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

Null Kähler structures, Symmetries and IntegrabilityOct 01 2003Jun 21 2006We review the integrable systems which arise as symmetry reductions of Plebanski's heavenly equations, and their generalisations. We also show that all four-dimensional null Kahler-Einstein (or type N hyper-heavenly) metrics with symmetry can be found ... More

On primitive integer solutions of the Diophantine equation $t^2=G(x,y,z)$ and related resultsFeb 25 2015In this paper we investigate Diophantine equations of the form $T^2=G(\overline{X}),\; \overline{X}=(X_{1},\ldots,X_{m})$, where $m=3$ or $m=4$ and $G$ is specific homogenous quintic form. First, we prove that if $F(x,y,z)=x^2+y^2+az^2+bxy+cyz+dxz\in\Z[x,y,z]$ ... More

Semi-supervised learning with Bidirectional GANsNov 28 2018In this work we introduce a novel approach to train Bidirectional Generative Adversarial Model (BiGAN) in a semi-supervised manner. The presented method utilizes triplet loss function as an additional component of the objective function used to train ... More

On formal inverse of the Prouhet-Thue-Morse sequenceJan 19 2016Let $p$ be a prime number and consider a $p$-automatic sequence ${\bf u}=(u_{n})_{n\in\N}$ and its generating function $U(X)=\sum_{n=0}^{\infty}u_{n}X^{n}\in\mathbb{F}_{p}[[X]]$. Moreover, let us suppose that $u_{0}=0$ and $u_{1}\neq 0$ and consider the ... More

On Construction of Recursion Operator and Algebra of Symmetries for Field and Lattice SystemsOct 19 2000In the paper, developing the idea of V. Sokolov et all. (J.Math.Phys. 40 (1999)6473 we construct recursion operators and hereditary algebra of symmetries for many field and lattice systems.

Kauffman bracket skein module of the connected sum of two projective spacesAug 05 2010Diagrams and Reidemeister moves for links in a twisted S^1-bundle over an unorientable surface are introduced. Using these diagrams, we compute the Kauffman Bracket Skein Module (KBSM) of the connected sum of two projective spaces. In particular, we show ... More

Multidimensional monopolist pricing problem with uncertain valuationsMay 04 2016May 18 2016We consider the problem of revenue maximization by a monopolist selling a set of substitutable goods to an unit-demand buyer of uncertain type. The Bayesian variant of this problem has received much interest in the computer science and economics communities ... More

Categories of diagrams with irreversible movesDec 31 2013We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every move of the ... More

Large N behavior of two dimensional supersymmetric Yang-Mills quantum mechanicsAug 21 2006Aug 23 2006We analyze the $N \to \infty $ limit of supersymmetric Yang-Mills quantum mechanics (SYMQM) in two spacetime dimensions. To do so we introduce a particular class of SU(N) invariant polynomials and give the solutions of 2D SYMQM in terms of them. We conclude ... More

A class of Einstein--Weyl spaces associated to an integrable system of hydrodynamic typeNov 13 2003Feb 09 2004HyperCR Einstein--Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can be in principle constructed from a twistor correspondence, thus establishing the integrability. ... More

Systematic construction of separable systems with quadratic in momenta first integralsSep 16 2003Liouville integrable separable systems with quadratic in momenta first integrals are considered. Particular attention is paid to the systems generated by the so-called special conformal Killing tensors, i.e. Benenti systems. Then, infinitely many new ... More

The number of gauge singlets in supersymmetric Yang-Mills quantum mechanicsAug 22 2007We compute generating functions for number of U(N) (SU(N)) singlets in Fock space in several space dimensions. The motivation to find the explicit form of the functions is from the numerical approach to supersymmetric Yang-Mills quantum mechanics, based ... More

Dirac equation for membranesMar 10 2011Sep 22 2011Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of positive and negative ... More

A note on Sierpiński problem related to triangular numbersOct 01 2008In this note we show that the system of equations t_{x}+t_{y}=t_{p},\quad t_{y}+t_{z}=t_{q},\quad t_{x}+t_{z}=t_{r}, where $t_{x}=x(x+1)/2$ is a triangular number, has infinitely many solutions in integers. Moreover we show that this system has rational ... More

Coloring invariants of spatial graphsDec 20 2009Jun 09 2010We define the fundamental quandle of a spatial graph and several invariants derived from it. In the category of graph tangles, we define an invariant based on the walks in the graph and cocycles from nonabelian quandle cohomology.

