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Results for "Jan Frenzel"

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Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More
A gradient system with a wiggly energy and relaxed EDP-convergenceJan 13 2018If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic effects. We introduce a notion of evolutionary Gamma-convergence that relates the microscopic energy ... More
Unusual composition dependence of transformation temperatures in Ti-Ta-X shape memory alloysApr 12 2018Ti-Ta-X (X = Al, Sn, Zr) compounds are emerging candidates as high-temperature shape memory alloys (HTSMAs). The stability of the one-way shape memory effect (1WE), the exploitable pseudoelastic (PE) strain intervals as well as the transformation temperature ... More
Atoms and Photons - Their Interaction DynamicsDec 18 2012The Jaynes-Cummings model (JCM) describes the interaction of a two-level atom with a single quantised field mode in an optical cavity. In this BSc project we derive the basic Rabi model Hamiltonian and show how it leads to the JCM Hamiltonian. The results ... More
Is the P300 Speller Independent?Jun 17 2010The P300 speller is being considered as an independent brain-computer interface. That means it measures the user's intent, and does not require the user to move any muscles. In particular it should not require eye fixation of the desired character. However, ... More
Coarse-grained hidden entropy production in partially inaccessible quantum jump trajectoriesSep 27 2016We consider an open quantum system for which only a subset of all possible transitions are accessible, while the remaining ones are hidden from direct observation. Using a modification of the notion of quantum jump trajectories we introduce the coarse-grained ... More
Latent Space Cartography: Generalised Metric-Inspired Measures and Measure-Based Transformations for Generative ModelsFeb 06 2019Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous results on Riemannian ... More
Matrix Product State Representation without explicit local Hilbert Space Truncation with Applications to the Sub-Ohmic Spin-Boson ModelNov 14 2012Jul 05 2013We present an alternative to the conventional matrix product state representation, which allows us to avoid the explicit local Hilbert space truncation many numerical methods employ. Utilising chain mappings corresponding to linear and logarithmic discretizations ... 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
Quasi-autonomous quantum thermal machines and quantum to classical energy flowAug 11 2015Nov 16 2015There are both practical and foundational motivations to consider the thermodynamics of quantum systems at small scales. Here we address the issue of autonomous quantum thermal machines that are tailored to achieve some specific thermodynamic primitive, ... 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
Reexamination of Pure Qubit Work ExtractionJun 16 2014Nov 19 2014Many work extraction or information erasure processes in the literature involve the raising and lowering of energy levels via external fields. But even if the actual system is treated quantum mechanically, the field is assumed to be classical and of infinite ... More
Thermodynamic constraints on neural dimensions, firing rates, brain temperature and sizeMay 22 2009There have been suggestions that heat caused by cerebral metabolic activity may constrain mammalian brain evolution, architecture, and function. This article investigates physical limits on brain wiring and corresponding changes in brain temperature that ... More
Scaling of brain metabolism and blood flow in relation to capillary and neural scalingNov 15 2011Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body resting metabolism ... More
Global and regional brain metabolic scaling and its functional consequencesMay 21 2007Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous reflecting complex activity patterns in the mammalian brain. Results: Here, it is found based on empirical ... More
Towards comparative theoretical neuroanatomy of the cerebral cortexApr 01 2004Despite differences in brain sizes and cognitive niches among mammals, their cerebral cortices posses many common features and regularities. These regularities have been a subject of experimental investigation in neuroanatomy for the last 100 years. It ... More
