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Mixed Threefolds Isogenous to a ProductMar 07 2017In this paper we study \emph{threefolds isogenous to a product of mixed type} i.e. quotients of a product of three compact Riemann surfaces $C_i$ of genus at least two by the action of a finite group $G$, which is free, but not diagonal. In particular, ... More

On Threefolds Isogenous to a Product of CurvesDec 19 2014Mar 08 2017A threefold isogenous to a product of curves $X$ is a quotient of a product of three compact Riemann surfaces of genus at least two by the free action of a finite group. In this paper we study these threefolds under the assumption that the group acts ... More

On Threefolds Isogenous to a Product of CurvesDec 19 2014Jan 14 2015A threefold isogenous to a product of curves $X$ is a quotient of a product of three compact Riemann surfaces of genus at least $2$ by the free action of a finite group. In this paper we study these threefolds under the assumption that the group acts ... More

A family of threefolds of general type with canonical map of high degreeFeb 08 2019In this note we provide a two-dimensional family of smooth minimal threefolds of general type with canonical map of degree 96, improving the previous known bound of 72.

New surfaces with canonical map of high degreeJul 31 2018We give an algorithm that, for a given value of the geometric genus $p_g,$ computes all regular product-quotient surfaces with abelian group that have at most canonical singularities and have canonical system with at most isolated base points. We use ... More

The pluricanonical systems of a product-quotient varietyOct 02 2018We give a method for the computation of the plurigenera of a product-quotient manifold. We give two different types of applications to it: to the construction of Calabi-Yau threefolds and to the determination of the minimal model of a product-quotient ... More

Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear SystemsMar 11 2015In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and discuss further ... More

A stabilizing iteration scheme for model predictive control based on relaxed barrier functionsMar 15 2016Apr 06 2016We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called relaxed logarithmic ... More

Differential Characters and Geometric ChainsMar 26 2013Apr 09 2013We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit ... More

Staggered domain wall fermionsSep 16 2016We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared ... More

Distances and large deviations in the spatial preferential attachment modelSep 26 2018Sep 27 2018We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. M\"orters (2013). First, in a regime of strong linear reinforcement, we show that typical distances are at most of doubly-logarithmic order. ... More

Thermal Quantum Fields without Cut-offs in 1+1 Space-time DimensionsMar 26 2004We construct interacting quantum fields in 1+1 dimensional Minkowski space, representing neutral scalar bosons at positive temperature. Our work is based on prior work by Klein and Landau and Hoegh-Krohn

On the relativistic KMS condition for the P(φ)_2 modelSep 29 2006The relativistic KMS condition introduced by Bros and Buchholz provides a link between quantum statistical mechanics and quantum field theory. We show that for the $P(\phi)_2$ model at positive temperature, the two point function for fields satisfies ... More

Friction force: from mechanics to thermodynamicsNov 17 2009Jul 01 2010We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws ... More

Thermal Quantum Fields with Spatially Cut-off Interactions in 1+1 Space-time DimensionsJul 25 2003We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Hoegh-Krohn. Generalized path ... More

Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger modelFeb 26 2016Jul 05 2016We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, ... More

On spatial and temporal multilevel dynamics and scaling effects in epileptic seizuresMar 30 2011Jul 29 2011Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of ... More

Duck Traps: Two-dimensional Critical Manifolds in Planar SystemsAug 30 2018Nov 05 2018In this work we consider two-dimensional critical manifolds in planar fast-slow systems near fold and so-called canard (=`duck') points. These higher-dimension, and lower-codimension, situation is directly motivated by the case of hysteresis operators ... More

Introduction to nuclear astrophysicsNov 20 2009In the first lecture of this volume, we will present the basic fundamental ideas regarding nuclear processes occurring in stars. We start from stellar observations, will then elaborate on some important quantum-mechanical phenomena governing nuclear reactions, ... More

A geometric approach to the diophantine Frobenius problemJul 12 2010It turns out that all instances of the diophantine Frobenius problem for three coprime a_i have a common geometric structure which is independent of arithmetic coincidences among the a_i. By exploiting this structure we easily obtain Johnson's formula ... More

