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Search results for: MARKOV OPERATORS
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On residualities in the set of Markov operators on C1
PublicationDowodzi się, że zbiór operatorów Markowa na klasie Schattena 1, które są mieszające w normie, jest normowo gęsty, otwarty. Natomiast w topologii mocno operatorowej operatory Markowa mocno mieszające są zbiorem I kategorii.
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Direct estimation of functional and density operators by local operations and classical communication.
PublicationWykazano, że można dokonywać detekcji splątania w paradygmacie odległych laboratoriów. Pokazano, jak można fizycznie zaimplementować strukturalne przybliżenie fizyczne niefizycznego odwzorowania w tym paradygmacie.
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublicationVarious 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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Applying Hidden Markov Models to Visual Activity Analysis for Simple Digital Control Panel Operations
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Application of hidden Markov models to eye tracking data analysis of visual quality inspection operations
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Mieszanie w klasie niejednorodnych łańcuchów Markowa i kwadratowych operatorów stochastycznych
PublicationRozprawa doktorska poświęcona jest zagadnieniu asymptotycznych własności w klasie nieskończenie wymiarowych niejednorodnych łańcuchów Markowa z czasem dyskretnym oraz w klasie kwadratowych operatorów stochastycznych. W pierwszej kolejności definiowane są różne rodzaje asymptotycznego zachowania (mieszania) niejednorodnych łańcuchów Markowa odpowiadające zbieżności w normowej i mocnej topologii operatorowej oraz omówione są relacje...
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Saturation of Bernstein Schnabl operators.
PublicationW pracy dowodzi się twierdzenia o nasyceniu dla operatorów Bernsteina-Schnabla nad sympleksem Bauera w przestrzeni Banacha.
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Quadratic stochastic operators on Banach lattices
PublicationWe study the convergence of iterates of quadratic stochastic operators that are mean monotonic. They are defined on the convex set of probability measures concentrated on a weakly compact order interval S = [0, f] of a fixed Banach lattice F. We study their regularity and identify the limits of trajectories either as the “infimum” or “supremum” of the support of initial distributions.
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Fractional differential equations with causal operators
PublicationWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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Shift invariant operators and a saturation theorem.
PublicationPraca jest kontynuacją wcześniejszych dwóch prac wydanych w Appl. Math. w latach 2001 i 2002. Główny wynik dotyczy wygładzania specjalnego ciągu zbieżnego słabo, tak iż dostajemy ciąg zbieżny w normie supremum.
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Boundary value problems with causal operators
PublicationPraca dotyczy istnienia rozwiązań dla równań różniczkowych z nieliniowymi dwu-punktowymi warunkami brzegowymi. Podano warunki dostateczne na istnienie rozwiązań takich zagadnień stosując metodę iteracji monotonicznych. Dyskutowano też nierówności różniczkowe rzędu pierwszego z dodatnimi operatorami liniowymi oraz problem rozwiązań ekstremalnych.
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On mixing in the class of quadratic stochastic operators
PublicationWe 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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Weak Stability of Centred Quadratic Stochastic Operators
PublicationWe consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...
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Asymptotic error expansions for Schoenberg type operators.
PublicationW pracy wyprowadzono rozwinięcie asymptotyczne dla błędu w L2 operatorówSchoenberga.
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Hubbard operators approach to the transport in molecular junctions
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Different types of solvability conditions for differential operators
PublicationSolvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differential equations on the real axis, and...
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Asymptotic error expansions for Schoenberg type operators
PublicationPrzedstawiono L^p błąd dla rozwinięć dla operatorów Schoenberga
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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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On asymptotic periodicity of kernel double Markovian operators
PublicationIt 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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Wybór operatora usług VOIP
PublicationW pracy przedstawiono propozycje algorytmu wyboru operatora VoIP, zapewniającego w danym momencie realizację połączenia o najlepszej jakości. Weryfikacja jakości realizowanego połączenia została dokonana metodami subiektywnymi. Zaproponowane 2 metody wyboru najlepszego operatora wykorzystują: pomiar maksymalnego opóźnienia przechodzenia danych z/do operatora (w oparciu o usługę PING) oraz pomiar czasu trwania zestawiania połączenia...
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A Note on Fractional Curl Operator
PublicationIn this letter, we demonstrate that the fractional curl operator, widely used in electromagnetics since 1998, is essentially a rotation operation of components of the complex Riemann–Silberstein vector representing the electromagnetic field. It occurs that after the wave decomposition into circular polarisations, the standard duality rotation with the angle depending on the fractional order is applied to the left-handed basis vector...