Wick's Theorem and a New Perturbation Theory Around the Atomic Limit of Strongly Correlated Electron SystemsSep 26 1994A new type of perturbation expansion in the mixing $V$ of localized orbitals with a conduction-electron band in the $U\to\infty$ Anderson model is presented. It is built on Feynman diagrams obeying standard rules. The local correlations of the unperturbed ... More
Deformed exponentials and logarithms in generalized thermostatisticsMar 24 2002Criteria are given that kappa-deformed logarithmic and exponential functions should satisfy. With a pair of such functions one can associate another function, called the deduced logarithmic function. It is shown that generalized thermostatistics can be ... More
Dual description of nonextensive ensemblesApr 06 1999Apr 13 1999In the case of a system with an unbounded hamiltonian the entropic index q of non-extensive thermodynamics has an upperbound q_c>1 beyond which the formalism becomes meaningless. The expression 1/(q_c-1) is the dimension of the state space (i.e. the manifold ... More
The q-exponential family in statistical physicsNov 28 2009The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical description of ... More
Generalized thermostatistics based on deformed exponential and logarithmic functionsNov 19 2003The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is shown that this ... More
The Quantum Geometer's Universe: Particles, Interactions and TopologyJul 31 2002With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the three other known ... More
The Cosmological Constant of One-Dimensional Matter Coupled Quantum Gravity is QuantizedFeb 20 2002Coupling any interacting quantum mechanical system to gravity in one dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantized, even though the gravity sector is free of any quantum dynamics, while physical ... More
On the Road Towards the Quantum Geometer's Universe: An Introduction to Four-Dimensional Supersymmetric Quantum Field TheoriesAug 03 2004This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a previous Workshop ... More
The AdS3 central charge in string theorySep 09 2011Oct 05 2011We evaluate the vacuum expectation value of the central charge operator in string theory in an AdS3 vacuum. Our calculation provides a rare non-zero one-point function on a spherical worldsheet. The evaluation involves the regularization both of a worldsheet ... More
Phase diagram of exciton condensate in doped two-band Hubbard modelOct 20 2014Using the dynamical mean-field approximation we investigate formation of excitonic condensate in the two-band Hubbard model in the vicinity of the spin-state transition. With temperature and band filling as the control parameters we realize all symmetry ... More
Synthetic Spectra and Light Curves of Interacting Binaries and Exoplanets with Circumstellar Material: SHELLSPECAug 15 2011Program SHELLSPEC is designed to calculate light-curves, spectra and images of interacting binaries and extrasolar planets immersed in a moving circumstellar environment which is optically thin. It solves simple radiative transfer along the line of sight ... More
Puiseux series polynomial dynamics and iteration of complex cubic polynomialsSep 21 2004We study polynomials with coefficients in a field L as dynamical systems where L is any algebraically closed and complete ultrametric field with dense valuation group and characteristic zero residual field. We give a complete description of the dynamical ... More
Aspects of Spontaneous N=2 -> N=1 Breaking in SupergravityMar 15 2002We discuss some issues related to spontaneous N=2-> N=1 supersymmetry breaking. In particular, we state a set of geometrical conditions which are necessary that such a breaking occurs. Furthermore, we discuss the low energy N=1 effective Lagrangian and ... More
The Darboux-Bianchi-Bäcklund transformation and soliton surfacesMar 21 2013In the first part of the paper we present the dressing method which generates multi-soliton solutions to integrable systems of nonlinear partial differential equations. We compare the approach of Neugebauer with that of Zakharov, Shabat and Mikhailov. ... More
Chiral Dynamics beyond the Standard ModelNov 09 2006The SM Lagrangian without physical scalars is rewritten as the LO of a Low-Energy Effective Theory invariant under a higher non linear symmetry S_{nat} \supset SU(2)_W \times U(1)_Y. Soft breaking of S_{nat} defines a hierarchy of non standard effects ... More