Isotropy of Angular Frequencies and Weak Chimeras With Broken SymmetryDec 04 2015Jul 18 2016The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here we generalize the definition weak chimera to a more general class of equivariant dynamical systems by characterizing ... More

Raiders of the lost spacetimeMay 21 2014Spacetime as we know and love it is lost in most approaches to quantum gravity. For many of these approaches, as inchoate and incomplete as they may be, one of the main challenges is to relate what they take to be the fundamental non-spatiotemporal structure ... More

A many-body approach to crystal field theoryAug 04 2003Oct 03 2003A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function of the density ... More

The structure of Green functions in quantum field theory with a general stateOct 30 2007In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are required. The ... More

Analytical solutions for two-level systems with dampingNov 23 2006A method is proposed to transform any analytic solution of the Bloch equation into an analytic solution of the Landau-Lifshitz-Gilbert equation. This allows for the analytical description of the dynamics of a two level system with damping. This method ... More

Perturbative Quantum Field Theory in the String-Inspired FormalismJan 05 2001Jan 06 2001We review the status and present range of applications of the ``string-inspired'' approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and S-matrix elements in a way which is similar in spirit ... More

Regular and Biregular module algebrasSep 30 2008Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in 1995 we investigate regular and biregular Hopf module algebras. If $A$ is an algebra with an action by an affine Hopf algebra $H$, then any $H$-stable ... More

Duality for partial group actionsNov 06 2007Given a finite group G acting as automorphisms on a ring A, the skew group ring A*G is an important tool for studying the structure of G-stable ideals of A. The ring A*G is G-graded, i.e.G coacts on A*G. The Cohen-Montgomery duality says that the smash ... More

The radial effective temperature distribution of steady-state, mass-losing accretion disksJun 10 1999Mass loss appears to be a common phenomenon among disk-accreting astrophysical systems. An outflow emanating from an accretion disk can act as a sink for mass, angular momentum and energy and can therefore alter the dissipation rates and effective temperatures ... More

The Evolution of Cataclysmic VariablesAug 23 2011Sep 02 2011I review our current understanding of the evolution of cataclysmic variables (CVs). I first provide a brief introductory "CV primer", in which I describe the physical structure of CVs, as well as their astrophysical significance. The main part of the ... More

Cataclysmic Variables: Eight Breakthroughs in Eight YearsJan 14 2011May 04 2011The last few years have seen tremendous progress in our understanding of cataclysmic variable stars. As a result, we are finally developing a much clearer picture of their evolution as binary systems, the physics of the accretion processes powering them, ... More

Characterising subspaces of Banach spaces with a Schauder basis having the shift propertyJun 02 2011We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of ... More

Two algebraic properties of thermal quantum field theoriesJan 05 1999May 05 2004We establish the Schlieder and the Borchers property for thermal field theories. In addition, we provide some information on the commutation and localization properties of projection operators.

Some Comments on Entanglement and Local Thermofield TheoryMay 05 2004We combine recent results of Clifton and Halvorson [1] with structural results of the author [2--5] concerning the local observables in thermofield theory. An number of interesting consequences are discussed.

The Relation Between KMS-states for Different TemperaturesMar 30 1998May 05 2004Given a thermal field theory for some temperature $\beta^{-1}$, we construct the theory at an arbitrary temperature $ 1 / \beta'$. Our work is based on a construction invented by Buchholz and Junglas, which we adapt to thermal field theories. In a first ... More

Decay of Spatial Correlations in Thermal StatesMar 27 1998We study the cluster properties of thermal equilibrium states in theories with a maximal propagation velocity (such as relativistic QFT). Our analysis, carried out in the setting of algebraic quantum field theory, shows that there is a tight relation ... More

Separation of acoustic waves in isentropic flow perturbationsFeb 14 2014Feb 22 2015The present contribution investigates the mechanisms of sound generation and propagation in the case of highly-unsteady flows. Based on the linearisation of the isentropic Navier-Stokes equation around a new pathline-averaged base flow, it is demonstrated ... More

