Preprints from
758  Wojciech M. Zajączkowski  On regular periodic solutions to the NavierStokes equations. Case C, March 2020 
Full Text Abstract Abstract: On regular periodic solutions to the NavierStokes equations. Case C
AbstractWe find a global a priori estimate for solutions to the NavierStokes equations with periodic boundary conditions guaranteeing inview of the Serrin type condition the existence of global regular solutions. We derive the following estimate‖V(t)‖H1(Ω)≤c,(1)whereVis the velocity of the fluid.The estimate (1) is proved in two steps. First we derive a globalestimate guaranteeing the existence of global regular solutions toweakly compressible NavierStokes equations with large second viscosity, density close to a constant and gradient part of velocity small.Next we show that solutions to the NavierStokes equations remainclose to solutions to the weakly compressible NavierStokes equationsif the corresponding initial data and external forces are sufficientlyclose 
757  Wojciech M. Zająaczkowski  On regular periodic solutions to the NavierStokes equations. Case B, March 2020 
Full Text Abstract Abstract: On regular periodic solutions to the NavierStokes equations. Case B
We find a global a priori estimate for solutions to the NavierStokes equations with periodic boundary conditions guaranteeing inview of the Serrin type condition the existence of global regular solutions. We derive the following estimate‖V(t)‖H1(Ω)≤c,(1)whereVis the velocity of the fluid.The estimate (1) is proved in two steps. First we derive a globalestimate guaranteeing the existence of global regular solutions toweakly compressible NavierStokes equations with large second viscosity, density close to a constant and gradient part of velocity small.Next we show that solutions to the NavierStokes equations remainclose to solutions to the weakly compressible NavierStokes equationsif the corresponding initial data and external forces are sufficientlyclose. 
756  Wojciech M. Zajączkowski  Global regular periodic solutions to equations of weakly compressible barotropic fluid motions. Case C, March 2020 
Full Text Abstract Abstract: Global regular periodic solutions to equations of weakly compressible barotropic fluid motions. Case C
We consider barotropic motions described by the compressibleNavierStokes equations in a box with periodic boundary conditions.We are looking for density%in the form%=a+η, whereais aconstant andηt=0is sufficiently small inH2norm. We assume existence of potentialsφandψsuch thatv=∇φ+ rotψ+ –∫vdx.Next we assume that∇φt=0is sufficiently small inH2norm too.Finally, we assume that the second viscosity coefficientνis sufficiently large. Then we prove long time existence of solutions suchthatv∈L∞(0,T;H2(Ω))∩L2(0,T;H3(Ω)),v,t∈L∞(0,T;H1(Ω))∩L2(0,T;H2(Ω)), where the existence timeTis proportional toν.Next forTsufficiently large we obtain thatv(T) is correspondinglysmall so global existence is proved using the methods appropriate forproblems with small data.Mathematical Subject Classification (2010):35A01, 35B10,76N10Key words and phrases:compressible NavierStokes equations,periodic solutions, density close to a constant, gradient part of velocity small, large second viscosity, existence of global regular solutions. 
755  Wojciech M. Zajączkowski  Global regular periodic solutions to equations of weakly compressible barotropic fluid motions. Case B, March 2020 
Full Text Abstract Abstract: Global regular periodic solutions to equations of weakly compressible barotropic fluid motions. Case B
We consider barotropic motions described by the compressibleNavierStokes equations in a box with periodic boundary conditions.We are looking for density%in the form%=a+η, whereais aconstant andηt=0is sufficiently small inH2norm. We assume existence of potentialsφandψsuch thatv=∇φ+ rotψ+ –∫vdx.Next we assume that∇φt=0is sufficiently small inH2norm too.Finally, we assume that the second viscosity coefficientνis sufficiently large. Then we prove long time existence of solutions suchthatv∈L∞(0,T;H2(Ω))∩L2(0,T;H3(Ω)),v,t∈L∞(0,T;H1(Ω))∩L2(0,T;H2(Ω)), where the existence timeTis proportional toν.Next forTsufficiently large we obtain thatv(T) is correspondinglysmall so global existence is proved using the methods appropriate forproblems with small data.Mathematical Subject Classification (2010):35A01, 35B10,76N10Key words and phrases:compressible NavierStokes equations,periodic solutions, density close to a constant, gradient part of velocity small, large second viscosity, existence of global regular solutions 
754  Jan Kisyński  CHARACTERIZATION OF RAPIDLY DECREASING DISTRIBUTIONS ON R^n BY CONVOLUTIONS WITH TEST FUNCTIONS, March 2019  Full Text 
753  Jan Kisyński  TOPOLOGIES IN THE SET OF RAPIDLY DECREASING DISTRIBUTIONS, February 2019  Full Text 
752  Jan Kisyński  ON RAPIDLY DECREASING DISTRIBUTIONS, May 2017  Full Text 
751  Jan Kisyński  ON THE EXCHANGE BETWEEN CONVOLUTION AND MULTIPLICATION VIA THE FOURIER TRANSFORMATION, February 2017  Full Text 
750  Jan Kisyński  ON THE LOCALLY CONVEX SPACE OF RAPIDLY DECREASING DISTRIBUTIONS, June 2016  Full Text 
749  P.J. GIBLIN AND S.JANECZKO  BIFURCATION SETS OF FAMILIES OF REFLEXIONS ON SURFACES IN R 3, September 2015  Full Text 
748  Takeo Fukuda and Stanisław Janeczko  Poisson algebras and singular symplectic forms associated to A_{k} type singularities., July 2015  Full Text 
