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A bicomplex of Khovanov homology for colored Jones polynomialJul 30 2009Sep 09 2010We construct a bicomplex for the categorification of the colored Jones polynomial. This work is motivated by the problem suggested by Anna Beliakova and Stephan Wehrli who discussed the categorification of the colored Jones polynomial in their paper.

Finite-type invariants for curves on surfacesMar 14 2008Oct 15 2008This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a higher-order ... More

Khovanov homology for an unnormalized Witten-Reshetikhin-Turaev invariant and 3-manifoldsMay 09 2011Jul 11 2011A problem about Khovanov homology and 3-manifolds is discussed in this paper.

On Reidemeister invariance of the Khovanov homology group of the Jones polynomialJan 26 2009Oct 06 2009As Oleg Viro describes in his paper, the most fundamental property of the Khovanov homology group is their invariance under Reidemeister moves. Viro constructes Khovanov complex and homology consisting of Jordan curves with sign and also gives a proof ... More

Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrasesAug 26 2010May 10 2017We introduce three spectral sequences which give some expressions of colored Jones polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of them are derived from a bicomplex of the colored Jones polynomial. The other is the ... More

Some chain maps on Khovanov complexes and Reidemeister movesOct 06 2009We introduce some chain maps between Khovanov complexes. Each of the chain maps commutes with a chain homotopy map and a retraction maps which obtain a Reidemeister invariance of Khovanov homology.

Invariants via word for curves and frontsMay 03 2007May 08 2007We construct the infinite sequence of invariants for curves in surfaces by using word theory that V. Turaev introduced. For plane closed curves, we add some extra terms, e.g. the rotation number. From these modified invariants, we get the Arnold's basic ... More

Spectral sequences of colored Jones polynomials, colored Rasmussen invariants and nanophrasesAug 26 2010Sep 24 2010We introduce three spectral sequences which give some expressions of colored Jones polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of them are derived from a bicomplex of the colored Jones polynomial. The other is the ... More

Chain homotopy maps and a universal differential for Khovanov-type homologyJul 13 2009Oct 06 2009We give chain homotopy maps of Khovanov-type link homology of a universal differential. The universal differential, discussed by Mikhail Khovanov, Marco Mackaay, Paul Turner and Pedro Vaz, contains the original Khovanov's differential and Lee's differential. ... More

Remarks on the categorification of colored Jones polynomialsAug 05 2010Sep 24 2010We introduce colored Jones polynomials of nanowords and their categorification. We also prove the existence of a Khovanov-type bicomplex which has three grades.

Remarks on the categorification of colored Jones polynomialsAug 05 2010May 10 2017We introduce colored Jones polynomials of nanowords and their categorification. We also prove the existence of a Khovanov-type bicomplex which has three grades.

On Goussarov-Polyak-Viro Conjecture of knots with degree threeMay 04 2019A knot invariant ordered by filtered finite dimensional vector spaces is called finite type. It has been conjectured that every finite type invariant of classical knots could be extended to a finite type invariant of long virtual knots (Goussarov-Polyak-Viro ... More

The half-twisted splice operation on reduced knot projectionsAug 05 2012We show that any nontrivial reduced knot projection can be obtained from a trefoil projection by a finite sequence of half-twisted splice operations and their inverses such that the result of each step in the sequence is reduced.

Khovanov homology and wordsJan 26 2009Mar 22 2010This paper is concerned with nanowords, a generalization of links, introduced by Turaev. It is shown that the system of bigraded homology groups is an invariant of nanowords by introducing a new notion. This paper gives two examples which show the independence ... More

On a Poincaré polynomial from Khovanov homology and Vassiliev invariantsMay 14 2019We introduce a Poincar\'{e} polynomial with two-variable $t$ and $x$ for knots, derived from Khovanov homology, where the specialization $(t, x)$ $=$ $(1, -1)$ is a Vassiliev invariant of order $n$. Since for every $n$, there exist non-trivial knots with ... More

