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A rigorous proof of the scallop theorem and a finite mass effect of a microswimmerJul 29 2011We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a proof is given to Purcell's scallop theorem including the body rotation. The breakdown of the theorem due to a finite Stokes ... More

The N-flagella problem: Elastohydrodynamic motility transition of multi-flagellated bacteriaApr 02 2019Peritrichous bacteria such as Escherichia coli swim in viscous fluids by forming a helical bundle of flagellar filaments. The filaments are spatially distributed around the cell body to which they are connected via a flexible hook. To understand how the ... More

Two-Point Functions and Logarithmic Boundary Operators in Boundary Logarithmic Conformal Field TheoriesMay 26 2004May 27 2004Amongst conformal field theories, there exist logarithmic conformal field theories such as $c_{p,1}$ models. We have investigated $c_{p,q}$ models with a boundary in search of logarithmic theories and have found logarithmic solutions of two-point functions ... More

Classical Hamiltonian Reduction On $D(2|1;α)$ Chern-Simons Gauge Theory and Large N=4 Superconformal SymmetryAug 15 1998May 07 19993d Chern-Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the $D(2|1;\alpha)$ CS theory in the similar context of the hamiltonian reduction of 2d superconformal algebras. There Hilbert ... More

Two-Point Functions and Boundary States in Boundary Logarithmic Conformal Field TheoriesDec 14 2003Our main aim in this thesis is to address the results and prospects of boundary logarithmic conformal field theories: theories with boundaries that contain the above Jordan cell structure. We have investigated c_{p,q} boundary theory in search of logarithmic ... More

Filament mechanics in a half-space via regularised Stokeslet segmentsApr 02 2019We present a generalisation of efficient numerical frameworks for modelling fluid-filament interactions via the discretisation of a recently-developed, non-local integral equation formulation to incorporate regularised Stokeslets with half-space boundary ... More

A new basis for filament simulation in three dimensionsJul 10 2019Jul 11 2019Simulations of slender inextensible filaments in a viscous fluid are often plagued by numerical stiffness. Recent coarse-graining studies have reduced the computational requirements of such systems, though have thus far been limited to the motion of planar ... More

Automated identification of flagella from videomicroscopy via the medial axis transformAug 03 2018Mar 21 2019Ubiquitous in eukaryotic organisms, the flagellum is a well-studied organelle that is well-known to be responsible for motility in a variety of organisms. Commonly necessitated in their study is the capability to image and subsequently track the movement ... More

Filament mechanics in a half-space via regularised Stokeslet segmentsApr 02 2019Apr 09 2019We present a generalisation of efficient numerical frameworks for modelling fluid-filament interactions via the discretisation of a recently-developed, non-local integral equation formulation to incorporate regularised Stokeslets with half-space boundary ... More

The pairwise hydrodynamic interactions of synchronized spermatozoaJun 01 2019The journey of mammalian spermatozoa in nature is well-known to be reliant on their individual motility. Often swimming in crowded microenvironments, the progress of any single swimmer is likely dependent on their interactions with other nearby swimmers. ... More

A new basis for filament simulation in three dimensionsJul 10 2019Simulations of slender inextensible filaments in a viscous fluid are often plagued by numerical stiffness. Recent coarse-graining studies have reduced the computational requirements of such systems, though have thus far been limited to the motion of planar ... More

Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germOct 15 2017May 01 2018In this paper, we prove that the set of all $F$-pure thresholds on a fixed germ of a strongly $F$-regular pair satisfies the ascending chain condition. As a corollary, we verify the ascending chain condition for the set of all $F$-pure thresholds on smooth ... More

Anomaly of Tensionless String in Light-cone GaugeMar 04 2015The classical tensionless string theory has the spacetime conformal symmetry. We expect and require that the quantum tensionless string theory has it too. In the BRST quantization method, the theory has no spacetime conformal anomaly in two dimensions. ... More

Quantum 3D Tensionless String in Light-cone GaugeMar 28 2013Feb 19 2014We discuss the quantization of a tensionless closed string in light-cone gauge. It is known that by using a Hamiltonian BRST scheme the tensionless p-branes have no Lorentz anomaly in any space-time dimensions and no anomaly of space-time conformal symmetry ... More

Log Iitaka conjecture for abundant log canonical fibrationsFeb 28 2019We prove that the log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.