Residues and filtered D-modulesMay 04 2010For an embedding of sufficiently high degree of a smooth projective variety X into projective space, we use residues to define a filtered holonomic D-module (M, F) on the dual projective space. This gives a concrete description of the intermediate extension ... More

One non-relativistic particle coupled to a photon fieldFeb 01 2002Feb 20 2003We investigate the ground state energy of an electron coupled to a photon field. First, we regard the self-energy of a free electron, which we describe by the Pauli-Fierz Hamiltonian. We show that, in the case of small values of the coupling constant ... More

Evolution variational inequality and Wasserstein control in variable curvature contextSep 07 2015Nov 08 2015In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study $(\kappa,N)$-convex functions on metric spaces where $\kappa$ is a lower semi-continuous function, and gradient flow curves in the sense ... More

Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebrasFeb 07 2013Oct 14 2013We define polynomial H-identities for comodule algebras over a Hopf algebra H and establish general properties for the corresponding T-ideals. In the case H is a Taft algebra or the Hopf algebra E(n), we exhibit a finite set of polynomial H-identities ... More

Breakdown points for maximum likelihood estimators of location-scale mixturesOct 05 2004ML-estimation based on mixtures of Normal distributions is a widely used tool for cluster analysis. However, a single outlier can make the parameter estimation of at least one of the mixture components break down. Among others, the estimation of mixtures ... More

Embedded surfaces and almost complex structuresDec 09 1998We prove necessary and sufficient conditions for a smooth surface in a 4-manifold X to be pseudoholomorphic with respect to some almost complex structure on X. This provides a systematic approach to the construction of pseudoholomorphic curves that do ... More

Canonical extensions of local systemsOct 15 2007Oct 16 2007A local system H on a complex manifold M can be viewed in two ways--either as a locally free sheaf, or as a union of covering spaces T = T(H). When M is an open set in a bigger manifold, the local system will generally not extend, because of local monodromy. ... More

Zero Sets of Solutions to Semilinear Elliptic Systems of First OrderMay 13 1998Consider a nontrivial solution to a semilinear elliptic system of first order with smooth coefficients defined over an $n$-dimensional manifold. Assume the operator has the strong unique continuation property. We show that the zero set of the solution ... More

Complete Invariant Graphs of Alternating KnotsApr 27 2004Chord diagrams and related enlacement graphs of alternating knots are enhanced to obtain complete invariant graphs including chirality detection. Moreover, the equivalence by common enlacement graph is specified and the neighborhood graph is defined for ... More

From Quantum Bäcklund Transforms to Topological Quantum Field TheoryAug 26 2015Feb 03 2016We derive the quantum analogue of a B\"acklund transformation for the quantised Ablowitz-Ladik chain, a space discretisation of the nonlinear Schr\"odinger equation. The quantisation of the Ablowitz-Ladik chain leads to the $q$-boson model. Using a previous ... More

A Q-operator for the twisted XXX modelNov 06 2005Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results for the XXX model. We show that quasi-periodic boundary conditions are ... More

Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatzApr 10 2004We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for the Bethe eigenvalues ... More

PT-invariance and representations of the Temperley-Lieb algebra on the unit circleDec 13 2007Jan 02 2008We present in detail a recent conjecture on self-adjoint representations of the Temperley-Lieb algebra for particular values on the unit circle. The formulation in terms of graphical calculus is emphasized and discussed for several examples. The role ... More

The Fluctuation Theorem as a Gibbs PropertyDec 18 1998Common ground to recent studies exploiting relations between dynamical systems and non-equilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) ... More

If all geodesics are closed on the projective planeOct 04 2007The paper shows that the curvature of RP2 is constant iff all geodesics are closed. Therefore RP2 is the first known manifold with only one G-structure. It took quiete a long time to find such a manifold. The author shows only that if all geodesics are ... More

Self-duality of Coble's quartic hypersurface and applicationsSep 27 2001The moduli space M_0 of semi-stable rank 2 vector bundles with fixed trivial determinant over a non-hyperelliptic curve C of genus 3 is isomorphic to a quartic hypersurface in P^7 (Coble's quartic). We show that M_0 is self-dual and that its polar map ... More

Effective Theory Approach to W-Pair Production near ThresholdAug 06 2007In this talk, I review the effective theory approach to unstable particle production and present results of a calculation of the process e- e+ ->mu- nubar_mu u dbar X near the W-pair production threshold up to next-to-leading order in GammaW/MW ~ alpha ... More

Top quark signatures of Higgsless modelsOct 09 2006In these proceedings I describe the use of tree level unitarity to constrain top quark signatures of Higgsless electroweak models and discuss implications for collider phenomenology.

