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Towards autonomous ocean observing systems using Miniature Underwater Gliders with UAV deployment and recovery capabilitiesFeb 08 2019This paper presents preliminary results towards the development of an autonomous ocean observing system using Miniature Underwater Gliders (MUGs) that can operate with the support of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vessels (USVs) ... More

Dense definiteness and boundedness of composition operators in $L^2$-spaces via inductive limitsSep 13 2014The questions of dense definiteness and boundedness of composition operators in $L^2$-spaces are studied by means of inductive limits of operators. Methods based on projective systems of measure spaces and inductive limits of $L^2$-spaces are developed. ... More

Quasinormal extensions of subnormal operator-weighted composition operators in $\ell^2$-spacesJun 08 2016We prove the subnormality of an operator-weighted composition operator whose symbol is a transformation of a discrete measure space and weights are multiplication operators in $L^2$-spaces under the assumption of existence of a family of probability measures ... More

On the Fine-Grained Complexity of Empirical Risk Minimization: Kernel Methods and Neural NetworksApr 10 2017Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM is still not ... More

New Method for Public Key Distribution Based on Social NetworksMar 11 2015The security of communication in everyday life becomes very important. On the other hand, all existing encryption protocols require from user additional knowledge end resources. In this paper we discuss the problem of public key distribution between interested ... More

A mirror conjecture for projective bundlesSep 18 2006Oct 25 2006We propose, motivate and give evidence for a relation between the $\mathcal D$-modules of the quantum cohomology of a smooth complex projective manifold $X$ and a projective bundle $\PP(\oplus L_i)$ over $X$.

Multidimensional spectral order for selfadjoint operatorsJul 04 2019The aim of this paper is to extend the notion of the spectral order for finite families of pairwise commuting bounded and unbounded selfadjoint operators in Hilbert space. It is shown that the multidimensional spectral order $\preccurlyeq$ is preserved ... More

Representation stability on the cohomology of complements of subspace arrangementsNov 24 2017We study representation stability in the sense of Church and Farb of sequences of cohomology groups of complements of arrangements of linear subspaces in real and complex space as $S_n$-modules. We consider arrangement of linear subspaces defined by sets ... More

Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisitedApr 12 2008Jan 19 2009We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4\alpha)z z_x, z_t &=& (1-2\alpha)z_{xx} - 4\alpha z w_x + (4-8\alpha)w z_x - (4+8\alpha)w^2 z + (-2+4\alpha)z^3, (*) for which no recursion operator or master symmetry ... More

Virtual Class of Zero Loci and Mirror TheoremsJul 30 2003Jan 26 2005Let $Y$ be the zero loci of a regular section of a convex vector bundle $E$ over $X$. We provide a new proof of a conjecture of Cox, Katz and Lee for the virtual class of the genus zero moduli of stable maps to $Y$. This in turn yields the expected relationship ... More

Locally small spaces with an applicationMar 03 2019We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

A Framework for App Store OptimizationMay 28 2019In this paper a framework for app store optimization is proposed. The framework is based on two main areas: developer dependent elements and user dependent elements. Developer dependent elements are similar factors in search engine optimization. User ... More

Recompression: a simple and powerful technique for word equationsMar 16 2012Mar 18 2014In this paper we present an application of a simple technique of local recompression, previously developed by the author in the context of compressed membership problems and compressed pattern matching, to word equations. The technique is based on local ... More

Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equationsJun 01 2008Jun 14 2009We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symmetries in question generalize those found by Chen, Kontsevich and Schwarz ... More

Bhomian Mechanics vs. Standard Quantum Mechanics: a Difference in Experimental PredictionsFeb 08 2010Standard Quantum Mechanics (QM) predicts an anti-intuitive fenomenon here referred to as "quantum autoscattering", which is excluded by Bhomian Mechanics. The scheme of a gedanken experiment testing the QM prediction is briefly discussed.

Fractional quantization of Hall resistance as a consequence of mesoscopic feedbackNov 08 2005A nonlinear single-particle model is introduced, which captures the characteristic of systems in the quantum Hall regime. The model entails the magnetic Shr\"odinger equation with spatially variable magnetic flux density. The distribution of flux is prescribed ... More

Integrability in the mesoscopic dynamicsSep 12 2004The Mesoscopic Mechanics (MeM), which has been introduced in a previous paper, is relevant to the electron gas confined to two spatial dimensions. It predicts a special way of collective response of correlated electrons to the external magnetic field. ... More

Infinitesimal perturbations of rational mapsSep 23 2001Feb 16 2002We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restrictions on the behavior of critical points.

