Filtry
wszystkich: 467
Wyniki wyszukiwania dla: QUADRATIC STOCHASTIC OPERATORS
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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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Quadratic stochastic operators on Banach lattices
PublikacjaWe 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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Weak Stability of Centred Quadratic Stochastic Operators
PublikacjaWe 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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Prevalence Problem in the Set of Quadratic Stochastic Operators Acting on L1
PublikacjaThis 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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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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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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A Noether theorem for stochastic operators on Schatten classes
PublikacjaWe 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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Random Operators and Stochastic Equations
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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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Stochastic intervals for the family of quadratic maps
Dane BadawczeNumerical analysis of chaotic dynamics is a challenging task. The one-parameter families of logistic maps and closely related quadratic maps f_a(x)=a-x^2 are well-known examples of such dynamical systems. Determining parameter values that yield stochastic-like dynamics is especially difficult, because although this set has positive Lebesgue measure,...
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Mieszanie w klasie niejednorodnych łańcuchów Markowa i kwadratowych operatorów stochastycznych
PublikacjaRozprawa 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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Rigorous numerics for critical orbits in the quadratic family
PublikacjaWe develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps fa(x)=a−x2. We illustrate the effectiveness of our approach by constructing a dynamically defined partition P of the parameter interval Ω=[1.4,2] into almost 4 million subintervals, for each of which we compute to high precision the...
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Stochastic resonance in measurements
PublikacjaNoise is usually associated with the negative phenomenon, hampering the measurements data and their analysis. This view has been broken in the '80s when the phenomenon of stochastic resonance (Stochastic Resonance - SR) was discovered. It is a phenomenon that occurs in nonlinear dynamic measurement systems when the selected input noise can optimize system performance. SR became a way to improve efficiency of weak signals detection....
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Kalman filters and stochastic control - winter 2022/2023
Kursy OnlineThe lecture focusses on designing of Kalman filters and stochastic control of dynamic systems.
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Kalman filters and stochastic control - winter 2023/2024
Kursy OnlineThe lecture focusses on designing of Kalman filters and stochastic control of dynamic systems.
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Fractional differential equations with causal operators
PublikacjaWe 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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Directed electromagnetic pulse dynamics: projecting operators method
PublikacjaIn 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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Concrete Operators
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Operators and Matrices
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Text-mining Similarity Approximation Operators for Opinion Mining in BI tools
PublikacjaThe 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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Neural Approximators for Variable-Order Fractional Calculus Operators (VO-FC)
PublikacjaThe 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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Distortional buckling of thin-walled columns of closed quadratic cross-section
PublikacjaThe elastic stability of axially compressed column related to the cross-section distortion is investigated. Two kinds of closed quadratic cross-sections are taken into consideration with internal walls and without it. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical loads for the simply supported columns are found in an analytical form and compared with...
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Evolutionary Sets of Safe Ship Trajectories: problem dedicated operators
PublikacjaThe 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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Multi-state vibronic interactions in the fluorobenzene radical cation: The importance of quadratic coupling terms
PublikacjaThe multi-mode multi-state vibronic interactions in the set of X^2B_1 - D^2A_1 electronic states of the monofluoro benzene radical cation are investigated theoretically, based on a quadratic vibronic coupling approach. The underlying ionization potentials and coupling constants are obtained from ab initio coupled-cluster calculations. Previous investigations (relying on the linear coupling approach) are extended by including all...
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Dynamical nonlocality in quantum time via modular operators
PublikacjaWe 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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Enhancing rheological muscle models with stochastic processes
PublikacjaPurpose: Biological musculoskeletal systems operate under variable conditions. Muscle stiffness, activation signals, and loads change during each movement. The presence of noise and different harmonic components in force production significantly influences the behaviour of the muscular system. Therefore, it is essential to consider these factors in numerical simulations. Methods: This study aims to develop a rheological mathematical...
