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ASYMPTOTIC ANALYSIS
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International Conference on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (Conference on Analysis of Algorithms)
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublikacjaQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently in the ℓ1 space. It turns out that in principle most of the results can be carried over to the L1 space. However, due to topological properties of this space one has to restrict in some situations to kernel quadratic stochastic operators. In this article we study the uniform and strong asymptotic...
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Robust asymptotic super twisting sliding mode observer for non-linear uncertain biochemical systems
PublikacjaThe problem of state estimation (reconstruction of the state vector) for a given class of biochemical systems under uncertain system dynamics has been addressed in this paper. In detail, the bioreactor at a water resource recovery facility represents the considered biochemical systems. The biochemical processes taking place in the bioreactor have been modelled using an activated sludge model. Based on this model, an appropriate...
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Asymptotic formulas for the error in linear interpolation
PublikacjaWyznaczono asymptotyczny wzór dla błędu w liniowej interpolacji z dowolnymi węzłami.
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The asymptotic formula for the error in orthogonal projection
PublikacjaW pracy podano formułę asymptotyczną błędu aproksymacji dla rzutów ortogonalnych w normie L^p.
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublikacjaWe study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L1(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure...
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Asymptotic error expansions for Schoenberg type operators
PublikacjaPrzedstawiono L^p błąd dla rozwinięć dla operatorów Schoenberga
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Asymptotic error expansions for Schoenberg type operators.
PublikacjaW pracy wyprowadzono rozwinięcie asymptotyczne dla błędu w L2 operatorówSchoenberga.
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On asymptotic periodicity of kernel double Markovian operators
PublikacjaIt is proved that a kernel, doubly Markovian operator T is asymptotically periodic if and only if its deterministic σ-field Σd(T)(equivalently Σd(T∗)) is finite. It follows that kernel doubly Markovian operator T is asymptotically periodic if and only if T∗ is asymptotically periodic.
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The work of Professor Andrzej Lasota on asymptotic stability and recent progress
PublikacjaPraca poświęcona jest wkładowi Profesora Andrzeja Lasoty w teorię asymptotycznej stabilności iteracji operatorów stochastycznych na przestrzeni ostatnich 36 lat. Podkreślono aplikacyjny charakter wyników, pokazując stosowne przykłady z modelowania rozwoju komórki, optymalizacji wierceń geologicznych i ewolucji modeli kwantowych.
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Mazur-Orlicz theorem and asymptotic formula for the error in supreme norm.
PublikacjaObliczono formułę asymptotyczną błędu interpolacji dla normy supremum.
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Asymptotic modelling and design of some microlayered functionally graded heat conductors
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Asymptotic Expansion Method with Respect to Small Parameter for Ternary Diffusion Models
PublikacjaTernary diffusion models lead to strongly coupled systems of PDEs. We choose the smallest diffusion coefficient as a small parameter in a power series expansion whose components fulfill relatively simple equations. Although this series is divergent, one can use its finite sums to derive feasible numerical approximations, e.g. finite difference methods (FDMs).
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Asymptotic approximations of lasing eigenvalues of an infinite grating of circular quantum wires in the free space
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Asymptotic numerical solver for the linear Klein–Gordon equation with space- and time-dependent mass
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ANALYSIS OF THE p53 PROTEIN GENE EXPRESSION MODEL
PublikacjaWe study the asymptotic behaviour of the solutions of the p53-Mdm2 model proposed by Monk (2003). The p53 gene is crucial for cellular inhibition of the angiogenesis process, while Mdm2 is a negative regulator of the p53 tumor-suppressor. We investigate the stability of the positive steady state and perform some numerical experiments.
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The smoothness test for a density function
PublikacjaThe problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...
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Free randomness amplification using bipartite chain correlations
PublikacjaA direct analysis of the task of randomness amplification from Santha-Vazirani sources using the violation of the chained Bell inequality is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. This analysis is used to find the exact threshold value of the initial randomness parameter from which perfect randomness can be extracted in the asymptotic limit of...
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Limiting distribution of Lempel Ziv'78 redundancy
PublikacjaWe show that the Lempel Ziv'78 redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper [3]. We present a new simplified proof of the Central Limit Theorem for the number of phrases in the LZ'78 algorithm. As in our 1995 paper, here we first analyze the asymptotic behavior of the total path length in a digital search tree (a DST) built from independent sequences....
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On the Limiting distribution of Lempel Ziv'78 Redundancy for Memoryles Sources
PublikacjaWe show that the Lempel Ziv'78 redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper [3]. We present a new simplified proof of the Central Limit Theorem for the number of phrases in the LZ'78 algorithm. As in our 1995 paper, here we first analyze the asymptotic behavior of the total path length in a digital search tree (a DST) built from independent sequences....