ACM line bundles on polarized K3 surfacesMar 30 2018An ACM bundle on a polarized algebraic variety is defined as a vector bundle whose intermediate cohomology vanishes. We are interested in ACM bundles of rank one with respect to a very ample line bundle on a K3 surface. In this paper, we give a necessary ... More

Unstable Lazarsfeld-Mukai bundles of rank 2 on a certain K3 surface of Picard number 2Jun 30 2017Let $g$ and $c$ be any integers satisfying $g\geq3$ and $0\leq c\leq \lfloor\frac{g-1}{2}\rfloor$. It is known that there exists a polarized K3 surface $(X,H)$ such that $X$ is a K3 surface of Picard number 2, and $H$ is a very ample line bundle on $X$ ... More

Semantics for a Quantum Programming Language by Operator AlgebrasDec 30 2014This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of the category ... More

Remarks on the abundance conjectureSep 15 2015Nov 03 2015We prove the abundance theorem for log canonical $n$-folds such that the boundary divisor is big assuming the abundance conjecture for log canonical $(n-1)$-folds. We also discuss the log minimal model program for log canonical $4$-folds.

Finite generation of adjoint ring for log surfacesMay 09 2015Jan 06 2016We prove the finite generation of the adjoint ring for $\mathbb{Q}$-factorial log surfaces over any algebraically closed field.

Incomplete Hypergeometric Systems Associated to 1-Simplex $\times$ (n-1)-SimplexDec 17 2010The A-hypergeometric system was introduced by Gel'fand, Kapranov and Zelevinsky in the 1980's. Among several classes of A-hypergeometric functions, those for 1-simplex $\times$ (n-1)-simplex are known to be a very nice class. We will study an incomplete ... More

Stability of non-proper functionsSep 07 2018The purpose of this paper is to give a sufficient condition for (strong) stability of non-proper smooth functions (with respect to the Whitney $C^\infty$--topology). We introduce the notion of end-triviality of smooth mappings, which concerns behavior ... More

Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundlesMar 23 2015Previously, many people have studied a stability of vector bundles of given rank and Chern classes on algebraic varieties. Recently, we are interested in the slope stability of the rank 2 Lazarsfeld-Mukai bundle $E_{C,Z}$ on a K3 surface $X$ associated ... More

A class of singularity of arbitrary pairs and log canonicalizationsApr 17 2018May 24 2019We define a class of singularity on arbitrary pairs of a normal variety and an effective $\mathbb{R}$-divisor on it, which we call pseudo-lc in this paper. This is a generalization of the usual lc singularity of pairs and log canonical singularity of ... More

The classification of ACM line bundles on quartic hypersurfaces on P^3Sep 07 2013In this paper, we give a complete classification of initialized and ACM line bundles on a smooth quartic hypersurface on P^3$.

On the non-vanishing conjecture and existence of log minimal modelsSep 01 2016Sep 08 2016We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.

On the non-vanishing conjecture and existence of log minimal modelsSep 01 2016Oct 03 2016We prove that the non-vanishing conjecture and the log minimal model conjecture for projective log canonical pairs can be reduced to the non-vanishing conjecture for smooth projective varieties such that the boundary divisor is zero.