747  W. Domitrz, S. Janeczko, P. DE M. Rios, and M.A.S. Ruas  Singularities of affine equidistants: Extrinsic geometry of surfaces in 4space. July 2015, July 2015  Full Text 
746  Teresa Ledwina and Grzegorz Wyłupek  Tests for firstorder stochastic dominance, December 2013  Full Text 
745  Zbigniew Jelonek  Simple examples of affine manifolds with infinitely many exotic models, July 2013  Full Text 
744  Takeo Fukuda and Stanisław Janeczko  Singularities of solvable Hamiltonian mappings, April 2013  Full Text 
743  Piotr M.Hajac and Elmar Wagner  The pullbacks of principal coactions, March 2013  Full Text 
742  Teresa Regińska  Discrete illposed problems: twoparameter regularization, November 2012  Full Text 
741  Hassan Babiker and Stanisław Janeczko  Combinatorial cycles of tetrahedral chains, November 2012  Full Text 
740  Jerzy Zabczyk  "A note on the paper ""Stability and stabilizability of infinite dimensional systems"" by A. J. Pritchard and J. Zabczyk, SIAM Review, 23 (1981), 2552", October 2012  Full Text 
739  S. Janeczko, Z. Jelonek, M. A. S. Ruas  Symmetry defect of algebraic varieties, September 2012  Full Text 
738  Jan Rudnik  The Ktheory of the tripleToeplitz deformation of the complex projective plane, July 2012  Full Text 
737  Piotr M. Hajac and Bartosz Zieliński  The cocycle condition for multipullbacks of algebras, July 2012  Full Text 
736  Takako Kuzumaki and Jerzy Urbanowicz  On congruences for the sums $\sum_{i=1}^{[n//r]}{\chi_n(i)\over nri}$ of E. Lehmer's type, July 2012  Full Text 
735  Shigeru Kanemitsu, Takako Kuzumaki and Jerzy Urbanowicz  On congruences for the sums $\sum_{i=1}^{[n//r]}{\chi_n(i)\over i^k}$ of E. Lehmer's type, July 2012  Full Text 
734  Ryszard Frankiewicz, Sławomir Szczepaniak  An easy proof of Gowers' FINk theorem, December 2011  Full Text 
733  Piotr M. Hajac, Adam Rennie and Bartosz Zieliński  The Ktheory of Heegaard quantum lens spaces, October 2011  Full Text 
732  Teresa Crespo, Zbigniew Hajto and Elżbieta Sowa  PiccardVessiot theory for real fields, October 2011  Full Text 
731  Teresa Regińska  Regularization methods for mathematical model of laser beams, October 2011  Full Text 
730  Erdem Altuntac  On convergence of an alternating method for a Cauchy problem for the Helmholtz equation, June 2011  Full Text 
729  Jan Kisyński  The Petrovski? condition!!and!!rapidly decreasing distritutions, January 2011  Full Text 
728  Bronisław Jakubczyk and Wojciech Kryński  Vector fields with distributions and invariants of ODEs, December 2010  Full Text 
727  Joanna Janczewska  Finding two almost homoclinic solutions for a class of second order perturbed Hamiltonian systems, December 2010  
726  Małgorzata Schroeder and Ryszard Zieliński  Estimating AR(1) with Entropy Loss Function, August 2010  Full Text 
725  Jan Kisyński  On the TarskiSeidenberg Theorem, June 2010  Full Text 
724  Tomasz Maszczyk  Computing GromovWitten Invariants of some Fano Varieties, May 2010  Full Text 
723  Tomasz Maszczyk  Division with Remainder in Algebras with Valuation, May 2010  Full Text 
722  Tomasz Maszczyk  On Splitting Polynomials in Noncommutative Extensions, May 2010  Full Text 
721  Tomasz Maszczyk  Maximal Commutative Subalgebras, Poisson Geometry and Hochschild Homology, May 2010  Full Text 
720  Tomasz Maszczyk  Distributive Lattices and Cohomology, May 2010  Full Text 
719  Piotr M. Sołtan  On Actions of of Compact Quantum Group, May 2010  Full Text 
718  Piotr M. Sołtan  Examples of Noncompact Quantum Group Actions, May 2010  Full Text 
717  Jan Janas, Sergei Naboko and Luis O. Silva  Proceedings of the 8th Research Seminar of Difference and Differential Operators, 714 July 2007, April 2010  Full Text 
716  Zbigniew Jelonek  On the Russell Problem, March 2010  Full Text 
715  Robert Dryło  On Constructing Optimal Families of Pairingfriendly Elliptic Curves, March 2010  Full Text 
714  Andrzej Pokrzywa  Regularization of linear operators, Hilbert space methods, March 2010  Full Text 
713  Danuta PrzeworskaRolewicz  Shifts and Periodicity in Algebraic Analysis, February 2010  Full Text 
712  Jan Kisyński  Convolution Semigroups of Rapidly Decreasing Distributions, February 2010  Full Text 
711  Piotr M. Hajac, Atabey Kaygun, Bartosz Zieliński  Finite Closed Coverings!!of Compact Quantum Spaces, February 2010  Full Text 
710  Emily Burgunder and Maria Ronco  Tridendriform Algebras and Combinatorial Hopf Algebras, December 2009 
Full Text Abstract Abstract: Tridendriform Algebras and Combinatorial Hopf AlgebrasAbstract 710 Abstract. We extend the denition of tridendriform bialgebra by in troducing a weight q. The subspace of primitive elements of a qtridendriform bialgebra is equipped with an associative product and a natural struc ture of brace algebra, related by a distributive law. This data is called q GerstenhaberVoronov algebras. We prove the equivalence between the categories of connected qtridendriform bialgebras and of qGerstenhaber Voronov algebras. The space spanned by surjective maps, as well as the space spanned by parking functions, have natural structures of q tridendriform bialgebras, denoted ST(q) and PQSym(q), in such a way that ST(q) is a subtridendriform bialgebra of PQSym(q). Finally we show that the bialgebra ofMpermutations dened by T. Lam and P. Pylyavskyy may be endowed with a natural structure of qtridendriform algebra which is a quotient of ST(q). 