Mixture-of-tastes Models for Representing Users with Diverse InterestsNov 22 2017Jan 29 2018Most existing recommendation approaches implicitly treat user tastes as unimodal, resulting in an average-of-tastes representations when multiple distinct interests are present. We show that appropriately modelling the multi-faceted nature of user tastes ... More

Strong Chain Rules for Min-Entropy under Few Bits SpoiledFeb 27 2017It is well established that the notion of min-entropy fails to satisfy the \emph{chain rule} of the form $H(X,Y) = H(X|Y)+H(Y)$, known for Shannon Entropy. Such a property would help to analyze how min-entropy is split among smaller blocks. Problems of ... More

Simulating Auxiliary Inputs, RevisitedMar 02 2015Jul 14 2016For any pair $(X,Z)$ of correlated random variables we can think of $Z$ as a randomized function of $X$. Provided that $Z$ is short, one can make this function computationally efficient by allowing it to be only approximately correct. In folklore this ... More

Towards a Total Cross Section Measurement with the ALFA Detector at ATLASSep 17 2014The main goals of the Absolute Luminosity For ATLAS (ALFA) detector is to provide an absolute luminosity and total cross section measurement. The measurement method used, the detector alignment and the quality of the collected data are discussed.

Four approaches to hydrodynamic Green's functions -- the Oseen tensorsDec 21 2013We present four different ways of deriving the Oseen tensor which is the fundamental solution to the Stokes equations for an incompressible viscous fluid. This solution corresponds to a point force acting on an infinite fluid. The derivations follow the ... More

On the Equivalence Principle and Electrodynamics of Moving BodiesMar 18 2015Feb 18 2018We consider a certain extension of the Einstein's elevator thought experiment by assuming that the elevator is charged and falls into an electromagnetic field. We argue, on grounds of the Equivalence Principle, that an observer-dependent metric should ... More

An example of a non non-archimedean Polish group with ample genericsMar 13 2015For an analytic $P$-ideal $I$, $S_I$ is the Polish group of all the permutations of $\mathbb{N}$ whose support is in $I$, with Polish topology given by the corresponding submeasure on $I$. We show that if $\mbox{Fin} \subsetneq I$, then $S_I$ has ample ... More

Multi-step Uniformization with Steady-State Detection in Nonstationary M/M/s Queuing SystemsOct 03 2014Oct 11 2014A new approach to the steady state detection in the uniformization method of solving continuous time Markov chains is introduced. The method is particularly useful in solving inhomogenous CTMC's in multiple steps, where the desired error bound of the ... More

Abelian pro-countable groups and non-Borel orbit equivalence relationsMay 24 2014Apr 25 2016We study topological groups that can be defined as Polish, pro-countable abelian groups, as non-archimedean abelian groups or as quasi-countable abelian groups, i.e., Polish subdirect products of countable, discrete groups, endowed with the product topology. ... More

Summary of session A4: Complex and conformal methods in classical and quantum gravityJan 08 2014This paper summarises oral contributions to the parallel session {\it Complex and conformal methods in classical and quantum gravity} which took place during the 20th International Conference on General Relativity and Gravitation held in Warsaw in July ... More

Rational solutions of certain Diophantine equations involving normsMay 27 2013In this note we present some results concerning the unirationality of the algebraic variety $\cal{S}_{f}$ given by the equation \begin{equation*} N_{K/k}(X_{1}+\alpha X_{2}+\alpha^2 X_{3})=f(t), \end{equation*} where $k$ is a number field, $K=k(\alpha)$, ... More

