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The inverses of tails of the Riemann zeta functionMar 01 2018Jul 05 2018We present some bounds of the inverses of tails of the Riemann zeta function on $0 < s < 1$ and compute the integer parts of the inverses of tails of the Riemann zeta function for $s=\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$.

Various 3x3 Nonnegative Matrices with Prescribed Eigenvalues and Diagonal EntriesOct 03 2016In this paper, we answer the various forms of nonnegative inverse eigenvalue problems with prescribed diagonal entries for order three: real or complex general matrices, symmetric stochastic matrices, and real or complex doubly stochastic matrices. We ... More

Various 3x3 Nonnegative Matrices with Prescribed Eigenvalues and Diagonal EntriesOct 03 2016Jun 21 2018In this paper, we answer the various forms of nonnegative inverse eigenvalue problems with prescribed diagonal entries for order three: real or complex general matrices, symmetric stochastic matrices, and real or complex doubly stochastic matrices. We ... More

On the structures of hive algebras and tensor product algebras for general linear groups of low rankDec 07 2017May 13 2019The tensor product algebra TA(n) for the complex general linear group GL(n), introduced by Howe et al., describes the decomposition of tensor products of irreducible polynomial representations of GL(n). Using the hive model for the Littlewood-Richardson ... More

Hive algebras and tensor product algebras for small GL(n)Dec 07 2017For the complex general linear group GL(n), the GL(n) tensor product algebra TA(n) introduced by Howe et al. describes the decomposition of the tensor products of two irreducible polynomial representations of GL(n). Using the hive model for the Littlewood-Richardson ... More

Minimality of $5$-adic polynomial dynamical systemsSep 05 2018We characterize the dynamical systems consisting of the set of 5-adic integers and polynomial maps which consist of only one minimal component.

Dynamic Structures of 2-adic Fibonacci PolynomialsMar 13 2019The dynamic structures of Fibonacci polynomials over the ring of 2-adic integers are described by investigating minimal decompositions which consist of minimal subsystems and attracting basins.

$J^+$-like invariants of periodic orbits of the second kind in the restricted three body problemAug 28 2017Sep 05 2018We determine three invariants: Arnold's $J^+$-invariant as well as $\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near the heavier primary in the restricted ... More

Mirror duality and noncommutative toriOct 06 2007In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence ... More

Application of Support Vector Machine to detect an association between a disease or trait and multiple SNP variationsApr 17 2001May 22 2001After the completion of human genome sequence was anounced, it is evident that interpretation of DNA sequences is an immediate task to work on. For understanding their signals, improvement of present sequence analysis tools and developing new ones become ... More

Geometrical Interpretation of Electromagnetism in a 5-Dimensional ManifoldJul 12 2015Aug 13 2017In this paper, Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ... More

Black holes with baryonic charge and $\mathcal{I}$-extremizationApr 10 2019We study $\mathcal{I}$-extremization of three-dimensional gauge field theories and its geometric dual, focusing in particular on a seven-dimensional Sasaki-Einstein manifold $M^{1,1,1}$. We generalize recent studies on relations among toric geometry, ... More

An lp-boundedness of stochastic singular integral operators and its application to spdesAug 31 2016Jun 08 2017In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y), Z=(r,z) \in (0,\infty) ... More

Volume invariant and maximal representations of discrete subgroups of Lie groupsMay 22 2012Sep 21 2012Let $\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\Gamma$ into $G$, which generalizes the volume invariant for representations of uniform ... More

Phase transition of quantum corrected Schwarzschild black holeJul 23 2012Nov 07 2012We study the thermodynamic phase transition of a quantum-corrected Schwarzschild black hole. The modified metric affects the critical temperature which is slightly less than the conventional one. The space without black holes is not the hot flat space ... More

A Novel Statistical Diagnosis of Clinical DataSep 02 2002In this paper, we present a diagnosis method of diseases from clinical data. The data are routine test such as urine test, hematology, chemistries etc. Though those tests have been done for people who check in medical institutes, how each item of the ... More

2D Electrophoresis Gel Image and Diagnosis of a DiseaseMay 28 2003The process of diagnosing a disease from the 2D gel electrophoresis image is a challenging problem. This is due to technical difficulties of generating reproducible images with a normalized form and the effect of negative stain. In this paper, we will ... More

A Representation of Changes of Images and its Application for Developmental BiolologyMay 13 2003In this paper, we consider a series of events observed at spaced time intervals and present a method of representation of the series. To explain an idea, by dealing with a set of gene expression data, which could be obtained from developmental biology, ... More

