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Approximation of fractals by manifolds and other graph-like spacesFeb 08 2018We define a distance between energy forms on a graph-like metric measure space and on a discrete weighted graph using the concept of quasi-unitary equivalence. We apply this result to metric graphs and graph-like manifolds (e.g. a small neighbourhood ... More

Surrogate cloud fields with measured cloud propertiesJun 09 2003This paper describes two new methods to generate 2D and 3D cloud fields based on 1D and 2D ground based profiler meas-urements. These cloud fields share desired statistical properties with real cloud fields. As they, however, are similar but not the same ... More

Downscaling near-surface atmospheric fields with multi-objective Genetic ProgrammingJul 07 2014The coupling of models for the different components of the Soil-Vegetation-Atmosphere-System is required to investigate component interactions and feedback processes. However, the component models for atmosphere, land-surface and subsurface are usually ... More

The countable Telescope Conjecture for module categoriesJan 25 2008May 16 2008By the Telescope Conjecture for Module Categories, we mean the following claim: "Let R be any ring and (A, B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct limits. Then (A, B) is of finite type." We prove a modification of this ... More

Singular compactness and definability for $Σ$-cotorsion and Gorenstein modulesApr 24 2018May 25 2018We introduce a general version of singular compactness theorem which makes it possible to show that being a $\Sigma$-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed along the way, ... More

Measuring switching processes in financial markets with the Mean-Variance spin glass approachMar 13 2015In this article we use the Mean-Variance Model in order to measure the current market state. In our study we take the approach of detecting the overall alignment of portfolios in the spin picture. The projection to the ground-states enables us to use ... More

A feasible interpolation for random resolutionApr 22 2016Sep 11 2016Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen clauses (modulo ... More

BPS invariants of semi-stable sheaves on rational surfacesSep 22 2011Feb 19 2013BPS invariants are computed, capturing topological invariants of moduli spaces of semi-stable sheaves on rational surfaces. For a suitable stability condition, it is proposed that the generating function of BPS invariants of a Hirzebruch surface takes ... More

BPS invariants of N=4 gauge theory on a surfaceFeb 28 2011Dec 19 2011Generating functions of BPS invariants for N=4 U(r) gauge theory on a Hirzebruch surface with r=2 and 3 are computed. The BPS invariants provide the Betti numbers of moduli spaces of semi-stable sheaves. The generating functions for r=2 are expressed ... More

Resonant Hypergeometric Systems and Mirror SymmetryNov 03 1997The Gamma-series of Gel'fand-Kapranov-Zelevinsky are adapted so that they give solutions for certain resonant systems of GKZ hypergeometric differential equations. For this some complex parameters in the Gamma-series are replaced by nilpotent elements ... More

Exact Simulation of the 3/2 ModelMay 17 2011May 18 2011This paper discusses the exact simulation of the stock price process underlying the 3/2 model. Using a result derived by Craddock and Lennox using Lie Symmetry Analysis, we adapt the Broadie-Kaya algorithm for the simulation of affine processes to the ... More

Topologies induced by group actionsDec 01 2014We introduce some canonical topologies induced by actions of topological groups on groups and rings. For $H$ being a group [or a ring] and $G$ a topological group acting on $H$ as automorphisms, we describe the finest group [ring] topology on $H$ under ... More

New examples of small Polish structuresJun 23 2012We answer some questions from a paper of Krupi\'nski by giving suitable examples of small Polish structures. First, we present a class of small Polish group structures without generic elements. Next, we construct a first example of a small non-zero-dimensional ... More

Morse Homology for the Yang-Mills Gradient FlowMar 04 2011Oct 26 2015We use the Yang-Mills gradient flow on the space of connections over a closed Riemann surface to construct a Morse-Bott chain complex. The chain groups are generated by Yang-Mills connections. The boundary operator is defined by counting the elements ... More