Finite type invariants of nanowords and nanophrasesJul 10 2010Oct 04 2010Homotopy classes of nanowords and nanophrases are combinatorial generalizations of virtual knots and links. Goussarov, Polyak and Viro defined finite type invariants for virtual knots and links via semi-virtual crossings. We extend their definition to ... More

Dual Ramanujan-Fourier seriesNov 21 2016Let $c_q(n)$ be the Ramanujan sums. Many results concerning Ramanujan-Fourier series $f(n)=\sum_{q=1}^\infty a_q c_q (n)$ are obtained by many mathematicians. In this paper we study series of the form $f(q)=\sum_{n=1}^\infty a_n c_q (n)$, which we call ... More

Ramanujan-Fourier series of certain arithmetic functions of two variablesApr 26 2016We study Ramanujan-Fourier series of certain arithmetic functions of two variables. We generalize Delange's theorem to the case of arithmetic functions of two variables and give sufficient conditions for pointwise convergence of Ramanujan-Fourier series ... More

On some generalizations of mean value theorems for arithmetic functions of two variablesApr 19 2016Let $f: \mathbb{N}^2 \mapsto \mathbb{C}$ be an arithmetic function of two variables. We study the existence of the limit: \[\displaystyle \lim_{x \to \infty} \frac{1}{x^2 (\log x)^{k-1}} \sum_{n_1 , n_2 \le x} f (n_1, n_2) \] where $k$ is a fixed positive ... More

Dual Ramanujan-Fourier seriesNov 21 2016Jan 17 2018Let $c_q(n)$ be the Ramanujan sums. Many results concerning Ramanujan-Fourier series $f(n)=\sum_{q=1}^\infty a_q c_q (n)$ are obtained by many mathematicians. In this paper we study series of the form $f(q)=\sum_{n=1}^\infty a_n c_q (n)$, which we call ... More

Off-shell invariant super Yang-Mills with gauged central charges for N=D=2 and N=D=4: "Do we need a constraint ?"Nov 14 2014We investigate to derive off-shell invariant twisted super Yang-Mills for N=2 in 2-dimensions and N=4 in 4-dimensions with a central charge by super connection ansatz formalism. We find off-shell invariant N=2 algebra with and without an extra constraint ... More

Multiplicative Nonholonomic/Newton -like AlgorithmFeb 09 2000We construct new algorithms from scratch, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has numerous merits ... More

Question on D=26 --- String Theory versus Quantum Gravity ---Oct 16 1997In the covariant-gauge two-dimensional quantum gravity, various derivations of the critical dimension D=26 of the bosonic string are critically reviewed, and their interrelations are clarified. It is shown that the string theory is not identical with ... More

Decoding Stacked Denoising AutoencodersMay 10 2016Data representation in a stacked denoising autoencoder is investigated. Decoding is a simple technique for translating a stacked denoising autoencoder into a composition of denoising autoencoders in the ground space. In the infinitesimal limit, a composition ... More

Anomaly Problem in a Simple Model Analogous to the Lightcone-Gauge Two-Dimensional Quantum GravityFeb 25 1997It was found in the two-dimensional quantum gravity both in the de Donder gauge and in the lightcone gauge that one of field equations breaks down at the level of the representation, though the breakdown is very little. It is shown that this anomalous ... More

Exact Solutions to the Two-dimensional BF and Yang-Mills Theories in the Light-cone GaugeNov 16 2001It is shown that the BRS-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated ... More

Note Added to ``Proof of the Gauge Independence of the Conformal Anomaly of Bosonic String in the Sense of Kraemmer and Rebhan''Mar 06 1998A comment is given to the reply of Kraemmer and Rebhan (hep-th/9711075) to our paper (hep-th/9710131).