Abelian vortices from Sinh--Gordon and Tzitzeica equationsDec 30 2011Feb 25 2012It is shown that both the sinh--Gordon equation and the elliptic Tzitzeica equation can be interpreted as the Taubes equation for Abelian vortices on a CMC surface embedded in $\R^{2, 1}$, or on a surface conformally related to a hyperbolic affine sphere ... More

Instability of Flat Space Enclosed in a CavityAug 14 2012Jan 20 2013We consider a spherically symmetric self-gravitating massless scalar field enclosed inside a timelike worldtube $R\times S^3$ with a perfectly reflecting wall. Numerical evidence is given that arbitrarily small generic initial data evolve into a black ... More

Top degree part in $b$-conjecture for unicellular bipartite mapsApr 12 2016Aug 11 2017Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series $\psi(x, y, z; 1, 1+\beta)$ with an additional parameter $\beta$ that may be interpreted as a continuous deformation of the rooted bipartite maps ... More

Quantum resonances and partial differential equationsApr 24 2003Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description emphasizes the ... More

Morse cohomology in a Hilbert space via the Conley IndexJan 30 2014Aug 04 2014Main theorem of this paper states that Floer cohomology groups in a Hilbert space are isomorphic to the cohomological Conley Index. It is also shown that calculating cohomological Conley Index does not require finite dimensional approximations of the ... More

Liftability of singularities and their Frobenius morphism modulo $p^2$Mar 16 2016We investigate the $W_2(k)$-liftability of singular schemes. We prove constructibility of the locus of $W_2(k)$-liftable schemes in a flat family $X \to S$. Moreover, we construct an explicit $W_2(k)$-lifting of a Frobenius split scheme $X$ over a perfect ... More

Categories of diagrams with irreversible movesDec 31 2013Oct 04 2017We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every move of the ... More

A rho-invariant of iterated torus knotsJun 19 2009Jun 20 2012We compute rho-invariant for iterated torus knots $K$ for the standard representation of the knot group given by abelianisation. For algebraic knots, this invariant turns out to be very closely related to an invariant of a plane curve singularity, coming ... More

Self-injective artin algebras without short cycles in the component quiverDec 12 2012We give a complete description of all self-injective artin algebras of infinite representation type whose component quiver has no short cycles.

Relationships between K-monotonicity and rotundity properties with applicationFeb 26 2018In this paper we investigate a relationship between fully k-rotundity properties, uniform K-monotonicity properties, reflexivity and K-order continuity in a symmetric spaces E. We also answer a crucial question whether fully k-rotundity properties might ... More

On the Equivalence Principle and Electrodynamics of Moving BodiesMar 18 2015Consider an observer surrounded by a charged, conducting elevator (assume that the charge is isolated from the observer). In the presence of the external electric field the elevator will accelerate however, due to the screening effect, the observer will ... More

Relativistic Black-Scholes modelJul 19 2013May 24 2016Black-Scholes equation, after a certain coordinate transformation, is equivalent to the heat equation. On the other hand the relativistic extension of the latter, the telegraphers equation, can be derived from the Euclidean version of the Dirac equation. ... More

Spiky membranesOct 20 2009We study spiky configurations of membranes in the SO(d)xSU(N) invariant matrix models. A class of exact solutions (analogous to plane-waves) of the corresponding Schroedinger equation for an arbitrary N is discussed. If the large N limit is performed ... More

Precision radial velocities of double-lined spectroscopic binaries with an iodine absorption cellOct 15 2004Feb 25 2005A spectroscopic technique employing an iodine absorption cell (I_2) to superimpose a reference spectrum onto a stellar spectrum is currently the most widely adopted approach to obtain precision radial velocities of solar-type stars. It has been used to ... More

Incompressible Couette FlowFeb 04 2003This project work report provides a full solution of simplified Navier Stokes equations for The Incompressible Couette Problem. The well known analytical solution to the problem of incompressible couette is compared with a numerical solution. In that ... More

Numerical modeling of fluid flow through porous media (Modelowanie numeryczne transportu plynow przez osrodki porowate)Jul 17 2009The aim of the thesis is to present and analyze two particular problems of transport in porous media flow. The first of them is related to the process of saturation of porous building materials. Recently, M. K\"untz and P. Laval\'ee, using a computer ... More

