Filtry
wszystkich: 668
wybranych: 608
Wyniki wyszukiwania dla: mathematical analysis
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Mathematical analysis of transformer insulation state by means of composite indicator
PublikacjaThe paper is presenting mathematical model – composite indicator (CI), which was utilized on insulating state of distribution transformer to analyze and sensibility of individual measurements methods mutual comparison. We can uniquely determine importance of these measurements methods with this mathematical apparatus in these measurements methods in insulating state of transformers.
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Mathematical analysis of a generalised p53-Mdm2 protein gene expression model
PublikacjaWe propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate...
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Mathematical analysis of the lasing eigenvalue problem for the optical modes in a layered dielectric cavity with a quantum well and distributed Bragg reflectors
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Mathematical Modelling and Effect Size Analysis in Support of Searching for the Proteomic Signature of Radiotherapy Toxicity
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Modeling of medium flow processes in transportation pipelines - the synthesis of their state-space models and the analysis of the mathematical properties of the models for leak detection purposes
PublikacjaThe dissertation concerns the issue of modeling the pipeline flow process under incompressible and isothermal conditions, with a target application to the leak detection and isolation systems. First, an introduction to the model-based process diagnostics is provided, where its basic terminology, tools, and methods are described. In the following chapter, a review of the state of the art in the field of leak detection and isolation...
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On the interspike-intervals of periodically-driven integrate-and-fire models
PublikacjaWe analyze properties of the firing map, which iterations give information about consecutive spikes, for periodically driven linear integrate-and-fire models. By considering locally integrable (thus in general not continuous) input functions, we generalize some results of other authors. In particular, we prove theorems concerning continuous dependence of the firing map on the input in suitable function spaces. Using mathematical...
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Conley type index applied to Hamiltonian inclusions
PublikacjaPodano dowód istnienia nietrywialnych rozwiązań okresowych dla inkluzji Hamiltonowskich, z potencjałem lokalnie Lipschitzowskim, okresowym, uogólniając klasyczne twierdzenie Ammana- Zehndera. Użyto techniki z teorii indeksu Conley'a dla wielowartościowych potoków w przestrzeni Hilberta.
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Stability by linear approximation for time scale dynamical systems
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Rotating rod and ball
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Homoclinic solutions for nonautonomous second order Hamiltonian
PublikacjaW pracy dowodzi się istnienia rozwiązań homoklinicznych dla pewnych typów równań różniczkowych zwyczajnych drugiego rzędu typu hamiltonowskiego.
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Comment on the orthogonality of the Macdonald functions of imaginary order
PublikacjaPrzeprowadzono dowód ortogonalności funkcji Macdonalda z urojonym indeksem. Zastosowana metoda jest znacznie prostsza od innych prezentowanych do tej pory w literaturze.
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Differential-algebraic systems with maxima
PublikacjaMetoda numeryczno-analityczna została zastosowana do układów równań różniczkowo-algebraicznych z operatorem maximum. Zakładając warunek Lipschitza na funkcje występujące w zagadnieniu pokazano, że ciąg iteracji prostych jest zbieżny do rozwiązania zagadnienia pomocniczego. Podano warunki dostateczne na istnienie rozwiązania problemu wyjściowego. Iteracje Seidla też były przedmiotem badań. W ostatniej części pracy był dyskutowany...
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First-order impulsive ordinary differential equations with advanced arguments
PublikacjaPraca dotyczy problemów istnienia rozwiązań dla równań różniczkowych z impulsami i nieliniowymi warunkami brzegowymi. Są to równania z argumentami wyprzedzonymi. Podano warunki dostateczne na istnienie rozwiązań. W pracy są również dyskutowane nierówności różniczkowe z impulsami. Podano też przykłady ilustrujące otrzymane wyniki.