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Concrete Operators
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Operators and Matrices
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On iterates of strong Feller operators on ordered phase spaces.
PublicationPraca dotyczy asymptotycznych własności iteracji operatorów Markowa. Udowodniono, że operatory Lasoty i ich wielowymiarowe uogólnienia są asymptotycznie stabilne. Wyniki mają zastosowanie w modelowaniu rozwoju komórki.
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Directed electromagnetic pulse dynamics: projecting operators method
PublicationIn this article, we consider a one-dimensional model of electromagnetic pulse propagation in isotropic media, takinginto account a nonlinearity of the third order. We introduce a method for Maxwell's equation transformation on thebasis of a complete set of projecting operators. The operators correspond to wave dispersion branches including thedirection of propagation. As the simplest result of applying the method, we derive a system...
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Boundary vlue problems for difference equations with causal operators
PublicationPraca dotyczy problemów brzegowych dla równań różnicowych.Podano warunki dostateczne na istnienie ekstremalnych rozwiązań stosując metodę iteracji monotonicznych.
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators
PublicationWe 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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Dynamical nonlocality in quantum time via modular operators
PublicationWe formalize the concept of the modular energy operator within the Page and Wootters timeless framework. As a result, this operator is elevated to the same status as the more studied modular operators of position and momentum. In analogy with dynamical nonlocality in space associated with the modular momentum, we introduce and analyze the nonlocality in time associated with the modular energy operator. Some applications of our...
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On quasi-compact Markov nets
PublicationAnalizuje się strukturę ergodyczną netów Markowa. W szczególności podano charakteryzację ściśle ergodycznych minimalnych (L-R) netów markowskich na zwartej przestrzeni fazowej. Uzyskano warunki równoważne quasi-zwartości (L-R) netów Markowa, rozszerzając tzw. ergodyczne twierdzenie Lotz'a.
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Types of Markov Fields and Tilings
PublicationThe method of types is one of the most popular techniques in information theory and combinatorics. However, thus far the method has been mostly applied to one-dimensional Markov processes, and it has not been thoroughly studied for general Markov fields. Markov fields over a finite alphabet of size m ≥ 2 can be viewed as models for multi-dimensional systems with local interactions. The locality of these interactions is represented...
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On the maximum principle of Bernstein-Schnabl operators over a Bauer simplex
PublicationW pracy bada się geometryczne własności sympleksy Bauera i dowodzi się zasady maksimum dla operatorów Bernsteina-Schnabla.
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Genetic operators of evolutionary algorithm in problem of collision avoidance at sea
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Specialized genetic operators in drinking water distribution systems control
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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
PublicationThis paper is devoted to the study of the problem of prevalence in the class of quadratic stochastic operators acting on the L1 space for the uniform topology. We obtain that the set of norm quasi-mixing quadratic stochastic operators is a dense and open set in the topology induced by a very natural metric. This shows the typical long-term behaviour of iterates of quadratic stochastic operators.
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An analysis of the current situation for Polish ferry operators in a transitional environment
PublicationArtykuł rozpoczyna analiza sytuacji polskiej żeglugi promowej na tle procesów zachadzących w otoczeniu. W dalszej części została przedstawiona analiza SWOT, która wskazała główne problemy, którym muszą stawić czoła polscy armatorzy promowi. W pracy zaproponowano strategie marketingowe i dokano oceny ich roli w dalszym rozwoju badanych przedsiębiorstw promowych.
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Evolutionary Sets of Safe Ship Trajectories: problem dedicated operators
PublicationThe paper presents the optimization process of the evolutionary sets of safe ship trajectories method, with a focus on its problem-dedicated operators. The method utilizes a customized evolutionary algorithm to solve a constrained optimization problem. This problem is defined as finding a set of cooperating trajectories (a set is an evolutionary individual) of all the ships involved in the encounter situation. The resulting trajectories...
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Asymptotic properties of quadratic stochastic operators acting on the L1 space
PublicationQuadratic 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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Existence of solutions for a coupled system of difference equations with cousal operators
PublicationPraca dotyczy układów równań różnicowych. Podano warunki dostateczne na istnienie rozwiązań takich problemów. Badano również nierówności różnicowe.
