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Spin dynamics of two bosons in an optical lattice site: a role of anharmonicity and anisotropy of the trapping potentialMar 21 2013Jun 17 2013We study a spin dynamics of two magnetic Chromium atoms trapped in a single site of a deep optical lattice in a resonant magnetic field. Dipole-dipole interactions couple spin degrees of freedom of the two particles to their motion in the site. The motion ... More

Classical field records of a quantum system: their internal consistency and accuracyApr 23 2015Nov 25 2015We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas results carry ... More

Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solutionJul 31 2017Number fluctuations in a one-dimensional Bose gas consist of contributions from many smaller independent localized fluctuations, the density grains. We have derived a set of extended integral equations from the Yang-Yang solution for finite temperature ... More

A semiclassical field theory that is freed of the ultraviolet catastropheApr 12 2019A more accurate semiclassical theory for ultracold gases is derived, in which the occupation of high energy modes is dynamically constrained to the Bose-Einstein distribution. This regularized version of the SGPE model preserves the proper nonlinear energy ... More

Tunneling-Induced Restoration of the Degeneracy and the Time-Reversal Symmetry Breaking in Optical LatticesApr 23 2013Nov 19 2013We study the ground-state properties of bosons loaded into the $p$-band of a one dimensional optical lattice. We show that the phase diagram of the system is substantially affected by the anharmonicity of the lattice potential. In particular, for a certain ... More

Correlation evolution in dilute Bose-Einstein condensates after quantum quenchesOct 04 2013Feb 19 2019The universal forms of quantum density and phase correlations after an interaction quench are found for dilute 1d, 2d, and 3d condensates. A Bogoliubov approach in a local density aproximation is used. We obtain compact expressions for the most visible ... More

Multifaceted phase ordering kinetics of an antiferromagnetic spin-1 condensateMay 02 2019We study phase domains coarsening after a quench of a weak magnetic field in a quasi one-dimensional spin-1 antiferromagnetic condensate. The system concurrently realizes two independent models of phase ordering kinetics, namely the binary mixture and ... More

Classical limit of entangled states of two angular momentaNov 26 2018May 13 2019We consider a system of two particles, each with large angular momentum $j$, in the singlet state. The probabilities of finding projections of the angular momenta on selected axes are determined. The generalized Bell inequalities involve these probabilities ... More

Tunable dipolar resonances and Einstein-de Haas effect in a Rb-87 atoms condensateFeb 08 2011We study a spinor condensate of Rb-87 atoms in F = 1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in mF = 1 component we observe a significant transfer of atoms to other, initially empty Zeeman states exclusively due ... More

A plactic algebra action on bosonic particle configurations: The classical caseJan 03 2019We study the plactic algebra and its action on bosonic particle configurations in the classical case. These particle configurations together with the action of the plactic generators can be identified with crystals of the quantum analogue of the symmetric ... More

Conformal mechanicsNov 19 2012Jan 08 2013The SL(2,R) invariant Hamiltonian systems are discussed within the frame- work of the orbit method. It is shown that both dynamics and symmetry trans- formations are globally well-defined on phase space. The flexibility in the choice of time variable ... More

The asymptotic strong Feller property does not imply the e-property for Markov-Feller semigroupsAug 22 2013T. Szarek [Stud. Math. 189 (2008), {\S} 4] have discussed the relationship between two important notions concerning Markov semigroups: the asymptotic strong Feller property and the e-property, asserting that the former property implies the latter one. ... More

Symbiotic Stars in the Magellanic CloudsFeb 24 2004Orbital periods and other parameters of symbiotic binaries in the LMC and SMC are presented and discussed. In particular, the symbiotic stars in the MCs are compared with those in the Milky Way.