Distortion elements in $Diff^\infty(R/Z)$Aug 18 2008We consider the group of smooth diffeomorphisms of the circle. We show that any recurrent $f$ (in the sense that $\{f^n\}_{n \in Z}$ is not discrete) is in fact a distortion element (in the sense that its iterates can be written as short compositions ... More

The Nonlinear Maxwell Theory---an OutlineMar 20 2001The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and static solutions ... More

Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: a new application for formal symmetriesMar 18 2003Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that under certain mild ... More

Encoding spatial data into quantum observablesSep 06 2016Aug 03 2017The focus of this work is a correspondence between the Hilbert space operators on one hand, and doubly periodic generalized functions on the other. The linear map that implements it, referred to as the Q-transform, enables a direct application of the ... More

Reduction of integration domain in Triebel-Lizorkin spacesOct 26 2018Jan 02 2019We investigate the comparability of generalized Triebel-Lizorkin and Sobolev seminorms on uniform and non-uniform sets when the integration domain is truncated according to the distance from the boundary. We provide numerous examples of kernels and domains ... More

Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)Dec 01 2014Apr 13 2015The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit distance between ... More

Which Regular Expression Patterns are Hard to Match?Nov 22 2015Sep 26 2016Regular expressions constitute a fundamental notion in formal language theory and are frequently used in computer science to define search patterns. A classic algorithm for these problems constructs and simulates a non-deterministic finite automaton corresponding ... More

Generalized Cauchy identities, trees and multidimensional Brownian motions. Part II: Combinatorial differential calculusAug 25 2007We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements of the considered ... More

Gravity as field - field oriented framework reproducing General RelativityApr 13 2014Sep 21 2015In the last article we have created foundations for gravitational field oriented framework (DaF) that reproduces GR. In this article we show, that using DaF approach, we can reproduce Schwarzschild solution with orbit equations, effective potential and ... More

Unbounded composition operators via inductive limits: cosubnormal operators with matrix symbols. IIOct 19 2015The paper deals with unbounded composition operators with infinite matrix symbols acting in $L^2$-spaces with respect to the gaussian measure on $\mathbb{R}^\infty$. We introduce weak cohyponormality classes $\EuScript{S}_{n,r}^*$ of unbounded operators ... More

3D PET image reconstruction based on Maximum Likelihood Estimation Method (MLEM) algorithmApr 26 2015Positron emission tomographs (PET) do not measure an image directly. Instead, they measure at the boundary of the field-of-view (FOV) of PET tomograph a sinogram that consists of measurements of the sums of all the counts along the lines connecting two ... More

Hausdorff dimension and conformal measures of Feigenbaum Julia setsAug 21 2004We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon'', there exist many Feigenbaum Julia sets $J(f)$ whose Hausdorff dimension is strictly smaller than two. We also ... More

The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of IntegersFeb 22 2015Dec 01 2015The distant graph $G = G(\mathbb{P}(Z),\triangle)$ of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein's geometric interpretation of Euclidean continued fractions. In case the ... More

Memory equations as reduced Markov processesApr 06 2018A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory ... More

An almost-solvable model of complex network dynamicsFeb 26 2019We discuss a specific model, which we refer to as RandLOE, of a large multi-agent network whose dynamic is prescribed via a combination of deterministic local laws and random exogenous factors. The RandLOE approach lies outside the framework of Stochastic ... More

Featured Snippets Results in Google Web Search: An Exploratory StudyJul 10 2019In this paper authors analyzed 163412 keywords and results with featured snippets collected from localized Polish Google search engine. A method-ology for retrieving data from Google search engine was proposed in terms of obtaining necessary data to study ... More

Knowledge Graph Development for App Store Data ModelingMar 17 2019These days usage of mobile applications has become quite a normal part of our lives, since every day we use our smartphones for communication, entertainment, business and even education. A high demand on various apps has led to significant growth of supply. ... More

Hyperbolic geometry for non-differential topologistsJan 22 2018A soft presentation of hyperbolic spaces, free of differential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean ... More