Twistor Theory and Differential EquationsFeb 02 2009Feb 13 2009This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon arise from holomorphic ... More

Presymplectic representation of bi-Hamiltonian chainOct 26 2004Liouville integrable systems, which have bi-Hamiltonian representation of the Gel'fand-Zakharevich type, are considered. Bi-presymplectic representation of one-Casimir bi-Hamiltonian chains and weakly bi-presymplectic representation of multi-Casimir bi-Hamiltonian ... More

A Laplace ladder of discrete Laplace equationsMar 08 2002The notion of a Laplace ladder for a discrete analogue of the Laplace equation is presented. The adjoint of the discrete Moutard equation and a discrete counterpart of the nonlinear form of Goursat equation are introduced.

Dynamics of a planar domain wall with oscillating thickness in λ Φ^{4} modelMar 22 1999Domain wall - type solution with oscillating thickness in a real, scalar field model is investigated with the help of a polynomial approximation. We propose a simple extension of the polynomial approximation method. In this approach we calculate higher ... More

Multiparticle collision dynamics in porous mediaOct 20 2016We adopt the multiparticle collision dynamics method to simulate fluid flows in porous media. For this, the particle-level drag force is introduced into the original algorithm. The force hinder the flow resulting in global resistance and decrease of permeability. ... More

Multigraded ApolarityJan 23 2016We generalize methods to compute various kinds of rank to the case of a toric variety $X$ embedded into projective space using a very ample line bundle $\mathcal{L}$. We use this to compute rank, border rank, and cactus rank of monomials in $H^0(X, \mathcal{L})^*$ ... More

Dirac equation for embedded 4-geometriesMar 14 2011Mar 24 2013We apply Dirac's square root idea to constraints for embedded 4-geometries swept by a 3-dimensional membrane. The resulting Dirac-like equation is then analyzed for general coordinates as well as for the case of a Friedmann-Robertson-Walker metric for ... More

Construction of exact solutions of Bloch-Maxwell equation based on Darboux transformationAug 06 2004A new strategy, using Darboux transformations, of finding self-switching solutions of $i\dot{\rho} = [H, f({\rho})]$ is introduced. Unlike the previous ones, working for any f but for Hamiltonians whose spectrum contains at least three equally spaced ... More

On arithmetic progressions on genus two curvesMay 21 2007We study arithmetic progression in the $x$-coordinate of rational points on genus two curves. As we know, there are two models for the curve $C$ of genus two: $C: y^2=f_{5}(x)$ or $C: y^2=f_{6}(x)$, where $f_{5}, f_{6}\in\Q[x]$, $\operatorname{deg}f_{5}=5, ... More

Homology of ternary algebras yielding invariants of knots and knotted surfacesJun 14 2017Sep 20 2018We define homology of ternary algebras satisfying axioms derived from particle scattering or, equivalently, from the third Reidemeister move. We show that ternary quasigroups satisfying these axioms appear naturally in invariants of Reidemeister, Yoshikawa, ... More

Entropy of Independent Experiments, RevisitedApr 28 2017The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for sources with independent ... More

Robust scheduling to minimize the weighted number of late jobs with interval due-date uncertaintyAug 08 2017We consider the class of single machine scheduling problems with the objective to minimize the weighted number of late jobs, under the assumption that completion due-dates are not known precisely at the time when decision-maker must provide a schedule. ... More

The observer-assisted method for adjusting hyper-parameters in deep learning algorithmsNov 30 2016This paper presents a concept of a novel method for adjusting hyper-parameters in Deep Learning (DL) algorithms. An external agent-observer monitors a performance of a selected Deep Learning algorithm. The observer learns to model the DL algorithm using ... More

Multiparticle collision dynamics in porous mediaOct 20 2016Oct 28 2016Multiparticle collision dynamics (MPCD) is a relatively new algorithm of fluid flow simulations that has been applied mostly to flows around simple objects. One might ask how it behaves in more complex flows. Therefore, we extend MPCD to simulate transport ... More

Non-autonomous Henon-Heiles system from Painleve classApr 10 2019Apr 29 2019We show how to deform separable Henon-Heiles system with isospectral Lax representation, related with the stationary flow of the $5th$-order KdV, to respective non-autonomous systems of Painleve type with isomonodromic Lax representation.