Replica Symmetry Breaking in Renormalization: Application to the Randomly Pinned Planar Flux ArrayMar 03 1995The randomly pinned planar flux line array is supposed to show a phase transition to a vortex glass phase at low temperatures. This transition has been examined by using a mapping onto a 2D XY-model with random an\-iso\-tropy but without vortices and ... More
Spin and quadrupole contributions to the motion of astrophysical binariesDec 10 2014Jul 18 2016Compact objects in general relativity approximately move along geodesics of spacetime. It is shown that the corrections to geodesic motion due to spin (dipole), quadrupole, and higher multipoles can be modeled by an extension of the point mass action. ... More
Non-existence of toroidal cohomogeneity-1 near horizon geometriesAug 03 2010We prove that $D\geq 5$ dimensional stationary, non-static near horizon geometries with (D-3) rotational symmetries subject to the vacuum Einstein equations including a cosmological constant cannot have toroidal horizon topology. In D=4 dimensions the ... More
A stabilization theorem for dynamics of continuous opinionsAug 22 2007A stabilization theorem for processes of opinion dynamics is presented. The theorem is applicable to a wide class of models of continuous opinion dynamics based on averaging (like the models of Hegselmann-Krause and Weisbuch-Deffuant). The analysis detects ... More
Universality in movie rating distributionsJun 13 2008Jul 10 2009In this paper histograms of user ratings for movies (1,...,10) are analysed. The evolving stabilised shapes of histograms follow the rule that all are either double- or triple-peaked. Moreover, at most one peak can be on the central bins 2,...,9 and the ... More
Jacob's ladders, $ζ$-factorization and infinite set of metamorphosis of a multiformJan 30 2015Feb 10 2015In this paper we use Jacob's ladders together with fundamental Hardy-Littlewood formula (1921) to prove the so-called $\zeta$-factorization formula on the critical line. Simultaneously, we obtain a set of control parameters of metamorphosis of a multiform ... More
Jacob's ladders and the nonlocal interaction of the function $|ζ(1/2+it)|$ with the function $\argζ(1/2+it)$ on the distance $\sim(1-c)π(t)$Apr 01 2010Jun 18 2010In this paper we obtain a new-type formula - \emph{a mixed formula} - which connects the functions $|\zeta(1/2+it)|$ and $\arg\zeta(1/2+it)$. This formula cannot be obtained in the classical theory of A. Selberg, and, all the less, in the theories of ... More
Jacob's ladders, new properties of the function $\arg\zf$ and corresponding metamorphosesJun 26 2015The notion of the Jacob's ladders, reversely iterated integrals and the $\zeta$-factorization is used in this paper in order to obtain new results in study of the function $\arg\zf$. Namely, we obtain new formulae for non-local and non-linear interaction ... More
Jacob's ladders and invariant set of constraints for the reversely iterated integrals (energies) in the theory of the Riemann zeta-functionDec 09 2014In this paper we obtain an extension of the set of non-local equalities by adding to it new set of local equalities. Namely, we obtain an invariant set of equalities on the set of reversely iterated integrals (energies). In other words, we obtain a new ... More
Jacob's ladders and laws that control chaotic behavior of the measures of reversely iterated segmentsApr 22 2014The main subject to study in this paper are properties of the sequence of reversely iterated segments. Especially, we will examine properties of chaotic behavior of the sequence of measures of corresponding segments. Our results are not accessible within ... More
Riemann's hypothesis and some infinite set of microscopic universes of the Einstein's type in the early period of the evolution of the UniverseMay 14 2013Jul 28 2013We obtain in this paper, as a consequence of the Riemann hypothesis, certain class of topological deformations of the graph of the function $|\zf|$. These are used to construct an infinite set of microscopic universes (on the Planck's scale) of the Einstein ... More
Jacob's ladders and some nonlinear integral equations connected with the Poisson-Lobachevsky integralJan 14 2011We obtain some new properties of the signal generated by the Riemann zeta-function in this paper. Namely, we show the connection between the function $\zf$ and a nonlinear integral equation related to the Poisson-Lobachevsky integral.