On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditionsMay 24 2018Jan 10 2019We study the non-autonomously forced Burgers equation $$ u_t(x,t) + u(x,t)u_x(x,t) - u_{xx}(x,t) = f(x,t) $$ on the space interval $(0,1)$ with two sets of the boundary conditions: the Dirichlet and periodic ones. For both situations we prove that there ... More

Maxwell-like picture of General Relativity and its Planck limitJan 13 2013Nov 29 2013We show that Geroch decomposition leads us to Maxwell-like representation of gravity in $(3+1)$ metrics decomposition that may be perceived as Lorentz invariant version of GEM. For such decomposition we derive four-potential $V^\mu$ and gravitational ... More

Unbounded composition operators via inductive limits: cosubnormals with matrical symbolsFeb 05 2015We prove, by use of inductive techniques, that assorted unbounded composition operators in $L^2$-spaces with matrical symbols are cosubnormal.

Plastic scintillators for positron emission tomography obtained by the bulk polymerization methodApr 26 2015This paper describes three methods regarding the production of plastic scintillators. One method appears to be suitable for the manufacturing of plastic scintillator, revealing properties which fulfill the requirements of novel positron emission tomography ... More

Uniform separation through intermediate pointsJan 27 2015It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is applied to improve ... More

The moduli space of generalized quiversMar 30 2017We construct the moduli space of finite dimensional representations of generalized quivers for arbitrary connected complex reductive groups using Geometric Invariant Theory as well as Symplectic reduction methods. We explicit characterize stability and ... More

Improving Viterbi is Hard: Better Runtimes Imply Faster Clique AlgorithmsJul 14 2016The classic algorithm of Viterbi computes the most likely path in a Hidden Markov Model (HMM) that results in a given sequence of observations. It runs in time $O(Tn^2)$ given a sequence of $T$ observations from a HMM with $n$ states. Despite significant ... More

Optical vortex coronagraphy from soft spin-orbit masksSep 19 2016We report on a soft route towards optical vortex coronagraphy based on self-engineered electrically tunable vortex masks based on liquid crystal topological defects. These results suggest that a Nature-assisted technological approach to the fabrication ... More

Efficient polarization analysis for focusing neutron instrumentsFeb 27 2017Polarized neutrons are a powerful probe to investigate magnetism in condensed matter on length scales from single atomic distances to micrometers. With the ongoing advancement of neutron optics, that allow to transport beams with increased divergence, ... More

A general renormalization procedure on the one-dimensional lattice and decay of correlationsJan 26 2017Dec 12 2017We present a general form of Renormalization operator $\mathcal{R}$ acting on potentials $V:\{0,1\}^\mathbb{N} \to \mathbb{R}$. We exhibit the analytical expression of the fixed point potential $V$ for such operator $\mathcal{R}$. This potential can be ... More

Scalar field deformations of Lambda-CDM cosmologyMay 26 2015Nov 04 2015This paper treats nonrelativistic matter and a scalar field $\phi$ with a monotonically decreasing potential minimally coupled to gravity in flat Friedmann-Lema\^{i}tre-Robertson-Walker cosmology. The field equations are reformulated as a three-dimensional ... More

Nuclear effects are relevant to the calorimetric reconstruction of neutrino energyApr 25 2017As the calorimetric method of neutrino-energy reconstruction is generally considered to be largely insensitive to nuclear effects, its application seems to be an effective way for reducing systematic uncertainties in oscillation experiments. To verify ... More

FFT-Based Fast Computation of Multivariate Kernel Estimators with Unconstrained Bandwidth MatricesAug 11 2015Sep 07 2016The problem of fast computation of multivariate kernel density estimation (KDE) is still an open research problem. In our view, the existing solutions do not resolve this matter in a satisfactory way. One of the most elegant and efficient approach utilizes ... More

Convergence and Summability of Multiple Fourier series and generalized variationApr 24 2014In this paper we present results on convergence and Ces\`{a}ro summability of Multiple Fourier series of functions of bounded generalized variation.