Pion spectra in Ar+Sc interactions at SPS energiesDec 05 2016This contribution discusses recent results from analysis of Ar+Sc interactions recorded with the NA61/SHINE detector at six beam momenta: 13A, 19A, 30A, 40A, 75A, 150A GeV/c at the CERN SPS. Rapidity and transverse mass spectra of pions obtained with ... More

On decompositions of quadrinomials and related Diophantine equationsDec 09 2015Let $A,B,C,D$ be rational numbers such that $ABC \neq 0$, and let $n_1>n_2>n_3>0$ be positive integers. We solve the equation $$ Ax^{n_1}+Bx^{n_2}+Cx^{n_3}+D = f(g(x)),$$ in $f,g \in \mathbb{Q}[x]$. In sequel we use Bilu-Tichy method to prove finitness ... More

A New Approximate Min-Max Theorem with Applications in CryptographyJun 22 2015We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and ... More

Lower bounds on $q$-wise independence tails and applications to min-entropy condensersApr 09 2015We present novel and sharp lower bounds for higher load moments in the classical problem of mapping $M$ balls into $N$ bins by $q$-universal hashing, specialized to the case when $M=N$. As a corollary we prove a tight counterpart for the result about ... More

Consequences of the existence of ample generics and automorphism groups of homogeneous metric structuresMay 07 2014Nov 25 2015We define a simple criterion for a homogeneous, complete metric structure $X$ that implies that the automorphism group $\mbox{Aut}(X)$ satisfies all the main consequences of the existence of ample generics: it has the small index property, the automatic ... More

Dirac equation for stringsFeb 24 2013Feb 14 2018Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there ... More

Decoherence free subspaces for two--access quantum channelsSep 01 2012Sep 04 2012In this paper we consider construction of decoherence free subspaces for two--access random unitary channels. First, we concentrate on hermitian unitary noise model $U$ for a bi--unitary channel and show that in this case a code exists if the space of ... More

Motion of the Local Group as a cosmological probeMay 09 2012In this thesis, we use the motion of the Local Group of galaxies (LG) through the Universe to measure the cosmological parameter of non-relativistic matter density, Omega_m. For that purpose, we compare the peculiar velocity of the LG with its gravitational ... More

The Twisted Photon Associated to Hyper-Hermitian Four-ManifoldsAug 31 1998The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a potential that generalises Plebanski's second heavenly equation for hyper-Kahler 4-manifolds. A class of examples of hyper-Hermitian metrics which depend on ... More

Resonances for asymptotically hyperbolic manifolds: Vasy's method revisitedNov 11 2015Dec 02 2015We revisit Vasy's method for showing meromorphy of the resolvent for (even) asymptotically hyperbolic manifolds. It provides an effective definition of resonances in that setting by identifying them with poles of inverses of a family of Fredholm differential ... More

Anti-self-dual four-manifolds with a parallel real spinorFeb 28 2001Oct 18 2001Anti-self-dual metrics in the $(++--)$ signature which admit a covariantly constant real spinor are studied. It is shown that finding such metrics reduces to solving a fourth order integrable PDE, and some examples are given. The corresponding twistor ... More

Harmonic functions, central quadrics, and twistor theoryMar 14 2003Jun 27 2003Solutions to the $n$-dimensional Laplace equation which are constant on a central quadric are found. The associated twistor description of the case $n=3$ is used to characterise Gibbons-Hawking metrics with tri-holomorphic $SL(2, \C)$ symmetry.