A Global Event Description using Particle Flow with the CMS DetectorOct 20 2008The CMS Detector consists of a large volume silicon tracker immersed in a high four Tesla magnetic field, together with a high resolution/granularity electromagnetic calorimeter and a nearly full solid angle coverage hadronic calorimeter. Particle flow ... More

Bivariate natural exponential families with quadratic diagonal of the variance functionApr 20 2015We characterize bivariate natural exponential families having the diagonal of the variance function of the form \[ \textrm{diag} V(m_1,m_2)=\left(Am_1^2+am_1+bm_2+e,Am_2^2+cm_1+dm_2+f\right), \] with $A<0$ and $a,\ldots,f\in\mathbb{R}$. The solution of ... More

Nonlinear realizations and the orbit methodMay 09 2013Aug 12 2013Given a symmetry group one can construct the invariant dynamics using the technique of nonlinear realizations or the orbit method. The relationship between these methods is discussed. Few examples are presented.

One more Turán number and Ramsey number for the loose 3-uniform path of length threeNov 29 2015Let $P$ denote a 3-uniform hypergraph consisting of 7 vertices $a,b,c,d,e,f,g$ and 3 edges $\{a,b,c\}, \{c,d,e\},$ and $\{e,f,g\}$. It is known that the $r$-color Ramsey number for $P$ is $R(P;r)=r+6$ for $r\le 9$. The proof of this result relies on a ... More

Three-dimensional gravity and instability of $\text{AdS}_{3}$Nov 28 2013This is an extended version of my lecture at the LIII Cracow School of Theoretical Physics in Zakopane in which I presented the results of joint work with Piotr Bizo\'n concerning (in)stability of the three-dimensional anti-de Sitter spacetime.

Orbital and stellar parameters of symbiotic starsOct 22 2002This paper reviews current knowledge of symbiotic binaries, with special emphasis on their multifrequency observational characteristics, and basic parameters of the symbiotic system components. We start with a brief presentation of variable phenomena ... More

On the nullification of threshold amplitudesJul 01 2002The nullification of threshold amplitudes is considered within the conventional framework of quantum field theory. The relevant Ward identities for the reduced theory are derived both on path-integral and diagrammatic levels. They are then used to prove ... More

Optical and Near-IR Monitoring of Symbiotic Binary SystemsMar 29 2001Symbiotic stars are long-period interacting binary systems in which an evolved red giant star transfers material to its much hotter compact companion. Such a composition places them among the most variable stars. In addition to periodic variations due ... More

Isometric uniqueness of a complementably universal Banach space for Schauder decompositionsNov 09 2012Jun 10 2013We present an isometric version of the complementably universal Banach space $\mathbb{P}$ with a Schauder decomposition. The space $\mathbb{P}$ is isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to Kadec' complementably universal ... More

On basic curvature identities for almost (para)contact metric manifoldsSep 21 2012In monograph of D. E. Blair "Riemannian geometry of contact and symplectic manifolds" and in the paper of S. Zamkovoy "Canonical connections on paracontact manifolds", the curvature identities respectively for contact and paracontact metric manifold are ... More

Para-CR Structures on almost Paracontact Metric ManifoldsFeb 28 2012Apr 01 2012Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. ... More

Eco-evolutionary "fitness" in 3 dimensions: absolute growth, absolute efficiency, and relative competitivenessJul 03 2014Oct 01 2015Competitions can occur on an absolute scale, to be faster or more efficient, or they can occur on a relative scale, to "beat" one's competitor in a zero-sum game. Ecological models have focused on absolute competitions, in which optima exist. Classic ... More

The Place of Recurrent Novae among the Symbiotic StarsMar 26 2008The observational properties of recurrent novae indicate that they can be divided into two subclasses:systems with a dwarf and a red giant secondary, respectively. The second type -- which includes RS Oph -- bears many similarities to symbiotic stars. ... More

Champagne subregions of the unit discJan 07 2011Jun 20 2011This paper concerns harmonic measure on the domains that arise when infinitely many disjoint closed discs are removed from the unit disc. It investigates which configurations of discs are unavoidable for Brownian motion, and obtains refinements of related ... More

Two component Bose-Hubbard model with higher angular momentum statesApr 13 2011May 09 2012We study a Bose-Hubbard Hamiltonian of ultracold two component gas of spinor Chromium atoms. Dipolar interactions of magnetic moments while tuned resonantly by ultralow magnetic field can lead to spin flipping. Due to approximate axial symmetry of individual ... More