A note on sections of broken Lefschetz fibrationsApr 06 2011Oct 02 2011We show that there exists a non-trivial simplified broken Lefschetz fibration which has infinitely many homotopy classes of sections. We also construct a non-trivial simplified broken Lefschetz fibration which has a section with non-negative square. It ... More

On genus-1 simplified broken Lefschetz fibrationsDec 18 2010Feb 23 2011Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefshcetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1 simplified broken ... More

Stability of test ideals of divisors with small multiplicityFeb 09 2016Aug 20 2017Let $(X, \Delta)$ be a log pair in characteristic $p>0$ and $P$ be a (not necessarily closed) point of $X$. We show that there exists a constant $\delta>0$ such that $\tau(X, \Delta)_P= \tau(X, \Delta + D)_P$ for each effective $\mathbb{Q}$-Cartier divisor ... More

Remarks on special kinds of the relative log minimal model programApr 04 2017We prove $\mathbb{R}$-boundary divisor versions of results proved by Birkar or Hacon-Xu on special kinds of the relative log minimal model program.

Cluster tilting modules and noncommutative projective schemesApr 08 2016In this paper, we study the relationship between equivalences of noncommutative projective schemes and cluster tilting modules. In particular, we prove the following result. Let $A$ be an AS-Gorenstein algebra of dimension $d\geq 2$ and ${\mathsf{tails}\,} ... More

Total and Partial Computation in Categorical Quantum FoundationsNov 05 2015This paper uncovers the fundamental relationship between total and partial computation in the form of an equivalence of certain categories. This equivalence involves on the one hand effectuses, which are categories for total computation, introduced by ... More

Minimal model theory for relatively trivial log canonical pairsJul 18 2016Sep 08 2016We study relative log canonical pairs with relatively trivial log canonical divisors. We fix such a pair $(X,\Delta) / Z$ as above, and we establish the minimal model theory for $(X,\Delta)$ assuming the minimal model theory for all Kawamata log terminal ... More

Proper 3-orientations of bipartite planar graphs with minimum degree at least 3Apr 01 2019We show that every bipartite planar graph with minimum degree at least 3 has proper orientation number at most 3.

Ascending chain condition for $F$-pure thresholds with fixed embedding dimensionMay 18 2018In this paper, we prove that the set of all $F$-pure thresholds of ideals with fixed embedding dimension satisfies the ascending chain condition. As a corollary, given an integer $d$, we verify the ascending chain condition for the set of all $F$-pure ... More

Log Iitaka conjecture for abundant log canonical fibrationsFeb 28 2019May 01 2019We prove that the log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.

Bubbly vertex dynamics: a dynamical and geometrical model for epithelial tissues with curved cell shapesMay 15 2014Oct 08 2014In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, the ... More

Low energy states of a semiflexible polymer chain with attraction and the whip-toroid transitionsDec 05 2005Jul 25 2006Based on our previous paper [cond-mat/0507477], we establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O(3) nonlinear sigma model on a line segment with the local inextensibility ... More

Feigin-Fuchs Representations for Nonequivalent Algebras of N=4 Superconformal SymmeterySep 24 1996The $N=4$ SU(2)$_k$ superconformal algebra has the global automorphism of SO(4) $\approx$ SU(2)$\times$SU(2) with the {\it left} factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by $\rho$ corresponding ... More

Analytic theory of DNA condensationJul 20 2005Jan 30 2007We introduce a novel model for DNA condensation (whip-toroid transition) using the path integral method in the framework of the non-linear sigma model on a line segment. We show that some of its classical configurations exhibit toroidal forms, and the ... More

Effect of interaction shape on the condensed DNA toroidJan 30 2007We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. ... More

Boundary behaviours of Leishmania mexicana: a hydrodynamic simulation studyJun 01 2018Nov 16 2018It is well established that the parasites of the genus Leishmania exhibit complex surface interactions with the sandfly vector midgut epithelium, but no prior study has considered the details of their hydrodynamics. Here, the boundary behaviours of motile ... More