An lp-boundedness of stochastic singular integral operators and its application to spdesAug 31 2016In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y), Z=(r,z) \in (0,\infty) ... More

Geometrical Interpretation of Electromagnetism in 5-Dimensional ManifoldJul 12 2015Sep 21 2016In this paper Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ... More

Concurrence of the Blandford-Payne Process and the Bardeen-Petterson Effect: Theoretical Prediction and its Observational EvidencesAug 21 2015Although the Blandford-Payne process, the standard model for the production of AGN jet outflow, has been fully acknowledged and long-known in both the theoretical Astrophysics and observational Astronomy communities, subsequent research works to gain ... More

Spin filtering in a magnetic barrier structure: in-plane spin orientationMar 01 2014We investigate ballistic spin transport in a two dimensional electron gas system through magnetic barriers of various geometries using the transfer matrix method. While most of the previous studies have focused on the effect of magnetic barriers perpendicular ... More

On deformation spaces of nonuniform hyperbolic latticesOct 04 2013Let $\Gamma$ be a nonuniform lattice acting on real hyperbolic n-space. We show that in dimension greater than or equal to 4, the volume of a representation is constant on each connected component of the representation variety of $\Gamma$ in SO(n,1). ... More

Projective Normality Of Algebraic Curves And Its Application To SurfacesJan 09 2006Let $L$ be a very ample line bundle on a smooth curve $C$ of genus $g$ with $\frac{3g+3}{2}<\deg L\le 2g-5$. Then $L$ is normally generated if $\deg L>\max\{2g+2-4h^1(C,L), 2g-\frac{g-1}{6}-2h^1(C,L)\}$. Let $C$ be a triple covering of genus $p$ curve ... More

Abstractive Summarization of Reddit Posts with Multi-level Memory NetworksNov 02 2018We address the problem of abstractive summarization in two directions: proposing a novel dataset and a new model. First, we collect Reddit TIFU dataset, consisting of 120K posts from the online discussion forum Reddit. We use such informal crowd-generated ... More

1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetryJun 14 2007Jul 06 2007In this paper we generalize the work of Lin, Lunin and Maldacena on the classification of 1/2-BPS M-theory solutions to a specific class of 1/4-BPS configurations. We are interested in the solutions of 11 dimensional supergravity with $SO(3)\times SO(4)$ ... More

Neural Network-Hardware Co-design for Scalable RRAM-based BNN AcceleratorsNov 06 2018Apr 15 2019Recently, RRAM-based Binary Neural Network (BNN) hardware has been gaining interests as it requires 1-bit sense-amp only and eliminates the need for high-resolution ADC and DAC. However, RRAM-based BNN hardware still requires high-resolution ADC for partial ... More

Abstractive Summarization of Reddit Posts with Multi-level Memory NetworksNov 02 2018Apr 09 2019We address the problem of abstractive summarization in two directions: proposing a novel dataset and a new model. First, we collect Reddit TIFU dataset, consisting of 120K posts from the online discussion forum Reddit. We use such informal crowd-generated ... More

Parabolic Littlewood-Paley inequality for $φ(-Δ)$-type operators and applications to Stochastic integro-differential equationsFeb 20 2013In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type $\phi(-\Delta)$, where $\phi$ is a Bernstein function. As an application, we construct an $L_p$-theory for the stochastic integro-differential ... More

Moduli Spaces of Standard Holomorphic Bundles on a Noncommutative Complex TorusDec 11 2003In this paper we study the moduli space of standard holomorphic structures on a noncommutative complex two torus. It will be shown that the moduli space is naturally identified with the moduli space of stable bundles on an elliptic curve. We also propose ... More

Comments on the symmetry of AdS$_6$ solutions in String/M-theory and Killing spinor equationsApr 27 2016Aug 22 2016It was recently pointed out in \cite{Kim:2015hya} that AdS$_6$ solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to $D=4$ internal space leads to a nonlinear sigma model with target $SL(3,\mathbb{R})/SO(2,1)$. ... More

Sequential Learning of Visual Tracking and Mapping Using Unsupervised Deep Neural NetworksFeb 26 2019We proposed an end-to-end deep learning-based simultaneous localization and mapping (SLAM) system following conventional visual odometry (VO) pipelines. The proposed method completes the SLAM framework by including tracking, mapping, and sequential optimization ... More

Unavoidable Subtournaments in Tournaments with Large Chromatic NumberApr 13 2018For a set H of tournaments, we say H is heroic if every tournament, not containing any member of H as a subtournament, has bounded chromatic number. Berger et al. explicitly characterized all heroic sets containing one tournament. Motivated by this result, ... More

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Jan 10 2019We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let $\Sigma$ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify the ... More

Simplicial volume of Q-rank one locally symmetric manifolds covered by the product of R-rank one symmetric spacesApr 24 2011Jan 10 2012In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly positive.