Reducible Quantum Electrodynamics. I. The Quantum Dimension of the Electromagnetic FieldMay 30 2015In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the Canonical Commutation ... More

Generalized thermostatistics and mean-field theoryNov 20 2002Sep 30 2003The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized thermostatistics. ... More

Generalised thermostatistics using hyperensemblesSep 03 2007The hyperensembles, introduced by Crooks in a context of non-equilibrium statistical physics, are considered here as a tool for systems in equilibrium. Simple examples like the ideal gas, the mean-field model, and the Ising interaction on small square ... More

Rigorous results in non-extensive thermodynamicsAug 25 1999This paper studies quantum systems with a finite number of degrees of freedom in the context of non-extensive thermodynamics. A trial density matrix, obtained by heuristic methods, is proved to be the equilibrium density matrix. If the entropic parameter ... More

Granular Collapse as a Percolation TransitionMay 18 1999Sep 17 1999Inelastic collapse is found in a two-dimensional system of inelastic hard disks confined between two walls which act as an energy source. As the coefficient of restitution is lowered, there is a transition between a state containing small collapsed clusters ... More

On Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron Systems: A New Approach Based on Wick's TheoremJul 25 1994A new perturbational approach to spectral and thermal properties of strongly correlated electron systems is presented: The Anderson model is reexamined for $U\to\infty$\,, and it is shown that an expansion of Green's functions with respect to the hybridization ... More

Self-Consistent Strong-Coupling-Perturbation Theory for the Anderson Model, Based on Wicks TheoremAug 12 1996A strong-coupling-perturbation theory around the Atomic Limit of the Anderson model with large $U$ for a localized $f$-orbital coupled to a conduction-electron band is presented. Although an auxiliary-particle representation is {\em not} used, application ... More

Symmetry Tests within the Standard Model and Beyond from Nuclear Muon CaptureSep 17 1998Precision measurements in nuclear muon capture on the proton and $^3$He allow for tests of the Standard Model for the strong and electroweak interactions, complementary to those achieved in high energy experiments. The present situation and future prospects ... More

Strangeness and Quark--Gluon PlasmaDec 21 2011I review the foundational motivation which led us to the ultra relativistic heavy ion collision research at SPS, RHIC and now LHC: the quantum vacuum structure; the deconfined nature of quark-gluon plasma (QGP) phase filling the Universe for the first ... More

Massless particles on supergroups and AdS3 x S3 supergravityFeb 01 2011Jun 27 2011Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the ... More

Models for ModulesFeb 09 2012Sep 14 2012We recall the structure of the indecomposable sl(2) modules in the Bernstein-Gelfand-Gelfand category O. We show that all these modules can arise as quantized phase spaces of physical models. In particular, we demonstrate in a path integral discretization ... More

A note on causality in the bulk and stability on the boundaryAug 06 2003Oct 06 2003By carefully analyzing the radial part of the wave-equation for a scalar field in AdS, we show that for a particular range of boundary conditions on the scalar field, the radial spectrum contains a bound state. Using the AdS/CFT correspondence, we interpret ... More

Exploration PotentialSep 16 2016Sep 28 2016We introduce exploration potential, a quantity for that measures how much a reinforcement learning agent has explored its environment class. In contrast to information gain, exploration potential takes the problem's reward structure into account. This ... More

Recent Developments in Superstring PhenomenologyMay 20 1992Recent developments in superstring phenomenology are summarized on a non-technical level. (Talk presented at the XXVIIth Rencontre de Moriond on Electroweak Interactions and Unified Theories.)