709  W. Domitrz, S. Janeczko and M. Zhitomirskii  Generic Singularities of Symplectic and Quasisymplectic Immersions, December 2009 
Full Text Abstract Abstract: Generic Singularities of Symplectic and Quasisymplectic ImmersionsAbstract 709 Abstract. For any k < 2n we construct a complete system of invariants in the problem of classifying singularities of immersed k dimensional submanifolds of a symplectic 2nmanifold at a generic double point. 
708  Stanisław Spież, Marian Srebrny and Jerzy Urbanowicz  Secret Sharing Matrices, September 2009  Full Text 
707  Andrzej Schinzel, Stanisław Spież and Jerzy Urbanowicz  Admissible Tracks in Shamir's Scheme, September 2009  Full Text 
706  Teresa Regińska and Ulrich Tautenhahn  Conditional stability estimates and regularization with applications to Cauchy problems for the Helmholtz equation, May 2009  Full Text 
705  Wojciech Niemiro and Ryszard Zieliński  Remarks of uniform convergence of random variables and statistics, May 2009  Full Text 
704  Goo Ishikawa and Stanisław Janeczko  Symplectic invariants of parametric singularities, May 2009  Full Text 
703  Dmitry Portnyagin  Regularity of Solutions to Nonlinear Nondiagonal Parabolic System, February 2009  Full Text 
702  Krzysztof Szajowski  On a Random Number of Disorders, February 2009  Full Text 
701  Jan Kisyński  Cauchy's problem for system of PDE with constant coefficients and semigroups of operators, January 2009  Full Text 
700  Elżbieta Ferenstein and Adam PasternakWiniarski  Optimal stopping of a risk process with disruption and interest rates, January 2009  Full Text 
699  Michał Baran and Jerzy Zabczyk  Completeness of bond market driven by Lévy process, December 2008  Full Text 
698  Jacek Jakubowski and Mariusz Niewęgłowski  FDoubly Stochastic Markov Chains  A New Class of Processes for Modeling Credit Rating , December 2008  Full Text 
697  Jacek Jakubowski and Mariusz Niewęgłowski  Defaultable bonds with an infinite number of Lévy factors, December 2008  Full Text 
696  Wojciech Sarnowski and Krzysztof Szajowski  Optimal detection of homogeneous segment of observations in stochastic sequence, December 2008  
695  Joanna Janczewska  Homoclinic solutions for a class of autonomous second order Hamiltonian systems with a superquadratic potential, November 2008  Full Text 
694  Zdzisław Brzeniak and Jerzy Zabczyk  Regularity of OrnsteinUhlenbeck processes driven by a Lévy white noise, November 2008  Full Text 
693  Danuta PrzeworskaRolewicz  Fourierlike methods for equations with separable variables, October 2008  Full Text 
692  Enrico Priola and Jerzy Zabczyk  Structual properties of semilinear SPDEs driven by cylindrical stable processes, October 2008  Full Text 
691  Danuta PrzeworskaRolewicz  Nonlinear separable equations in linear spaces and commutative Leibniz algebras, September 2008  Full Text 
690  Michał Baran, Jacek Jakubowski and Jerzy Zabczyk  On incompleteness of bond markets with infinite number of random factors, September 2008  Full Text 
689  Piotr Miło  A note on small branching fluctuation limits of catalytic superprocesses with immigration, September 2008  Full Text 
688  Danuta PrzeworskaRolewicz  Möj mistrz i promotor Witold Pogorzelski (18951963), August 2008  Full Text 
687  Marcin Styborski  Conley index in Hilbert spaces and the LeraySchauder degree, March 2008  Full Text 
686  Łukasz Kuciński  Equivalence of measures corresponding to the Hilbert space valued Lévy processes, December 2007  Full Text 
685  Jerzy Zabczyk and Anna Rusinek  Positivity of crredit spreads, August 2007 
Full Text Abstract Abstract: Positivity of crredit spreadsCredit spread is defined as a difference between forward rates corresponding to bond facing the default risk and forward rates corresponding to riskfree bond. We give conditions under which credit spread is a positive process, considering joint model for rates. 