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On noncausal identification of nonstationary stochastic systems
PublikacjaIn this paper we consider the problem of noncausal identification of nonstationary,linear stochastic systems, i.e., identification based on prerecorded input/output data. We show how several competing weighted least squares parameter smoothers, differing in memory settings, can be combined together to yield a better and more reliable smoothing algorithm. The resulting parallel estimation scheme automatically adjusts its smoothing...
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublikacjaIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublikacjaIn this study a thin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical load for the simply supported bar is found in analytical form and it is compared with the FEM solution. Sufficient accuracy...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublikacjaIn this study a tin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equatio is derived with aid of the principle of stationary potential energy. The critical load for simply supported bar is found in an analytical form and it is copared with the FEM solution. Sufficient accuracy of the...
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Quadratic Cohen representations in spectral analysis of serration process in Al–Mg alloys
PublikacjaImportant from mechanical point of view the Portevin–Le Chatelier serration phenomenon is being characterized by a complicated spectral profile. As a typical example of nonstationary processes it demands a special treatment allowing to follow the evolution of energy of stress fluctuations as a function of strain. The authors suggest the utilization of a compact system of quadratic transformations, known as Cohen class, as a technique...
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On DoA estimation for rotating arrays using stochastic maximum likelihood approach
PublikacjaThe flexibility needed to construct DoA estimators that can be used with rotating arrays subject to rapid variations of the signal frequency is offered by the stochastic maximum likelihood approach. Using a combination of analytic methods and Monte Carlo simulations, we show that for low and moderate source correlations the stochastic maximum likelihood estimator that assumes noncorrelated sources has accuracy comparable to the...
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An idea of an approach to self-testing of mixed signal systems based on a quadratic function stimulation
PublikacjaA new approach to self-testing of the analog parts of mixed-signal electronic systems controlled by microcontrollers equipped with an ADC and a DAC is presented. It is based on a BIST and a new fault diagnosis method. A novelty is the use of the DAC as a component of the BIST, allowing to generate a stimulating signal with a quadratic function shape. It contributes to a better extraction of information about the state of the circuit...
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Stochastic equivalence scales in log-normal distributions of expenditures
PublikacjaIn the paper, the properties of the stochastic equivalence scales (SES) are analysed when expenditure distributions are log-normal. The SES provides the equivalent distribution of expenditures when the population of households is heterogeneous with respect to such attributes as household size, demographic cpmposition, etc. For log-normal expenditure distributions, the non-parametric SES deflators are proportional to the ration...
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Stochastic Systems
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STOCHASTIC MODELS
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Fast Basis Function Estimators for Identification of Nonstationary Stochastic Processes
PublikacjaThe problem of identification of a linear nonsta-tionary stochastic process is considered and solved using theapproach based on functional series approximation of time-varying parameter trajectories. The proposed fast basis func-tion estimators are computationally attractive and yield resultsthat are better than those provided by the local least squaresalgorithms. It is shown that two...
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Saturation of Bernstein Schnabl operators.
PublikacjaW pracy dowodzi się twierdzenia o nasyceniu dla operatorów Bernsteina-Schnabla nad sympleksem Bauera w przestrzeni Banacha.
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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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Asynchronous Networked Estimation System for Continuous Time Stochastic Processes
PublikacjaIn this paper we examine an asynchronous networked estimation system for state estimation of continuous time stochastic processes. Such a system is comprised of several estimation nodes connected using a possibly incomplete communication graph. Each of the nodes uses a Kalman filter algorithm and data from a local sensor to compute local state estimates of the process under observation. It also performs data fusion of local estimates...
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On noncausal weighted least squares identification of nonstationary stochastic systems
PublikacjaIn this paper, we consider the problem of noncausal identification of nonstationary, linear stochastic systems, i.e., identification based on prerecorded input/output data. We show how several competing weighted (windowed) least squares parameter smoothers, differing in memory settings, can be combined together to yield a better and more reliable smoothing algorithm. The resulting parallel estimation scheme automatically adjusts...
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Random Processes and Stochastic Control - project
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Investigation of long-range dependencies in the stochastic part of daily GPS solutions
PublikacjaThe long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series...