Jacob's ladders and the oscillations of the function $|ζ(1/2+it)|^2$ around its mean-value; law of the almost exact equality of corresponding areasJun 22 2010The oscillations of the function $Z^2(t),\ t\in [0,T]$ around the main part $\sigma(T)$ of its mean-value are studied in this paper. It is proved that an almost equality of the corresponding areas holds true. This result cannot be obtained by methods ... More
Jacob's ladders and the asymptotic formula for short and microscopic parts of the Hardy-Littlewood integral of the function $|ζ(1/2+it)|^4$Jan 22 2010The elementary geometric properties of Jacob's ladders of the second order lead to a class of new asymptotic formulae for short and microscopic parts of the Hardy-Littlewood integral of $|\zeta(1/2+it)|^4$. These formulae cannot be obtained by methods ... More
Jacob's ladders and the asymptotic formula for the integral of the eight order expression $|ζ(1/2+i\vp_2(t))|^4|ζ(1/2+it)|^4$Jan 13 2010Jan 19 2010It is proved in this paper that there is a fine correlation between the values of $|\zeta(1/2+i\vp_2(t))|^4$ and $|\zeta(1/2+it)|^4$ where $\vp_2(t)$ stands for the Jacob's ladder of the second order. This new asymptotic formula cannot be obtained in ... More
Jacob's ladders and the first asymptotic formula for the expression of the fifth order $Z^3[...]\hat{Z}^2(t)$ for the collection of disconnected setsDec 01 2009It is shown in this paper that there is a fine correlation of the fifth order between the values $Z[\phi(t)/2+\rho_1]Z[\phi(t)/2+\rho_2]Z[\phi(t)/2+\rho_3]$ and $\hat{Z}^2(t)$ which correspond to two collections of disconnected sets. This new asymptotic ... More
Jacob's ladders and the first asymptotic formula for the expression of the sixth order $|ζ(1/2+i\varphi(t)/2)|^4|ζ(1/2+it)|^2$Nov 06 2009Jan 12 2010t is proved in this paper that there is a fine correlation between the values of $|\zeta(1/2+i\varphi(t)/2)|^4$ and $|\zeta(1/2+it)|^2$ which correspond to two segments with gigantic distance each from other. This new asymptotic formula cannot be obtained ... More
Automatic segmentation of HeLa cell imagesJan 12 2011In this work, the possibilities for segmentation of cells from their background and each other in digital image were tested, combined and improoved. Lot of images with young, adult and mixture cells were able to prove the quality of described algorithms. ... More
The $C^0$-inextendibility of the Schwarzschild spacetime and the spacelike diameter in Lorentzian GeometryJul 02 2015Apr 25 2016The maximal analytic Schwarzschild spacetime is manifestly inextendible as a Lorentzian manifold with a twice continuously differentiable metric. In this paper, we prove the stronger statement that it is even inextendible as a Lorentzian manifold with ... More
Visual Representation of 3D Language Constructs Specified by Generic DepictionsNov 20 2013Several modeling domains make use of three-dimensional representations, e.g., the "ball-and-stick" models of molecules. Our generator framework DEViL3D supports the design and implementation of visual 3D languages for such modeling purposes. The front-end ... More
Effective CP violation in the Standard ModelJul 14 2004We study the strength of effective CP violation originating from the CKM matrix in the effective action obtained by integrating out the fermions in the Standard Model. Using results obtained by Salcedo for the effective action in a general chiral gauge ... More
A Brief Tutorial on the Ensemble Kalman FilterJan 23 2009The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman filter for ... More
Validity of the Impulse Approximation and Quasielastic (e,e'p) Reactions from NucleiDec 20 2000We assess the combined effect of ground-state correlations, meson-exchange and isobar currents upon the cross sections for quasielastic (e,e'p) reactions from nuclei. Four-momenta in the range 0.1 \leq Q^2 \leq 1 GeV^2 are addressed. We observe that for ... More
History of Solar Magnetic Fields since George Ellery HaleAug 13 2015As my own work on the Sun's magnetic field started exactly 50 years ago at Crimea in the USSR, I have been a participant in the field during nearly half the time span since Hale's discovery in 1908 of magnetic fields in sunspots. The present historical ... More
Soficity for monoids, semigroups, and general dynamical systemsAug 09 2015We examine several definitions of soficity for monoids obtained by generalizing various definitions of sofic groups. They are not all equivalent and include the definition recently introduced by Ceccherini-Silberstein and Coornaert. One of these definitions ... More
Recent progress in the theory of random surfaces and simplicial quantum gravityDec 01 1994Dec 02 1994Some of the recent developments in the theory of random surfaces and simplicial quantum gravity is reviewed. For 2d quantum gravity this includes the failure of Regge calculus, our improved understanding of the $c>1$ regime, some surprises for q-state ... More
A counterexample to the pseudo 2-factor isomorphic graph conjectureDec 10 2014May 27 2015A graph $G$ is pseudo 2-factor isomorphic if the parity of the number of cycles in a 2-factor is the same for all 2-factors of $G$. Abreu et al. conjectured that $K_{3,3}$, the Heawood graph and the Pappus graph are the only essentially 4-edge-connected ... More
Jacob's ladders, $\mathcal{Z}_{ζ,Q^2}$-transformation of real elementary functions and telegraphic signals generated by the power functionsFeb 16 2016In this paper we show that the $\mathcal{Z}_{\zeta,Q^2}$-transformation of every unbounded signal based on increasing power function is a telegraphic signal, i.e. the unit rectangular signal.