684  Erwin Deriaz, Valérie Perrier  Direct Numerical Simulation of turbulence using divergencefree wavelets, June 2007  Full Text 
683  Stefan Rolewicz  How to define convex functions on differentiable manifolds, June 2007  Full Text 
682  Michał Baran  Approximations for solutions of Lévytype stochastic differential equations, May 2007  Full Text 
681  Wojciech Kryński  Contact Equivalence and characteristic Cones of Ordinary Differential Equations, May 2007  Full Text 
680  Erwin Deriaz, Valérie Perrier  Orthogonal Helmholtz decomposition in arbitrary dimension using divergencefree and curlfree wavelets, May 2007  Full Text 
679  Zbigniew Jelonek  On the Cancellation Problem, April 2007  Full Text 
678  Stanisław Janeczko, Zbigniew Jelonek  Diffeomorphisms that are Symplectomorphisms, March 2007  Full Text 
677  Szymon Peszat and Jerzy Zabczyk  HeathJarrowMortonMusiela Equation of Bond Market, February 2007  Full Text 
676  Erwin Deriaz  Shannon wavelet approximations of linear differential operators, January 2007  Full Text 
675  B. Jakubczyk, W. Kryński, F. Pelletier  Characteristic vector fields of generic distributions of corank 2, December 2006  Full Text 
674  Michał Baran, Jacek Jakubowski, Jerzy Zabczyk  A note on completeness of bond market in infinite dimension, December 2006  Full Text 
673  Jacek Jakubowski and Jerzy Zabczyk  Exponential moments for HJM models with jumps, November 2006 
Full Text Abstract Abstract: Exponential moments for HJM models with jumpsGeneral HJM models driven by a Lévy process are considered. Necessary moment conditions for the discounted bond prices to be local martingales are derived. It is proved, under the moment conditions, that the discounted bond prices are local martingales if and only if a generalized HJM condition holds. 
672  W. Domitrz, S. Janeczko, M. Zhitomirskii  Symplectic Singularities of Varieties: The Method of Algebraic Restrictions, October 2006  Full Text 
671  Zbigniew Jelonek  Manifolds with a Unique Embedding, September 2006  Full Text 
670  Özer Öztürk  On Thom polynomials for A4 () via Schur functions, September 2006  Full Text 
669  Anna Rusinek  Invariant measures for forward rate HJM model with Lévy noise, September 2006 
Full Text Abstract Abstract: Invariant measures for forward rate HJM model with Lévy noiseWe give a sufficient condition for the existence of an invariant measure for HeathJarrowMorton model of forward rate function driven by a Levy process. We also prove that there exists an invariant measure for the model, if noise is small enough. 
668  Wojciech Niemiro, Ryszard Zieliński  Uniform asymptotic normality for the Bernoulli scheme, June 2006  Full Text 
667  Anna Rusinek  Invariant measures for a class of stochastic evolution equations, March 2006 
Full Text Abstract Abstract: Invariant measures for a class of stochastic evolution equationsWe give a sufficient condition for the existence of an invariant measure for a stochastic evolution equation with noise driven by a Lévy process. 
666  Jan Kisyński  On Fourier transforms of distribution semigroups, March 2006 
Full Text Abstract Abstract: On Fourier transforms of distribution semigroupsAbstract 666 A onetoone correspondence is established between Fourier transforms of ultradistribution semigroups in the sense of Beurling and some class of pseudoresolvents characterized by conditions concerning their domains of existence and growth. 
665  Tadeusz Inglot and Teresa Ledwina  Data driven score tests of fit for a semiparametric homoscedastic linear regression model, January 2006 
Full Text Abstract Abstract: Data driven score tests of fit for a semiparametric homoscedastic linear regression modelAbstract 665 We propose new tests for testing the validity of a semiparametric randomdesign linear regression model. The construction consists of several steps. First, we follow the classical idea of overfitting and replace the basic problem by a series of auxiliary subproblems. Next, to test whether extra terms are significant we construct a counterpart of classic score statistic. In passing, a handy way of deriving the efficient score is proposed and developed. Finally, we com bine the solution with smoothing methods providing guidelines to choose the right subproblem. This leads to data driven score tests for the initial testing problem. We show that under the null model our construction is asymptotically distribution free and illustrate this result by a small simulation study. We also compare the finite sample performace of our tests with the the recent solution introduced by Guerre and Lavergne (2005), as well as to Cram?ervon Mises type construction. The simulation experiment indicates the very good performance of the proposed tests. 
664  Goo Ishikawa and Stanisław Janeczko  The complex symplectic moduli spaces of unimodel parametric plane curve singularities, January 2006 
Full Text Abstract Abstract: The complex symplectic moduli spaces of unimodel parametric plane curve singularitiesAbstract 664 Classification of zeromodal singularities of parametric plane curves under diffeomorphism equivalence is extended to unimodal singularities. Both the simple and unimodal singularities of parametric plane curves are classified further under symplectomorphic equivalence. In particular the corresponding cyclic symplectic moduli spaces are reconstructed as a canonical ambient spaces for the diffeomorphism moduli spaces which are no longer Hausdorff spaces. 