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MODEL OF MULTILEVEL STOCHASTIC ANALYSIS OF ROAD SAFETY ON REGIONAL LEVEL
PublikacjaIn this paper multilevel approach to the issue of road safety level on the road network of European regions, classified as NUTS 2 in statistical databases of the European Union, has been presented. Following the pattern of many publications on road safety it has been assumed that the risk calculated as the number of death casualties in road accidents per 100,000 inhabitants of a given region has Poisson distribution. Therefore,...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublikacjaIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublikacjaIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Application of a stochastic compartmental model to approach the spread of environmental events with climatic bias
PublikacjaWildfires have significant impacts on both environment and economy, so understanding their behaviour is crucial for the planning and allocation of firefighting resources. Since forest fire management is of great concern, there has been an increasing demand for computationally efficient and accurate prediction models. In order to address this challenge, this work proposes applying a parameterised stochastic model to study the propagation...
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Asynchronous distributed state estimation for continuous-time stochastic processes
PublikacjaWe consider the problem of state estimation of a continuous-time stochastic process using an asynchronous distributed multi-sensor estimation system (ADES). In an ADES the state of a process of interest is estimated by a group of local estimators. Each local estimator based, for example, on a Kalman filter, performs single sensor filtration but also fusion of its local results and results from other (remote) processors to compute...
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Variations of Ship’s Deck Elevation Due to Stochastic Process of Containers Loading
PublikacjaThe stochastic process of container loading is described in the paper with special emphasis to ship motion when she is lying at a quay. The 3 DOF system was applied to describe rolling, pitching and heaving of a vessel which may cause a significant variations of momentary deck elevation. The realistic range of such variations are assessed for a variety of cargo locations on-board and a phase shift between two independent gantries...
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Locally Adaptive Cooperative Kalman Smoothing and Its Application to Identification of Nonstationary Stochastic Systems
PublikacjaOne of the central problems of the stochastic approximation theory is the proper adjustment of the smoothing algorithm to the unknown, and possibly time-varying, rate and mode of variation of the estimated signals/parameters. In this paper we propose a novel locally adaptive parallel estimation scheme which can be used to solve the problem of fixed-interval Kalman smoothing in the presence of model uncertainty. The proposed solution...
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Boundary value problems with causal operators
PublikacjaPraca 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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Shift invariant operators and a saturation theorem.
PublikacjaPraca 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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On residualities in the set of Markov operators on C1
PublikacjaDowodzi 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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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublikacjaThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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HCI-Based Wireless System for Measuring the Concentration of Mining Machinery and Equipment Operators
PublikacjaMaintaining stable and reliable working conditions is a matter of vital importance for various companies, especially those involving heavy machinery. Due to human exhaustion, as well as unpredicted hazards and dangerous situations, the personnel has to take actions and wisely plan each move. This paper presents a human–computer interaction (HCI)-based system that uses a concentration level measurement function to increase the safety...
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Mathematical model to assess energy consumption using water inflow-drainage system of iron-ore mines in terms of a stochastic process
PublikacjaPurpose is to develop a unified mathematical model to assess energy efficiency of a water inflow-drainage process as the real variant of stochastic method for water pumping from underground workings of iron-ore mines. Methods. The research process was based upon the methods of probability theory as well as stochastic modelling methods. The stochastic function integration has been reduced to summation of its ordinates and further...
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Quadratic programming approach to coupled resonator filter cad
PublikacjaArtykuł prezentuje technikę komputerowego wspomagania procesu projektowania filtrów zbliżeniowych. Polega ona na sformułowaniu macierzy sprzężeń jako problemu programowania kwadratowego (QP). Dzięki zdefiniowaniu procedury optymalizacyjnej jako problemu QP, przy założeniu liniowej zależności współczynników sprzężeń od wymiarów geometrycznych struktury, uzyskano znaczącą redukcję liczby pełnofalowych symulacji prowadzących do uzyskania...
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Uniform Expansivity Outside a Critical Neighborhood in the Quadratic Family
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Four-state stochastic model of changes in the reliability states of a motor vehicle
PublikacjaThe properties of semi-Markov processes have been generally characterized and the applicability of the theory of such processes to the determining of the reliability of motor cars and other road vehicles has been explained. A formal description of the process of changes in the motor vehicle technical states considered as reliability states and a model of this process in the form of a one-dimensional stochastic process have been...