Description of the emotional states of communicating people by mathematical modelJul 30 2015Oct 29 2015The model we study is a generalization of the model considered by Liebovitch et al. (2008) and Rinaldi et al. (2010), and is related to the discrete model of the emotional state of communicating couples described by Gottman et al. (2002). Considered system ... More

Modelling of lung cancer survival data for critical illness insurancesFeb 28 2016We derive a general multiple state model for critical illness insurances. In contrast to the classical model, we take into account that the probability of death for a dread disease sufferer may depend on the duration of the disease, and the payment of ... More

Periodic Longitude-Stationary Non-Drift Emission in Core-Single Radio Pulsar B1946+35Mar 29 2017Radio pulsar PSR B1946+35 is a classical example of a core/cone triple pulsar where the observer's line-of-sight cuts the emission beam centrally. In this paper we perform a detailed single-pulse polarimetric analysis of B1946+35 using sensitive Arecibo ... More

Ebola impact and quarantine in a network modelDec 20 2015Much effort has been directed towards using mathematical models to understand and predict contagious disease, in particular Ebola outbreaks. Classical SIR (susceptible-infected-recovered) compartmental models capture well the dynamics of the outbreak ... More

Refined Turán numbers and Ramsey numbers for the loose 3-uniform path of length threeOct 20 2015Let $P$ denote a 3-uniform hypergraph consisting of 7 vertices $a,b,c,d,e,f,g$ and 3 edges $\{a,b,c\}, \{c,d,e\},$ and $\{e,f,g\}$. It is known that the $r$-color Ramsey number for $P$ is $R(P;r)=r+6$ for $r\le 7$. The proof of this result relies on a ... More

Pulse chirp increasing pulse compression followed by positive resonant radiation in fibersJan 04 2016Pulse self-compression followed by the generation of resonant radiation is a well known phenomenon in non-linear optics. Resonant radiation is important as it allows for efficient and tunable wavelength conversion. We vary the chirp of the initial pulse ... More

On Kuratowski partitionsJun 27 2017In 1935 K. Kuratowski posed the problem whether a function f:X ! Y , (X is completely metrizable and Y is metrizable), with the property that a preimage of each open has the Baire property, is continuous apart from a meager set. This paper is a selection ... More

The base size of a primitive diagonal groupMay 09 2012A base B for a finite permutation group G acting on a set X is a subset of X with the property that only the identity of G can fix every point of B. We prove that a primitive diagonal group G has a base of size 2 unless the top group of G is the alternating ... More

On multicolor Ramsey number for 3-paths of length threeNov 24 2016We show that if we color the hyperedges of the complete $3$-uniform complete graph on $2n+\sqrt{18n+1}+2$ vertices with $n$ colors, then one of the color classes contains a loose path of length three.

Anomalous diffusion models: different types of subordinator distributionOct 13 2011Subordinated processes play an important role in modeling anomalous diffusion-type behavior. In such models the observed constant time periods are described by the subordinator distribution. Therefore, on the basis of the observed time series, it is possible ... More

Asymmetric truncated Toeplitz operators on finite-dimensional spacesNov 02 2016In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric truncated Toeplitz ... More

Critical collapse of a rotating scalar field in $2+1$ dimensionsFeb 15 2017Mar 29 2017We carry out numerical simulations of the collapse of a complex rotating scalar field of the form $\Psi(t,r,\theta)=e^{im\theta}\Phi(t,r)$, giving rise to an axisymmetric metric, in 2+1 spacetime dimensions with cosmological constant $\Lambda<0$, for ... More

Disjointness properties for Cartesian products of weakly mixing systemsDec 23 2011Jul 18 2012For $n\geq 1$ we consider the class JP($n$) of dynamical systems whose every ergodic joining with a Cartesian product of $k$ weakly mixing automorphisms ($k\geq n$) can be represented as the independent extension of a joining of the system with only $n$ ... More

The multipartite Ramsey number for the 3-path of length threeJun 27 2017We study the Ramsey number for the 3-path of length three and $n$ colors and show that $R(P^3_3;n)\le \lambda_0 n+7\sqrt{n}$, for some explicit constant $\lambda_0=1.97466\dots$.