662  Teresa Regińska and Andrzej Wakulicz  Wavelet moment method for Cauchy problem fo the Helmhotz equation, December 2005 
Full Text Abstract Abstract: Wavelet moment method for Cauchy problem fo the Helmhotz equationAbstract 662 The paper is concerned with the problem of reconstruction of acoustic or electromagnetic field from unexact data given on an open part of the boundary of a given domain. A regularization concept is presented for the illposed moment problem equivalent to a Cauchy problem for the Helmholtz equation. A method of regularization by projection with application of Meyer wavelet subspaces is introduced and analyzed. The derived formula, describing the projection level in terms of the error bound of unexact Cauchy data, allows to prove convergence and stability of the method. 
661  Agata Boratyńska  Gammaminimax prediction in exponential families with quadratic variance function, November 2005 
Full Text Abstract Abstract: Gammaminimax prediction in exponential families with quadratic variance functionAbstract 661 The problem of prediction of a random variable Y , distribution of which belongs to the one parameter exponential family with the quadratic variance function is considered. The knowledge about priors is introduced by a class Γ of all distributions, where the first two moments are within some given convex and compact set. The Γminimax predictor under the squared error loss is obtained. 
660  Teresa Regińska and Kazimierz Regiński  Approximate solution of a Cauchy problem for the Helmholtz equation, September 2005 
Full Text Abstract Abstract: Approximate solution of a Cauchy problem for the Helmholtz equationAbstract 660 A problem of reconstruction of the radiation field in a domain in R^{3} from experimental data on a part of boundary is considered. For the model problem described by a Cauchy problem for the Helmholtz equation, an approximate method based on regularization in the frequency space is analyzed. Convergence and stability are proved under a suitable choice of regularization parameter. Numerical implementation of the method is discussed. 
659  Halszka TutajGasińska  Symplectic packing of a torus, July 2005 
Full Text Abstract Abstract: Symplectic packing of a torusAbstract 659 We show a construction of a symplectic packing of a fourdimensional ball into a torus. 
658  Jacek Jakubowski, Mariusz Niewęgłowski and Jerzy Zabczyk  Lévy modelling of defaultable bonds, July 2005 
Full Text Abstract Abstract: Lévy modelling of defaultable bondsAbstract 658 A market with defaultable bonds modelled by equations with L?vy noise is considered. Conditions under which the market is free of arbitrage are derived. 
657  Ryszard Zieliński  Lstatistics as nonparametric Quantile Estimators, June 2005 
Full Text Abstract Abstract: Lstatistics as nonparametric Quantile EstimatorsAbstract 657 Key Words: quantiles, HarrellDavis estimator, KaighCheng estimator; Lstatistics; optimal estimation. 
656  Ryszard Zieliński  Estimating quantiles with Linex Loss Function. Approximation to VaR Estimation, April 2005 
Full Text Abstract Abstract: Estimating quantiles with Linex Loss Function. Approximation to VaR EstimationAbstract 656 Sometimes, e.g. in the context of estimating V aR (Value at Risk), underestimating a quantile is less desirable than overestimating it which suggest to measure the error of estimation by an asymmetric loss function. As a loss function when estimat ing a parameter by an estimator T we take the well known Linex Function exp{f(αT  θ )}g (T ) 1. To estimate the quan tile of order q 2 (0; 1) of a normal distribution N(; ), we con struct the optimal estimator in the class of all estimators of the form ?x + k; 1 < k < 1, if is known, or of the form ?x + s, if both parameters and are unknown; here ?x and s are standard estima tors of and , respectively. To estimate a quantile of an unknown distribution F from the family F of all continuous and strictly in creasing distribution functions we construct the optimal estimator in the class T of all estimators which are equivariant with respect to monotone transformations of data. 
655  Tomasz Maszczyk  On a pairing between super Lie and periodic homology, March 2005  
654  Tomasz Maszczyk  Differential operators of k[x]/(xn+1), December 2004  
653  Ryszard Zieliński  Optimal quantile estimators. Small sample approach, November 2004  Full Text 
652  Paul Baum, Piotr M. Hajac, Rainer Mathes, Wojciech Szymański  The KTheiry of HeegaardType Quantum 3Spheres, September 2004  Full Text 
651  Jacek Jakubowski, Jerzy Zabczyk  HJM condition for models with Levy noise, September 2004  Full Text 
650  Marcin Bobieński, Tomasz Maszczyk  Twistor spaces of complex grassmannians, April 2004  
649  Jan Palczewski, Jerzy Zabczyk  Portfolio diversification Markovian prices, April 2004  Full Text 
648  Danuta PrzeworskaRolewicz, Stefan Rolewicz  Historical remarks on bounded sets, April 2004  
647  Piotr M. Hajac, Masoud Khalkhali, Bahram Rangipour, Yorck Sommerhäuser  Stable antiYetterDrinfeld modules, March 2004  Full Text 
646  K. Twardowska, J. Zabczyk  A note on Stochastic Burgers' System of Equations, December 2003  Full Text 
645  W. Domitrz, S. Janeczko, M. Zhitomirskii  Relative Poincare lemma, contractibility, quasihomogeneity and vector fields tangent to a singular variety, October 2003 
Full Text Abstract Abstract: Relative Poincare lemma, contractibility, quasihomogeneity and vector fields tangent to a singular varietyAbstract 645 We study the interplay between the properties of the germ of a singular variety N \subset R^{n} given in the title and the algebra of vector fields tangent to N. The Poincare lemma property means that any closed differential (p+1)form vanishing at any point of N is a differential of a pform which also vanishes at any point of N. In particular, we show that the classical quasihomogeneity is not a necessary condition for the Poincare lemma property, it can be replaced by quasihomogeneity with respect to a smooth submanifold of R^n or a chain of smooth submanifolds. We prove that N is quasihomogeneous if and only if there exists a vector field V, V(0) = 0, which is tangent to N and has positive eigenvalues. We also generalize this theorem to quasihomogeneity with respect to a smooth submanifold of R^{n}. 