Consistent analysis of neutral- and charged-current neutrino scattering off carbonMay 22 2012Sep 11 2012Background: Good understanding of the cross sections for (anti)neutrino scattering off nuclear targets in the few-GeV energy region is a prerequisite for correct interpretation of results of ongoing and planned oscillation experiments. Purpose: Clarify ... More

Absolute Monte Carlo estimation of integrals and partition functionsJan 28 2010Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly designed to compute ... More

Tuning the exchange interaction by electric field in laterally coupled quantum dotsDec 10 2008The effect of external electric field on the exchange interaction has been studied by an exact diagonalization method for two electrons in laterally coupled quantum dots (QD's). We have performed a systematic study of several nanodevices that contain ... More

Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical CouplingNov 27 2007We show that the integrated density of states of the almost Mathieu operator is absolutely continuous if and only if the coupling is non-critical. We deduce for subcritical coupling that the spectrum is purely absolutely continuous for almost every phase, ... More

Algebraic perturbation theory for dense liquids with discrete potentialsDec 28 2006A simple theory for the leading-order correction g_1(r) to the structure of a hard-sphere liquid with discrete (e.g. square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle ... More

Simplicity of Lyapunov spectra: a sufficient criterionJul 28 2006We exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. This builds on work of Guivarc'h-Raugi and Gol'dsheid-Margulis, who considered products of random matrices, and of Bonatti-Viana, ... More

Reciprocal transformations for Stackel-related Liouville integrable systemsJul 25 2006We consider the St\"ackel transform, also known as the coupling-constant metamorphosis, which under certain conditions turns a Hamiltonian dynamical system into another such system and preserves the Liouville integrability. We show that the corresponding ... More

Effective Constraints and Physical Coherent States in Quantum Cosmology: A Numerical ComparisonNov 25 2009A cosmological model with a cyclic interpretation is introduced, which is subject to quantum back-reaction and yet can be treated rather completely by physical coherent state as well as effective constraint techniques. By this comparison, the role of ... More

High-energy limit of neutrino quasielastic cross sectionMar 18 2005Mar 23 2005It's a common knowledge that the quasielastic neutrino-neutron and antineutrino-proton cross sections tend to the same constant as (anti)neutrino energy becomes high. In this paper we calculate the exact expression of the limit in terms of the parameters ... More

Generic singular continuous spectrum for ergodic Schrödinger operatorsSep 06 2004We consider Schr\"odinger operators with ergodic potential $V_\omega(n)=f(T^n(\omega))$, $n \in \Z$, $\omega \in \Omega$, where $T:\Omega \to \Omega$ is a non-periodic homeomorphism. We show that for generic $f \in C(\Omega)$, the spectrum has no absolutely ... More

Exponential decay of correlations for the Rauzy-Veech-Zorich induction mapOct 20 2006We prove exponential mixing for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations (Theorem 3)

Ergodicity and the Classical Lambda Phi^4 Lattice Field TheoryOct 15 2000In this talk we present some studies in the approach to equilibrium of the classical lambda phi^4 theory on the lattice, giving particular emphasis to its pedagogical usefulness in the context of classical statistical field theory (such as both the analytical ... More

Natural coordinates for a class of Benenti systemsApr 10 2006Jan 09 2007We present explicit formulas for the coordinates in which the Hamiltonians of the Benenti systems with flat metrics take natural form and the metrics in question are represented by constant diagonal matrices.

Symmetry relations in chemical kinetics arising from microscopic reversibilitySep 08 2005Dec 06 2005It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. ... More

(Non)existence of static scalar field configurations in finite systemsAug 22 2002Aug 28 2002Derrick's theorem on the nonexistence of stable time-independent scalar field configurations [G. H. Derrick, J. Math. Phys. 5, 1252 (1964)] is generalized to finite systems of arbitrary dimension. It is shown that the "dilation" argument underlying the ... More

Internal clock formulation of quantum mechanicsJun 02 2017Sep 18 2017The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational field, which is ... More

On the Interaction Effects Between Prediction and ClusteringJul 18 2018Dec 28 2018Machine learning systems increasingly depend on pipelines of multiple algorithms to provide high quality and well structured predictions. This paper argues interaction effects between clustering and prediction (e.g. classification, regression) algorithms ... More

Clustering on the Edge: Learning Structure in GraphsMay 05 2016With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most likely number ... More

Dynamic Quantum Tomography Model for Phase-Damping ChannelsSep 30 2015Dec 30 2015In this article we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the Hadamard product ... More