Learning Not to Learn: Training Deep Neural Networks with Biased DataDec 26 2018Apr 15 2019We propose a novel regularization algorithm to train deep neural networks, in which data at training time is severely biased. Since a neural network efficiently learns data distribution, a network is likely to learn the bias information to categorize ... More

KoulMde: An R Package for Koul's Minimum Distance EstimationJun 14 2016This article provides a full description of the R package KoulMde which is designed for Koul's minimum distance estimation method. When we encounter estimation problems in the linear regression and autogressive models, this package provides more efficient ... More

Ansatz of Leptonic Mixing: The Alliance of Bi-Maximal Mixing with a Single-Angle RotationAug 13 2012We introduce an ansatz of the PMNS matrix that consists of specific types of transformations. Bi-maximal mixing is taken for the neutrino masses, while a single-angle rotation in the 1-2 block is taken for the charged lepton masses. Motivated by the implications ... More

Toward a Possible Solution to the Cosmic Coincidence ProblemFeb 02 2002Oct 18 2002It is a mystery why the density of matter and the density of vacuum energy are nearly equal today when they scale so differently during the expansion of the Universe. We suggest a paradigm that might allow for a non-anthropic solution to this cosmic coincidence ... More

The Search for the Dark Matter: WIMPs and MACHOsMar 13 1993Review talk presented at the Texas/PASCOS Symposium, Berkeley, CA, Dec 1992. We review the status of experiments and ideas relevant for the detection of the dark matter which is suspected to be the dominant constituent of the Universe. Great progress ... More

Rapoport-Zink spaces of Hodge typeAug 26 2013Jan 07 2016When $p>2$, we construct a Hodge-type analogue of Rapoport-Zink spaces under the unramifiedness assumption, as formal schemes parametrising "deformations" (up to quasi-isogeny) of $p$-divisible groups with certain crystalline Tate tensors. We also define ... More

Quot schemes for flags and Gromov invariants for flag varietiesDec 04 1995Using Quot schemes and a localization theorem we study Gromov-Witten invariants for partial flag varieties. The strategy is to extend A. Bertram's result of Gromov-Witten invariants for special Schubert varieties of Grassmannians to the case of partial ... More

Homology Class of a Deligne-Lusztig variety and its analoguesMar 30 2016Jun 01 2016In this paper we consider Deligne-Lusztig varieties and their analogues when the Frobenius endomorphism is replaced with conjugation by an element in a group, especially a regular semisimple or regular unipotent one. We calculate their classes in the ... More

A Comparison of Two ComplexesMar 12 2016Apr 17 2016In this paper we prove the conjecture of Lusztig in "Generic character sheaves on groups over $\mathbf{k}[\epsilon]/(\epsilon^r)$." Given a reductive group over $\mathbb{F}_q$ for some $r\geq 2$, there is a notion of a character sheaf defined in "Character ... More

Molecules of the Euler problem of two fixed centers and its applicationsJun 17 2016We study the molecules of negative energy hypersurfaces of the Euler problem. As an application, we determine the knot types of periodic orbits. More precisely, we show that for energies below the critical Jacobi energy, every periodic orbits is a torus ... More

Constraints on the I=1 hadronic tau decay and e^+e^- --> hadrons data sets and implications for (g-2)_muApr 22 2005Dec 16 2005Sum rule tests are performed on the spectral data for (i) flavor 'ud' vector- current-induced hadronic tau decays and (ii) e^+ e^- hadroproduction, in the region below s~3-4 GeV^2, where discrepancies exist between the isospin- breaking-corrected charged ... More

The Strange Quark Mass, alpha_s and the Chiral Limit Electroweak Penguin Matrix Elements From Hadronic Tau Decay DataSep 09 2002Hadronic tau decay data provides access to the light quark vector (V) and axial vector (A) spectral functions. This makes possible investigations of the dynamics of QCD at intermediate scales and improved determinations of certain QCD/Standard Model parameters. ... More