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Asymptotic error expansions for Schoenberg type operators
PublikacjaPrzedstawiono L^p błąd dla rozwinięć dla operatorów Schoenberga
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Hubbard operators approach to the transport in molecular junctions
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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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Different types of solvability conditions for differential operators
PublikacjaSolvability 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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Communications on Stochastic Analysis
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Global and Stochastic Analysis
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Theory of Stochastic Processes
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STOCHASTIC ANALYSIS AND APPLICATIONS
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STOCHASTIC PROCESSES AND THEIR APPLICATIONS
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Deterministic versus stochastic modelling of unsaturated flow in a sandy field soil based on dual tracer breakthrough data
PublikacjaThe 216 km2 Neuenhagen Millcreeck catchment can be characterized as a drought sensitive landscape in NE Germany. It is therefore a fundamental human interest to understand how water that fell as precipitation moves through the unsaturated soils and recharges groundwater. Additionally, a better knowledge of nutrient transport from soil to groundwater is important also, especially in landscapes with light sandy soils. For a better...
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Quadratic convergence of monotone iterations to systems of differential-algebraic equations
PublikacjaZastosowano tu metodę dolnych i górnych rozwiązań do skonstruowania monotonicznych ciągów, które są zbieżne kwadratowo do jedynego rozwiązania układu równań różniczkowo-algebraicznych z warunkiem początkowym.
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Quadratic approximation of solutions for differential equations with nonlinear boundary conditions.
PublikacjaZastosowano metodę kwazilinearyzacji i sformułowano warunki dostateczne przy których iteracje monotoniczne są kwadratowo zbieżne do jedynego rozwiązania wymienionego w tytule zagadnienia różniczkowego. Uzyskane wyniki uogólniają niektóre wcześniej publikowane rezultaty gdy warunek brzegowy był liniowy.
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Stochastic approach to movements of a multihull on waves
PublikacjaW artykule przedstawiono metodę wyznaczania różniczkowych równań ruchu.Układ równań różniczkowych został przedstwaiony dla ruchów antysymetrycznych jednoski wielokadłubowej (poprzeczne ruchy liniowe, poprzeczne ruchy kątowe, poziome ruchy kątowe). Dla tych ruchów zbudowano stochastyczne równania różniczkowe.
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Multihull vessel excitations in stochastic formulation
PublikacjaPraca dotyczy określania wymuszeń wielokadłubowej jednostki pływającej w ujęciu stochastycznym. Wymuszenia ruchu jednostek pływających pochodzą od ruchu fal morskich i działania wiatru. Najczęściej jest to falowanie nieregularne i dlatego w badaniach dynamiki takich jednostek zakłada się, że proces falowania ma charakter probabilistyczny. Przeprowadzono analizę dynamiki jednostki wielokadłubowej na liniowym modelu, na który działa...
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Tribology of stochastic phenomena on the hard tissue.
PublikacjaPraca przedstawia model matematyczny zjawisk tribologicznych podczas hodowli tkanek twardych, w tym chrząstek stawowych. Uwzględnia się chropowatości powierzchni hodowanych chrząstek. Problem tribologiczny uzewnętrzniony został koniecznością sterowania wartościami sił tarcia jakie powstają w cienkiej warstewce przyściennej opływanej tkanki cieczą biologiczną w trakcie hodowli. Taki model matematyczny nie był do tej pory rozpatrywany.
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Boundary vlue problems for difference equations with causal operators
PublikacjaPraca dotyczy problemów brzegowych dla równań różnicowych.Podano warunki dostateczne na istnienie ekstremalnych rozwiązań stosując metodę iteracji monotonicznych.
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On iterates of strong Feller operators on ordered phase spaces.