Application of Facial Reduction to $H_\infty$ State Feedback Control ProblemJun 11 2016One often encounters numerical difficulties in solving linear matrix inequality (LMI) problems obtained from $H_\infty$ control problems. We discuss the reason from the viewpoint of optimization, and provide necessary and sufficient conditions for LMI ... More

Neural Network with Unbounded Activation Functions is Universal ApproximatorMay 14 2015Nov 29 2015This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de-facto standard of deep learning. The ReLU network can be analyzed ... More

Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravityJul 16 2002We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for $-2 \leq c \leq 1$. We reformulate Q-state Potts model into the model which can be identified as a weighted percolation cluster ... More

Effects of the difference between the charge and matter deformations on fusion reactions of unstable nucleiJun 26 2002Relativistic mean field calculations suggest that the charge and matter deformations significantly differ in some of the unstable neutron and proton rich nuclei. We discuss the effects of the difference on the fusion reactions induced by them at energies ... More

Notes on Unfair Papers by Mebarki et al. on ``Quantum Nonsymmetric Gravity''Dec 06 1999It is pointed out that the essential parts of some recent papers by Mebarki {\it et al.} (hep-th/9911045, hep-th/9911046, hep-th/9911048, hep-th/9911049, dated 6 Nov.1999) are taken from a book written by Nakanishi and Ojima, published in 1990.

Dirac-Kaehler Fermion from Clifford Product with Noncommutative Differential Form on a LatticeMay 12 2003May 18 2003We formulate Dirac-Kaehler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kaehler action requires to choose the lattice structure having both orientabilities on a link. ... More

N=2 Supersymmetric Model with Dirac-Kahler Fermions from Generalized Gauge Theory in Two DimensionsMay 31 1999We investigate the generalized gauge theory which has been proposed previously and show that in two dimensions the instanton gauge fixing of the generalized topological Yang-Mills action leads to a twisted N=2 supersymmetric action. We have found that ... More

Receiver Design for Realizing On-Demand WiFi Wake-up using WLAN SignalsSep 27 2012In this paper, we design a simple, low-cost, and low-power wake-up receiver which can be used for an IEEE 802.11-compliant device to remotely wake up the other devices by utilizing its own wireless LAN (WLAN) signals. The employed wake-up mechanism utilizes ... More

Two-Body Dirac Equation and Its WFOOct 24 1995Dec 05 1995A relativistic equation is proposed for the bound state of two particles, which is in accord with the boundary condition for the propagation of the negative-energy states and reduces to the (one-body)Dirac equation in the infinite limit of one of the ... More

Warped Geometry in Higher Dimensions with an Orbifold Extra DimensionMay 19 2001Oct 24 2001We solve the Einstein equations in higher dimensions with warped geometry where an extra dimension is assumed to have orbifold symmetry $S^{1}/Z_{2}$. The setup considered here is an extension of the five-dimensional Randall-Sundrum model to $5+D$ dimensions, ... More

Anisotropic Evolution Driven by Kinetic TermMar 30 2009Apr 26 2009We present a simple model where anisotropic evolution is driven by kinetic term in extra dimensions. By introducing a canonical or a ghost kinetic term, the possibility of anisotropy is studied.

Newton's law in braneworlds with an infinite extra dimensionDec 23 2001Apr 01 2002We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the ... More

On Fluid mechanics formulation of Monge-Kantorovich Mass Transfer ProblemFeb 08 2007The Monge-Kantorovich mass transfer problem is equivalently formulated as a convex optimization problem for a potential function. In the light of this formulation an interative algorithm is developed for determining the solution. It is a gradient flow ... More

Picard-Fuchs Equations and Prepotential in N=2 Supersymmetric G_{2} Yang-Mills TheoryMar 26 1997Jun 03 1997We study the low-energy effective theory of N=2 supersymmetric Yang-Mills theory with the exceptional gauge group $G_{2}$. We obtain the Picard-Fuchs equations for the $G_{2}$ spectral curve and compute multi-instanton contribution to the prepotential. ... More

The $W$ algebra structure of $N=2$ $CP_{n}$ coset modelsOct 28 1992We discuss the $N=2$ super $W$ algebras from the hamiltonian reduction of affine Lie superalgebras $A(n|n-1)^{(1)}$ and $A(n|n)^{(1)}$. From the quantum hamiltonian reduction of $A(n|n-1)^{(1)}$ we get the free field realization of $N=2$ $CP_{n}$ super ... More