Algebraic Properties of Valued Constraint Satisfaction ProblemMar 03 2014Apr 01 2015The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005]. We introduce ... More

Adaptive quantum teleportationOct 16 2008Jun 07 2009We consider multiple teleportation in the Knill-Laflamme-Milburn (KLM) scheme. We introduce adaptive teleportation, i.e., such that the choice of entangled state used in the next teleportation depends on the results of the measurements performed during ... More

Optimal state in the Knill-Laflamme-Milburn scheme of linear optical teleportationJul 05 2007Dec 15 2007We discuss some properties of the Knill-Laflamme-Milburn scheme for quantum teleportation with both maximally and nonmaximally entangled states. We derive the error correction scheme when one performs teleportation with nonmaximally entangled states and ... More

Nonmaximally entangled states can be better for multiple linear optical teleportationAug 05 2007Mar 17 2008We investigate multiple linear optical teleportation in the Knill-Laflamme-Milburn scheme with both maximally and nonmaximally entangled states. We show that if the qubit is teleported several times via nonmaximally entangled state then the errors introduced ... More

Quantum network protocol for qudits with use of quantum repeaters and Pauli Z-type operational errorsApr 13 2016In this chapter a quantum communication protocol with use of repeaters is presented. The protocol is constructed for qudits i.e. the generalized quantum information units. One-dit teleportation is based on the generalized Pauli-Z (phase-flip) gate's correction. ... More

The center of the affine nilTemperley-Lieb algebraMay 11 2015We give a description of the center of the affine nilTemperley-Lieb algebra based on a certain grading of the algebra and on a faithful representation of it on fermionic particle configurations. We present a normal form for monomials, hence construct ... More

Identification of new Galactic symbiotic stars with SALT. I. Initial discoveries and other emission line objectsNov 04 2013Feb 10 2014We introduce the first results from an ongoing, systematic survey for new symbiotic stars selected from the AAO/UKST SuperCOSMOS H$\alpha$ Survey (SHS). The survey aims to identify and characterise the fainter population of symbiotic stars underrepresented ... More

Transfers of entanglement qudit states in quantum networksFeb 02 2013The issue of quantum states' transfer -- in particular, for so-called Perfect State Transfer (PST) -- in the networks represented by the spin chains seems to be one of the major concerns in quantum computing. Especially, in the context of future communication ... More

Fair valuation of Lévy-type drawdown-drawup contracts with general insured and penalty functionsDec 12 2017Feb 19 2018In this paper, we analyse some equity-linked contracts that are related to drawdown and drawup events based on assets governed by a geometric spectrally negative L\'evy process. Drawdown and drawup refer to the differences between the historical maximum ... More

Feedback and the fudamental line of low-luminosity LSB/dwarf galaxiesOct 20 2002Dec 12 2003We study in simple terms the role of feedback in establishing the scaling relations of low-surface-brightness and dwarf galaxies with stellar masses in the range 6x10^5 <M*< 3x10^10 Msun. These galaxies, as measured from SDSS and in the Local Group, show ... More

An immune system-tumour interactions model with discrete time delay: model analysis and validationMay 08 2015Nov 04 2015In this article a generalized mathematical model describing the interactions between malignant tumour and immune system with discrete time delay incorporated into the system is considered. Time delay represents the time required to generate an immune ... More

On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFSJul 24 2007May 06 2008We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We ... More

Finite homogeneous effect algebras with trivial sharp elementsSep 16 2016In this paper we describe finite homogeneous effect algebras whose sharp elements are only $0$ and $1$.