PublikacjaPraca 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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Investigations of the Methods of Time Delay Measurement of Stochastic Signals Using Cross-correlation with the Hilbert Transform
PublikacjaThe article presents the results of simulation studies of four methods of estimating time delay for random signals using cross-correlation with the Hilbert Transform. Selected models of mutually delayed stochastic signals were used in the simulations, corresponding to the signals obtained from scintillation detectors in radioisotope measurements of liquid-gas two-phase flow. Standard deviations of the values of the individual functions...
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New Approach to Noncasual Identification of Nonstationary Stochastic FIR Systems Subject to Both Smooth and Abrupt Parameter Changes
PublikacjaIn this technical note, we consider the problem of finite-interval parameter smoothing for a class of nonstationary linear stochastic systems subject to both smooth and abrupt parameter changes. The proposed parallel estimation scheme combines the estimates yielded by several exponentially weighted basis function algorithms. The resulting smoother automatically adjusts its smoothing bandwidth to the type and rate of nonstationarity...
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Non-quadratic quality criteria in parameter estimation of continuous-time models
PublikacjaW pracy wykorzystuje się procedury estymacji parametrycznej do identyfikacji modeli z czasem ciągłym. Rozważane algorytmy minimalizują wskaźnik jakości w postaci sumy lub całki wartości bezwzględnej błędu predykcji. Zastosowanie techniki zmiennych instrumentalnych umożliwia ponadto znaczące polepszenie dokładności ocen parametrów, a wprowadzony do w procedur estymacji mechanizm ważenia błędów predykcji pozwala identyfikować modele...
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Quadratic convergence of monotone iterations for differential equations with initial time difference
PublikacjaPodano warunki dostateczne na to, aby iteracje monotoniczne były zbieżne do jedynego rozwiązania równania różniczkowego przy różnych warunkach początkowych. Pokazano, że jest to zbieżność kwadratowa.
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Stochastic approach to the dynamics of a linear floating object
PublikacjaArtykuł stanowi prezentację metody różniczkowych równań stochastycznych w zastosowaniu do analizy dynamiki obiektów pływających. Analizowany jest ruch jednostki pływającej jako obiektu liniowego z uwzględnieniem w równaniach stochastycznych nieliniowości, występującej w wymuszeniach zewnętrznych działających na obiekt. Stochastyczne równania różniczkowe są zapisane dla sprzężonych ruchów symetrycznych.
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Stochastic approach to the dynamics of marine floating object
PublikacjaAnalizowany jest ruch jednostki pływającej z uwzględnieniem w równaniach stochastycznych nieliniowości, występującej w wymuszeniach zewnętrznych działających na obiekt. Stochastyczne równania różniczkowe są zapisane dla sprzężonych ruchów symetrycznych.
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Approximation of Covariance Function with Application to Stochastic Mechanics.
PublikacjaW pracy przedstawiono koncepcję rozwinięć kanonicznych dla funkcji losowych oraz możliwość ich zastosowania w stochastycznej mechanice gruntów. Rozpatrzono rozkład widmowy, rozwinięcia Karhunena-Loevego oraz rozwinięcia ortogonalne zmodyfikowanymi wielomianami Hermite'a. Przeprowadzono analizę błędów dla zagadnienia warstwy gruntu o losowych parametrach sprężystych, uzyskano analityczne rozwiązanie systemu stochastycznego.
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Limit Analysis of a Strip Footing on Stochastic Subsoil.
PublikacjaW pracy analizowana jest ława fundamentowa posadowiona na losowym podłożu.Poszukiwane są oszacowania nośności podłoża na podstawie twierdzeń o dolnej i górnej ocenie obciążenia granicznego. Dla różnych statycznie dopuszczalnych pól naprężenia i kinematycznie dopuszczalnych pól prędkości, wyznaczono wartości oczekiwane i wariancje obciążenia granicznego. Pozwoliło to na określenie odpowiednich dystrybuant, rozumianych...
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Stochastic model of the process of diesel engine operation.