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Nonlinear boundary value problems for second order differential equations with causal operators
PublikacjaW pracy rozważane są równania różniczkowe rzędu drugiego z nielinowymi warunkami brzegowymi. Prawa strona takich zagadnień zawiera operatory typu ''causal''. Podane zostały warunki dostateczne na istnienie rozwiązań tego typu problemów. Badano też nierówności różniczkowe związane z w/w równaniami różniczkowymi. Podano przykład ilustrujący otrzymane wyniki teoretyczne.
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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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Stability by linear approximation for time scale dynamical systems
PublikacjaWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
PublikacjaZnaleziono cztery nowe wyrażenia dla pochodnej stowarzyszonej funkcji Legendre'a pierwszego rodzaju względem jej stopnia w przypadku, gdy rząd i stopień są liczbami naturalnymi. Wyniki wykorzystano do podania nowych wyrażeń dla stowarzyszonych funkcji Legendre'a drugiego rodzaju z naturalnymi rzędem i stopniem.
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublikacjaUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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Anisotropic Orlicz–Sobolev spaces of vector valued functions and Lagrange equations
PublikacjaIn this paper we study some properties of anisotropic Orlicz and Orlicz–Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give conditions which ensure that the principal part of variational functional is finitely defined and continuously differentiable on Orlicz–Sobolev space.
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Mountain pass type periodic solutions for Euler–Lagrange equations in anisotropic Orlicz–Sobolev space
PublikacjaUsing the Mountain Pass Theorem, we establish the existence of periodic solution for Euler–Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part and a forcing term. We consider two situations: G satisfying at infinity and globally. We give conditions on the growth of the potential near zero for both situations.
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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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Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive
PublikacjaWe study one-dimensional integrate-and-fire models of the general type x˙=F (t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F (t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle...
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A PAIR OF PERFECTLY CONDUCTING DISKS IN AN EXTERNAL FIELD
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Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method
PublikacjaIn this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...
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Dynamics of Field Line Mappings in Magnetic Flux Tubes
PublikacjaWe study the topological constraints on the dynamics of magnetic field lines in flux tubes. Our approach is based on the application of the topological invariant: fixed point index. We consider periodic flux tubes and find various restrictions on the field lines that come from the sequence of fixed point indices of iterations. We also analyze the case of a tube with a cylindrical obstacle, deducing some special dynamical properties...
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Boundary value problems for dynamic equations of Volterra type on time scales
PublikacjaPraca dotyczy równań i nierówności dla problemów dynamicznych typu Volterry. Podano warunki dostateczne na istnienie ekstremalnych rozwiązań w obszarze ograniczonym przez dolne i górne rozwiązania. Praca zawiera również pewne uwagi dla konkretnych zagadnień różniczkowych i dyskretnych.
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Positive solutions to second order four-point impulsive problems with deviating arguments
PublikacjaStosując tw. Leggetta-Williamsa, podano warunki dostateczne na istnienie dodatnich rozwiązań dla czteropunktowych problemów brzegowych dla równań różniczkowych rzędu drugiego z odchylonymi argumentami. Dyskutowane były problemy gdy argument odchylony był typu opóźnionego lub wyprzedzonego.
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Dynamic inequalities and equations of Volterra type on time scales
PublikacjaPraca dotyczy całkowo-różniczkowych równań dynamicznych typu Volterry z warunkami początkowymi. Stosując twierdzenie Banacha o punkcie stałym pokazano istnienie jedynego rozwiązania liniowego równania dynamicznego. Stosując metodę iteracji monotonicznych pokazano istnienie rozwiązań ekstremalnych dla problemów nieliniowych. Badano też nierówności dynamiczne. Praca zawiera również uwagi dotyczące zagadnień różniczkowych i różnicowych.
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublikacjaIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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On integro-differential equations with delayed arguments
PublikacjaPraca dotyczy problemów różniczkowo-całkowych z warunkami początkowymi oraz brzegowymi typu okresowego. Podano warunki na istnienie i jednoznaczność rozwiązania. Badania dotyczyły również nierówności różniczkowo-całkowych z argumentami typu opóżnionego. Podano przykłady, które mogą mieć zastosowanie w problemach inżynierskich.