Birational smooth minimal models have equal Hodge numbers in all dimensionsSep 20 2002Nov 24 2002This is a resume of the author's talk at the Worhshop on Arithmetic, Geometry and Physics around Calabi-Yau Varieties and Mirror Symmetry (July 23-29, 2001), the Fields Institute. The aim of this note is to prove that birational smooth minimal models ... More

A remark on Alexander polynomial criterion for bi-orderability of fibered 3-manifold groupsDec 03 2010We observe that Clay-Rolfsen's obstruction of bi-orderability, which uses the classical Alexander polynomial, is not strengthened by using the twisted Alexander polynomials for finite representations unlike many known applications of the Alexander polynomial. ... More

Finite orbits of Hurwitz actions on braid systemsDec 02 2009Apr 19 2010There are natural actions of the braid groups on the products of the braid groups, called the Hurwitz action. We first study the roots of centralizers in the braid groups. By using the structure of the roots, we provide a criterion for the Hurwitz orbit ... More

Okounkov bodies and Seshadri constantsFeb 29 2012May 31 2013Okounkov bodies, which are closed convex sets defined for big line bundles, have rich information on the line bundles. On the other hand, Seshadri constants are invariants which measure the positivity of line bundles. In this paper, we prove that Okounkov ... More

On a structure of random open books and closed braidsApr 17 2015Jun 21 2015A result of Malyutin shows that a random walk on the mapping class group gives rise to an element whose fractional Dehn twist coefficient is large or small enough. We show that this leads to several properties of random 3-manifolds and links. For example, ... More

Every property is testable on a natural class of scale-free multigraphsApr 03 2015Jul 23 2015In this paper, we introduce a natural class of multigraphs called hierarchical-scale-free (HSF) multigraphs, and consider constant-time testability on the class. We show that a very wide subclass, specifically, that in which the power-law exponent is ... More

Cosmological solutions for model with a $1/H^{2}$ termNov 07 2006Mar 14 2007We drive the cosmological solutions of five-dimensional model with $1/H^{2}$ term $(H^{2}\equiv H_{MNPQ}H^{MNPQ})$, where $H_{MNPQ}$ is 4-form field strength. The behaviors of the scale factors and the scalar potential in effective theory are examined.As ... More

Refined Topological Vertex and Duality of Gauge Theories in Generic Omega BackgroundsNov 29 2012The partition functions of refined topological strings(A-models) are computed, which give rise to the circle-compactified five-dimensional supersymmetric linear quiver gauge theories in generic (not necessarily self-dual) Omega backgrounds. Based on the ... More

Analysis of ZH recoil massFeb 18 2009The precise measurement of the Higgs mass is the most important program at International Linear Collider (ILC). Using e+e- -> ZH process, the mass of Higgs boson can be measured by two lepton tracks from decay of Z boson, even if the Higgs boson decays ... More

A-D-E Singularity and the Seiberg-Witten TheoryJun 03 1999We study the low-energy effective theory of N=2 supersymmetric Yang-Mills theory with ADE gauge groups in view of the spectral curves of the periodic Toda lattice and the A-D-E singularity theory. We examine the exact solutions by using the Picard-Fuchs ... More

Examples of Mori dream spaces with Picard number twoApr 30 2013Mar 09 2014In this note, we give a sufficient condition such that a projective variety with Picard number two is a Mori dream space. Using this condition, we obtain examples of Mori dream spaces with Picard number two.

Construction of isolated left orderings via partially central cyclic amalgamationJul 04 2011Feb 20 2013We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples of isolated ... More

Finite Thurston type orderings on dual braid monoidsFeb 05 2009Dec 14 2009For a finite Thurston type ordering < of the braid group B_{n}, we introduce a new normal form of a dual positive braid which we call the C-normal form. This normal form extends Fromentin's rotating normal form and the author's C-normal form of positive ... More

Curve diagram for Artin group of type BOct 02 2013May 08 2014We develop a theory of curve diagrams for Artin groups of type B. We define the winding number labeling and the wall crossing labeling of curve diagrams, and show that these labelings detect the classical and the dual Garside length, respectively. A remarkable ... More

On the supersingular reduction of K3 surfaces with complex multiplicationSep 30 2017Nov 29 2018We study the good reduction modulo p of K3 surfaces with complex multiplication. If a K3 surface with complex multiplication has good reduction, we calculate the Picard number and the height of the formal Brauer group of the reduction. Moreover, if the ... More

Braid ordering and knot genusMay 14 2008Dec 10 2009The genus of knots is a one of the fundamental invariant and can be seen as a complexity of knots. In this paper, we give a lower bound of genus using Dehornoy floor, which is a measure of complexity of braids in terms of braid ordering.