Differential Equations in Special Kahler GeometryAug 21 1992Sep 09 1992The structure of differential equations as they appear in special \K\ geometry of $N=2$ supergravity and $(2,2)$ vacua of the heterotic string is summarized. Their use for computing couplings in the low energy effective Lagrangians of string compactifications ... More

Rescaling limits of complex rational mapsNov 14 2012We discuss rescaling limits for sequences of complex rational maps in one variable which approach infinity in parameter space.It is shown that any given sequence of maps of degree $d \ge 2$ has at most $2d-2$ dynamically distinct rescaling limits which ... More

Frobenius Manifolds from Yang-Mills InstantonsOct 29 1997We present an elementary self-contained account of semisimple Frobenius manifolds in three dimensions, and exhibit a new family of explicit examples. These examples are constructed from Yang-Mills instantons with a certain symmetry.

Spin gauge symmetry in the action principle for classical relativistic particlesJan 20 2015We suggest that the physically irrelevant choice of a representative worldline of a relativistic spinning particle should correspond to a gauge symmetry in an action approach. Using a canonical formalism in special relativity, we identify a (first-class) ... More

How to See the Chiral Structure of QCD Vacuum in Low Energy $π-π$ ScatteringOct 17 1995Precise measurement of the $\pi\pi$-phase shift $\delta^0_0(E)$ at very low energies would provide, for the first time, the experimental evidence in favour of or against the existence of a large quark condensate in the QCD vacuum, which is standardly ... More

Jacob's ladders and properties of complete additivity and complete multiplicativity in the set of reverse iterated integrals (energies)Sep 02 2014New class of integral identities concerning constraints on behavior of the Riemann's zeta function on the critical line is introduced in this paper. Namely, we have obtained new kind of $\sigma$-additivity and $\sigma$-multiplicativity in the class of ... More

Jacob's ladders, heterogeneous quadrature formulae, big asymmetry and related formulae for the Riemann zeta-functionJan 13 2014In this paper we obtain as our main result new class of formulae expressing correlation integrals of the third-order in $Z$ on disconnected sets $\mathring{G}_1(x),\mathring{G}_2(y)$ by means of an autocorrelative sum of the second order in $Z$. Moreover, ... More

New consequences of the Riemann-Siegel formula and a law of asymptotic equality of signum-areas of $Z(t)$ functionDec 17 2013In this paper we obtain the first mean-value theorems for the function $Z(t)$ on some disconnected sets. Next, we obtain a geometric law that controls chaotic behavior of the graph of the function $Z(t)$. This paper is the English version of the papers ... More

Jacob's ladders, their iterations and the new class of integrals connected with parts of the Hardy-Littlewood integral of the function $|ζ(1/2+it)|^2$Sep 21 2012In this paper we introduce the iterations of the Jacob's ladder and the new type of integral containing certain product of the factors $|\zeta|^2$ corresponding to the components of some disconnected set of the critical line. Next, we obtain an asymptotic ... More

Jacob's ladders and certain asymptotic multiplicative formula for the function $|\zf|^2$Jan 16 2012In this paper it is proved that a mean-value of the product of some factors $|\zeta|^2$ is asymptotically equal to the product of the mean-values of $\zeta|^2$, and this holds true for every fixed number of the factors.

On the order of the Titchmarsh's sum in the theory of the Riemann zeta-function and on the biquadratic effect in the information theoryDec 27 2011We obtain in this paper the solution of the classical problem on the order of the Titchmarsh's sum (1934). Simultaneously, we obtain a connection of this problem and the Kotelnikoff-Whittaker-Nyquist's theorem from the information theory.

The validity of the analog of the Riemann hypothesis for some parts of $ζ(s)$ and the new formula for $π(x)$Sep 05 2011An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the solutions of the ... More

Jacob's ladders and the multiplicative asymptotic formula for short and microscopic parts of the Hardy-Littlewood integralJul 02 2009The elementary geometric properties of Jacob's ladders lead to a class of new asymptotic formulae for short and microscopic parts of the Hardy-Littlewood integral. This class of asymptotic formulae cannot be obtained by methods of Balasubramanian, Heath-Brown ... More

On some properties of Riemann zeta function on critical lineOct 04 2007The aim of this paper is to show further results following those published in [5], and to relate the Riemann zeta function to the relativistic cosmology.