Non-congruence of homology Veech groups in genus twoJan 28 2013Feb 13 2014We study the action of the Veech group of square-tiled surfaces of genus two on homology. This action defines the homology Veech group which is a subgroup of $\textrm{SL}_2(\mathcal{O}_D)$ where $\mathcal{O}_D$ is a quadratic order of square discriminant. ... More

A discrete log gas, discrete Toeplitz determinants with Fisher-Hartwig singularities, and Gaussian Multiplicative ChaosSep 11 2015We consider a log-gas on a discretization of the unit circle. We prove that if the gas is not too dense, or the number of particles in the gas is not too large compared to the scale of the discretization, the absolute value of the characteristic polynomial ... More

Precise model of Hawking radiation from the tunnelling mechanismNov 05 2014Aug 07 2015We recently improved the famous result of Parikh and Wilczek, who found a probability of emission of Hawking radiation which is compatible with a non-strictly thermal spectrum, showing that such a probability of emission is really associated to two non-strictly ... More

A clarification on the debate on "the original Schwarzschild solution"Oct 28 2010Mar 25 2011Now that English translations of Schwarzschild's original paper exist, that paper has become accessible to more people. Historically, the so-called "standard Schwarzschild solution" was not the original Schwarzschild's work, but it is actually due to ... More

Interferometric detection of gravitational waves arising from extended theories of gravityFeb 13 2009Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this letter Proceeding ... More

Using long-baseline interferometric gravitational waves detectors for high precision measures of the gravitational accelerationNov 07 2006Jan 25 2007A derivation of the optical axis lenght fluctations due by tilts of the mirrors of the Fabry-Perot cavity of long-baseline interferometers for the detection of gravitational waves in presence of the gravitational field of the earth is discussed. By comparing ... More

Time-Dependent Schrodinger Equation for Black Hole Evaporation: no Information LossApr 06 2013Nov 06 2014In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state" (Verbatim from ref. 2). This was the starting ... More

Radiation dominated era and the power of general relativityMay 31 2012An analysis in the framework of the radiation dominated era permits to put bounds on the weak modification of general relativity which arises from the Lagrangian R^{1+epsilon}. Such a theory has been recently discussed in various papers in the literature. ... More

Primordial gravity's breathOct 08 2011By releasing a formula that directly connects the average amplitude of the relic stochastic gravitational-wave background (SGWB) with the Inflaton field and the equation for the characteristic amplitude h_c for the relic SGWB, in this paper the upper ... More

Interferometric detection of gravitational waves: the definitive test for General RelativityMay 15 2009Jun 08 2009Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this essay we show that, ... More

Conformal Transformation Properties of the B-type SupercurrentOct 19 1999We investigate the superconformal transformation properties of the supercurrent as well as of the superconformal anomalies themselves in d=4, N=1 supersymmetric quantum field theory. Matter supercurrent and anomalies are coupled to a classical background ... More

Baryon number and charge fluctuations from lattice QCDDec 18 2012We calculate electric and baryonic charge fluctuations on the lattice. Results have been obtained with the highly improved staggered quark action (HISQ) and almost physical quark masses on lattices with spacial extent of $N_\tau=6,8,12$. Higher order ... More

Net-baryon number fluctuations in (2+1)-flavor QCDJul 29 2010We present a lattice study of net-baryon number fluctuations in (2+1)-flavor QCD. The results are based on a Taylor expansion of the pressure with respect to the baryon chemical potential. We calculate higher moments of the net-baryon number fluctuations ... More

The QCD equation of state from improved staggered fermionsJun 22 2009We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent $N_{\tau}=8$. Calculations have been performed with two different improved ... More