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Mathematical modelling: Lessons from composite indicators
PublikacjaWe discuss here composite indicators as mathematical models, which can be looked at through the lenses of the five rules discussed in this volume. Composite indicators sit between analysis and advocacy, and their use has social and political implications. For this reason, the lenses of the manifesto can be used to build them better, to make them more transparent, as well as to inspect incumbent indicators for methodological or...
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The use of mathematical models for diagnosis of activated sludge systems in WWTP
PublikacjaIn this study diagnosis of activated sludge systems in wastewater treatment plant (WWTP) was investigated. Diagnosis of technical objects can be realized in many ways. One of the divisions of the diagnostic methods include modelling with or without a model of the object. The first of these is the analysis of the symptoms for which, based on the parameter values, the abnormality in the diagnosed objects are sought. Another way is...
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Mathematical modelling of the overhead contact line for the purpose of diagnostics of pantographs
PublikacjaThe overhead contact line (OCL) is the most effective way for supplying railway electric vehicles. The increase of the speed of the vehicles increases power consumption and requires ensuring proper cooperation of pantographs with OCL. The paper describes the novel mathematical model of the OCL system and the simulation results. The primary objective is a more accurate analysis to increase the reliability of the evaluation of monitoring...
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A Novel Approach to Fully Nonlinear Mathematical Modeling of Tectonic Plates
PublikacjaThe motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the...
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Mathematical Modeling of Ice Dynamics as a Decision Support Tool in River Engineering
PublikacjaThe prediction of winter flooding is a complicated task since it is affected by many meteorological and hydraulic factors. Typically, information on river ice conditions is based on historical observations, which are usually incomplete. Recently, data have been supplemented by information extracted from satellite images. All the above mentioned factors provide a good background of the characteristics of ice processes, but are not...
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Mathematical approach to design 3D scaffolds for the 3D printable bone implant
PublikacjaThis work demonstrates that an artificial scaffold structure can be designed to exhibit mechanical properties close to the ones of real bone tissue, thus highly reducing the stress-shielding phenomenon. In this study the scan of lumbar vertebra fragment was reproduced to create a numerical 3D model (this model was called the reference bone sample). New nine 3D scaffold samples were designed and their numerical models were created....
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Mathematical Modeling of the Impact Range of Sewage Discharge on the Vistula Water Quality in the Region of Włocławek
PublikacjaThe paper presents results of analysis of the industrial sewage discharge influence at km 688 + 250 of the Vistula River on water quality. During the analysis, two-dimensional models of flow, impurities and temperature transport were used. Hydrological conditions of the analyzed section of the river, characteristic flows and bathymetry of the riverbed in the first instance were defined. Calculations of velocity distribution at...
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Effectiveness of a mathematical model in simulating nonlinear mechanical behaviour of a seismic isolation system made of polymeric bearings
PublikacjaThe present study was focused on determining the effectives of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system made of Polymeric Bearings. The proposed mathematical model defines the lateral force as a nonlinear function of the shear displacement and the deformation velocity. The effectiveness of the proposed mathematical model was verified by comparing the seismic response...
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Mathematical Modelling of Drive System with an Elastic Coupling Based on Formal Analogy between the Transmission Shaft and the Electric Transmission Line
PublikacjaIn the paper, the kinematic structure of the transmission shaft between the driving motor and the working mechanism is studied. The analysis is based on electrical and mechanical similarities. The equivalent circuits, typical for electrical systems, are defined for the transmission shaft concerned. Modelling of the transmission shaft based on a formal analogy between the transmission shaft and the electric transmission line is...
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Influence of service ageing on polyester-reinforced polyvinyl chloride-coated fabrics reported through mathematical material models
PublikacjaIn this paper the coupled service (constructional tension) and environmental (sunlight, rainfalls, temperature variations) ageing influence on the polyester-reinforced polyvinyl chloride (PVC)-coated fabric VALMEX is studied. Two cases of the same fabric have been analyzed: one USED for 20 years on the real construction of the Forest Opera in Sopot (Poland), and one kept as a spare material (NOT USED). The following tests have...