PublikacjaStreszczenie: Najistotniejszym problemem eksploatacji silników o zapłonie samoczynnym jest problem racjonalnego (a zwłaszcza optymalnego) sterowania procesem eksploatacji tych silników. Sterowanie takie może ułatwić zastosowanie iteracyjnego algorytmu wyznaczania optymalnych strategii opracowanego przez R.A. Howarda. Wykorzystanie jednak tego algorytmu do sterowania procesem eksploatacji silników wymaga między innymi opracowania...
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PREDICTION OF SHIP MOTIONS IN IRREGULAR WAVES BASED ON RESPONSE AMPLITUDE OPERATORS EVALUATED EXPERIMENTALLY IN NOISE WAVES
PublikacjaThe most common methods for predicting ship roll motions in a specified sea state are direct measurements of motions in a representative irregular wave realisation (time domain) or calculations of motions from response amplitude operators (RAOs) in the frequency domain. The result of the first method is valid only for the tested sea state, whilst the second method is more flexible but less accurate. RAO-based predictions are calculated...
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Journal of Pseudo-Differential Operators and Applications
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An analysis of the current situation for Polish ferry operators in a transitional environment
PublikacjaArtykuł 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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Existence of solutions for a coupled system of difference equations with cousal operators
PublikacjaPraca dotyczy układów równań różnicowych. Podano warunki dostateczne na istnienie rozwiązań takich problemów. Badano również nierówności różnicowe.
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Specialized genetic operators in drinking water distribution systems control
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Genetic operators of evolutionary algorithm in problem of collision avoidance at sea
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On the maximum principle of Bernstein-Schnabl operators over a Bauer simplex
PublikacjaW pracy bada się geometryczne własności sympleksy Bauera i dowodzi się zasady maksimum dla operatorów Bernsteina-Schnabla.
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Quadratic Cohen representations in spectral analysis of serration process in Al-Mg alloys
PublikacjaIstotny z mechanicznego punktu widzenia efekt Portevina Le-Chateliera charakteryzuje się skomplikowanym profilem widmowym. Jako typowy przykład procesu niestacjonarnego, wymaga specjalnego podejścia umożliwiającego analizę zmian rozkładu energii fluktuacji naprężenia w funkcji odkształcenia. Jako narzędzie umożliwiające realizację powyższego założenia autorzy proponują zastosowanie rodziny przekształceń kwadratowych znanych jako...
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application of linear quadratic regulator (lqr) for nonlinear systems based on the parameter sensitivity
PublikacjaMetoda LQR jest znaną metodą optymalizacyjną dla liniowych układów sterowania. W referacie przedstawiono oryginalny algorytm dotyczący zastosowania tej metody dla nieliniowych układów sterowania przy wykorzystaniu analizy wrażliwości układu. Algorytm ten poddany jest weryfikacji na przykładzie układu sterowania napędu statku.
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International Journal of Stochastic Analysis
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Statistical Inference for Stochastic Processes
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Robust-adaptive dynamic programming-based time-delay control of autonomous ships under stochastic disturbances using an actor-critic learning algorithm
PublikacjaThis paper proposes a hybrid robust-adaptive learning-based control scheme based on Approximate Dynamic Programming (ADP) for the tracking control of autonomous ship maneuvering. We adopt a Time-Delay Control (TDC) approach, which is known as a simple, practical, model free and roughly robust strategy, combined with an Actor-Critic Approximate Dynamic Programming (ACADP) algorithm as an adaptive part in the proposed hybrid control...
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A stochastic approach to the problem of bearing capacity by the method of characteristics
PublikacjaW pracy omówiono zagadnienie nośności granicznej podłoża o własnościach losowych, przy obciążeniu od spoczywającego na nim fundamentu. Zaproponowano stochastyczną modyfikację metody charakterystyk bazującej na metodzie różnic skończonych. Analizowano zagadnienia związane z dyskretyzacją losowego ośrodka gruntowego, symulacją pola losowego oraz ze zbieżnością i stabilnością rozwiązania. Przedstawione podejście umożliwiło uwzględnienie...
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Application exaples of wide area monitoring for system operators within UCTE
PublikacjaW referacie przedstawiono przykładowe zastosowania pomiarów uzyskiwanych w systemie WAMS dla potrzeb systemu elektroenergetycznego.