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causalityMay 01 2016Sep 21 2016The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the ... More

A functor-valued extension of knot quandlesJun 10 2010Jul 05 2010For an oriented knot $K$, we construct a functor from the category of pointed quandles to the category of quandles in three different ways. We also extend the quandle cocycle invariants of knots by using these quandle-valued invariant of knots, and study ... More

Holographic dark energy model with non-minimal couplingMay 31 2004Aug 02 2005We find that holographic dark energy model with non-minimally coupled scalar field gives rise to an accelerating universe by choosing Hubble scale as IR cutoff. We show viable range of a non-minimal coupling parameter in the framework of this model.

A First Order $q$-Difference System for the $BC_1$-Type Jackson Integral and Its ApplicationsApr 03 2009We present an explicit expression for the $q$-difference system, which the $BC_1$-type Jackson integral ($q$-series) satisfies, as first order simultaneous $q$-difference equations with a concrete basis. As an application, we give a simple proof for the ... More

Accelerating Universe from Modified Kasner Model in Extra DimensionsDec 23 2008Mar 11 2009This paper has been withdrawn by the author.

Non-adiabatic dynamics in 10Be with the microscopic alpha+alpha+N+N modelAug 17 2005Mar 02 2006The alpha+6He low-energy reactions and the structural changes of 10Be in the microscopic alpha+alpha+N+N model are studied by the generalized two-center cluster model with the Kohn-Hulthen-Kato variation method. It is found that, in the inelastic scattering ... More

Correction terms to Newton law due to induced gravity in AdS backgroundNov 27 2002Jan 12 2003We calculate small correction terms to gravitational potential on Randall-Sundrum brane with an induced Einstein term. The behaviors of the correction terms depend on the magnitudes of $AdS$ radius $k^{-1}$ and a characteristic length scale $\l$ of model. ... More

Localized gravity on de Sitter brane in five dimensionsApr 14 2002Oct 25 2003We consider a single brane embedded in five dimensions with vanishing and positive bulk cosmological constant. In this setup, the existence of $dS_{4}$ brane is allowed. We explore the gravitational fluctuations on the brane, and we point out that the ... More

Linearized gravity in flat braneworlds with anisotropic brane tensionFeb 25 2002Oct 29 2002We study the four-dimensional gravitational fluctuation on anisotropic brane tension embedded in braneworlds with vanishing bulk cosmological constant. In this setup, warp factors have two types (A and B) and we point out that the two types correspond ... More

Various Types of Five-Dimensional Warp Factor and Effective Planck ScaleSep 19 2001Nov 10 2001Based on the assumption that the warp factor of four-dimensional spacetime and the one of fifth dimension are tied through a parameter $\alpha$, we consider five-dimensional gravity with a 3-brane coupled to a bulk scalar field. For arbitrary value of ... More

A note on chirally cosmetic surgery on cable knotsMay 16 2019We show that a $(p,q)$-cable of a non-trivial knot $K$ does not admit chirally cosmetic surgery for $q\neq 2$, or $q=2$ with additional assumptions. In particular, we show that $(p,q)$-cable of non-trivial knot $K$ does not admit chirally cosmetic surgery ... More

On continuous extension of grafting mapsNov 06 2004The definition of the grafting operation for quasifuchsian groups is extended by Bromberg to all $b$-groups. Although the grafting maps are not necessarily continuous at boundary groups, in this paper, we show that the grafting maps take every "standard" ... More

Convergence and divergence of Kleinian punctured torus groupsJan 12 2007Jul 01 2011In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due ... More

A homological representation formula of colored Alexander invariantsMay 12 2015We give a formula of the colored Alexander invariant in terms of the homological representation of the braid groups which we call truncated Lawrence's representation. This formula generalizes the famous Burau representation formula of the Alexander polynomial. ... More

Framing functions and strengthened version of Dehn's lemmaJul 19 2013Sep 28 2014We give a lower estimate of the framing function of knots, and prove a strengthened version of Dehn's lemma conjectured by Greene-Wiest.