Jacob's ladders and multiplicative algebra of reversely iterated integrals (energies) on the critical lineJun 13 2014Certain completely logarithmic formula for a set of reversely iterated integrals (energies) is proved in this paper. Namely, in this case we have that integral powers of $\ln T$ are contained on input as well as on output of corresponding integrals (energies). ... More

Riemann hypothesis and the arc length of the Riemann $Z(t)$-curveApr 07 2014On Riemann hypothesis it is proved in this paper that the arc length of the Riemann $Z$-curve is asymptotically equal to the double sum of local maxima of the function $Z(t)$ on corresponding segment. This paper is English remake of our paper \cite{9}, ... More

Jacob's ladders and some generalizations of certain Ramachandra's inequalityAug 01 2013In this paper we obtain some essential generalizations of certain Ramachandra's inequality, i. e. we obtain new lower estimates for the energies of some complicated signals generated by the Riemann zeta-function on the critical line.

Jacob's ladders, conjugate integrals, external mean-values and other properties of a multiply $π(T)$-autocorrelation of the function $|\zf|^2$Feb 15 2013Feb 18 2013In this paper we obtain a new class of transformation formulae (without an explicit presence of a derivative) for the integrals containing products of factors $|\zf|^2$ with respect to two components of a disconnected set on the critical line.

Jacob's ladders and the $\tilde{Z}^2$-transformation of the orthogonal system of trigonometric functionsJul 01 2010Oct 29 2010It is shown in this paper that there is a continuum set of orthogonal systems relative to the weight function $\tilde{Z}^2(t)$. The corresponding integrals cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.

Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integralJun 03 2009Feb 04 2010The elementary geometric properties of the Jacob's ladders \cite{7} lead to a class of new formulae for short parts of the Hardy-Littlewood integral. This class of formulae cannot be obtained by methods of Balasubramanian, Heath-Brown and Ivic.

Jacob's ladders and the almost exact asymptotic representation of the Hardy-Littlewood integralJan 26 2009In this paper we introduce a nonlinear integral equation such that the system of global solution to this equation represents a class of a very narrow beam at $T\to\infty$ (an analogue to the laser beam) and this sheaf of solutions leads to an almost-exact ... More

Steady-State Flow-Force Compensation in a Hydraulic Spool ValveDec 04 2013A high-speed jet flowing inside of a partially-open hydraulic valve is accompanied by a reaction force, also referred to as flow force. The nature of this force has remained a mystery despite an extensive research effort spanning many decades. The momentum ... More

Construction of operator product expansion coefficients via consistency conditionsJun 30 2009In this thesis an iterative scheme for the construction of operator product expansion (OPE) coefficients is applied to determine low order coefficients in perturbation theory for a specific toy model. We use the approach to quantum field theory proposed ... More

Convergence to consensus in multiagent systems and the lengths of inter-communication intervalsJan 14 2011Apr 20 2011A theorem on (partial) convergence to consensus of multiagent systems is presented. It is proven with tools studying the convergence properties of products of row stochastic matrices with positive diagonals which are infinite to the left. Thus, it can ... More

Cold Electroweak BaryogenesisSep 01 2004We present arguments that the CKM CP-violation in the standard model may be sufficient for the generation of the baryon asymmetry, if the electroweak transition in the early universe was of the cold, tachyonic, type after electroweak-scale inflation. ... More

Numerical study of plasmon properties in the SU(2)-Higgs modelAug 29 1997We discuss an explorative computation of real time autocorrelation functions, in the classical approximation. The results for the `plasmon' frequencies and damping rates appear compatible with the divergencies expected from perturbation theory.