The snippets taxonomy in web search enginesJun 11 2019In this paper authors analyzed 50 000 keywords results collected from localized Polish Google search engine. We proposed a taxonomy for snippets displayed in search results as regular, rich, news, featured and entity types snippets. We observed some correlations ... More

Bornological quasi-metrizability in generalized topologyMay 17 2015Oct 17 2018A concept of quasi-metrizability with respect to a bornology of a generalized topological space in the sense of Delfs and Knebusch is introduced. Quasi-metrization theorems for generalized bornological universes are deduced. A uniform quasi-metrizability ... More

Size and power properties of some tests in the Birnbaum-Saunders regression modelMay 18 2010The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order $n^{-1/2}$ and under a sequence of ... More

Continuous-mode effects and photon-photon phase gate performanceDec 08 2010Mar 07 2012The effects arising from the inherent continuous-mode nature of photonic pulses were poorly understood but significantly influence the performance of quantum devices employing photonic pulse interaction in nonlinear media. Such effects include the entanglement ... More

A formula for the Entropy of the Convolution of Gibbs probabilities on the circleFeb 10 2017Apr 24 2018Consider the transformation $T:S^1 \to S^1$, such that $T(x)=2\, x$ (mod 1), and where $S^1$ is the unitary circle. Suppose $J:S^1 \to \mathbb{R}$ is Holder continuous and positive, and moreover that, for any $y\in S^1$, we have that $\sum_{x\,\,\text{such ... More

Quantization of dynamical symplectic reductionJun 11 2019A long-standing problem in quantum gravity and cosmology is the quantization of systems in which evolution is generated by a constraint that must vanish on solutions. Here, an algebraic formulation of this problem is presented, together with new structures ... More

Saddle point solutions in Yang-Mills-dilaton theorySep 26 1992The coupling of a dilaton to the $SU(2)$-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analitical and numerical methods. In the abelian sector of the theory there are finite-energy ... More

Geometria nieortodoksyjnaJun 18 2001This is an introductory text to differential geometry (written in Polish) aimed for high-school students.

Interstellar H2 toward HD 37903Feb 26 2010Mar 14 2011We present an analysis of interstellar H2 toward HD 37903, which is a hot, B 1.5 V star located in the NGC 2023 reflection nebula. Meyer et al. (2001) have used a rich spectrum of vibrationally excited H2 observed by the HST to calculate a model of the ... More

On Value at Risk for foreign exchange rates - the copula approachAug 18 2006The aim of this paper is to determine the Value at Risk (VaR) of the portfolio consisting of long positions in foreign currencies on an emerging market. Basing on empirical data we restrict ourselves to the case when the tail parts of distributions of ... More

The Distance to the Large Magellanic CloudJan 31 2000I demonstrate that the two unexpected results in the local Universe: anomalous intrinsic (V-I)_0 colors of RR Lyrae stars and clump giants in the Galactic center, and very short distances to Magellanic Clouds inferred from clump giants, can be at least ... More

Harmonizing the RR Lyrae and Clump Distance Scales - Stretching the Short Distance Scale to Intermediate Ranges?Jan 26 2000Sep 26 2000I explore the consequences of making the RR Lyrae and clump giant distance scales consistent in the solar neighborhood, Galactic bulge and Large Magellanic Cloud (LMC). I employ two major assumptions: 1) that the absolute magnitude - metallicity, M_V(RR) ... More

Weak convergence of the sequences of homogeneous Young measures associated with a class of oscillating functionsJul 11 2018Feb 12 2019We consider the sequences of oscillating functions which are sums of the functions having continuously differentiable inverses. We show that if the total slopes of the elements of these sequences form monotonic sequence then the sequence of the respective ... More

On a certain family of U(b)-modulesMar 01 2016Oct 08 2016We report on results of Kra\'skiewicz and the author, and Watanabe on KP modules materializing Schubert polynomials, and filtrations having KP modules as their subquotients. We discuss applications of KP filtrations and ample KP bundles to positivity, ... More

A Purely Algebraic Proof of the Fundamental Theorem of AlgebraApr 21 2015Proofs of the fundamental theorem of algebra can be divided up into three groups according to the techniques involved: proofs that rely on real or complex analysis, algebraic proofs, and topological proofs. Algebraic proofs make use of the fact that odd-degree ... More

