total 1232took 0.09s

Probing weakly hybridized magnetic molecules by spin-polarized tunnelingJun 11 2019Advances in molecular spintronics rely on the in-depth characterization of the molecular building blocks in terms of their electronic and, more importantly, magnetic properties. For this purpose, inert substrates that interact only weakly with adsorbed ... More

Compilation as a Typed EDSL-to-EDSL TransformationMar 29 2016Apr 05 2016This article is about an implementation and compilation technique that is used in RAW-Feldspar which is a complete rewrite of the Feldspar embedded domain-specific language (EDSL) (Axelsson et al. 2010). Feldspar is high-level functional language that ... More

Two weight $L^{p}$-inequalities for dyadic shifts and the dyadic square functionApr 22 2015We consider two weight $L^{p}\to L^{q}$-inequalities for dyadic shifts and the dyadic square function with general exponents $1<p,q<\infty$. It is shown that if a so-called quadratic $\mathscr{A}_{p,q}$-condition related to the measures holds, then a ... More

The Light Cone in String TheoryApr 08 1993Apr 12 1993The causal boundary of string propagation -- defined as the hypersurface in loop space bordering the timelike(spacelike) domains in which two successive measurements of the string field do(do not) interfere with one another -- is argued to be $0=\int ... More

An Introduction to 2d Gravity and Solvable String ModelsDec 09 1991Continuum and discrete approaches to 2d gravity coupled to $c<1$ matter are reviewed.

Strictly nilpotent elements and bispectral operators in the Weyl algebraJun 18 2002In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of ... More

The Existence of Quasimeromorphic Mappings in Dimension 3Nov 16 2003Mar 03 2004We prove that a Kleinian group $G$ acting upon $\mathbb{H}^{3}$ admits a non-constant $G$-automorphic function, even if it has torsion elements, provided that the orders of the elliptic (i.e torsion) elements are uniformly bounded. This is accomplished ... More

$d$-Orthogonal Analogs of Classical Orthogonal PolynomialsSep 20 2016Jun 26 2018Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only ... More

Open induction in a bounded arithmetic for TC^0Apr 29 2014May 28 2014The elementary arithmetic operations $+,\cdot,\le$ on integers are well-known to be computable in the weak complexity class $\mathrm{TC}^0$, and it is a basic question what properties of these operations can be proved using only $\mathrm{TC}^0$-computable ... More

Reproducible Research: Best Practices and Potential MisuseMay 02 2019The scientific world is becoming more open to the public and fellow researchers. Open access publishing is becoming accepted, even if some publishers are resisting. The next step is the open code and data paradigm, which was briefly discussed in the "From ... More

The uniform distribution of sequences generated by iterated polynomialsSep 20 2017Assume that $m,s\in\mathbb N$, $m>1$, while $f$ is a polynomial with integer coefficients, $\text{deg}~f>1$, $f^{(i)}$ is the $i$th iteration of the polynomial $f$, $\kappa_n$ has a discrete uniform distribution on the set $\{0,1,\ldots,m^n - 1\}$. We ... More

On the Dipole Swing and the Search for Frame Independence in the Dipole ModelSep 10 2007Nov 06 2007Small-x evolution in QCD is conveniently described by Mueller's dipole model which, however, does not include saturation effects in a way consistent with boost invariance. In this paper we first show that the recently studied zero and one dimensional ... More

Period-doubled breathing in trapped Bose-Einstein condensatesMay 14 2004The response of a trapped Bose-Einstein condensed gas to a periodic driving force is studied theoretically in the framework of the nonlinear Gross-Pitaevskii equation. The monopole mode is driven by periodical modulation of the frequency of the isotropic ... More

Dust clouds and plasmoids in Saturn's Magnetosphere as seen with four Cassini instrumentsFeb 06 2017We revisit the evidence for a "dust cloud" observed by the Cassini spacecraft at Saturn in 2006. The data of four instruments are simultaneously compared to interpret the signatures of a coherent swarm of dust that would have remained near the equatorial ... More

Scalar Gravitational Waves in the Effective Theory of GravityJun 29 2016Oct 03 2018As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective ... More