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Modern Platform for Parallel Algorithms Testing: Java on Intel Xeon Phi
PublikacjaParallel algorithms are popular method of increasing system performance. Apart from showing their properties using asymptotic analysis, proof-of-concept implementation and practical experiments are often required. In order to speed up the development and provide simple and easily accessible testing environment that enables execution of reliable experiments, the paper proposes a platform with multi-core computational accelerator:...
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A hierarchical observer for a non-linear uncertain CSTR model of biochemical processes
PublikacjaThe problem of estimation of unmeasured state variables and unknown reaction kinetic functions for selected biochemical processes modelled as a continuous stirred tank reactor is addressed in this paper. In particular, a new hierarchical (sequential) state observer is derived to generate stable and robust estimates of the state variables and kinetic functions. The developed hierarchical observer uses an adjusted asymptotic observer...
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On mixing in the class of quadratic stochastic operators
PublikacjaWe study different types of limit behavior of quadratic stochastic operators acting on ℓ^1 (or ℓ^1_d) spaces in both strong and uniform topologies. The main motif of the paper is to express the uniform and strong asymptotic stability of the quadratic stochastic operator in terms of convergence of the associated (linear) nonhomogeneous Markov chain. We also examine which type of uniform convergence of iterates of the quadratic...
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On the Limiting Distribution of Lempel-Ziv’78 Redundancy for Memoryless Sources
PublikacjaWe study the Lempel-Ziv'78 algorithm and show that its (normalized) redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper, in particular, by presenting a new simplified proof of the central limit theorem (CLT) for the number of phrases in the LZ'78 algorithm. We first analyze the asymptotic behavior of the total path length in the associated digital search...
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Jeffreys heat conduction in coupled semispaces subjected to interfacial heating
PublikacjaA Jeffreys heat conduction problem for coupled semispaces subjected to the action of an interfacial heat source was defined. An analytical solution of the problem was derived for a polynomial specific power of the heat source using the Laplace transform approach. The asymptotic and parametric analysis was performed for different ratios of thermal conductivities , thermal diffusivities , thermal relaxation times and coefficients...
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Nonlinear planar modeling of massive taut strings travelled by a force-driven point-mass
PublikacjaThe planar response of horizontal massive taut strings, travelled by a heavy point-mass, either driven by an assigned force, or moving with an assigned law, is studied. A kinematically exact model is derived for the free boundary problem via a variational approach, accounting for the singularity in the slope of the deflected string. Reactive forces exchanged between the point-mass and the string are taken into account via Lagrange...
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Wavepacket of the Universe and its Spreading
PublikacjaWavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined on space-time. Space-time is static but the Universe is dynamic. Spreading analogous to expansion known from observational cosmology is obtained if one regards time evolution as a dynamical process...
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Asymmetric Renyi Problem and > PATRICIA Tries
PublikacjaIn 1960 R´enyi asked for the number of random queries necessary to recover a hidden bijective labeling of n distinct objects. In each query one selects a random subset of labels and asks, what is the set of objects that have theselabels? Weconsider here anasymmetric version of the problem in which in every query an object is chosenwith probability p > 1/2 and we ignore “inconclusive” queries. We study the number of queries needed...
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Infiltration in a double-porosity medium: Experiments and comparison with a theoretical model
PublikacjaThis paper presents experimental verification of the mathematical model of unsaturated flow in double‐porosity soils developed by the asymptotic homogenization method. A series of one‐dimensional infiltration experiments was carried out in a column filled with a double‐porosity medium composed of a mixture of sand and sintered clayey spheres arranged in a periodic manner. The unsaturated hydraulic properties of each porous material...
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Rotating rod and ball
PublikacjaWe consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time...
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Wear of electroplated diamond tools in lap-grinding of Al2O3 ceramic materials
PublikacjaCurrent development of modern products, together with ever-increasing demands for their operation and usage, necessitate the search for new processing methods. Abrasive machining is widely used in many industrial areas, especially for processing difficult-to-machine materials such as advanced ceramics. Grinding with lapping kinematics, also called lap-grinding, is still one of the innovative methods of abrasive processing being...
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Surface effects of network materials based on strain gradient homogenized media
PublikacjaThe asymptotic homogenization of periodic network materials modeled as beam networks is pursued in this contribution, accounting for surface effects arising from the presence of a thin coating on the surface of the structural beam elements of the network. Cauchy and second gradient effective continua are considered and enhanced by the consideration of surface effects. The asymptotic homogenization technique is here extended to...
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Structured populations with diffusion and Feller conditions
PublikacjaWe prove a weak maximum principle for structured population models with dynamic boundary conditions. We establish existence and positivity of solutions of these models and investigate the asymptotic behaviour of solutions. In particular, we analyse so called size profile.