On Homeomorphically Irreducible Spanning Trees in Cubic GraphsJul 28 2015Jun 12 2017A spanning tree without a vertex of degree two is called a Hist which is an abbreviation for homeomorphically irreducible spanning tree. We provide a necessary condition for the existence of a Hist in a cubic graph. As one consequence, we answer affirmatively ... More

Minimal String Theory is LogarithmicJun 29 2004Dec 24 2004We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity (Liouville field theory). In the Liouville sector, we show that four-point correlation functions ... More

Equilibrium Configurations of Strongly Magnetized Neutron Stars with Realistic Equations of StateAug 27 2007We investigate equilibrium sequences of magnetized rotating stars with four kinds of realistic equations of state (EOSs) of SLy (Douchin et al.), FPS (Pandharipande et al.), Shen (Shen et al.), and LS (Lattimer & Swesty). Employing the Tomimura-Eriguchi ... More

Electroweak bremsstrahlung in bino-like dark matter annihilationsJun 25 2013Sep 17 2013We investigate the effects of electroweak bremsstrahlung on bino-like neutralino dark matter pair annihilations in the minimal supersymmetric standard model (MSSM). We calculate the nonrelativistic pair annihilation cross sections via $W$-strahlung from ... More

$Ab$ $initio$ evaluation of Hamaker constantsMay 02 2016Nov 08 2016We propose a computational scheme to evaluate Hamaker constants, $A$, of molecules with practical sizes and anisotropies. Upon the increasing feasibility of diffusion Monte Carlo methods to evaluate binding curves for such molecules to extract the constants, ... More

Spatially-Coupled MacKay-Neal Codes with No Bit Nodes of Degree Two Achieve the Capacity of BECJan 28 2014Obata et al. proved that spatially-coupled (SC) MacKay-Neal (MN) codes achieve the capacity of BEC. However, the SC-MN codes codes have many variable nodes of degree two and have higher error floors. In this paper, we prove that SC-MN codes with no variable ... More

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

Thermofield Duality for Higher Spin Rindler GravityAug 31 2015Jan 20 2016We study the Thermo-field realization of the duality between the Rindler-AdS higher spin theory and $O(N)$ vector theory. The CFT represents a decoupled pair of free $O(N)$ vector field theories. It is shown how this decoupled domain CFT is capable of ... More

Bi-Local Holography in the SYK Model: PerturbationsAug 26 2016Nov 04 2016We continue the study of the Sachdev-Ye-Kitaev model in the Large $N$ limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. ... More

Stable Categories of Graded Maximal Cohen-Macaulay Modules over Noncommutative Quotient SingularitiesJul 23 2015Jan 27 2016Tilting objects play a key role in the study of triangulated categories. A famous result due to Iyama and Takahashi asserts that the stable categories of graded maximal Cohen-Macaulay modules over quotient singularities have tilting objects. This paper ... More

The classification of 3-dimensional noetherian cubic Calabi-Yau algebrasJun 01 2016Jul 11 2016It is known that every 3-dimensional noetherian Calabi-Yau algebra generated in degree 1 is isomorphic to a Jacobian algebra of a superpotential. Recently, S. P. Smith and the first author classified all superpotentials whose Jacobian algebras are 3-dimensional ... More

General hyperplane sections of threefolds in positive characteristicMar 02 2017In this paper, we study the singularities of a general hyperplane section $H$ of a three-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>0$. We prove that if $X$ has only canonical singularities, then $H$ ... More

Coupled Painleve VI system with E_6^{(1)} symmetryJan 13 2007Apr 19 2007We present an new system of ordinary differential equations with affine Weyl group symmetry of type E_6^{(1)}. This system is expressed as a Hamiltonian system of sixth order with a coupled Painleve VI Hamiltonian.

