the boundary of meridian disks uniformly. Then ... More
Higher Order Correction to the GHS String Black HoleJun 14 1994We study the order $\alpha'$ correction to the string black hole found by Garfinkle, Horowitz, and Strominger. We include all operators of dimension up to four in the Lagrangian, and use the field redefinition technique which facilitates the analysis. ... More
Zero Mode Divergence Problem in String TheoryJan 06 1994For $2D$ string theory, the perturbative $S$-matrices are not well-defined due to a zero mode divergence. Although there exist formal procedures to make the integral convergent, their physical meanings are unclear. We describe a method to obtain finite ... More
Slope equality of non-hyperelliptic Eisenbud--Harris special fibrations of genus $4$Apr 17 2018The Horikawa index and the local signature are introduced for relatively minimal fibered surfaces whose general fiber is a non-hyperelliptic curve of genus $4$ with unique trigonal structure.
Strange examples of local signatures for fibered surfaces of small genusApr 28 2017We give examples of local signatures, completely different from the usual ones, for general fibrations of genus $2$ and genus $3$.
Slopes of Fibered Surfaces with a Finite Cyclic AutomorphismApr 16 2015Apr 17 2016We study slopes of finite cyclic covering fibrations of a fibered surface. We give the best possible lower bound of the slope of these fibrations. We also give the slope equality of finite cyclic covering fibrations of a ruled surface and observe the ... More
On sets of marked once-holed tori allowing holomorphic mappings into Riemann surfaces with marked handleApr 18 2016In our previous work, for a given Riemann surface $Y_0$ with marked handle, we investigated geometric properties of the set of marked once-holed tori $X$ allowing holomorphic mappings of $X$ into $Y_0$. It turned out that it is a closed domain with Lipschitz ... More
Unknotting submanifolds of the 3-sphere by twistingsSep 21 2016Dec 01 2016By the Fox's re-embedding theorem, any compact submanifold of the 3-sphere can be re-embedded in the 3-sphere so that it is unknotted. It is unknown whether the Fox's re-embedding can be replaced with twistings. In this paper, we will show that any closed ... More
Non-minimal bridge positions of torus knots are stabilizedJun 05 2010We show that any non-minimal bridge decomposition of a torus knot is stabilized and that $n$-bridge decompositions of a torus knot are unique for any integer $n$. This implies that a knot in a bridge position is a torus knot if and only if there exists ... More
Additivity of free genus of knotsNov 08 1998We show that free genus of knots is additive under connected sum.
The Heterotic EnhanconNov 06 2001Mar 12 2002The enhancon mechanism is studied in the heterotic string theory. We consider the N_L=0 winding strings with momentum (NS1-W*) and the Kaluza-Klein dyons (KK5-NS5*). The NS1-W* and KK5-NS5* systems are dualized to the D4-D0* and D6-D2* systems, respectively, ... More
Natural Generalization of Bosonic String AmplitudesFeb 26 1993Jun 04 1993The similarity between tree-level string theory scalar amplitudes, the Koba-Nielsen form ($S^{1}$) and the Virasoro-Shapiro form ($S^{2}$) suggests a natural $S^{n}$ generalization for a scalar amplitude. It is shown that the $S^{n}$ amplitude shares ... More
Pregeometrical Formulation of Berkovits' Open RNS Superstring Field TheoriesDec 15 2001We propose a pregeometrical formulation of Berkovits' open Ramond-Neveu-Schwarz (RNS) superstring field theories. We show that Berkovits' open RNS superstring field theories arise by expanding around particular solutions of the classical equations of ... More
Super-Brownian motion in random environment as a limit point of critical branching random walks in random environmentJul 07 2012Apr 24 2013We focus on the existence and its characterization of limit for a certain critical branching random walks in time-space random environment in 1 dimension which was introduced by Birkner Each particle performs simple random walk on $\mathbb{Z}$ ... More
Nuclear Force in the Skyrme Model: Quasistatic ApproachApr 13 1993Dynamics of two-Skyrmion systems is studied in the quasistatic approach. The quasistatic approach enables us to formulate the collective coordinate quantization of two-Skyrmion systems consistently with the 1/Nc expansion. By constructing quasistatic ... More
QCD Analysis of the H dibaryonOct 20 1995The status of theoretical studies of the $H$ dibaryon is reviewed. Some recent developments including the effect of the instanton induced interaction and the QCD sum rule results are discussed in detail.