Structure of Chinese algebrasSep 29 2010Jul 08 2011The structure of the algebra K[M] of the Chinese monoid M over a field K is studied. The minimal prime ideals are described. They are determined by certain homogeneous congruences on M and they are in a one to one correspondence with diagrams of certain ... More

Premium valuation for a multiple state model containing manifold premium-paid statesJan 25 2017The aim of this contribution is to derive a general matrix formula for the net period premium paid in more than one state. For this purpose we propose to combine actuarial technics with the graph optimization methodology. The obtained result is useful ... More

Indo-Pacific variability on seasonal to multidecadal timescales. Part I: Intrinsic SST modes in models and observationsApr 06 2016Sep 29 2016The variability of Indo-Pacific SST on seasonal to multidecadal timescales is investigated using a recently introduced technique called nonlinear Laplacian spectral analysis (NLSA). Through this technique, drawbacks associated with ad hoc pre-filtering ... More

Globally regular instability of $AdS_3$Jun 03 2013We consider three-dimensional AdS gravity minimally coupled to a massless scalar field and study numerically the evolution of small smooth circularly symmetric perturbations of the $AdS_3$ spacetime. As in higher dimensions, for a large class of perturbations, ... More

Comparison of sampling techniques for Bayesian parameter estimationAug 12 2013Jan 06 2014The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the posterior probability ... More

On threshold amplitudes III: 2 into n processesSep 04 2003The 2 into n scattering with final particles at rest is discussed. The comparison with purely soft processes allows to identify symmetries responsible for vanishing of certain 2 into n amplitudes. Some examples are given.

On threshold amplitudes II: Amplitudes nullification via classical symmetriesJun 25 2003The Ward identities for amplitudes at the tree level are derived from symmetries of the corresponding classical dynamical systems. The results are applied to some 2 into n amplitudes.

Deep Analyses of Nulling in Arecibo Pulsars Reveal Further Periodic BehaviorFeb 06 2008Sensitive Arecibo observations provide an unprecedented ability to detect nulls for an accurate pulse-modulation quelling (PMQ) analysis. We demonstrate that a number of conal pulsars show "periodic nulling" similar to the phenomenon found earlier in ... More

Quantum behaviour near a spacelike boundary in the c=1 matrix modelNov 19 2007Mar 30 2008Certain time dependent configurations in the c=1 matrix model correspond to string theory backgrounds which have spacelike boundaries and appear geodesically incomplete. We investigate quantum mechanical properties of a class of such configurations in ... More

Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Isomorphism ProblemFeb 07 2018The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that this reduction ... More

Proof Complexity Meets AlgebraNov 20 2017Sep 25 2018We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of pp-interpretability, ... More

Dynamical systems associated to the $β$-core in the repeated prisoner's dilemmaNov 29 2017We consider the repeated prisoner's dilemma (PD). We assume that players make their choices knowing only average payoffs from the previous stages. A player's strategy is a function from the convex hull $\mathfrak{S}$ of the set of payoffs into the set ... More

A hierarchy of maximal intersecting triple systemsAug 22 2016We reach beyond the celebrated theorems of Erd\H{o}s-Ko-Rado and Hilton-Milner, and, a recent theorem of Han-Kohayakawa, and determine all maximal intersecting triples systems. It turns out that for each $n\ge7$ there are exactly 15 pairwise non-isomorphic ... More

An isometrically universal Banach space with a monotone Schauder basisFeb 11 2014Mar 12 2014We present an isometric version of the complementably universal Banach space $\mathcal{B}$ with a monotone Schauder basis. The space $\mathcal{B}$ is isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to Kadec' complementably universal ... More

Remarks on Gurarii spacesNov 24 2011We present selected known results and some of their improvements, involving Gurarii spaces. A Banach space is Gurarii if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the word "almost", ... More

Accuracy of the lepton-nucleus scattering models in the quasielastic regionJun 21 2017We present a discussion of models of nuclear effects used to describe an inclusive electron-nucleus scattering in the quasielastic (QE) peak region, aiming to compare them and draw conclusion of their reliability when applied in neutrino-nucleus interactions. ... More

A Widom-Rowlinson Jump Dynamics in the ContinuumApr 26 2016We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact. The states of ... More