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

Spatially Coupled Codes over the Multiple Access ChannelFeb 14 2011We consider spatially coupled code ensembles over a multiple access channel. Convolutional LDPC ensembles are one instance of spatially coupled codes. It was shown recently that, for transmission over the binary erasure channel, this coupling of individual ... More

Topology of holomorphic Lefschetz pencils on the four-torusMar 28 2016In this paper we discuss topological properties of holomorphic Lefschetz pencils on the four-torus. Relying on the theory of moduli spaces of polarized abelian surfaces, we first prove that, under some mild assumption, the (smooth) isomorphism class of ... More

Radiative Transfer Simulations for Neutron Star Merger EjectaJun 17 2013Jul 17 2013The merger of binary neutron stars (NSs) is among the most promising gravitational wave (GW) sources. Next-generation GW detectors are expected to detect signals from the NS merger within 200 Mpc. Detection of electromagnetic wave (EM) counterpart is ... More

Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos CodesFeb 22 2011Jan 25 2013Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the ... More

Fourier Domain Decoding Algorithm of Non-Binary LDPC codes for Parallel ImplementationAug 25 2010For decoding non-binary low-density parity check (LDPC) codes, logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing quantization effects of SP algorithm in conjunction with FFT. Since FFT is not applicable in the logarithm domain, ... More

On (2,3) torus decompositions of QL-configurationsMay 09 2010Let $Q$ be an affine quartic which does not intersect transversely with the line at infinity $L_{\infty}$. In this paper, we show the existence of a $(2,3)$ torus decomposition of the defining polynomial of $Q$ and its uniqueness except for one class. ... More

The sixth Painleve equation arising from Drinfel'd-Sokolov hierarchyJan 26 2006Apr 01 2010This paper has been withdrawn by the authors due to double submitting.

Extending automorphisms of the genus-2 surface over the 3-sphereMar 14 2018Mar 17 2018An automorphism $f$ of a closed orientable surface $\Sigma$ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \Sigma)$ with respect to some embedding $\Sigma \hookrightarrow S^3$. We prove that if an ... More

Robust Image Identification for Double-Compressed and Resized JPEG ImagesSep 02 2018In the case that images are shared via social networking services (SNS) and cloud photo sharing services (CPSS), it is known that the JPEG images uploaded to the services are often re-compressed and resized by the providers. Because of such a situation, ... More

Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural NetworksMar 24 2019Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previously analyzed optimal CNNs are unrealistically wide and difficult to obtain ... More

On Asymptotic Behaviors of Graph CNNs from Dynamical Systems PerspectiveMay 27 2019Graph Convolutional Neural Networks (graph CNNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up more layers and ... More

Testing Properties of Functions on Finite GroupsSep 03 2015We study testing properties of functions on finite groups. First we consider functions of the form $f:G \to \mathbb{C}$, where $G$ is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to an irreducible ... More

Bi-Local Holography in the SYK Model: PerturbationsAug 26 2016Sep 04 2016We continue the study of the Sachdev-Ye-Kitaev model in the Large $N$ limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. ... More

Composite nature of Lambda(1405) from the spacial structure of KbarN systemDec 09 2015We discuss the spacial structure of the resonance state, Lambda(1405), solving the Schrodinger equation with the KbarN local potential. The potential is constructed by paying attention to the two points, the constraint from the recent experimental data ... More

Mass ejection from neutron star mergers: different components and expected radio signalsJan 08 2015In addition to producing a strong gravitational signal, a short gamma-ray burst (GRB), and a compact remnant, neutron star mergers eject significant masses at significant kinetic energies. This mass ejection takes place via dynamical mass ejection and ... More

Spin Current Generation as a Nonequilibrium Kondo Effect in a Spin-orbit Mesoscopic InterferometerOct 24 2012We study nonequilibrium generation of spin-dependent transport through a single-level quantum dot embedded in a ring with the Rashba spin-orbit coupling. We consider nonmagnetic systems, involving no magnetic field nor ferromagnetic leads. It is theoretically ... More