Point Process Analysis of Vortices in a Periodic BoxJun 07 2007The motion of assemblies of point vortices in a periodic parallelogram can be described by the complex position $z_j(t)$ whose time derivative is given by the sum of the complex velocities induced by other vortices and the solid rotation centered at $z_j$. ... More
Determinantal Martingales and Correlations of Noncolliding Random WalksJul 07 2013Dec 20 2014We study the noncolliding random walk (RW), which is a particle system of one-dimensional, simple and symmetric RWs starting from distinct even sites and conditioned never to collide with each other. When the number of particles is finite, $N < \infty$, ... More
Characteristic Polynomials of Random Matrices and Noncolliding Diffusion ProcessesFeb 23 2011Dec 17 2015We consider the noncolliding Brownian motion (BM) with $N$ particles starting from the eigenvalue distribution of Gaussian unitary ensemble (GUE) of $N \times N$ Hermitian random matrices with variance $\sigma^2$. We prove that this process is equivalent ... More
Dissipative Abelian Sandpile ModelsMay 02 2015We introduce a family of abelian sandpile models with two parameters $n, m \in {\bf N}$ defined on finite lattices on $d$-dimensional torus. Sites with $2dn+m$ or more grains of sand are unstable and topple, and in each toppling $m$ grains dissipate from ... More
O'Connell's process as a vicious Brownian motionOct 09 2011Dec 10 2011Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two of them meet they kill each other. We consider the vicious Brownian motion conditioned never ... More
Determinantal process starting from an orthogonal symmetry is a Pfaffian processApr 11 2011Oct 03 2011When the number of particles $N$ is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index $\nu > -1$ (BESQ$^{(\nu)}$) are determinantal processes for arbitrary fixed initial configurations. In the present ... More
Waist and trunk of knotsMay 27 2009Jun 01 2009We introduce two numerical invariants, the waist and the trunk of knots. The waist of a closed incompressible surface in the complement of a knot is defined as the minimal intersection number of all compressing disks for the surface in the 3-sphere and ... More
Transparent tiles of silica aerogels for high-energy physicsFeb 14 2019Silica aerogels are important to be used as photon radiators in Cherenkov counters for high-energy-physics experiments because of their optical transparency and intermediate refractive indices between those of gases and liquids or solids. Cherenkov counters ... More
On subfactors arising from asymptotic representations of symmetric groupsDec 04 2009Mar 29 2011We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each finite factorial ... More
Deformation of algebras associated to group cocyclesJul 13 2011We define a deformation of algebras endowed with coaction of the reduced group algebras. The deformation parameter is given by a 2-cocycle over the group. We prove K-theory isomorphisms for the cocycles which can be perturbed to the trivial one.
Operator algebra of foliations with projectively invariant transverse measureNov 06 2007Apr 18 2013We study the structure of operator algebras associated with the foliations which have projectively invariant measures. When a certain ergodicity condition on the measure preserving holonomies holds, the lack of holonomy invariant transverse measure can ... More
Phase diagram and collective excitation in excitonic insulator: from the orbital physics viewpointFeb 25 2016May 06 2016Excitonic insulating system is studied from the viewpoints of the orbital physics in strongly correlated electron systems. An effective model Hamiltonian for low-energy electronic states is derived from the two-orbital Hubbard model with a finite energy ... More
Wireless Full-duplex Medium Access Control for Enhancing Energy EfficiencyMar 31 2017Recent years have witnessed a proliferation of battery-powered mobile devices, e.g., smartphones, tablets, sensors, and laptops, which leads a significant demand for high capacity wireless communication with high energy efficiency. Among technologies ... More
Spin and Charge Fluctuations near Metal-Insulator Transition in Dimer-Type Molecular SolidFeb 28 2017Spin and charge fluctuations at vicinity of metal-to-Mott insulator transitions are studied in an organic solid with molecular dimers. The extended Hubbard model taking account of the internal electronic degree of freedom in a molecular dimer is analyzed ... More