Two weight $L^{p}$-inequalities for dyadic shifts and the dyadic square functionApr 22 2015Jan 24 2017We consider two weight $L^{p}\to L^{q}$-inequalities for dyadic shifts and the dyadic square function with general exponents $1<p,q<\infty$. It is shown that if a so-called quadratic $\mathscr{A}_{p,q}$-condition related to the measures holds, then a ... More

L^{p}(μ)-L^{q}(ν) characterization for well localized operatorsDec 05 2014Jan 26 2016We consider a two weight $L^{p}(\mu) \to L^{q}(\nu)$-inequality for well localized operators as defined and studied by F. Nazarov, S. Treil and A. Volberg when $p=q=2$. A counterexample of F. Nazarov shows that the direct analogue of these results fails ... More

General Belief MeasuresFeb 27 2013Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of firstorder ... More

In Love With a Robot: the Dawn of Machine-To-Machine MarketingFeb 18 2013Aug 03 2016The article looks at mass market artificial intelligence tools in the context of their ever-growing sophistication, availability and market penetration. The subject is especially relevant today for these exact reasons - if a few years ago AI was the subject ... More

The Non-Commutative Geometry of the Complex Classes of Topological InsulatorsFeb 28 2014Jun 13 2014Alain Connes' Non-Commutative Geometry program [Connes 1994] has been recently carried out [Prodan, Leung, Bellissard 2013, Prodan, Schulz-Baldes 2014] for the entire A- and AIII-symmetry classes of topological insulators, in the regime of strong disorder ... More

Mott insulator dynamicsMay 06 2011Jun 13 2011The hydrodynamics of a lattice Bose gas in a time-dependent external potential is studied in a mean-field approximation. The conditions under which a Mott insulating region can melt, and the local density adjust to the new potential, are determined. In ... More

Sequence encoding without inductionJan 27 2012We show that the universally axiomatized, induction-free theory PA^- is a sequential theory in the sense of Pudl\'ak [5], in contrast to the closely related Robinson's arithmetic.

Ueber die Geometrie der alten AegypterJun 05 2008Lecture given before the Royal Academy Vienna that summarizes the state of knowledge about the mathematics of the ancient Egyptians, up to 1884. Contains all relevant references to classical Greek texts, and the 'latest' archeology results. Later published ... More

Process Description of COM Object Life CycleDec 20 2009The objective of this article is to provide for the reader a basic description of all the steps involved in the COM object life-cycle process. COM is a software technology and process performer. The first section briefly introduces the Component Object ... More

The edge spectrum of Chern insulators with rough boundariesSep 15 2008Feb 04 2009Chern insulators are periodic band insulators with the property that their projector onto the occupied bands have non-zero Chern number. Chern insulator with a homogeneous boundary display continuum spectrum that fills the entire insulating gap. The local ... More

Saturation In Deep Inelastic ScatteringJun 14 2004The solution to the BFKL equation grows like a power of center of mass energy, s, violating unitarity conditions at high energies. The growth of the cross section can be tamed by taking into account multiple pomeron exchanges. This is known as saturation ... More

Spacelike Singularities and String TheoryDec 08 1994Dec 21 1994An interpretation of spacelike singularities in string theory uses target space duality to relate the collapsing Schwarzschild geometry near the singularity to an inflationary cosmology in dual variables. An appealing picture thus results whereby gravitational ... More

Multiply quantized vortices in trapped Bose-Einstein condensatesMar 13 2001Oct 05 2001Vortex configurations in rotating Bose-Einstein condensed gases trapped in power-law and anharmonic potentials are studied. When the confining potential is steeper than harmonic in the plane perpendicular to the axis of rotation, vortices with quantum ... More

A Computational Non-Commutative Geometry Program for Disordered Topological InsulatorsNov 29 2016A computational program based on the principles of non-commutative geometry is presented. This includes the general algebraic principles, the algorithms themselves, the error estimates and the applications. The latter are mainly on the integer quantum ... More

Vector orthogonal polynomials with Bochner's propertySep 20 2016Classical orthogonal polynomial systems of Jacobi, Hermite, Laguerre and Bessel have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a classical theorem by Bochner they ... More

Recursive functions and existentially closed structuresOct 26 2017The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$ does not interpret ... More

Intrinsic Differential Geometry and the Existence of Quasimeromorphic MappingsDec 31 2008We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.