644  Jan Kisyński  Representations of the convolution algebra D(R) and distrubution groups, July 2003  
643  Piotr M. Hajac, Masoud Khalkhali, Bahram Rangipour, Yorck Sommerhäuser  Hopfcyclic homology and cohomology with coefficients, July 2003  Full Text 
642  Tomasz Brzeziński, Piotr M. Hajac  The ChernGalois character, July 2003  Full Text 
641  Zbigniew Jelonek  On the Łojasiewicz exponent and effective nullstellensatz, June 2003  Full Text 
640  Agnieszka Rossa  Unbiased estimation of survival probability for censored data with known censoring times, April 2003  
639  Piotr M.Hajac, Rainer Matthes and Wojciech Szymański  Chern numbers for two families of noncommutative Hopf fibrations, March 2003  Full Text 
638  Ryszard Zieliński  Effective WLLN, SLLN and CLN in statistical models, March 2003 
Full Text Abstract Abstract: Effective WLLN, SLLN and CLN in statistical modelsAbstract 638 Weak laws of large numbers (WLLN), strong laws of large numbers (SLLN), and central limit theorems (CLT) in statistical models differ from those in probability theory in that they should hold uniformly in the family of distributions specified by the model. If a limit law states that for every \eps > 0 there exists N such that for all n > N the inequalities \xi_n < \eps are satisfied and N = N(\eps) is explicitly given than we call the law effective. It is trivial to obtain the effective statistical version of WLLN in the Bernoulli scheme, to get SLLN takes a little while, but CLT does not hold uniformly. Other statistical schemes are also considered. 
637  Grzegorz Łysik  Nonanalycity in time of solutions of KdV equation, February 2003  Full Text 
636  Agnieszka Kałamajska  On new geometric conditions for some weakly lower semicontinous functionals with application to the rankone conjecture of Morrey (to apperar in Proc. Roy. Soc. Edingburgh), January 2003 
Abstract Abstract: On new geometric conditions for some weakly lower semicontinous functionals with application to the rankone conjecture of Morrey (to apperar in Proc. Roy. Soc. Edingburgh)Abstract 636 We obtain new geometric necessary conditions for a function $f$ to define a lower semicontinuous functional of the form $I_{f}(u)=\int_{\Omega }f(u)dx$, where $u$ satisfies a given conservation law: $Pu=0$, defined by a differential operator $P$ of degree one with constant coefficients. Those conditions imply the socalled $\Lambda $convexity condition, known as the rankone condition when we deal with a functional of the calculus of variations. In particular we derive some new geometric properties of quasiconvex functions and state some new questions related to the rankone conjecture of Morrey. . 
635  Agnieszka Kałamajska  Between the classical theorem of Young and Convergence Teorem in SetValued Analysis, January 2003 
Full Text Abstract Abstract: Between the classical theorem of Young and Convergence Teorem in SetValued AnalysisAbstract 635 We obtain a version of Young's Theorem, where Younglike measures can control discontinuous functions. It determines the weak limit of $f(u^{\nu })$ in the space of measures where $f$ is (possibly) discontinuous scalar function, while $\{u^{\nu }\}$ is a sequence of vectorvalued functions, which is weakly convergent in some $L^{p}$space. The Representation Theorem we derive unifies the two wellknown theorems in nonlinear analysis: the classical Young's theorem, where continuity of $f$ is assumed, and Convergence Theorem known in setvalued analysis, where $f$ may be discontinuous, but the sequence $\{u^{\nu }\}$ converges strongly. Such approach is dictated by the wide range of discontinuous problems arising in nonlinear PDE. The motivations and applications to various convergence problems are discussed. 
634  Piotr M.Hajac, Rainer Matthes and Wojciech Szymański  Graph C*algebras and Z2quotients of Quantum Spheres, November 2002  Full Text 
633  Ilona Królak  Haagerup inequality and contractivity properties of OrnsteinUhlenbeck semigroup for general commutation relations, October 2002  Full Text 
632  Ilona Królak  Property Gamma for von Neumann algebras connected with general commutation relations, October 2002  Full Text 
631  Rémi Léandre  Hypoeliptic diffusions and cyclic cohomology, October 2002  
630  Teresa Regińska  Regularizatin of discrete illposed problems, September 2002 
Full Text Abstract Abstract: Regularizatin of discrete illposed problemsAbstract 630 The paper concerns conditioning aspects of finite dimensional problems arisen when the Tikhonov regularization is applied to discrete illposed problems. A relation between a regularization parameter and sensitivity of regularized solution is investigated. Moreover, it is shown that choice of regularization parameter optimal with respect to the condition number of finite dimensional operator approximating a compact operator gives regularized discrete solutions convergent to the exact generalized solution when dimension of discrete equation and data error are related in a proper way and the data error tends to 0. As an example the method of truncated singular value decomposition with regularization is considered. 