Galaxy rotation curve from classical CepheidsSep 06 2018Jan 11 2019The Galaxy rotation curve is usually assumed to be flat. However, some galaxies have Keplerian rotation curves in the outer part of the galaxy. In our Galaxy the Keplerian rotation of interstellar clouds in the galactic longitude l=135 was observed. We ... More

Boosting Question Answering by Deep Entity RecognitionMay 27 2016In this paper an open-domain factoid question answering system for Polish, RAFAEL, is presented. The system goes beyond finding an answering sentence; it also extracts a single string, corresponding to the required entity. Herein the focus is placed on ... More

A characterization of Keller mapsSep 09 2011Dec 09 2011Let k be a field of characteristic zero. Let phi be a k-endomorphism of the polynomial algebra k[x_1,...,x_n]. It is known that phi is an automorphism if and only if it maps irreducible polynomials to irreducible polynomials. In this paper we show that ... More

Primes of the form x^2+n*y^2 in function fieldsNov 15 2009Mar 17 2011Let n be a square-free polynomial over F_q, where q is an odd prime power. In this paper, we determine which irreducible polynomials p in F_q[x] can be represented in the form X^2+nY^2 with X, Y in F_q[x]. We restrict ourselves to the case where X^2+nY^2 ... More

Spatial CLT for the supercritical Ornstein-Uhlenbeck superprocessMar 29 2012In this paper we consider a superprocess being a measure-valued diffusion corresponding to the equation $u_{t}=Lu+\alpha u-\beta u^{2}$, where $L$ is the infinitesimal operator of the \emph{Ornstein-Uhlenbeck process} and $\beta>0,\:\alpha>0$. The latter ... More

Permutations without long decreasing subsequences and random matricesMar 16 2006Dec 31 2006We study the shape of the Young diagram \lambda associated via the Robinson-Schensted-Knuth algorithm to a random permutation in S_n such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other words we study ... More

Small growth vectors of the compactifications of the contact systems on $J^{\,r}(1,1)$Feb 23 2011It is well known that the compactifications of the canonical contact systems living on real jet spaces $J^{\,r}(1,1)$, $r \ge 2$, are locally universal Goursat distributions, $\Delta^r$, living on compact manifolds (called Goursat monsters) having open ... More

Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spacesMay 28 2011An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with respect to ideals) ... More

On CR (Cauchy-Riemann) almost cosymplectic manifoldsSep 09 2012Oct 05 2012In the paper we develop a framework for the alternative way of the study of a local geometry of almost cosymplectic manifolds with Kahlerian leaves. The main idea is to apply the concept of a geometry and analysis of CR manifolds. Locally the almost cosymplectic ... More

Hyperbolicity and Averaging for the Srzednicki-Wójcik equationJul 09 2016For the Srzednicki-W\'ojcik equation, the planar nonautonomous ODE parameterized by $\kappa \in \mathbb{R}$, $$ z'=\overline{z}(1+ |z|^2 \exp(i \kappa t)), \qquad z(t) \in \mathbb{C} $$ using averaging we show how the region of hyperbolicty grows with ... More

Weak convergence of the sequences of homogeneous Young measures associated with a class of oscillating functionsJul 11 2018Mar 09 2019We take under consideration Young measures with densities. The notion of density of a Young measure is introduced and illustrated with examples. It is proved that the density of a Young measure is weakly sequentially closed set. In the case when density ... More

Symmetric polynomials and divided differences in formulas of intersection theoryMay 28 1996The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci; some explicit ... More

Consistency of modified versions of Bayesian Information Criterion in sparse linear regression with subgaussian errorsNov 15 2014May 29 2018We consider a sparse linear regression model, when the number of available predictors, $p$, is much larger than the sample size, $n$, and the number of non-zero coefficients, $p_0$, is small. To choose the regression model in this situation, we cannot ... More

Quantum information approach to normal representation of extensive gamesJul 16 2011Jul 19 2011We modify the concept of quantum strategic game to make it useful for extensive form games. We prove that our modification allows to consider the normal representation of any finite extensive game using the fundamental concepts of quantum information. ... More

Simple error bounds for the multivariate Laplace approximation under weak local assumptionsNov 01 2015Apr 11 2016The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is presented. ... More

Bounded convergence theoremsSep 10 2013There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such ... More