Localised Relative Energy and Finite Speed of Propagation for Compressible FlowsDec 15 2017Dec 20 2017For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt classical arguments ... More

On the Generation of Pythagorean Triples and Representation of Integers as a Difference of Two SquaresNov 07 2017The general formulas for finding the quantity of all primitive and nonprimitive triples generated by the given number x have been proposed. Also the formulas for finding the complete quantity of the representations of the integers as a difference of two ... More

Weak-strong uniqueness in fluid dynamicsMay 11 2017We give a survey of recent results on weak-strong uniqueness for compressible and incompressible Euler and Navier-Stokes equations, and also make some new observations. The importance of the weak-strong uniqueness principle stems, on the one hand, from ... More

Normal modes. The true storyJan 18 2016The aim of this article is a comprehensive description of normal modes of molecular vibrations. The starting point is chosen to be a general molecular system with separated center of mass and an arbitrary embedding of body-fixed axes. This allows to focus ... More

Deletion-correcting codes and dominant vectorsJul 05 2016In this paper we describe all pairs of binary vectors $({\bf u}, {\bf v})$ such that the set of vectors obtained by $t$ deletions in ${\bf v}$ is a subset of the set of vectors obtained by $t$ deletions in ${\bf u}$ for $t=1,2$. Such pairs play an important ... More

Intrinsic Chern-Connes Characters for Crossed Products by $\mathbb Z^d$Jan 14 2015Jan 19 2015We present a natural imbedding of the crossed product $\mathcal A \rtimes_\xi \mathbb Z^d$ into the $C^\ast$-algebra of adjointable operators over the standard Hilbert $\mathcal A$-module $\mathcal H_{\mathcal A}$. By replacing the representations on ... More

Cluster expansion and the boxdot conjectureAug 05 2013The boxdot conjecture asserts that every normal modal logic that faithfully interprets T by the well-known boxdot translation is in fact included in T. We confirm that the conjecture is true. More generally, we present a simple semantic condition on modal ... More

Rules with parameters in modal logic IMay 21 2013Apr 03 2015We study admissibility of inference rules and unification with parameters in transitive modal logics (extensions of K4), in particular we generalize various results on parameter-free admissibility and unification to the setting with parameters. Specifically, ... More

Quantum transport in disordered systems under magnetic fields: A study based on operator algebrasApr 29 2012Sep 19 2012The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. \cite{BELLISSARD:1994xj,Schulz-Baldes:1998vm,Schulz-Baldes:1998oq}. This formula was derived directly in the thermodynamic ... More

Root finding with threshold circuitsDec 16 2011Oct 23 2012We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials---given by a list of coefficients in binary---can be computed to a given accuracy by a uniform TC^0 algorithm (a uniform family of constant-depth ... More

Blending margins: The modal logic K has nullary unification typeAug 31 2011Oct 11 2013We investigate properties of the formula $p \to \Box p$ in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins $\phi \to \Box\phi / \phi, \neg\phi$, and as a consequence, we obtain various negative results ... More

Disordered Topological Insulators: A Non-Commutative Geometry PerspectiveOct 04 2010Dec 22 2010This review deals with strongly disordered topological insulators and covers some recent applications of a well established analytic theory based on the methods of Non-Commutative Geometry (NCG) and developed for the Integer Quantum Hall-Effect. Our main ... More

LXG Compiler - Design and ImplementationJan 07 2010LXG is a simple Pascal-like language. It is a functional programming language developed for studying compiler design and implementation. The language supports procedure and variable declarations, but no classes. This paper reports the design and implementation ... More

Enterprise Multi-Branch Database Synchronization with MSMQDec 11 2009When we talk about databases there have always been problems concerning data synchronization. The latter is a technique for maintaining consistency among different copies of data (often called replicas). In general, there is no universal solution to this ... More

Symmetry breaking in self-consistent models: Lessons from an exactly solvable many-fermion modelNov 11 2009This work presents a many-fermion Hamiltonian with the following properties: 1) is exactly solvable, 2) has a second order insulator-metal quantum phase transition, 3) has a well defined mean field approximation and 4) its mean-field ground state displays ... More