Improvements in calibration of GSO scintillators in the Suzaku Hard X-ray DetectorJul 25 2011Improvements of in-orbit calibration of GSO scintillators in the Hard X-ray Detector on board Suzaku are reported. To resolve an apparent change of the energy scale of GSO which appeared across the launch for unknown reasons, consistent and thorough re-analyses ... More
An operator theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivityJul 01 2016Sep 14 2018We first show some properties such as smoothness and monotone decreasingness of the solution to the BCS-Bogoliubov gap equation for superconductivity. Moreover we give the behavior of the solution with respect to the temperature near the transition temperature. ... More
On projective manifolds swept out by cubic varietiesOct 12 2010Nov 01 2011We study structures of embedded projective manifolds swept out by cubic varieties. We show if an embedded projective manifold is swept out by high-dimensional smooth cubic hypersurfaces, then it admits an extremal contraction which is a linear projective ... More
A mathematical proof that the transition to a superconducting state is a second-order phase transitionAug 26 2008We deal with the gap function and the thermodynamical potential in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature $T$ only. We show that the squared gap function is of class $C^2$ on the closed ... More
An Algebra Associated with a Flag in a Subspace Lattice over a Finite Field and the Quantum Affine Algebra $U_q(\widehat{\mathfrak{sl}}_2)$Sep 19 2017Sep 25 2018In this paper, we introduce an algebra $\mathcal{H}$ from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra $\mathcal{H}$ and the quantum affine ... More
Classification of embedded projective manifolds swept out by rational homogeneous varieties of codimension oneJan 09 2011We give a classification of embedded smooth projective varieties swept out by rational homogeneous varieties whose Picard number and codimension are one.
Association schemes on the Schubert cells of a GrassmannianNov 17 2017Let $\mathbb{F}$ be any field. The Grassmannian $\mathrm{Gr}(m,n)$ is the set of $m$-dimensional subspaces in $\mathbb{F}^n$, and the general linear group $\mathrm{GL}_n(\mathbb{F})$ acts transitively on it. The Schubert cells of $\mathrm{Gr}(m,n)$ are ... More
Fano manifolds of coindex three admitting nef tangent bundleApr 23 2019We prove that any Fano manifold of coindex three admitting nef tangent bundle is homogeneous.
The solution to the BCS gap equation for superconductivity and its temperature dependenceOct 28 2013From the viewpoint of operator theory, we deal with the temperature dependence of the solution to the BCS gap equation for superconductivity. When the potential is a positive constant, the BCS gap equation reduces to the simple gap equation. We first ... More
The BCS Gap Equation on a Banach Space Consisting of Functions both of the Temperature and of the Wave VectorOct 31 2008Jun 04 2010In previous mathematical studies of the BCS gap equation of superconductivity, the gap function was regarded as an element of a space consisting of functions of the wave vector only. But we regard it as an element of a Banach space consisting of functions ... More
Compressible-incompressible two-phase flows with phase transition: model problemMay 10 2017Oct 05 2017We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in $\mathbb{R}^N$, and the Navier-Stokes-Korteweg equations is used in the ... More
Strong solutions for compressible-incompressible two-phase flows with phase transitionsAug 22 2018We consider the compressible-incompressible two-phase flows with phase transitions in a general domain of $N$-dimensional Euclidean space. The compressible fluid and the incompressible fluid are separated by a sharp interface, and the surface tension ... More
Observations of Umbral Dots and their Physical ModelsJul 17 2014The Hinode satellite opens a new era to the sunspots research, because of its high spatial resolution and temporal stability. Fine scale structures in sunspots, called umbral dots (UDs), have become one of the hottest topics in terms of the close observation ... More
The h-expansion of Macdonald operators and their expression by Dunkl operatorsApr 11 2012Apr 12 2012Macdonald operators are well known as the 'commutative family' acting on the symmetric functions over Q(q,t). If we suppose that q=exp(h) and t=exp(beta h) and observe the Taylor expansion around h=0, we can see the second-degree Dunkl operator appear ... More
Triviality of hierarchical O(N) spin model in four dimensions with large NNov 04 2003The renormalization group transformation for the hierarchical O(N) spin model in four dimensions is studied by means of characteristic functions of single-site measures, and convergence of the critical trajectory to the Gaussian fixed point is shown for ... More