Existence of global weak solutions for Navier-Stokes equations with large fluxSep 28 2010Global existence of weak solutions to the Navier-Stokes equation in a cylindrical domain under the slip boundary conditions and with inflow and outflow was proved. To prove the energy estimate, crucial for the proof, we use the Hopf function. This makes ... More

On embeddability of automorphisms into measurable flows from the point of view of self-joining propertiesApr 10 2013Sep 02 2014We compare self-joining- and embeddability properties. In particular, we prove that a measure preserving flow $(T_t)_{t\in\mathbb{R}}$ with $T_1$ ergodic is 2-fold quasi-simple (2-fold distally simple) if and only if $T_1$ is 2-fold quasi-simple (2-fold ... More

On the strong convolution singularity propertyNov 16 2012Jan 24 2013We develop a new method for proving that a flow has the so-called strong convolution singularity property, i.e. the Gaussian system induced by its (reduced) maximal spectral type has simple spectrum. We use these methods to give examples of smooth flows ... More

Black swans or dragon kings? A simple test for deviations from the power lawFeb 17 2011We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity ... More

Quantum qubit switch: entropy and entanglementSep 07 2017The quantum entanglement is considered as one of the most important notions of quantum computing. The entanglement is a feature of quantum systems and it is used as a basis for many quantum algorithms and protocols. In this paper we analyze the level ... More

Distinguishing between symbiotic stars and planetary nebulaeAug 17 2017Number of known symbiotic stars (SySt) is still significantly lower than their predicted population. One of the main problems in finding complete population of SySt is the fact that their spectrum can be confused with other objects, such as planetary ... More

Indo-Pacific variability on seasonal to multidecadal timescales. Part II: Multiscale atmosphere-ocean linkagesSep 29 2016The coupled atmosphere-ocean variability of the Indo-Pacific on interannual to multidecadal timescales is investigated in a millennial control run of CCSM4 and in observations using a family of modes recovered in Part~I of this work from unprocessed SST ... More

Multicore Noncommutative BionsOct 25 2004Nov 13 2004The noncommutative bion core of Constable, Myers and Tafjord (hep-th/9911136) describes the BPS D1-D3 brane intersection (where a single bundle of D1-branes is attached to the D3 brane) in the nonabelian Born-Infeld theory of D1-branes. The possibility ... More

"Isochronic" dynamical systems and nullification of amplitudesMay 13 2003We construct the set of theories which share the property that the tree-level amplitudes nullify even if both initial and final states contain the same type of particles. The origin of this phenomenon lies in the fact that the reduced classical dynamics ... More

QTM: computational package using MPI protocol for quantum trajectories methodOct 06 2018The Quantum Trajectories Method (QTM) is one of {the} frequently used methods for studying open quantum systems. { The main idea of this method is {the} evolution of wave functions which {describe the system (as functions of time). Then,} so-called quantum ... More

On Kuratowski partitions in the Marczewski structure and Ellentuck topologyJun 27 2017Nov 06 2017We show that large sets in Ellentuck topology (i.e. sets which are not nowhere Ramsey) do not admit Kuratowski's partition. The similar result is true for the Sacks real forcing.

A short mathematical proof of Frankiewicz - Kunen theoremJun 27 2017Nov 06 2017In this paper there is proved without any metamathematical techniques that the existence of precipitous ideals immediately follows from Kuratowski partitions.

Restricted size Ramsey number for $P_3$ versus cyclesJun 25 2017Nov 20 2018Let $F$, $G$ and $H$ be simple graphs. We say $F \rightarrow (G, H)$ if for every $2$-coloring of the edges of $F$ there exists a monochromatic $G$ or $H$ in $F$. The Ramsey number $r(G, H)$ is defined as $r(G, H) = min\{|V (F)|: F \rightarrow (G, H)\}$, ... More

Asymmetric truncated Toeplitz operators equal to the zero operatorSep 13 2016Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of asymmetric truncated ... More

Free Jump Dynamics in ContinuumAug 27 2014The evolution is described of an infinite system of hopping point particles in $\mathbb{R}^d$. The states of the system are probability measures on the space of configurations of particles. Under the condition that the initial state $\mu_0$ has correlation ... More