The Evolution of GalaxiesAug 07 2007The evolution of galaxies results from a combination of internal and external processes. The star formation is an internal process transforming cold and dense cores of molecular clouds to stars. It may be triggered internally by expanding shells, or externally, ... More

Galaxy Collisions, Gas Stripping and Star Formation in the Evolution of GalaxiesDec 23 2004A review of gravitational and hydrodynamical processes during formation of clusters and evolution of galaxies is given. Early, at the advent of N-body computer simulations, the importance of tidal fields in galaxy encounters has been recognized. Orbits ... More

Calculation of QCD loops using tree-level matrix elementsMay 17 2010The possibility of treating colour in one-loop amplitude calculations alike the other quantum numbers is briefly discussed for semi-numerical algorithms based on generalized unitarity and parametric integration techniques. Numerical results are presented ... More

CDT as a scaling limit of matrix modelsMay 09 2011It is shown that generalized CDT, the two-dimensional theory of quantum gravity, constructed as a scaling limit from so-called causal dynamical triangulations, can be obtained from a cubic matrix model. It involves taking a new scaling limit of matrix ... More

An analytic method for bounding $ψ(x)$Nov 06 2015In this paper we present an analytic altorithm which calculates almost sharp bounds for the normalized error term $(t-\psi(t))/\sqrt{t}$ for $t\leq x$ in expected run time $O(x^{1/2+\varepsilon})$ for every $\varepsilon>0$. The method has been implemented ... More

Cortical composition hierarchy driven by spine proportion economical maximization or wire volume minimizationOct 28 2015The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e., axons and dendrites ... More

SUSY with R-symmetry: confronting EW precision observables and LHC constraintsOct 22 2015After motivation and short presentation of the minimal supersymmetric model with R-symmetry (MRSSM), we address the question of accomodating the measured Higgs boson mass in accordance with electroweak precision observables and LHC constraints.

Reducible Quantum Electrodynamics. II. The charged states of the vacuumOct 09 2015May 28 2016An explicit construction is given of field operators satisfying the free Dirac equation. The quantum expectation of these field operators forms a spinor which satisfies the original Dirac equation. The current operators are defined as pair correlation ... More

Homogeneous rank one perturbationsNov 11 2016A holomorphic family of closed operators with a rank one perturbation given by the function $x^{\frac{m}{2}}$ is studied. The operators can be used in a toy model of renormalization group.

Contour curves and isophotes on rational ruled surfacesSep 26 2016The ruled surfaces, i.e., surfaces generated by one parametric set of lines, are widely used in the~field of applied geometry. An~isophote on a surface is a curve consisting of surface points whose normals form a constant angle with some fixed vector. ... More

A feasible interpolation for random resolutionApr 22 2016Oct 19 2016Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen clauses (modulo ... More

X-rays from magnetic intermediate mass Ap/Bp starsJan 19 2016The X-ray emission of magnetic intermediate mass Ap/Bp stars is reviewed and put into context of intrinsic as well as extrinsic hypotheses for its origin. New X-ray observations of Ap/Bp stars are presented and combined with an updated analysis of the ... More

Jacob's ladders, interactions between $ζ$-oscillating systems and $ζ$-analogue of an elementary trigonometric identitySep 29 2016In our previous papers, we have introduced within the theory of the Riemann zeta function the following notions: Jacob's ladders, oscillating systems, $\zeta$-factorization, metamorphoses, \dots In this paper we obtain $\zeta$-analogue of an elementary ... More

Exploring Dirac neutralinos and EW adjoint scalars of N=1/N=2 hybrid SUSY at collidersDec 04 2010Properties of Dirac neutralinos and the corresponding EW scalar gauge bosons, as predicted by the N=1/N=2 hybrid supersymmetric model, and prospects for their discovery at colliders are discussed.

SUSY StudiesAug 15 2005Aug 21 2005This report summarizes the progress in SUSY studies performed since the last International Linear Collider Workshop in Paris (LCWS04).