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Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein
PublikacjaWe analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop. The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account. We consider three, possibly different, time scales connected with: (i) the process of binding to/dissolving from a binding site, (ii) formation and dissociation of dimers, (iii) production and degradation of Hes1...
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Solution of coupled integral equations for quantum scattering in the presence of complex potentials
PublikacjaIn this paper, we present a method to compute solutions of coupled integral equations for quantum scattering problems in the presence of a complex potential. We show how the elastic and absorption cross sections can be obtained from the numerical solution of these equations in the asymptotic region at large radial distances.
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Generalized Dobrushin Coefficients on Banach Spaces
PublikacjaThe asymptotic behavior of iterates of bounded linear operators (not necessarily positive), acting on Banach spaces, is studied. Through the Dobrushin ergodicity coefficient, we generalize some ergodic theorems obtained earlier for classical Markov semigroups acting on L1 (or positive operators on abstract state spaces).
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Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait
PublikacjaQuadratic stochastic operators can exhibit a wide variety of asymptotic behaviours and these have been introduced and studied recently. In the present work we discuss biological interpretations that can be attributed to them. We also propose a computer simulation method to illustrate the behaviour of iterates of quadratic stochastic operators.
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Are quantum correlations symmetric?
PublikacjaWe provide operational definition of symmetry of entanglement: An entangled state contains symmetric entanglement if its subsystems can be exchanged (swapped) by means of local operations and classical communication. We show that in general states have asymmetric entanglement. This allows to construct nonsymmetric measure of entanglement, and a parameter that reports asymmetry of entanglement contents of quantum state. We propose...
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Stable indirect adaptive control based on discrete-time T-S fuzzy model
PublikacjaThis paper presents an indirect adaptive fuzzy control scheme for uncertain nonlinear asymptotically stable plants.A discrete-time T-S fuzzy input-output model is employed to approximate the unknown plant dynamics. The T-S fuzzy model is fed with its own states, which are indeed its past outputs, rather than the measurements from the plants. Entirely based on this model, a feedback linearization control law is designed by using...
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Stable indirect adaptive control based on discrete-time T-S fuzzy model
PublikacjaThis paper presents an indirect adaptive fuzzy control scheme for uncertain nonlinear asymptotically stable plants.A discrete-time T-S fuzzy input-output model is employed to approximate the unknown plant dynamics. The T-S fuzzy model is fed with its own states, which are indeed its past outputs, rather than the measurements from the plants. Entirely based on this model, a feedback linearization control law is designed by using...
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Broadcast copies reveal the quantumness of correlations
PublikacjaWe study the quantumness of bipartite correlations by proposing a quantity that combines a measure of total correlations-mutual information-with the notion of broadcast copies-i.e., generally nonfactorized copies-of bipartite states. By analyzing how our quantity increases with the number of broadcast copies, we are able to classify classical, separable, and entangled states. This motivates the definition of the broadcast regularization...
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Transition dipole moments of the lithium dimer
PublikacjaIn addition to knowledge of interatomic adiabatic potential energy curves of diatomic systems, it is essential to know electronic transition dipole moments. They are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping. Here, we present electronic transition dipole moments calculated for 74 allowed transitions between 26 states of Li2 [P. Jasik, J.E. Sienkiewicz, Chem. Phys. 323 (2006)...
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Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform
PublikacjaBirth–and–death models are now a common mathematical tool to describe branching patterns observed in real–world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth–and–death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the...
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublikacjaVarious equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....
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Identification of Shear Modulus Parameters of Half-space Inhomogeneous by Depth
PublikacjaThe paper propose a method for determining of the parameters of the exponential shear modulus of a functionally graded half-space based on the solution of the problem of a pure shear of an elastic functionally graded half-space by a strip punch. The solution of the integral equation of the contact problem is constructed by asymptotic methods with respect to the dimensionless parameter. The dependence of contact stresses on the...
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On the influence of a surface roughness on propagation of anti-plane short-length localized waves in a medium with surface coating
PublikacjaWe discuss the propagation of localized surface waves in the framework of the linear Gurtin–Murdoch surface elasticity and taking into account a roughness of a free boundary. We derive a boundary-value problem for anti-plane motions with curvilinear boundary and surface stresses. Using the asymptotic technique developed earlier, we obtain the form of a localized wave and analyze its amplitude evolution. As the main result we present...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublikacjaIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublikacjaIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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System information propagation for composite structures
PublikacjaWe study in details decoherence process of a spin register, coupled to a spin environment. We use recently developed methods of information transfer study in open quantum systems to analyze information flow between the register and its environment. We show that there are regimes when not only the register decoheres effectively to a classical bit string, but this bit string is redundantly encoded in the environment, making it available...