Locally triangular graphs and normal quotients of the $n$-cubeJul 06 2015For an integer $n\geq 2$, the triangular graph has vertex set the $2$-subsets of $\{1,\ldots,n\}$ and edge set the pairs of $2$-subsets intersecting at one point. Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected ... More

Dust evolution and satellitesimal formation in circumplanetary disksJul 07 2018Sep 11 2018It is believed that satellites of giant planets form in circumplanetary disks. Many of the previous contributions assumed that their formation process proceeds similarly to rocky planet formation, via accretion of the satellite seeds, called satellitesimals. ... More

Smart Policies for Artificial IntelligenceAug 29 2016We argue that there already exists de facto artificial intelligence policy - a patchwork of policies impacting the field of AI's development in myriad ways. The key question related to AI policy, then, is not whether AI should be governed at all, but ... More

Three solutions for elliptic Dirichlet boundary value problem with singular weightJul 05 2016In this paper we prove the~existence of two non-trivial weak solutions of Dirichlet boundary value problem for p-Laplacian problem with a~singular part and two disturbances satisfying the~proper assumptions. The~abstract existence result we use is the~famous ... More

Sharp and principal elements in effect algebrasApr 02 2015Jul 02 2015In this paper we characterize the effect algebras whose sharp and principal elements coincide. We also give examples of two non-isomorphic effect algebras having the same universum, partial order and orthosupplementation.

Goldie rank of primitive quotients via lattice point enumerationDec 21 2012Let k be an algebraically closed field of characteristic 0. Musson and vandenBergh classified primitive ideals for rings of torus invariant differential operators. This classification applies in particular to subquotients of localized extended Weyl algebras ... More

The Global Evolution of States of a Continuum Kawasaki Model with RepulsionMar 27 2016An infinite system of point particles performing random jumps in $\mathds{R}^d$ with repulsion is studied. The states of the system are probability measures on the space of particle's configurations. The result of the paper is the construction of the ... More

Everywhere divergence of the one-sided ergodic Hilbert transform and Liouville numbersJun 10 2016We prove some results on the behavior of infinite sums of the form $\Sigma f\circ T^n(x)\frac{1}{n}$, where $T:S^1\to S^1$ is an irrational circle rotation and $f$ is a mean-zero function on $S^1$. In particular, we show that for a certain class of functions ... More

Paths in hypergraphs: a rescaling phenomenonJun 26 2017Let $P^k_\ell$ denote the loose $k$-path of length $\ell$ and let define $f^k_\ell(n,m)$ as the minimum value of $\Delta(H)$ over all $P^k_\ell$-free $k$-graphs $H$ with $n$ vertices and $m$ edges. In the paper we study the behavior of $f^4_2(n,m)$ and ... More

Exponential ergodicity of some Markov dynamical system with application to a Poisson driven stochastic differential equationJan 20 2018Feb 21 2018We are concerned with the asymptotics of the Markov chain given by the post-jump locations of a certain piecewise-deterministic Markov process with a state-dependent jump intensity. We provide sufficient conditions for such a model to possess a unique ... More

Two Growing Modes Lead to the Morphology-Quiescence Relation in GalaxiesOct 29 2018Quiescence in galaxies correlates strongly with the central density/morphology of the stellar distribution. We investigate two possible explanations for this morphology-quiescence relation: 1) the central density results from a dissipative core-building ... More

The dependence structure for PARMA models with alpha-stable innovationsAug 13 2006In this paper we investigate the dependence structure for PARMA models (i.e. ARMA models with periodic coefficients) with symmetric alpha-stable innovations. In this case the covariance function is not defined and therefore other measures of dependence ... More

The universal Banach space with a $K$-suppression unconditional basisJan 23 2018Jan 05 2019Using the technique of Fra\"iss\'e theory, for every constant $K\ge 1$ we consruct a universal object in the class of Banach spaces with normalized $K$-suppression unconditional Schauder bases.