The classification of Wada-type representations of braid groupsMay 13 2011Mar 02 2012We give a classification of Wada-type representations of the braid groups, and solutions of a variant of the set-theoretical Yang-Baxter equation adapted to the free-product group structure. As a consequence, we prove Wada's conjecture: There are only ... More

On finite Thurston type orderings of braid groupsOct 22 2008May 11 2010We prove that for any finite Thurston-type ordering $<_{T}$ on the braid group\ $B_{n}$, the restriction to the positive braid monoid $(B_{n}^{+},<_{T})$ is a\ well-ordered set of order type $\omega^{\omega^{n-2}}$. The proof uses a combi\ natorial description ... More

Hurwitz equivalences of positive group generatorsAug 08 2010Jan 20 2011For a positively presented group G, we provide a criterion for two tuples of positive group generators of G to be Hurwitz equivalent or Hurwitz-conjugation equivalent. We also present an algorithmic approach to solve the Hurwitz equivalence and the Hurwitz ... More

Linear slices close to a Maskit sliceMar 29 2013We consider linear slices of the space of Kleinian once-punctured torus groups; a linear slice is obtained by fixing the value of the trace of one of the generators. The linear slice for trace 2 is called the Maskit slice. We will show that if traces ... More

Reading the dual Garside length of braids from homological and quantum representationsMay 23 2012We show that Lawrence's representation and linear representations from quantum sl_2 called generic highest weight vectors detect the dual Garside length of braids in a simple and natural way. That is, by expressing a representation as a matrix over a ... More

Isolated orderings on amalgamated free productsMay 06 2014We show that an amalgamated free product $G*_{A}H$ admits a discrete isolated ordering, under some assumptions of $G,H$ and $A$. This generalizes the author's previous construction of isolated orderings, and unlike known constructions of isolated orderings, ... More

Braid ordering and the geometry of closed braidMay 10 2008Oct 22 2008The relationships between braid ordering and the geometry of its closure is studied. We prove that if an essential closed surface $F$ in the complements of closed braid has relatively small genus with respect to the Dehornoy floor of the braid, $F$ is ... More

Polynomial-Space Approximation of No-Signaling ProversAug 17 2009Oct 20 2009In two-prover one-round interactive proof systems, no-signaling provers are those who are allowed to use arbitrary strategies, not limited to local operations, as long as their strategies cannot be used for communication between them. Study of multi-prover ... More

Existence of supersingular reduction for families of K3 surfaces with large Picard number in positive characteristicNov 15 2016We focus on non-isotrivial families of $K3$ surfaces in positive characteristic $p$ whose geometric generic fibers satisfy $\rho \geq 21-2h$ and $h \geq 3$, where $\rho$ is the Picard number and $h$ is the height of the formal Brauer group. We show that, ... More

Two-Body Dirac Equation and Its Wave Function at the OriginAug 07 1997A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of the constituent ... More

Two-Body Dirac Equation and Its Wave Function at the OriginDec 21 1996A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of the constituent ... More

On analogues of Arakawa-Kaneko zeta functions of Mordell-Tornheim typeMar 14 2016In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among Mordell-Tornheim multiple ... More

From ALE-instanton Moduli to Super Yang-Mills Theories via BranesDec 24 1997A large class of equivalence relations between the moduli spaces of instantons on ALE spaces and the Higgs branches of supersymmetric Yang-Mills theories, are found by means of a certain kind of duality transformation between brane configurations in superstring ... More

On birational geometry of the space of parametrized rational curves in GrassmanniansAug 31 2014Sep 11 2014In this paper, we study the birational geometry of the Quot schemes of trivial bundles on $\mathbb{P}^1$ by constructing small $\mathbb{Q}$-factorial modifications of the Quot schemes as suitable moduli spaces. We determine all the models which appear ... More