Robustness of the Spin-Chern numberApr 13 2009Aug 19 2009The Spin-Chern ($C_s$) was originally introduced on finite samples by imposing spin boundary conditions at the edges. This definition lead to confusing and contradictory statements. On one hand the original paper by Sheng and collaborators revealed robust ... More

Image and Transfer FunctionsMay 12 2009We describe three transfer functors P, P', P" of an inverse exact category which arise from three transfer functions. We concentrate on some of the basic results which emerge from the theory of projections in inverse exact categories.

Rotating states for trapped bosons in an optical latticeSep 12 2008Rotational states for trapped bosons in an optical lattice are studied in the framework of the Hubbard model. Critical frequencies are calculated and the main parameter regimes are identified. Transitions are observed from edge superfluids to vortex lattices ... More

Topological quantization of ensemble averagesMar 22 2008Oct 04 2008We define the current of a quantum observable and, under well defined conditions, we connect its ensemble average to the index of a Fredholm operator. The present work builds on a formalism developed by Kellendonk and Schulz-Baldes \cite{Kellendonk:2004p597} ... More

A note on the substructural hierarchyJul 02 2015Oct 19 2015We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the $\mathcal N_3$ level of the substructural hierarchy.

Fat Triangulations and Differential GeometryAug 17 2011We study the differential geometric consequences of our previous result on the existence of fat triangulations, in conjunction with a result of Cheeger, M\"{u}ller and Schrader, regarding the convergence of Lipschitz-Killing curvatures of piecewise-flat ... More

Rules with parameters in modal logic IIMay 30 2019We analyze the computational complexity of admissibility and unifiability with parameters in transitive modal logics. The class of cluster-extensible (clx) logics was introduced in the first part of this series of papers. We completely classify the complexity ... More

On a construction of Burago and ZalgallerSep 29 2010The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of $PL$ isometric embeddings of $PL$ compact surfaces into $\mathbb{R}^3$. We conclude that their proof does not admit a direct extension to higher dimensions. ... More

Curvature based triangulation of metric measure spacesJan 29 2010We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower ... More

The Data Singular and the Data Isotropic Loci for Affine ConesJul 10 2015The generic number of critical points of the Euclidean distance function from a data point to a variety is called the Euclidean distance degree. The two special loci of the data points where the number of critical points is smaller then the ED degree ... More

On the properties of the combinatorial Ricci flow for surfacesApr 11 2011Jun 07 2011We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for the combinatorial ... More

Metric Ricci curvature for $PL$ manifoldsMar 07 2012We introduce a metric notion of Ricci curvature for $PL$ manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers Theorem, for surfaces as well as for a large class of higher dimensional manifolds.

M-theory and N=2 StringsOct 15 1997N=2 heterotic strings may provide a window into the physics of M-theory radically different than that found via the other supersymmetric string theories. In addition to their supersymmetric structure, these strings carry a four-dimensional self-dual structure, ... More

Scalar Gravitational Waves in the Effective Theory of GravityJun 29 2016As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective ... More

Functional Integration Over GeometriesFeb 17 1995The geometric construction of the functional integral over coset spaces ${\cal M}/{\cal G}$ is reviewed. The inner product on the cotangent space of infinitesimal deformations of $\cal M$ defines an invariant distance and volume form, or functional integration ... More

The homology of Heisenberg Lie algebras over fields of characteristic twoDec 05 2003The generating function of the Betti numbers of the Heisenberg Lie algebra over a field of characteristic 2 is calculated using discrete Morse theory.