Algebraic representations of von Neumann algebrasSep 08 2006Mar 09 2010An algebraic extended bilinear Hilbert semispace is proposed as being the natural representation space for the algebras of von Neumann.This bilinear Hilbert semispace has a well defined structure given by the representation space of an algebraic general ... More

Quantized gravito-electro-magnetic interactions of bilinear typeJul 26 2006The interactions inside the (bisemi)particles are envisaged from two points of view: The first approach, based on the reducible representations of algebraic bilinear semigroups, allows to describe explicitly the interactions between (bisemi)particles ... More

Schur function identities and the number of perfect matchings of holey Aztec rectanglesNov 26 1997Dec 21 1997We compute the number of perfect matchings of an $M\times N$ Aztec rectangle where $|N-M|$ vertices have been removed along a line. A particular case solves a problem posed by Propp. Our enumeration results follow from certain identities for Schur functions, ... More

Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitionsNov 26 1997We prove a constant term conjecture of Robbins and Zeilberger (J. Combin. Theory Ser. A 66 (1994), 17-27), by translating the problem into a determinant evaluation problem and evaluating the determinant. This determinant generalizes the determinant that ... More

A (conjectural) 1/3-phenomenon for the number of rhombus tilings of a hexagon which contain a fixed rhombusJan 01 2001Jul 13 2001We state, discuss, provide evidence for, and prove in special cases the conjecture that the probability that a random tiling by rhombi of a hexagon with side lengths $2n+a,2n+b,2n+c,2n+a,2n+b,2n+c$ contains the (horizontal) rhombus with coordinates $(2n+x,2n+y)$ ... More

On generalized Ramanujan primesJan 28 2014Jan 12 2016In this paper we establish several results concerning the generalized Ramanujan primes. For $n\in\mathbb{N}$ and $k \in \mathbb{R}_{> 1}$ we give estimates for the $n$th $k$-Ramanujan prime which lead both to generalizations and to improvements of the ... More

Conformal scalar fields, isotropic singularities and conformal cyclic cosmologiesDec 07 2013We analyse spacetimes with a conformal scalar field source, a cosmological constant and a quartic self-interaction term for the scalar field. We also consider additional matter contents in the form of Maxwell and Yang-Mills fields or radiation fluids. ... More

L^2-Invariants of Finite Aspherical CW-ComplexesMay 27 2008Let $X$ be a finite aspherical CW-complex whose fundamental group $\pi_1(X)$ possesses a subnormal series $\pi_1(X) \rhd G_m \rhd ... \rhd G_0$ with a non-trivial elementary amenable group $G_0$. We investigate the $L^2$-invariants of the universal covering ... More

Proof of a Conjecture by Lewandowski and ThiemannApr 01 2003It is proven that for compact, connected and semisimple structure groups every degenerate labelled web is strongly degenerate. This conjecture by Lewandowski and Thiemann implies that diffeomorphism invariant operators in the category of piecewise smooth ... More

The Bivariate Normal CopulaDec 15 2009We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved ... More

Dynamic Composition of Evolving Process TypesDec 25 2011Classical approaches like process algebras or labelled transition systems deal with static composition to model non-trivial concurrent or distributed systems; this is not sufficient for systems with dynamic architecture and with variable number of components. ... More

Tool-Assisted Multi-Facet Analysis of Formal Specifications (Using Alelier-B and ProB)Oct 09 2009Tool-assisted analysis of software systems and convenient guides to practise the formal methods are still motivating challenges. This article addresses these challenges. We ex periment on analysing a formal speci?cation from multiple aspects. The B method ... More

Can Component/Service-Based Systems Be Proved Correct?Oct 10 2009Component-oriented and service-oriented approaches have gained a strong enthusiasm in industries and academia with a particular interest for service-oriented approaches. A component is a software entity with given functionalities, made available by a ... More

Dining Cryptographers with 0.924 Verifiable Collision ResolutionFeb 07 2014Jan 03 2015The dining cryptographers protocol implements a multiple access channel in which senders and recipients are anonymous. A problem is that a malicious participant can disrupt communication by deliberately creating collisions. We propose a computationally ... More