Deforming nonnormal isolated surface singularities and constructing 3-folds with $\mathbb{P}^1$ as exceptional setDec 11 2015Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as isolated, non ... More
Jacob's ladders, factorization and metamorphoses as an appendix to the Riemann functional equation for $ζ(s)$ on the critical lineOct 01 2015In this paper we obtain a new set of metamorphoses of the oscillating Q-system by using the Euler's integral. We split the final state of mentioned metamorphoses into three distinct parts: the signal, the noise and finally appropriate error term. We have ... More
The extended states in disordered 1D systems in the presence of the generalized $N$-mer correlationsJul 07 2016Oct 07 2016We have been investigating the problem of the Anderson localization in a disordered one dimensional tight-binding model. The disorder is created by the interaction of mobile particles with other species, immobilized at random positions. We introduce a ... More
Random Matrices and Matrix CompletionSep 26 2016The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited linear information ... More
Solving Reachability Problems with Singular and Indefinite Hessian by Sequential Quadratic ProgrammingNov 03 2016The problem of finding a solution of a dynamical system that originates and terminates in given sets of states is considered. We formulate it as an equality constrained nonlinear programming problem and compare line search and trust-region approaches ... More
Long-lived charged sleptons at the ILC/CLICNov 09 2012Supersymmetric scenarios with a very weakly interacting lightest superpartner (LSP) - like the gravitino or axino - naturally give rise to a long-lived next-to-LSP (NLSP). If the NLSP is a charged slepton it leaves a very distinct signature in a collider ... More
Quantum E(2) groups and Lie bialgebra structuresMar 12 1996Lie bialgebra structures on $e(2)$ are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical $r$-matrix) we solve the cocycle condition, find the Lie-Poisson brackets and obtain quantum group ... More
TOTEM Results on Elastic Scattering and Total Cross-SectionOct 11 2013TOTEM is an LHC experiment dedicated to forward hadronic physics. In this contribution, two main parts of its physics programme - proton-proton elastic scattering and total cross-section - are discussed. The analysis procedures are outlined and their ... More
Searches for Particle Dark Matter with gamma-raysOct 16 2012In this contribution I review the present status and discuss some prospects for indirect detection of dark matter with gamma-rays. Thanks to the Fermi Large Area Telescope, searches in gamma-rays have reached sensitivities that allow to probe the most ... More
Standard Model physics at the LHCMar 28 2018Mar 30 2018In this contribution to the volume "From My Vast Repertoire -- The Legacy of Guido Altarelli" I discuss selected topics of Standard Model (SM) physics at the LHC and their connection to the work of Guido Altarelli. An overarching connection is given by ... More
Operator formalism of quantum mechanicsDec 29 2000This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The mathematical ... More
An example of a Fraïssé class without a Katětov functorApr 01 2016We disprove a conjecture from [W. Kubi\'s, D. Ma\v{s}ulovi\'c, Kat\v{e}tov functors, preprint, http://arxiv.org/abs/1412.1850] by showing the existence of a Fra\"iss\'e class $\mathcal{C}$ which does not admit a Kat\v{e}tov functor. On the other hand, ... More
A Blackbox Polynomial System Solver on Parallel Shared Memory ComputersApr 11 2018Jun 17 2018A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods are applied ... More
Longtime behavior of coupled wave equations for semiconductor lasersAug 09 2013Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial differential ... More
Double polarisation experiments in meson photoproductionSep 22 2016One of the remaining challenges within the standard model is to gain a good understanding of QCD in the non-perturbative regime. A key step towards this aim is baryon spectroscopy, investigating the spectrum and the properties of baryon resonances. To ... More