Isospin Breaking and the Extraction of $m_s$ from the $τ$-Decay-Like Vector Current Sum RuleApr 15 1998Narison's $\tau$-decay-like sum rule for determining the strange quark mass is re-investigated, taking into account isospin-breaking corrections in the extraction of the input spectral functions from $e^+e^-\to hadrons$ data. The corrections, estimated ... More

Two Model-Independent Results for the Momentum Dependence of Rho-Omega MixingJun 28 1995Two model-independent results on the momentum-dependence of $\rho$-$\omega$ mixing are described. First, an explicit choice of interpolating fields for the vector mesons is displayed for which both the mixing in the propagator and the isospin-breaking ... More

Results of the Mixed Tau-Electroproduction Sum Rule For V_usJun 26 2009A sum rule for determining |V_us| from a combination of hadronic tau decay and electroproduction data is discussed. Indications of problems with analogous, purely tau-decay-based analyses, most likely associated with slow convergence of the relevant D=2 ... More

Resolving the tau versus electroproduction discrepancy for the I=1 vector spectral function and implications for the SM prediction for a_muSep 23 2005Using only independent high-scale OPE input, we investigate QCD sum rule constraints on two currently incompatible versions of the I=1 vector spectral function, one obtained from electroproduction data, the other from hadronic tau decay data. Sum rules ... More

The Mixed-Isospin Vector Current Correlator in Chiral Perturbation Theory and QCD Sum RulesApr 06 1995The mixed-isospin vector current correlator, $\langle 0\vert T(V^\rho_\mu V^\omega_\nu )\vert 0\rangle$ is evaluated using both QCD sum rules and Chiral Perturbation Theory (ChPT) to one-loop order. The sum rule treatment is a modification of previous ... More

On relative computability for curvesFeb 10 2005We discuss a rational version of a conjecture of Matiyasevich, Davis, and Putnam on the relative decidability of the finiteness problem for Diophantine equations with respect to the existence problem. We formulate a suspicion that for rational solutions, ... More

Quantizing TimeJan 13 2003May 22 2003A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum mechanical description ... More

Secure direct communication using entanglementMar 14 2002Mar 15 2002A novel communication protocol based on an entangled pair of qubits is presented, allowing secure direct communication from one party to another without the need for a shared secret key. Since the information is transferred in a deterministic manner, ... More

Poisson deformations of ruled surfaces over an elliptic curveOct 04 2016We determine obstructedness or unobstructedness of (holomorphic) Poisson deformations of ruled surfaces over an elliptic curve.

Coinductive properties of Lipschitz functions on streamsSep 24 2008A simple hierarchical structure is imposed on the set of Lipschitz functions on streams (i.e. sequences over a fixed alphabet set) under the standard metric. We prove that sets of non-expanding and contractive functions are closed under a certain coiterative ... More

Friends of 12Aug 19 2016A friend of 12 is a positive integer different from 12 with the same abundancy index. By enlarging the supply of methods of Ward [1], it is shown that (i) if n is an odd friend of 12, then n=m^2, where m has at least 5 distinct prime factors, including ... More

A Condition for Hopf bifurcation to occur in Equations of Lotka - Volterra Type with DelaySep 04 2013Oct 27 2013It is known that Lotka - Volterra type differential equations with delays or distributed delays have an important role in modeling ecological systems. In this paper we study the effects of distributed delay on the dynamics of the harvested one predator ... More

The Effect of Data Swapping on Analyses of American Community Survey DataOct 21 2015Nov 24 2015Researchers from a growing range of fields and industries rely on public-access census data. These data are altered by census-taking agencies to minimize the risk of identification; one such disclosure avoidance measure is the data swapping procedure. ... More

The Backreacted Kähler Geometry of Wrapped BranesJun 07 2012Jun 11 2012For supersymmetric solutions of D3(M2) branes with AdS3(AdS2) factor, it is known that the internal space is expressible as U(1) fibration over K\"ahler space which satisfies a specific partial differential equation involving the Ricci tensor. In this ... More

On a degenerate parabolic equation arising in pricing of Asian optionsMay 08 2008We study a certain one dimensional, degenerate parabolic partial differential equation with a boundary condition which arises in pricing of Asian options. Due to degeneracy of the partial differential operator and the non-smooth boundary condition, regularity ... More

On Network Coding Capacity - Matroidal Networks and Network Capacity RegionsMar 02 2011One fundamental problem in the field of network coding is to determine the network coding capacity of networks under various network coding schemes. In this thesis, we address the problem with two approaches: matroidal networks and capacity regions. In ... More

On the equivalence of the definitions of volume of representationsApr 15 2014Let G be a rank 1 simple Lie group and M be a connected orientable aspherical tame manifold. Assume that each end of M has amenable fundamental group. There are several definitions of volume of representations of the fundamental group of M into G. We ... More

A closed symplectic four-manifold has almost Kaehler metrics of negative scalar curvatureMay 17 2006We show that every closed symplectic four-dimensional manifold admits compatible almost Kaehler metrics of negative scalar curvature.