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Markov Model of Disease Development and Recovery
PublicationMarkov models are commonly used to simulate diseases and allow modeling of multiple health states and outcomes. Starting with the well known Le Bras multistate model (cascading failure model) with time-independent transitions we will see how simple Markov mortality models may be pressed into the service of survival and event history analysis. We will focus on more complex models which will be able to take into account remission,...
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COMPARATIVE ANALYSIS OF RESULTS OF APPLICATION OF MARKOV AND SEMI-MARKOV PROCESSES TO RELIABILITY MODELS OF MULTI-STATE TECHNICAL OBJECTS
PublicationDuring rational operation of technical objects and systems various operational decisions are made and decision-making process itself should be consisted in selecting that considered most favourable out of all possible to be taken. Choice of such decision is possible after taking into account many different information items but it never be completely correct without accounting for data and indices dealing with reliability. In...
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Reactive Energy Billing in Operator Tariffs in Poland
PublicationThe paper describes the current method of reactive energy billing in the tariffs of distribution grid operators in Poland. The current solutions are subject to critical assessment. Issues related to the motivation effect of the current solutions on consumers are analysed. Problems that occur in relation with connecting distributed generators to the distribution grid and challenges related to prosumer billing are indicated.
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A Population-Based Method with Selection of a Search Operator
PublicationThis paper presents a method based on a population in which the parameters of individuals can be processed by operators from various population-based algorithms. The mechanism of selecting operators is based on the introduction of an additional binary parameters vector located in each individual, on the basis of which it is decided which operators are to be used to modify individuals’ parameters. Thus, in the proposed approach,...
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Text-mining Similarity Approximation Operators for Opinion Mining in BI tools
PublicationThe concept of the Text-mining Similarity Approximation Operators for Opinion Mining as extensions to Natural Language Interface Database is defined. The new operators: “keywords of” dimension; subsetting operator “about C is q”; aggregation operator “by similar C” are proposed. These operators are based on the Latent Semantic Analysis and Social Network Analysis
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Application exaples of wide area monitoring for system operators within UCTE
PublicationW referacie przedstawiono przykładowe zastosowania pomiarów uzyskiwanych w systemie WAMS dla potrzeb systemu elektroenergetycznego.
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Mobile operators at war: opinion mining and sentiment analysis on social media
PublicationConsidering hermetic and very competitive market such as mobile operator ones, social media has become best alternative for contact with customer and gathering data and opinions. Different style of running social media profiles is giving different results. The research presented in this paper aims to show the number of responses gathered from polish Internet users and its sentiment for mobile operator brands. It also presents practical...
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Quadratic stochastic operators as a tool in modelling the dynamics of a distribution of a population trait
PublicationQuadratic 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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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublicationThe paper presents research on the approximation of variable-order fractional operators by recurrent neural networks. The research focuses on two basic variable-order fractional operators, i.e., integrator and differentiator. The study includes variations of the order of each fractional operator. The recurrent neural network architecture based on GRU (Gated Recurrent Unit) cells functioned as a neural approximation for selected...
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Covariant forms of lax one-field operators: from abelian to noncommutative
PublicationBadamy kowariancje w odniesieniu do transformacji Darboux wielomianowych operatorów różniczkowych o współczynnikach określonych przez funkcje jednego bazowego pola. W przypadku komutatywnym rozważana para Laxa równań typu Boussinesqa. Wprowadza się pewne zbudowane niezmiennicze formy i nie-abeliowe funkcje specjalne.
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The Effectiveness of Operations Implementing Changes
PublicationW niniejszym rozdziale zdefiniowano pojęcie efektywności zmian organizacyjnych. Scharakteryzowano również składowe elementy efektywności, jakimi są skuteczność, korzystność i ekonomiczność. Pokazano również miejsce oceny efektywności zmian w procesie realizacji przekształceń. Przedstawiono również model oceny efektywności zmian procesu planowania i sterowania umożliwiający ocenę skuteczności, korzystności i ekonomiczności zmian.
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Average Redundancy of the Shannon Code for Markov Sources
PublicationIt is known that for memoryless sources, the average and maximal redundancy of fixed–to–variable length codes, such as the Shannon and Huffman codes, exhibit two modes of behavior for long blocks. It either converges to a limit or it has an oscillatory pattern, depending on the irrationality or rationality, respectively, of certain parameters that depend on the source. In this paper, we extend these findings, concerning the Shannon...