629  Stefan Rolewicz  Abstract convex analysis in metric spaces, August 2002  Full Text 
628  Marian Grendar  Frequency moments inverse problem and maximum (Shannon vs. RenyiTsallis) entropy, August 2002 
Full Text Abstract Abstract: Frequency moments inverse problem and maximum (Shannon vs. RenyiTsallis) entropyAbstract 628 An illposed inverse problem which lays in making a choice of probability distribution from set H of distributions is considered, in a nonstandard setting where H is given by constraints  known as frequency moment constraints  which are nonlinear (in probabilities). From perspective of their probabilistic justification(s) two methods for making the choice are studied: a) maximization of Shannon's entropy (MaxEnt), b) maximization of RenyiTsallis entropy (maxTent). Concerning MaxEnt, its large deviations asymptotic justification, known as conditioned weak law of large numbers, seems to be yet not developed for this case (of nonconvex H and nonunique maximum). Hovewer, MaxProb justification of MaxEnt is valid also in this setting, implying that distribution chosen by maxTent is not the most probable one. The case of Tsallis' Xfrequency constraints is studied, as well. Two subclasses of the feasible set are constructed, where it can be directly seen that maxTent choice is not only different than the most probable distribution, it is also asymptotically improbable. The findings, taken together, brings from probability viewpoint maxTent under suspect. 
627  Stanisław Spież, Jerzy Urbanowicz, Paul van Wamelen  Divisibility properties of generalized Vandermonde and Cauchy determinants,, August 2002  Full Text 
626  Ryszard Zieliński  Constructing medianunbiased estimators in oneparameter families of distributions via optimal nonparametric estimation and stochastic ordering,, July 2002 
Full Text Abstract Abstract: Constructing medianunbiased estimators in oneparameter families of distributions via optimal nonparametric estimation and stochastic ordering,Abstract 611 If \theta \in \Theta is an unknown real parameter of a distribution under consid eration, we are interested in constructing an exactly medianunbiased estimator \hat\theta of \theta, i.e. an estimator \hat\theta such that a median Med(\hat\theta) of the estimator equals \theta, uniformly over theta \in \Theta. We shall consider the problem in the case of a fixed sample size n (nonasymptotic approach). 
625  Danuta PrzeworskaRolewicz  Generalized Sturm separation theorem,, April 2002 
Abstract Abstract: Generalized Sturm separation theorem,Abstract 625 A generalization of Sturm separation theorem was given in Advantages of onedimensional kernels. (Math Nachrichten, 149(1990), 122147) in the case when a right invertible operator under consideration had the onedimensional dernel. The purpose of the present paper is to shoe the Sturm theorem without this restrictive assumption 
624  Piotr M. Hajac, Rainer Matthes, Wojciech Szymański  Locally trivial quantum Hopf fibration,, March 2002 
Full Text Abstract Abstract: Locally trivial quantum Hopf fibration,Abstract 625 The irreducible *representations of the polynomial algebra 0(S^{3}_{pq}) of quantum 3sphere introduced by Calow and Mathes are classified. The Kgroups of its universal C*algebra are shown to coincide with their classical counterparts. The U(1)actions on 0(S^{3}_{pq}) corresponding to the classical Hopf fibration is proven to be a Galois action. The thus obrained HopfGalois extension is shown to be relatively projective (admitting a strong connection) for any p,q in (0,1), and noncleft at least in the symmetric case p=q. The latter is obtained by computing an appropriate ChernConnes pairing. 
623  Ryszarda Rempała  Joint replenishment multiproduct inventory problem with continous production and discrete demands, February 2002 
Full Text Abstract Abstract: Joint replenishment multiproduct inventory problem with continous production and discrete demandsAbstract 623 The basic, deterministic, multiitem inventory problem is considered. The production rates (decision variables) are represented by nonnegative functions defined on the interval $[0,T],$ $T 
622  Zbigniew Ciesielski, Anna Kamont  Survey on the Orthogonal Franklin System, February 2002  
kis  Jan Kisyński  The Wider spaces, representations of the convolution algebra L1(R+) and one parameter semigroups of operators,, January 2001 
Full Text Abstract Abstract: The Wider spaces, representations of the convolution algebra L1(R+) and one parameter semigroups of operators,Abstract  kis A short proof is presented of the isometric isomorphosm between teh Widder space W(K^{+};E) and the space L(L^{1}(R^{+});E). The HilleYosida generation theorem from the theory of operator semigroups is reproved by an argument involving representations of the convolution algebra L^{1}(R^{+}). 