A geometric construction of panel-regular lattices in buildings of types ~A_2 and ~C_2Aug 19 2009May 04 2010Using Singer polygons, we construct locally finite affine buildings of types ~A_2 and ~C_2 which admit uniform lattices acting regularly on panels. This construction produces very explicit descriptions of these buildings as well as very short presentations ... More
Faith's problem on R-projectivity is undecidableOct 28 2017In \cite{F}, Faith asked for what rings $R$ does the Dual Baer Criterion hold in Mod-$R$, that is, when does $R$-projectivity imply projectivity for all right $R$-modules? Such rings $R$ were called right testing. Sandomierski proved that if $R$ is right ... More
On the Hadamard condition on Robertson-Walker spacetimeSep 04 2006Using construction of adiabatic vacuum states of a free scalar field on Robertson-Walker spacetime, using results of Luders and Roberts we prove that validity of the Hadamard condition implies smoothness of the scale factor.
Computation of Principal A-determinants through Dimer DynamicsJan 23 2009In this note we translate the pictorial description of Gulotta's efficient inverse algorithm (arXiv:0807.3012) into matrix operations, so that it can be implemented on a computer. As an application we point out that this in combination with results from ... More
Generalised Hilbert Numerators IIMar 16 2000We associate to each $r$-multigraded, locally finitely generated ideal in the "large polynomial ring" on countably many indeterminates a power series in $r$ variables; this power series is the limit in the adic topology of the numerators of the rational ... More
The maximality principle revisited: on certain optimal stopping problemsMay 13 2004May 27 2005We investigate the optimal stopping problems involving the supremum of a diffusion. The starting point is the link between works of Peskir and Meilijson, which we describe in a unified manner. The description developped follows mainly the work of Peskir ... More
C*-Multipliers, crossed product algebras, and canonical commutation relationsJul 09 1999Mar 20 2000The notion of a multiplier of a group X is generalized to that of a C*-multiplier by allowing it to have values in an arbitrary C*-algebra A. On the other hand, the notion of the action of X in A is generalized to that of a projective action of X as linear ... More
Vortex invariants and toric manifoldsDec 01 2008We consider the symplectic vortex equations for a linear Hamiltonian torus action. We show that the associated genus zero moduli space itself is homotopic (in the sense of a homotopy of regular G-moduli problems) to a toric manifold with combinatorial ... More
A conjecture on the Poincar{é}-Betti series of modules of differential operators on a generic hyperplane arrangementAug 31 2004Sep 03 2004Holm studied modules of higher order differential operators (generalising derivations) on generic (central) hyperplane arrangements. We use his results to determine the Hilbert series of these modules. We also give a conjecture about the Poincar{\'e}-Betti ... More
Semistable K3-surfaces with icosahedral symmetryJun 15 2001In a Type III degeneration of K3-surfaces the dual graph of the central fibre is a triangulation of the 2-sphere. We realise the tetrahedral, octahedral and especially the icosahedral triangulation in families of K3-surfaces, preferably with the associated ... More
Universal abelian covers of superisolated singularitiesJan 27 2006Jan 30 2008We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo-Velasco, Melle-Hernandez and Nemethi, thereby providing counterexamples to the ... More
Poincare series and zeta function for an irreducible plane curve singularityOct 15 2003The Poincare series of an irreducible plane curve singularity equals the zeta function of its monodromy, by a result of Campillo, Delgado and Gusein-Zade. We derive this fact from a formula of Ebeling and Gusein-Zade relating the Poincare series of a ... More
Existence of piecewise weak solutions of a discrete Cucker-Smale's flocking model with a singular communication weightFeb 18 2013We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight $\psi(s)=s^{-\alpha}, 0<\alpha<1.$ We also discuss the possibility of finite in time alignment of the velocities of ... More