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Innovations in Wastewater Treatment: Harnessing Mathematical Modeling and Computer Simulations with Cutting-Edge Technologies and Advanced Control Systems
PublikacjaThe wastewater treatment landscape in Central Europe, particularly in Poland, has undergone a profound transformation due to European Union (EU) integration. Fueled by EU funding and rapid technological advancements, wastewater treatment plants (WWTPs) have adopted cutting-edge control methods to adhere to EU Water Framework Directive mandates. WWTPs contend with complexities such as variable flow rates, temperature fluctuations,...
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Mathematical model of pennate muscle
PublikacjaThe purpose of this study is to create a new mathematical model of pennate striated skeletal muscle. This new model describes behaviour of isolated flat pennate muscle in two dimensions (2D) by taking into account that rheological properties of muscle fibres depend on their planar arrangement. A new mathematical model is implemented in two types: 1) numerical model of unipennate muscle (unipennate model); 2) numerical model of...
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A dressing method in mathematical physics
PublikacjaMetodę ubierania stosuje się do równań nieliniowych całkowalnych i w teorii potencjałów całkowalnych mechaniki kwantowej.
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Mathematical Approach to Assess a Human Gait
PublikacjaA purpose of the paper was to create a mathematical approach to assess a human gait. The scope of the study was to model a normal gait in the sagittal plane and frontal plane of the body. Applying the Newton-Euler formulation, three multibody biomechanical models were derived to describe single support phase and double support phase of the gait. To model a gait in the sagittal plane the open-close sagittal 6DOF model and the open-close...
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Mathematical Modelling in Diagnosis of Wastewater Treatment Plant
PublikacjaThe paper reports development of mathematical modeling in diagnosis of the WWTP. The algorithm is based on a comparition of data from the mathematical modeling and measurments of real datefrom WWTP, until it will detect any malfunction of the sensors in th case of study.
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Duhem and Natanson: Two Mathematical Approaches to Thermodynamics
PublikacjaIn this article, the previously unrecognized contributions of Pierre Duhem and Ladislavus Natanson in thermodynamics are shown. The mathematical remodelling of a few of their principal ideas is taken into consideration, despite being neglected in the literature. To emphasize these ideas in an appropriate epistemological order, it would be crucial to first revalue and reconstruct some underrepresented parts of the proceedings process...
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Mathematical Models in Design Process of Ship Bow Thrusters
PublikacjaThe paper describes an application of simulation models for computer-aided design of ship bow thrusters. Generation of simulation models of ship bow thruster requires development and verifying of mathematical models of system component elements. Using the results of simulation the expert system is able to determine, that the rules of classification societies are met. Design procedures and mathematical models are part of an expert...
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Mathematical Models in Design Process of Ship Bow Thrusters
PublikacjaThe presentation is about an application of simulation models for computer-aided design of ship bow thrusters. Generation of simulation models of ship bow thruster requires development and verifying of mathematical models of system component elements. Using the results of simulation the expert system is able to determine, that the rules of classification societies are met. Design procedures and mathematical models are part of an...
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Multibody models for gait analysis
PublikacjaThe aim of this study was to create multibody biomechanical models to analyze a normal gait of the human. Proposed models can be used to identify joint moments of the lower limbs during normal gait in the single and double support phases. Applying Newton-Euler formulation, following planar models were developed: 1) a mathematical 6DOF model describing a gait in the sagittal plane of the body for single support phase and double...
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Identification of ship’s hull mathematical model with numerical methods
PublikacjaThe modern maritime industry is moving toward the development of technology that will allow for full or partial autonomy of ship operation. This innovation places high demands on ship performance prediction techniques at the design stage. The researchwork presented in the article is related to the design stage of the ship and concerns methods for prognosis and evaluation of the specific operational condition of the ship, namely...