621b  Zbigniew Jelonek  On ramification values of a polynomial mapping, December 2001 
Abstract Abstract: On ramification values of a polynomial mappingAbstract 621a Let C_{1},...,C_{n} be affine algebraic varietes of dimension n1. There is a proper polynomial mapping F:C^{n} > C^{n}, such that the set of its ramification values containes hypersurfaces C'_{1},...,C'_{k}, which are birationally equivalent to C_{1},...,C_{k} 
621a  Zbigniew Jelonek  On generalized critical values of a polynomial mapping, December 2001 
Abstract Abstract: On generalized critical values of a polynomial mappingAbstract 621a Let f=(f_{1},...,f_{n}):C^{n}>C^{n} be a polynomial mapping and let deg f_{i} 
620  Ewa Zadrzyńska, Wojciech Zajšczkowski  On an inequality for a free boundary problem for equations of a viscous compressible heat conducting capilary fluid, September 2001 
Full Text Abstract Abstract: On an inequality for a free boundary problem for equations of a viscous compressible heat conducting capilary fluidAbstract 620 We derive an inequality for a local solution of a free boundary problem for a viscous compressible heatconducting capillary fluid. This inequality is crucial in proving the global existence of solutions belonging to certain anisotropic SobolevSlobodetskii space and close to an equilibrium state. 
619  Ryszard Zieliński  The most stable estimator of location under integrable contaminants, September 2001 
Full Text Abstract Abstract: The most stable estimator of location under integrable contaminantsAbstract 619 if a symmetric distribution is epscontaminated and contaminants have finite first moments, then median may cease to bi the most robust estimator of location.

618  Zofia Adamowicz  On Tableau consistency in weak theories, June 2001 
Full Text Abstract Abstract: On Tableau consistency in weak theoriesAbstract 618 We prove that the G\"odel second incompleteness theorem holds for\hfil\break Tableau consistency and weak arithmetic. Exactly, we prove that $$\D+\Omega_m\not\vdash Tabcons(\D+\Omega_m),$$ for $m\ge 1$. Also, we show that it is consistent with $\D+\Omega_m$ that a Tableau inconsistency proof of $\D+\Omega_m$ can be found in a cut which is ``slightly" larger than the cut determined by the $m1$th iteration of $\log$ (theorem 1.1 and 1.2). 
617  Jan Kisyński  Pseudoresolvents and distributions semigroups, July 2001 
Full Text Abstract Abstract: Pseudoresolvents and distributions semigroupsAbstract 617 For predistribution semigroups in Kunstmann's sense [K] the generators are defined and their characterization is given in terms of the corresponding pseudoresolvents. 
616  Wojciech Zajšczkowski  On global special solutions for NavierStokes equations with boundary slip conditions in a cylindrical domain. Existence, June 2001 
Full Text Abstract Abstract: On global special solutions for NavierStokes equations with boundary slip conditions in a cylindrical domain. ExistenceAbstract 616 Global existence and uniquness of solutions to NavierStokes equations in a cylinder and with boundary slip conditions is proved under the assumptions that the initial motion is sufficiently close to the axially symmetric motion. Then the solution remains close to the axially symmetric solution for all time. Moreover the solution has some properties of the axially symmetric solution. Therfore the existence is proved in the Sobolev weighed spaces where the weight is a power function of the distance to the axis of symmetry. The existence is proved in such classes that velocity belongs to H^{3} locally. 
615  Waldemar Korczyński  On some presentation of graphs, May 2001 
Full Text Abstract Abstract: On some presentation of graphsAbstract 615 The paper contains a survey of some mathematical results inspired by investigations in system theory. In part, these results are of purely mathematical character (e.g. a characterization theorem for the category of graph algebras), and partly they are new presentations of known mathematical notins (e.g. the power object catagory). These new presentations give rise to some applications of these mathematical notions in system theory, which will be discussed in the second part of the paper. 
614b  Zbigniew Jelonek, Krzysztof Kurdyka  On assymptotic critical values of a complex polynomial, April 2001  
614a  Zbigniew Jelonek  On biffurcation points of a complex polynomial, April 2001  
613  Urszula SkórnikPokarowska  Holomorphic Characterizations of Certains Classes of Distributions, January 2001 
Full Text Abstract Abstract: Holomorphic Characterizations of Certains Classes of DistributionsAbstract 613 We give two holomorphic characterizations of the space D'_{Lp} of distributions for 1<p<∞. Using the almost analytic continuation method we have found sufficient conditions for a function f holomorphic in C\R or even in a smaller region, a stripe along the real line, to have its boundary values in the space D'_{Lp}(R) for 1 < p <∞. We will also give another characterization of holomorphic functions whose boundary values are in D'_{Lp} for 1 < p <∞. We are also concerned with the holomorphic representation of integrable distributions. We present some applications of the holomorphic representation of distributions. 
612  Anna Kwiecińska  Almost sure and moment stability of stochastic partial differential equations, January 2001 
Full Text Abstract Abstract: Almost sure and moment stability of stochastic partial differential equationsAbstract 612 We study the almost sure and moment stability of a class of stochastic partial differential equations and we present an infinitedimensional version of a theorem proved for stochastic ordinary differential equations by Arnold, Oeljeklaus and Pardoux. We also investigate how adding a term with white noise influences the stability of a deterministic system. The outcome is quite surprising. It turns out that regardless whether the deterministic system was stable or unstable, after adding a term with sufficiently large noise, it becomes pathwise exponentially stable and unstable in the pth mean, for p > 1. Keywords: stochastic partial differential equation, almost sure stability, moment stability, deterministic partial differential equation, stabilization by noise, destabilization by noise. AMS 2000 Classifications: Primary: 60H15, 35K10; Secondary: 65N25. 
611  Gianmario Tessitore & Jerzy Zabczyk  Pricing Option for Markovian Models, January 2001 