The Bernstein--von Mises theorem for the proportional hazard modelNov 08 2006We study large sample properties of Bayesian analysis of the proportional hazard model with neutral to the right process priors on the baseline hazard function. We show that the posterior distribution of the baseline cumulative hazard function and regression ... More

Endpoint bounds for quasiradial Fourier multipliersOct 30 2015Jul 18 2016We consider quasiradial Fourier multipliers, i.e. multipliers of the form $m(a(\xi))$ for a class of distance functions $a$. We give a necessary and sufficient condition for the multiplier transformations to be bounded on $L^p$ for a certain range of ... More

Accelerated Proximal Point Method for Maximally Monotone OperatorsMay 13 2019This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex optimization methods, ... More

Quantum Hyperplane Section Theorem For Homogeneous SpacesDec 05 1997Jan 02 1998We formulated a mirror-free approach to the mirror conjecture, namely, quantum hyperplane section conjecture, and proved it in the case of nonnegative complete intersections in homogeneous manifolds. For the proof we followed the scheme of Givental's ... More

Almost-Kähler anti-self-dual metrics on $K3\#3\overline{\mathbb{CP}_{2}}$Feb 24 2019Donaldson-Friedman constructed anti-self-dual classes on $K3\#3\overline{\mathbb{CP}_{2}}$ using twistor space. We show that some of these conformal classes have almost-K\"ahler representatives.

Degeneration of strictly convex real projective structures on surfaceNov 28 2018Dec 12 2018In this paper we study the degeneration of convex real projective structures on bordered surfaces.

4-dimensional Riemannian manifolds with a harmonic 2-form of constant lengthNov 01 2017It was shown by Seaman that if a compact, oriented 4-dimensional riemannian manifold (M, g) of positive sectional curvature admits a harmonic 2-form of constant length, its intersection form is definite and such a harmonic form is unique up to constant ... More

Almost-Kahler Anti-Self-Dual MetricsNov 24 2015We show the existence of strictly almost-Kahler anti-self-dual metrics on certain 4-manifolds by deforming scalar-flat Kahler metrics. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of Seiberg-Witten ... More

Field-induced dynamics in the quantum Brownian oscillator: An exact treatmentFeb 15 2010Jul 23 2010We consider a quantum linear oscillator coupled to a bath in equilibrium at an arbitrary temperature and then exposed to an external field arbitrary in form and strength. We then derive the reduced density operator in closed form of the coupled oscillator ... More

Comment on "note on the derivative of the hyperbolic cotangent"May 10 2007In a couple of articles (Ford G W and O'Connell R F 1996 Nature 380 113 and 2002 J. Phys. A: Math. Gen. 35 4183) it was argued that the standard result for the derivative of the hyperbolic cotangent in the literature, d \coth y/dy = -{csch}^2 y is incomplete ... More

Novel Grey Interval Weight Determining and Hybrid Grey Interval Relation Method in Multiple Attribute Decision-MakingJul 11 2012This paper proposes a grey interval relation TOPSIS for the decision making in which all of the attribute weights and attribute values are given by the interval grey numbers. The feature of our method different from other grey relation decision-making ... More

Knots having the same Seifert form and primary decomposition of knot concordanceAug 20 2017Aug 24 2017We show that for each Seifert form of an algebraically slice knot with nontrivial Alexander polynomial, there exists an infinite family of knots having the Seifert form such that the knots are linearly independent in the knot concordance group and not ... More

Degenerate Euler zeta functionAug 29 2015Recently, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with degenerate Euler ... More

Identities involving Laguerre polynomials derived from umbral calculusJan 15 2013In this paper, we investigate some identities of Laguerre polynomials involving Bernoulli and Euler polynomials which are derived from umbral calculus.

On the q-Euler numbers and polynomials with weight 0Oct 10 2011The purpose of this paper is to investigate some properties of q-Euler numbers and polynomials with weight 0. From those q-Euler numbers with weight 0, we derive some identities on the q-Euler numbers and polynomials with weight 0.