Slepton Flavour Violation at CollidersJul 03 2002Jul 12 2002In supersymmetric extensions of the Standard Model, the lepton flavour violation (LFV) is closely related to the structure of slepton masses and mixing. Allowing for the most general flavour structure of the slepton sector, consistent with the experimental ... More

Reflection Scan: an Off-Path Attack on TCPJan 10 2012Jan 24 2012The paper demonstrates how traffic load of a shared packet queue can be exploited as a side channel through which protected information leaks to an off-path attacker. The attacker sends to a victim a sequence of identical spoofed segments. The victim ... More

Approximations and Mittag-Leffler conditions --- the toolsDec 04 2016Mittag-Leffler modules occur naturally in algebra, algebraic geometry, and model theory, [18], [12], [17]. If $R$ is a non-right perfect ring, then it is known that in contrast with the classes of all projective and flat modules, the class of all flat ... More

Representations and isomorphism identities for infinitely divisible processesJul 26 2016Jul 27 2016We propose isomorphism type identities for nonlinear functionals of general infinitely divisible processes. Such identities can be viewed as an analogy of the Cameron-Martin formula for Poissonian infinitely divisible processes but with random translations. ... More

Statistical Issues in Astrophysical Searches for Particle Dark MatterJul 24 2014Oct 14 2014In this review statistical issues appearing in astrophysical searches for particle dark matter, i.e. indirect detection (dark matter annihilating into standard model particles) or direct detection (dark matter particles scattering in deep underground ... More

GRVI Phalanx: A Massively Parallel RISC-V FPGA Accelerator AcceleratorJun 03 2016GRVI is an FPGA-efficient RISC-V RV32I soft processor. Phalanx is a parallel processor and accelerator array framework. Groups of processors and accelerators form shared memory clusters. Clusters are interconnected with each other and with extreme bandwidth ... More

On the computational complexity of finding hard tautologiesDec 08 2012Jul 18 2013It is well-known (cf. K.-Pudl\'ak 1989) that a polynomial time algorithm finding tautologies hard for a propositional proof system $P$ exists iff $P$ is not optimal. Such an algorithm takes $1^{(k)}$ and outputs a tautology $\tau_k$ of size at least $k$ ... More

A feasible interpolation for random resolutionApr 22 2016Feb 01 2017Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is a sound propositional proof system that extends the resolution proof system by the possibility to augment any set of initial clauses by a set of randomly chosen clauses (modulo ... More

Billiards and the Five Distance Theorem IIJul 28 2012We consider a billiard table rectangle. If a billiard ball is sent out from position F(1) at the angle of $\pi/4$, then the ball will rebound against the sides of the rectangle consecutively in points $F(2),F(3),...$. Let $n\geq5$ and $\Phi= \{F(j): 1\leq ... More

The Bousso entropy bound in selfgravitating gas of massless particlesFeb 20 2007Jul 12 2008The Bousso entropy bound is investigated in a static spherically symmetric spacetime filled with an ideal gas of massless bosons or fermions. Especially lightsheets generated by spheres are considered. Statistical description of the gas is given. Conditions ... More

An explicit Skorokhod embedding for functionals of Markovian excursionsSep 23 2005We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of Markovian excursions. Our setting allows to solve the Skorokhod embedding problem, in particular, for diffusions and their ... More

A poset classifying non-commutative term ordersJan 10 2002We study a certain poset on the free monoid on a countable alphabet. This poset is determined by the fact that its total extensions are precisely the standard term orders. We also investigate the poset classifying degree-compatible standard term orders, ... More

Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functionsNov 13 2002We call a set of positive integers closed under taking unitary divisors a unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical function on such a set corresponds to a function on the simplicial complex with ... More

The Hitchin fibration under degenerations to noded Riemann surfacesSep 16 2016In this note we study some analytic properties of the linearized self-duality equations on a family of smooth Riemann surfaces $\Sigma_R$ converging for $R\searrow0$ to a surface $\Sigma_0$ with a finite number of nodes. It is shown that the linearization ... More