Threshold Saturation on Channels with Memory via Spatial CouplingFeb 02 2011We consider spatially coupled code ensembles. A particular instance are convolutional LDPC ensembles. It was recently shown that, for transmission over the memoryless binary erasure channel, this coupling increases the belief propagation threshold of ... More

PSD estimation in Beamspace for Estimating Direct-to-Reverberant Ratio from A Reverberant Speech SignalOct 30 2015A method for estimation of direct-to-reverberant ratio (DRR) using a microphone array is proposed. The proposed method estimates the power spectral density (PSD) of the direct sound and the reverberation using the algorithm \textit{PSD estimation in beamspace} ... More

Coil--globule transition of a polymer involved in excluded-volume interactions with macromoleculesSep 21 2015Polymers adopt extended coil and compact globule states according to the balance between entropy and interaction energies. The transition of a polymer between an extended coil state and compact globule state can be induced by changing thermodynamic force ... More

Gravitational waves from remnant massive neutron stars of binary neutron star merger: Viscous hydrodynamics effectsMay 16 2017Employing a simplified version of the Israel-Stewart formalism of general-relativistic shear-viscous hydrodynamics, we explore the evolution of a remnant massive neutron star of binary neutron star merger and pay special attention to the resulting gravitational ... More

Von Neumann Algebras form a Model for the Quantum Lambda CalculusMar 07 2016We present a model of Selinger and Valiron's quantum lambda calculus based on von Neumann algebras, and show that the model is adequate with respect to the operational semantics.

Hochschild cohomology related to graded down-up algebras with weights $(1,n)$Apr 01 2019Let $A=A(\alpha, \beta)$ be a graded down-up algebra with $({\rm deg}\,x, {\rm deg}\,y)=(1,n)$ and $\beta \neq 0$, and let $\nabla A$ be the Beilinson algebra of $A$. If $n=1$, then a description of the Hochschild cohomology group of $\nabla A$ is known. ... More

Extending automorphisms of the genus-2 surface over the 3-sphereMar 14 2018Apr 25 2019An automorphism $f$ of a closed orientable surface $\Sigma$ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \Sigma)$ with respect to some embedding $\Sigma \hookrightarrow S^3$. We prove that if an ... More

Hochschild cohomology related to graded down-up algebras with weights $(1,n)$Apr 01 2019Jul 01 2019Let $A=A(\alpha, \beta)$ be a graded down-up algebra with $({\rm deg}\,x, {\rm deg}\,y)=(1,n)$ and $\beta \neq 0$, and let $\nabla A$ be the Beilinson algebra of $A$. If $n=1$, then a description of the Hochschild cohomology group of $\nabla A$ is known. ... 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

Structure of Lambda(1405) and construction of KbarN local potential based on chiral SU(3) dynamicsJun 18 2015Dec 08 2015We develop the single-channel local potential for the KbarN system, which is applicable to quantitative studies of Kbar bound states in nuclei. Because the high precision measurement of the kaonic hydrogen by SIDDHARTA reduces the uncertainty of the KbarN ... More

Ample Group Action on AS-regular Algebras and Noncommutative Graded Isolated SingularitiesApr 20 2014Oct 06 2014In this paper, we introduce a notion of ampleness of a group action $G$ on a right noetherian graded algebra $A$, and show that it is strongly related to the notion of $A^G$ to be a graded isolated singularity introduced by the second author of this paper. ... More

Elimination of cusps in dimension 4 and its applicationsOct 22 2012Dec 08 2014Several new combinatorial descriptions of closed 4-manifolds have recently been introduced in the study of smooth maps from 4-manifolds to surfaces. These descriptions consist of simple closed curves in a closed, orientable surface and these curves appear ... More

Fountain Codes with Multiplicatively Repeated Non-Binary LDPC CodesJul 06 2010Jul 11 2010We study fountain codes transmitted over the binary-input symmetric-output channel. For channels with small capacity, receivers needs to collects many channel outputs to recover information bits. Since a collected channel output yields a check node in ... More