A note on the generalized Euler numbers and polynomialsJul 28 2009In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

On the multiple q-Genocchi and Euler numbersJan 07 2008The purpose of this paper is to present a systemic study of some families of multiple q-Genocchi and euler numbers by using multivariate q-Volkenborn integral. From the studies of those q-Genocchi numbers and polynomials of higher order we derive some ... More

Lebesque-Radon-Nikodym theorem with respect to p-adic invariant measure on ZpSep 01 2009In this paper we derive the analogue of Lebesque-Radon Nikody theorem with respect to fermionic p-adic invariant measures on Zp

An Identity of the Symmetry for the Frobenius-Euler polynomials associated with the fermionic p-adic invariant q-integrals on Z_pApr 29 2008The main purpose of this paper is to prove an identity of symmetry for the Frobenius-Euler polynomials.

Analytic Continuation of q-Euler numbers and polynomialsJan 03 2008In this paper we study that the $q$-Euler numbers and polynomials are analytically continued to $E_q(s)$. A new formula for the Euler's $q$-Zeta function $\zeta_{E,q}(s)$ in terms of nested series of $\zeta_{E,q}(n)$ is derived. Finally we introduce the ... More

A note on q-Euler numbers and polynomialsAug 26 2006The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.

p-adic l-functions and sums of powersMay 27 2006The purpose of this paper is to give the explicit formulae of p-adic l-functions and sums of powers which are related to Euler numbers.

q-Analogue of Euler-Barnes Multiple Zeta Functions (= a note on q-zeta functions)Mar 06 2006Recently (see [1]) I has introduced an interesting the Euler-Barnes multiple zeta function. In this paper we construct the q-analogue of Euler-Barnes multiple zeta function which interpolates the q-analogue of Frobenius-Euler numbers of higher order at ... More

A note on the alternating sums of powers of consecutive integersAug 13 2005Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.

q-analogues of the sums of powers of consecutive integersFeb 06 2005Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.

An analogue of Lebesgue-Radon-Nikodym theorem with respect to p-adic q-invariant distribution on $\Bbb Z_p$Mar 09 2005The purpose of this paper is to derive the analogue of Lebesgue-Radon-Nikodym theorem with respect to $p$-adic $q$-invariant distribution on $\Bbb Z_p$ which is defined by author in [1].

New obstructions to doubly slicing knotsNov 06 2004A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's filtration of ... More

Explicit presentations of nonspecial line bundles and secant spacesMay 01 2012A line bundle L on a smooth curve X is nonspecial if and only if L admits a presentation L=K_X -D +E for some effective divisors D and E>0 on X with gcd (D, E)=0 and h^0 (X, O_X (D))=1. In this work, we define a minimal presentation of L which is minimal ... More

On families of periodic orbits in the restricted three-body problemJan 31 2018Sep 06 2018Since Poincar\'e, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at obvious periodic ... More

Galois theory and Diophantine geometryAug 05 2009This is an essay to accompany the author's lecture at the introductory workshop on `Nonabelian fundamental groups in arithmetic geometry' at the Newton Institute, Cambridge in July, 2009.

On the Largest Integer that is not a Sum of Distinct Positive $n$th PowersOct 07 2016Jul 09 2017It is known that for an arbitrary positive integer \(n\) the sequence \(S(x^n)=(1^n, 2^n, \ldots)\) is complete, meaning that every sufficiently large integer is a sum of distinct \(n\)th powers of positive integers. We prove that every integer \(m\geq ... More

Local Conjugacy in $\text{GL}_2(\mathbb{Z}/p^2\mathbb{Z})$May 30 2017Aug 08 2017Subgroups $H_1$ and $H_2$ of a group $G$ are said to be locally conjugate if there is a bijection $f: H_1 \rightarrow H_2$ such that $h$ and $f(h)$ are conjugate in $G$ for every $h \in H_1$. This paper studies local conjugacy among subgroups of $\text{GL}_2(\mathbb{Z}/p^2\mathbb{Z})$, ... More

Unstable minimal surfaces of annulus type in manifoldsMar 27 2006May 30 2008Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal ... More

A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifoldsMar 27 2006Given two Jordan curves in a Riemannian manifold, a minimal surface of annulus type bounded by these curves is described as the harmonic extension of a critical point of some functional (the Dirichlet integral) in a certain space of boundary parametrizations. ... More

Coloring the Real Line with Monochromatic IntervalsAug 19 2016Let D be a finite set of positive real numbers. The distance graph G(R,D) is the graph with vertex set R (set of real numbers), and two vertices x, y are adjacent if |x-y| belongs to D. We prove that every positive integer t>1 there is a distance set ... More