Note on a Theorem of MunkresMar 02 2004Mar 14 2004We prove that given a $\mathcal{C^\infty}$ Riemannian manifold with boundary, any fat triangulation of the boundary can be extended to the whole manifold. We also show that this result holds extends to $\mathcal{C}^1$ manifolds, and that in dimensions ... More

Energy Conservation and Pomeron Loops in High Energy EvolutionOct 04 2006Oct 31 2006We present a formalism which modifies the Mueller Dipole Model such that it incorporates energy-momentum conservation and also important colour suppressed effects. We implement our formalism in a Monte Carlo simulation and compare the results to inclusive ... More

Probing the Standard Model via rare pion and muon decaysJun 12 2006The PIBETA collaboration has used a non-magnetic pure CsI calorimeter operating at the Paul Scherrer Institute to collect the world's largest sample of rare pion and muon decays. We have extracted the absolute pi+ -> pi0 e+ nu decay branching ratio with ... More

Calculation of collective modes for the Bose-Hubbard model with confinementAug 26 2004Aug 30 2004The collective excitations in the Bose-Hubbard model in a trap are studied by means of numerical diagonalization in one dimension. The strength function is calculated for monopole and dipole perturbations, and moments of the strength function are utilized ... More

Computational Many-Body Physics via $\mathcal M_{2^q}$ AlgebraJun 17 2019The many-body Hamiltonians and other fermionic physical observables are expressed in terms of fermionic creation and annihilation operators, which form the algebra of canonical anti-commutation relations (CAR). In this work we use a canonical isomorphism ... More

On the Category of Partial BijectionsMar 05 2009Categories of partial functions have become increasingly important principally because of their applications in theoretical computer science. In this note we prove that the category of partial bijections between sets as an inverse-Baer*-category with ... More

The Trace Anomaly and Dynamical Vacuum Energy in CosmologyJun 17 2010The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical ... More

Non-Commutative Tools for Topological InsulatorsNov 14 2009Dec 15 2009This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in ... More

Generalized Wannier FunctionsNov 09 2007Nov 24 2015We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are exponentially localized ... More

Isometric Embeddings in Imaging and Vision: Facts and FictionApr 29 2010May 11 2010We explore the practicability of Nash's Embedding Theorem in vision and imaging sciences. In particular, we investigate the relevance of a result of Burago and Zalgaller regarding the existence of isometric embeddings of polyhedral surfaces in $\mathbb{R}^3$ ... More

Proof complexity of intuitionistic implicational formulasDec 17 2015Sep 18 2016We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of intuitionistic ... More

Metric Curvatures and their Applications 2: Metric Ricci Curvature and FlowFeb 09 2019In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our previous studies ... More

Generalized Gould-Hopper polynomialsSep 20 2016Classical orthogonal polynomial systems of Jacobi, Hermite, Laguerre and Bessel have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are ... More

Bispectral operators of prime orderJun 18 2002The aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number. More precisely we give a complete list of such bispectral operators. We use systematically the operator approach and in particular - Dixmier ... More

Fermionic Topological Order on TriangulationsJul 23 2019Fermion models belong to the CAR algebra. Following Kitaev's work on toric models, we identify a sub-algebra of CAR, generated by elements associated with the triangles and vertices of a finite triangulation of a surface $M$ of genus $g$. We show that ... More

New Horizons in Gravity: Dark Energy and Condensate StarsJul 25 2011Black holes are an apparently unavoidable prediction of classical General Relativity, at least if matter obeys the strong energy condition rho + 3p > 0. However quantum vacuum fluctuations generally violate this condition, as does the eq. of state of ... More

Integer factoring and modular square rootsJul 22 2012Jul 28 2015Buresh-Oppenheim proved that the NP search problem to find nontrivial factors of integers of a special form belongs to Papadimitriou's class PPA, and is probabilistically reducible to a problem in PPP. In this paper, we use ideas from bounded arithmetic ... More

TMD factorization and the gluon distribution in high energy QCDMar 08 2012Apr 02 2012This paper is a part of a series of works where we in detail examine the concept of Transverse Momentum Dependent (TMD), or k_T, factorization, which is frequently encountered in the literature and is widely used in the phenomenological applications of ... More

On the understanding and use of "unintegrated" parton distributions in small-x QCDAug 04 2011We review and discuss the use of TMD, or "unintegrated", gluon distributions in the domain of small-x physics. The definitions employed, and the hazards of the naive applications of the TMD factorization and the associated gluon distributions are discussed. ... More