Estimating $π(x)$ and related functions under partial RH assumptionsOct 26 2014Nov 09 2015The aim of this paper is to give a direct interpretation of the validity of the Riemann hypothesis up to a certain height $T$ in terms of the prime-counting function $\pi(x)$. This is done by proving the well-known explicit Schoenfeld bound on the RH ... More

Relative entropy in multi-phase models of 1d elastodynamics: Convergence of a non-local to a local modelMay 09 2014In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The arguments are ... More

Hwang-Mok rigidity of cominuscule homogeneous varieties in positive characteristicMay 23 2013Jun-Muk Hwang and Ngaiming Mok have proved the rigidity of irreducible Hermitian symmetric spaces of compact type under Kaehler degeneration. I adapt their argument to the algebraic setting in positive characteristic, where cominuscule homogeneous varieties ... More

Stably Newton non-degenerate singularitiesJun 02 2014Jan 28 2015We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. The answer is negative. The easiest example can be given in characteristic $p$: the function $x^p$ is not stably equivalent ... More

Modularity, Atomicity and States in Archimedean Lattice Effect AlgebrasJan 08 2010Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there exists an $(o)$-continuous ... More

Homomorphisms and Structural Properties of Relational SystemsOct 24 2007Two main topics are considered: The characterisation of finite homomorphism dualities for relational structures, and the splitting property of maximal antichains in the homomorphism order.

The ring of arithmetical functions with unitary convolution: Divisorial and topological propertiesJan 10 2002We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical functions with ... More

Uniform measures and convolution on topological groupsAug 06 2006May 14 2010Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on an arbitrary ... More

Coherent ultrafilters and nonhomogeneityApr 14 2014We introduce the notion of a coherent $P$-ultrafilter on a complete ccc Boolean algebra, strenghtening the notion of a $P$-point on $\omega$, and show that these ultrafilters exist generically under ${\mathfrak c} = {\mathfrak d}$. This improves the known ... More

The sum of two measurable functionsDec 22 2005The paper describes two Borel-measurable functions from a measure space into a locally convex space such that the image measure for each function is Radon but their sum is not Borel-measurable.

Degenerations of elliptic curves and cusp singularitiesDec 21 1995We give more or less explicit equations for all two-dimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein's equations for universal curves with level n structure. The main technical result is a description ... More

Non-embeddable 1-convex manifoldsSep 27 2012Nov 11 2013We show that every small resolution of a three-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve ... More

Non-classical correlations in reducible Quantum ElectrodynamicsDec 26 2018The question is discussed whether the momentum of a photon has a quantum uncertainty or whether it is a classical quantity. The latter assumption is the main characteristic of reducible Quantum Electrodynamics (rQED). Recent experiments in Quantum Optics ... More

Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approachMar 12 2019Apr 15 2019Recent theoretical and experimental studies have shown significance of the phenomenon of quantum information scrambling (i.e. a spread of quantum information over a systems degrees of freedom) for problems encountered in high-energy physics, quantum information, ... More

Partial correlation hypersurfaces in Gaussian graphical modelsJun 01 2018Sep 21 2018We derive a combinatorial sufficient condition for a partial correlation hypersurface in the parameter space of a directed Gaussian graphical model to be nonsingular, and speculate on whether this condition can be used in algorithms for learning the graph. ... More

Tree modules and limits of the approximation theoryJan 09 2018In this expository paper, we present a construction of tree modules and combine it with (infinite dimensional) tilting theory and relative Mittag-Leffler conditions in order to explore limits of the approximation theory of modules. We also present a recent ... More

Roots of Markoff quadratic forms as strongly badly approximable numbersJun 09 2011For a real number $x$, $\| x\| = \min \{|x-p|: p\in Z\}$ is the distance of $x$ to the nearest integer. We say that two real numbers $\theta$, $\theta'$ are $\pm$ equivalent if their sum or difference is an integer. Let $\theta$ be irrational and put ... More