Exotic projective structures and quasifuchsian spaces IIMar 03 2006Let $P(S)$ be the space of projective structures on a closed surface $S$ of genus $g >1$ and let $Q(S)$ be the subset of $P(S)$ of projective structures with quasifuchsian holonomy. It is known that $Q(S)$ consists of infinitely many connected components. ... More

Gorenstein Quotient Singularities of Monomial Type in Dimension ThreeJun 11 1994Jul 22 1994The purpose of this paper is to construct a crepant resolution of quotient singularities by finite subgroups of SL(3,C) of monomial type, and prove that the Euler number of the resolution is equal to the number of conjugacy classes. This result is a part ... More

A generalized Landau kinetic equation for weakly-coupled probability distribution of N-stars in dense star clusterAug 29 2018The secular evolution of a collisional star cluster of $N$-'point' stars have been conventionally discussed based on cumulative two-body relaxation process. The relaxation process requires a cut-off on the range of two-body encounter between stars in ... More

Ramond sector of super Liouville theory from instantons on an ALE spaceOct 10 2011We propose that N=2 U(2) gauge theories on the A_1 ALE space, with asymptotic holonomies not in SU(2), correspond to the Ramond sector of super Liouville theory. As evidence, we show that the instanton partition functions for the theories with and without ... More

Non-left-orderable double branched coveringsJun 08 2011Sep 26 2011We develop a method to show the fundamental group of the double branched covering of a link is not left-orderable by introducing the notion of the coarse presentation. As in the usual group presentations, a coarse presentation is given by a set of generators ... More

Notes on the divisibility of the class numbers of certain imaginary quadratic fieldsDec 07 2012In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.

Seshadri constants via toric degenerationsFeb 29 2012Jan 31 2013We give a method to estimate Seshadri constants on toric varieties at any point. By using the estimations and toric degenerations, we can obtain some new computations or estimations of Seshadri constants on non-toric varieties. In particular, we investigate ... More

Parametrizations of infinite biconvex sets in affine root systemsNov 26 1999Feb 19 2003We investigate in detail relationships between the set ${\mathfrak B}^\infty$ of all infinite ``biconvex'' sets in the positive root system $\Delta_+$ of an arbitrary untwisted affine Lie algebra ${\mathfrak g}$ and the set ${\mathcal W}^\infty$ of all ... More

Finiteness of Brauer groups of K3 surfaces in characteristic 2Apr 20 2017Jan 04 2018For a K3 surface over a field of characteristic 2 which is finitely generated over its prime subfield, we prove that the cokernel of the natural map from the Brauer group of the base field to that of the K3 surface is finite modulo the 2-primary torsion ... More

Existence of supersingular reduction for families of K3 surfaces with large Picard number in positive characteristicNov 15 2016Jul 29 2017We study non-isotrivial families of $K3$ surfaces in positive characteristic $p$ whose geometric generic fibers satisfy $\rho\geq21-2h$ and $h\geq3$, where $\rho$ is the Picard number and $h$ is the height of the formal Brauer group. We show that, under ... More

Unconditional construction of K3 surfaces over finite fields with given L-function in large characteristicDec 16 2016Nov 23 2018We give an unconditional construction of K3 surfaces over finite fields with given L-function, up to finite extensions of the base fields, under some mild restrictions on the characteristic. Previously, such results were obtained by Taelman assuming semistable ... More

Weight-monodromy conjecture for certain threefolds in mixed characteristicDec 09 2002Jul 31 2003The weight-monodromy conjecture claims the coincidence of the weight filtration and the monodromy filtration, up to shift, on the $l$-adic \'etale cohomology of a proper smooth variety over a complete discrete valuation field. Although it has been proved ... More

Weight-monodromy conjecture over equal characteristic local fieldsAug 14 2003Jan 26 2005The aim of this paper is to study certain properties of the weight spectral sequences of Rapoport-Zink by a specialization argument. By reducing to the case over finite fields previously treated by Deligne, we prove that the weight filtration and the ... More