Mott transition in anharmonic confinementAug 10 2007Two effects are identified that affect the visibility of the Mott transition in an atomic gas in an optical lattice confined in a power-law potential. The transition can be made more pronounced by increasing the power law, but at the same time, experimental ... More

Dipole and monopole modes in the Bose-Hubbard model in a trapApr 21 2004The lowest-lying collective modes of a trapped Bose gas in an optical lattice are studied in the Bose-Hubbard model. An exact diagonalization of the Hamiltonian is performed in a one-dimensional five-particle system in order to find the lowest few eigenstates. ... More

A Computational Non-Commutative Geometry Program for Disordered Topological InsulatorsNov 29 2016Apr 05 2017It has been some time since non-commutative geometry was proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, Bellissard's approach has been enthusiastically adopted in the relatively ... More

Automorphisms of algebras and Bochner`s property for discrete vector orthogonal polynomialsFeb 13 2016We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our approach lie in ... More

Topological Insulators at Strong DisorderJan 31 2016Topological insulators are newly discovered materials with the defining property that any boundary cut into such crystal supports spectrum which is immune to the Anderson localization. The present paper summarizes our efforts on the rigorous characterization ... More

The Existence of Quasimeromorphic MappingsApr 30 2004We prove that a Kleinian group $G$ acting upon $\mathbb{H}^{n}$ admits a non-constant $G$-automorphic function, even if it has torsion elements, provided that the orders of the elliptic (torsion) elements are uniformly bounded. This is accomplished by ... More

Two-weight commutator estimates: general multi-parameter frameworkJun 26 2019We provide an explicit technical framework for proving very general two-weight commutator estimates in arbitrary parameters. The aim is to both clarify existing literature, which often explicitly focuses on two parameters only, and to extend very recent ... More

Induction rules in bounded arithmeticSep 27 2018We study variants of Buss's theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on $\hat\Pi^b_i$ induction schemes, which were so ... More

The complexity of admissible rules of Łukasiewicz logicAug 31 2011Feb 28 2012We investigate the computational complexity of admissibility of inference rules in infinite-valued {\L}ukasiewicz propositional logic (\L). It was shown in [13] that admissibility in {\L} is checkable in PSPACE. We establish that this result is optimal, ... More

Fermionic Topological Order on TriangulationsJul 23 2019Jul 24 2019Fermionic physical models belong to the CAR algebra. Following Kitaev's work on toric models, we identify a sub-algebra of CAR, generated by elements associated with the triangles and vertices of a finite triangulation of a surface $M$ of genus $g$. We ... More

Resolutions of modules with initially linear syzygiesJun 09 2011Dec 16 2011We introduce the class of modules with initially linear syzygies, which includes ideals with linear quotients, and study their minimal resolutions. Using a contracting homotopy for the resolutions, we see that the minimal resolution of a matroidal monomial ... More

The minimal resolution of a cointerval edge ideal is multiplicativeSep 23 2016We show that the minimal resolution of the quotient of the polynomial algebra over a field by a cointerval edge ideal can be given the structure of a DG-algebra.

Recursive functions and existentially closed structuresOct 26 2017Jul 23 2019The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$ does not interpret ... More

Existence of Weak Solutions for the Incompressible Euler EquationsFeb 17 2011Using a recent result of C. De Lellis and L. Sz\'{e}kelyhidi Jr. we show that, in the case of periodic boundary conditions and for dimension greater or equal 2, there exist infinitely many global weak solutions to the incompressible Euler equations with ... More

The Two-Dimensional Quantum Galilei GroupsApr 09 1998The Poisson structures on two-dimensional Galilei group, classified in the author previous paper are quantized. The dual quantum Galilei Lie algebras are found.

Lie Bialgebra Structures on Twodimensional Galilei Algebra and their Lie-Poisson CounterpartsApr 10 1997All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie-Poisson structures on Galilei group are found.

Geometrical Structures of M-TheoryAug 03 1996N=(2,1) heterotic string theory provides clues about hidden structure in M-theory related to string duality; in effect it geometrizes some aspects of duality. The program whereby one may deduce this hidden structure is outlined, together with the results ... More

Estimating Global Errors in Time SteppingMar 17 2015Apr 13 2016This study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky's procedure; however, the proposed approach ... More