Macdonald cumulants, $G$-inversion polynomials and $G$-parking functionsJul 09 2017Sep 18 2018We prove a combinatorial formula for Macdonald cumulants which generalizes the celebrated formula of Haglund for Macdonald polynomials. We provide several applications of our formula. Firstly, it gives a new, constructive proof of a strong factorization ... More

On Directed Lattice Paths With Additional Vertical StepsOct 20 2014The paper is devoted to the study of lattice paths that consist of vertical steps $(0,-1)$ and non-vertical steps $(1,k)$ for some $k\in \mathbb Z$. Two special families of primary and free lattice paths with vertical steps are considered. It is shown ... More

Morse theory for plane algebraic curvesJan 10 2011May 24 2011We use Morse theoretical arguments to study algebraic curves in C^2. We take an algebraic curve C in C^2 and intersect it with a family of spheres with fixed origin and varying radii. We explain in detail how does the resulting link change when we cross ... More

Puiseux coefficients and parametric deformation of plane curve singularitiesSep 24 2009Mar 19 2012We study deformations of plane curve singularities from an analytic point of view and obtain some new concrete results. We show some rather unexpected properties of Puiseux coefficients treated as functions on a suitably defined parameter space. The methods ... More

Number of singular points of a genus $g$ curve with one point at infinityAug 31 2009We bound the maximal number N of singular points of a plane algebraic curve C that has precisely one place at infinity with one branch in terms of its first Betti number $b_1(C)$. Asymptotically we prove that $N<\sim{17/11}b_1(C)$ for large $b_1$. In ... More

Weighted and multivariate Johnson--Schechtman inequalities with application to interpolation theoryJun 04 2019We prove a weighted version of a classical inequality of Johnson and Schechtman from which we derive a decomposition theorem for $p$-th moments ($0<p\leq 1$) of nonnegative generalized $U$-statistics with constant not dependent on $p$. In particular, ... More

Degenerate Poisson pencils on curves: new separability theoryApr 01 2000Apr 01 2000A review of a new separability theory based on degenerated Poisson pencils and the so-called separation curves is presented. This theory can be considered as an alternative to the Sklyanin theory based on Lax representations and the so-called spectral ... More

Hyper-complex four-manifolds from the Tzitzéica equationAug 10 2001Oct 05 2001It is shown how solutions to the Tzitz\'eica equation can be used to construct a family of (pseudo) hyper-complex metrics in four dimensions.

Poisson Formula for Resonances in Even DimensionsJan 21 1999We consider scattering by an abstract compactly supported perturbation in R^n. To include the traditional cases of potential, obstacle and metric scattering without going into their particular nature we adopt the "black box" formalism developed jointly ... More

Supersymmetry and Lie groupsJul 26 2007We construct all vacuum states of $\mathcal{N}=2$ supersymmetric Yang-Mills quantum mechanics (for SU(N) group) and discuss their origin from the SU(N) real cohomology.

The study of SU(3) super Yang-Mills quantum mechanicsSep 27 2005Dec 16 2005We present the hamiltonian study of super Yang-Mills quantum mechanics (SYMQM). The recently introduced method based on Fock space representation allows to analyze SYMQM numerically. The detailed analysis for SYMQM in two dimensions for SU(3) group is ... More

Oriented straight lines and twistor correspondenceAug 10 2004Nov 23 2004The tangent bundle to the $n$--dimensional sphere is the space of oriented lines in $\R^{n+1}$. We characterise the smooth sections of $TS^n\to S^n$ which correspond to points in $\R^{n+1}$ as gradients of eigenfunctions of the Laplacian on $S^n$ with ... More

Quantum mechanics in a cut Fock spaceJul 08 2004Jul 09 2004A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between discrete and continuous ... More

Reexamination of determinant-based separability test for two qubitsOct 03 2010Jun 22 2011It was shown in [Augusiak et al.,\;Phys. Rev. A \textbf{77}, 030301(R) (2008)] that discrimination between entanglement and separability in a two qubit state can be achieved by a measurement of a single observable on four copies of it. Moreover, a pseudo ... More

Interpolating Dispersionless Integrable SystemApr 08 2008Jun 07 2008We introduce a dispersionless integrable system which interpolates between the dispersionless Kadomtsev-Petviashvili equation and the hyper-CR equation. The interpolating system arises as a symmetry reduction of the anti--self--dual Einstein equations ... More