Residues : The gateway to higher arithmetic INov 18 2012Residues to a given modulus have been introduced to mathematics by Carl Friedrich Gauss with the definition of congruence in the `Disquisitiones Arithmeticae'. Their extraordinary properties provide the basis for a change of paradigm in arithmetic. By ... More

Einselection without pointer statesAug 20 2009May 21 2010We consider small subsystems of large, closed quantum systems that evolve according to the von Neumann equation. Without approximations and without making any special assumptions on the form of the interaction we prove that, for almost all initial states ... More

CP Violation and the Future of Flavor PhysicsAug 04 2009With the nearing completion of the first-generation experiments at asymmetric $e^+ e^-$ colliders running at the $\Upsilon(4S)$ resonance ("B-Factories") a new era of high luminosity machines is at the horizon. We report here on the plans at KEK in Japan ... More

Odd-graceful labelings of trees of diameter 5Jul 23 2008Jul 23 2008A difference vertex labeling of a graph G is an assignment f of labels to the vertices of G that induces for each edge xy the weight |f(x)-f(y)|. A difference vertex labeling f of a graph G of size n is odd-graceful if f is an injection from V(G) to {0,1,...,2n-1} ... More

Characterizing Slow Exit and Entrance PointsJan 29 2012Feb 02 2012Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easier for singular perturbation problems. In this paper, we will revisit Conley's ... More

Exploring Parameter Spaces in Dynamical SystemsJul 12 2008The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on parameters. ... More

Girsanov theory under a finite entropy conditionJan 20 2011Jan 31 2011This paper is about Girsanov's theory. It (almost) doesn't contain new results but it is based on a simplified new approach which takes advantage of the (weak) extra requirement that some relative entropy is finite. Under this assumption, we present and ... More

Stochastic derivatives and generalized h-transforms of Markov processesFeb 15 2011Let $R$ be a continuous-time Markov process on the time interval $[0,1]$ with values in some state space $X$. We transform this reference process $R$ into $P:=f(X_0)\exp (-\int_0^1 V_t(X_t) dt) g(X_1)\,R$ where $f,g$ are nonnegative measurable functions ... More

Spectral Bounds for Dirac Operators on Open ManifoldsOct 31 2008We extend several classical eigenvalue estimates for Dirac operators on compact manifolds to noncompact, even incomplete manifolds. This includes Friedrich's estimate for manifolds with positive scalar curvature as well as the author's estimate on surfaces. ... More

Jet-like QED processes : on general properties of impact factorsJan 17 2014In this article, general properties of impact factors involved in jet-like QED processes are explored. In particular, a general link is established between their helicity properties and their order of magnitude as defined by jet-like kinematics. Exact ... More

Bijections for hook pair identitiesDec 13 1999Short, bijective proofs of identities for multisets of `hook pairs' (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.

A large deviation approach to optimal transportOct 08 2007A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle with an optimal ... More

Mutations and short geodesics in hyperbolic 3-manifoldsJun 23 2014Jun 22 2016In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in ... More

On the differential equation $y" - (b'(x)/2b(x))y' + λb(x)y = 0$Jul 28 2009The Hamilton-Jacobi method which can be used for solving this equation has been presented. The solution of the equation suggests that there exist some second order linear ordinary differential equations whose resolution can be done by means of characteristic ... More

Rectangle Gell-Mann MatricesNov 22 2006Aug 31 2007We call rectangle Gell-Mann matrices rectangle matrices which make generalization of the expression of a tensor commutation matrix $n \otimes n$ in terms of tensor products of square Gell-Mann matrices.

Matrices de commutation tensorielle: de l'équation de Dirac vers une application en physique des particulesMay 26 2014We construct two sets of representations of the Dirac equation. They transform themselves from one to another in multiplying by the tensor commutation matrix (TCM) $2\otimes 2$. The Gauss matrix can lead us to the Cholesky decomposition. The TCMs can ... More

Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebraOct 28 2011Sep 06 2012We define cylindric generalisations of skew Macdonald functions when one of their parameters is set to zero. We define these functions as weighted sums over cylindric skew tableaux: fixing two integers n>2 and k>0 we shift an ordinary skew diagram of ... More