A note on the grid Ramsey problemSep 27 2017The grid Ramsey number $ G(r) $ is the smallest number $ n $ such that every edge-colouring of the grid graph $\Gamma_{n,n} := K_n \times K_n$ with $r$ colours induces a rectangle whose parallel edges receive the same colour. We show $ G(r) \leq r^{\binom{r+1}{2}} ... More
The Ordinary Limit for Varieties over Z[x_1,...,x_r]Dec 04 2002Dec 18 2002We investigate for families of smooth projective varieties over a localized polynomial ring Z[x_1,...,x_r][D^{-1}] the conjugate filtration on De Rham cohomology tensored with Z/NZ. As N tends to infinity this leads to the concept of the ordinary limit, ... More
Octonion-valued forms and the canonical 8-form on Riemannian manifolds with a $Spin(9)$-structureAug 07 2018It is well-known that there is a unique $Spin(9)$-invariant 8-form on the octonionic plane that naturally yields a canonical differential 8-form on any Riemannian manifold with a weak $Spin(9)$-structure. Over the decades, this invariant has been studied ... More
Jacob's ladders and new synergetic formula generating infinite set of $ζ$-cooperative three-parametric invariantsOct 03 2018In this paper we obtain new $\zeta$-synergetic formula namely an exact secondary complete hybrid formula. This one is generated by some set of trigonometric and power functions together with the square of module of the Riemann's zeta-function on the critical ... More
Jacob's ladders and grafting of the complete hybrid formulas into $ζ$-synergetic meta-functional equation for Riemann's zeta-functionSep 14 2018In this paper we prove that there is a grafting of complete hybrid formula on meta-functional equation. This synergetic formula gives the result of a $\zeta$-chemical reaction between different sets of values of Riemann's zeta-function on the critical ... More
Jacob's ladders, crossbreeding, secondary crossbreeding and synergetic phenomena generated by Riemann's zeta-function and some elementary functions on disconnected sets of the critical lineJun 19 2018In this paper we obtain new complete hybrid formula for corresponding class of $\zeta$-factorization formulas. We demonstrate that this formula is the synergetic one. Namely, this one describes the cooperation between some class of elementary functions ... More
Weighted transverse spin asymmetries in 2015 COMPASS Drell-Yan dataDec 20 2018Muon pairs created in the Drell-Yan process of a negative pion beam of 190 GeV/c momentum impinging on a transversely polarised NH$_3$ target were detected with the COMPASS spectrometer at CERN in 2015. In addition to the extraction of the transverse ... More
On convexity and solution concepts in cooperative interval gamesNov 09 2018Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study convexity, core and ... More
On very restricted arithmetic progressions in symmetric sets in finite field modelNov 25 2018We consider a problem motivated by an attempt to generalize Szemer\'edi's theorem in the finite field model: Given a set $S \subseteq \mathbb{Z}_q^n$ containing $|S| = \mu \cdot q^n$ elements, must $S$ contain at least $\delta(q, \mu) \cdot q^n \cdot ... More
Motives from DiffractionNov 19 2005We look at geometrical and arithmetical patterns created from a finite subset of Z^n by diffracting waves and bipartite graphs. We hope that this can make a link between Motives and the Melting Crystals/Dimer models in String Theory.
Almost conformally almost Fedosov structuresOct 16 2017We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free torsion sharing ... More
On the Hard Lefschetz property of stringy Hodge numbersMar 08 2008For projective varieties with a certain class of 'mild' isolated singularities and for projective threefolds with arbitrary Gorenstein canonical singularities, we show that the stringy Hodge numbers satisfy the Hard Lefschetz property. This result fits ... More
Ambitable topological groupsMar 24 2008May 25 2009A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit. For n=0,1,2,..., every locally aleph_n bounded topological group is either ... More