Rational points on certain elliptic surfacesMay 21 2007Let $\mathcal{E}_{f}:y^2=x^3+f(t)x$, where $f\in\Q[t]\setminus\Q$, and let us assume that $\op{deg}f\leq 4$. In this paper we prove that if $\op{deg}f\leq 3$, then there exists a rational base change $t\mapsto\phi(t)$ such that on the surface $\cal{E}_{f\circ\phi}$ ... More

Einstein--Maxwell--Dilaton metrics from three--dimensional Einstein--Weyl structuresJan 04 2006Feb 12 2006A class of time dependent solutions to $(3+1)$ Einstein--Maxwell-dilaton theory with attractive electric force is found from Einstein--Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and $SU(\infty)$ Toda equations. ... More

On the Complexity of Searching Maximum of a Function on a Quantum ComputerJul 06 2005Oct 13 2005We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the algorithm ... More

Two-loop QCD corrections to top quark decayApr 27 2004We present a determination of a new class of Feynman diagrams relevant for second-order QCD corrections to the top quark decay t -> b W. Modern computing techniques allow us to perform a reduction of the original loop integrals to master integrals. We ... More

Rational points on certain quintic hypersurfacesOct 01 2008Let $f(x)=x^5+ax^3+bx^2+cx \in \Z[x]$ and consider the hypersurface of degree five given by the equation \cal{V}_{f}: f(p)+f(q)=f(r)+f(s). Under the assumption $b\neq 0$ we show that there exists $\Q$-unirational elliptic surface contained in $\cal{V}_{f}$. ... More

On some Diophantine systems involving symmetric polynomialsMay 27 2013Let $\sigma_{i}(x_{1},\ldots, x_{n})=\sum_{1\leq k_{1}<k_{2}<\ldots <k_{i}\leq n}x_{k_{1}}\ldots x_{k_{i}}$ be the $i$-th elementary symmetric polynomial. In this note we generalize and extend the results obtained in a recent work of Zhang and Cai \cite{ZC,ZC2}. ... More

Untwisting number and Blanchfield pairingsSep 29 2017In this note we use Blanchfield forms to study knots that can be turned into an unknot using a single $\overline{t}_{2k}$ move.

Systems, environments, and soliton rate equations (II): Toward realistic modelingMar 12 2018In order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) Find a `Lax representation' where all the kinetic variables are combined into a single matrix $\rho$, all the kinetic ... More

Approximation of maps into spheres by regulous mapsJun 15 2017Let $X$ be a compact real algebraic set of dimension $n$. We prove that every Euclidean continuous map from $X$ into the unit $n$-sphere can be approximated by regulous map. This strengthens and generalizes previously known results.

RKFD Methods - a short reviewOct 31 2016In this paper, a recently published method [Hussain, Ismail, Senua, Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method, J. Comput. Appl. Math. 306 (2016) 179-199] for solving fourth-order ordinary differential ... More

Dynamics of Nonlinear Waves on Bounded DomainsMar 03 2016This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy ... More

Rational cuspidal curves in projective surfaces. Topological versus algebraic obstructionsNov 18 2015We study rational cuspidal curves in projective surfaces. We specify two criteria obstructing possible configurations of singular points that may occur on such curves. One criterion generalizes the result of Fernandez de Bobadilla, Luengo, Melle--Hernandez ... More

Abelian pro-countable groups and orbit equivalence relationsMay 04 2014Apr 15 2015We study groups that can be defined as Polish, pro-countable groups, as non-archimedean groups with an invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable, discrete groups, endowed with the product topology. We ... More

Bayesian DEJD model and detection of asymmetric jumpsApr 08 2014News might trigger jump arrivals in financial time series. The "bad" and "good" news seems to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion ... More

Transfinite Asymptotic DimensionOct 02 2013Asymptotic property C for metric spaces was introduced by Dranishnikos as generalization of finite asymptotic dimension - asdim. It turns out that this property can be viewed as transfinite extension of asymptotic dimension. The original definition was ... More