Photonic Topological Insulating Phase Induced Solely by Gain and LossOct 25 2017Jul 04 2018We reveal a one-dimensional topological insulating phase induced solely by gain and loss control in non-Hermitian optical lattices. The system comprises units of four uniformly coupled cavities, where successive two have loss, the others experience gain ... More

Robust Image Identification for Double-Compressed JPEG ImagesJun 23 2018It is known that JPEG images uploaded to social networks (SNs) are mostly re-compressed by the social network providers. Because of such a situation, a new image identification scheme for double-compressed JPEG images is proposed in this paper. The aim ... More

Noncommutative Knörrer's periodicity theorem and noncommutative quadric hypersurfacesMay 29 2019Noncommutative hypersurfaces, in particular, noncommutative quadric hypersurfaces are major objects of study in noncommutative algebraic geometry. In the commutative case, Kn\"orrer's periodicity theorem is a powerful tool to study Cohen-Macaulay representation ... More

Incomplete A-Hypergeometric SystemsJul 04 2009Sep 01 2011The incomplete beta function is an important special function in statistics. In modern theory of hypergeometric functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles. However, the incomplete beta function cannot ... More

Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural NetworksMar 24 2019May 25 2019Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous analyzed optimal CNNs are unrealistically wide and difficult to obtain via ... More

Higher order Painleve system of type D^{(1)}_{2n+2} arising from integrable hierarchyApr 19 2007A higher order Painleve system of type D^{(1)}_{2n+2} was introduced by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry. It is also expressed as a Hamiltonian system of order 2n with a coupled Painleve VI ... More

The sixth Painleve equation arising from D_4^{(1)} hierarchyJan 26 2006Apr 20 2006The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.

On the circumradius condition for piecewise linear triangular elementsAug 09 2013Dec 21 2014We discuss the error analysis of linear interpolation on triangular elements. We claim that the circumradius condition is more essential then the well-known maximum angle condition for convergence of the finite element method. Numerical experiments show ... More

An algorithm of computing inhomogeneous differential equations for definite integralsMay 19 2010Jul 14 2010We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\"obner basis method in the ring ... More

Diffusion Monte Carlo methods applied to Hamaker Constant evaluationsMay 02 2016We applied diffusion Monte Carlo (DMC) methods to evaluate Hamaker constants of liquids for wettabilities, with practical size of a liquid molecule, Si$_6$H$_{12}$ (cyclohexasilane). The evaluated constant would be justified in the sense that it lies ... More

Construction of KbarN potential and structure of Lambda(1405) based on chiral unitary approachAug 31 2015Based on chiral unitary approach, we construct the realistic KbarN local potential, which is useful for the quantitative calculation of Kbar-nuclei. Since the resonance pole structure of the KbarN system seems important for the Kbar-nuclei and the spacial ... More

Hidden symmetries, null geodesics, and photon capture in the Sen black holeMay 20 2008Aug 07 2008Important classes of null geodesics and hidden symmetries in the Sen black hole are investigated. First, we obtain the principal null geodesics and circular photon orbits. Then, an irreducible rank-two Killing tensor and a conformal Killing tensor are ... More

Nature of hard X-ray (3-24 keV) detected luminous infrared galaxies in the COSMOS fieldMar 08 2017May 18 2017We investigate the nature of far-infrared (70 um) and hard X-ray (3-24 keV) selected galaxies in the COSMOS field detected with both Spitzer and Nuclear Spectroscopic Telescope Array (NuSTAR). By matching the Spitzer-COSMOS catalog against the NuSTAR-COSMOS ... More

Phenomenological model for ordered onions under shear flowNov 17 2010Sep 02 2011We propose a phenomenological model for the multi-lamellar vesicles (onions) formation induced by shear flow. In a nonionic surfactant (C$_{12}$E$_4$) system, onion phases under a fixed shear flow within a certain range show the order-disorder transition ... More