On the sections of universal hyperelliptic curvesSep 14 2016In this paper, we will give an algebraic proof for determining the sections for the universal pointed hyperelliptic curves, when $g\geq 3$ and the image of the $\ell$-adic cyclotomic character $G_k\to \Z^\times$ is infinite. Furthermore, we will study ... More
Global existence and decay estimates for quasilinear wave equations with nonuniform dissipative termNov 26 2013We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space $H^L \times H^{L-1}$, where $L \geq [d/2]+3$. The linear dissipative terms depend on space variable coefficient, and these terms may ... More
An operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity (final version)Dec 14 2017Apr 09 2019We show that the transition from a normal conducting state to a superconducting state is a second-order phase transition in the BCS-Bogoliubov model of superconductivity from the viewpoint of operator theory. Here we have no magnetic field. Moreover we ... More
Global solvability of compressible-incompressible two-phase flows with phase transitions in bounded domainsAug 22 2018Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains $\Omega_{t+}, \Omega_{t-} \subset \mathbb{R}^N$ where the domains are separated by a sharp compact interface $\Gamma_t ... More
The solution to the BCS gap equation and the second-order phase transition in superconductivityJun 04 2010May 17 2011The existence and the uniqueness of the solution to the BCS gap equation of superconductivity is established in previous papers, but the temperature dependence of the solution is not discussed. In this paper, in order to show how the solution varies with ... More
Higher order generalization of Fukaya's Morse homotopy invariant of 3-manifolds I. Invariants of homology 3-spheresFeb 26 2012May 07 2015We give a generalization of Fukaya's Morse homotopy theoretic approach for 2-loop Chern--Simons perturbation theory to 3-valent graphs with arbitrary number of loops at least 2. We construct a sequence of invariants of integral homology 3-spheres with ... More
Local cut points and metric measure spaces with Ricci curvature bounded belowOct 05 2006A local cut point is by definition a point that disconnectes its sufficiently small neighborhood. We show that there exists an upper bound for the degree of a local cut point in a metric measure space satisfying the generalized Bishop--Gromov inequality. ... More
Lengths of chains of minimal rational curves on Fano manifoldsOct 11 2010In this paper, we consider a natural question how many minimal rational curves are needed to join two general points on a Fano manifold X of Picard number 1. In particular, we study the minimal length of such chains in the cases where the dimension of ... More
Empirical observations of ultraslow diffusion driven by the fractional dynamics in languages: Dynamical statistical properties of word counts of already popular wordsJan 24 2018Jun 29 2018Ultraslow diffusion (i.e. logarithmic diffusion) has been extensively studied theoretically, but has hardly been observed empirically. In this paper, firstly, we find the ultraslow-like diffusion of the time-series of word counts of already popular words ... More
Morse theory and Lescop's equivariant propagator for 3-manifolds with $b_1=1$ fibered over $S^1$Mar 31 2014Sep 02 2014For a 3-manifold $M$ with $b_1(M)=1$ fibered over $S^1$ and the fiberwise gradient $\xi$ of a fiberwise Morse function on $M$, we introduce the notion of amidakuji-like path (AL-path) on $M$. An AL-path is a piecewise smooth path on $M$ consisting of ... More
ACM bundles on K3 surfaces of genus 2Jul 07 2014Let $\pi:X\rightarrow \mathbb{P}^2$ be a K3 surface of genus 2 and $L=\pi^{\ast}\mathcal{O}_{\mathbb{P}^2}(3)$, and assume that $\pi^{\ast}\mathcal{O}_{\mathbb{P}^2}(1)$ is ample as a line bundle on $X$. In this paper, we give a numerical characterization ... More
Is the solution to the BCS gap equation continuous in the temperature ?Aug 26 2010Apr 02 2013One of long-standing problems in mathematical studies of superconductivity is to show that the solution to the BCS gap equation is continuous in the temperature. In this paper we address this problem. We regard the BCS gap equation as a nonlinear integral ... More
BPS states carrying fermionic brane chargesJan 31 2000Feb 14 2000The Green-Siegel central extension of superalgebras for BPS branes is studied. In these cases commutators of usual bosonic brane charges only with the broken supersymmetry charges allow this central extension. We present an interpretation of these fermionic ... More