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Search results for: LINEAR DIOPHANTIE EQUATIONS
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Numerical analysis of open channel steady gradually varied flow using the simplified saint-venant equations
PublicationFor one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear...
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Highly linear self-assembled porphyrin wires
PublicationAn efficient noncovalent assembly process involving high geometrical control was applied to a linear bis(imidazolyl zinc porphyrin) 7Zn, bearing C18 substitutents, to generate linear multiporphyrin wires. The association process is based on imidazole recognition within the cavity of the phenanthroline-strapped zinc porphyrin. In chlorinated solvents, discrete soluble oligomers were obtained after (7Zn)n was end-capped with a terminal...
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The description of non-linear interactions of wave and non-wave modes in a non-adiabatic plasma flow
PublicationThe method of derivation of non-linear equations for interacting modes is explained and applied to a plasma's flow affected by a magnetic field. It is based on the linear projecting of the total perturbation field into specific variations of variables in individual modes of a flow. The method may be applied in many examples of fluid flows with different mechanisms of non-adiabaticity. It is of special importance in complex flows...
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Coupled nonlinear Schrödinger equations in optic fibers theory
PublicationIn this paper a detailed derivation and numerical solutions of CoupledNonlinear Schr¨odinger Equations for pulses of polarized electromagnetic wavesin cylindrical fibers has been reviewed. Our recent work has been compared withsome previous ones and the advantage of our new approach over other methods hasbeen assessed. The novelty of our approach lies is an attempt to proceed withoutloss of information within the frame of basic...
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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Implicit difference methods for first order partial differential functional equations
PublicationKlasyczne rozwiązania problemów początkowo brzegowych przybliżane są rozwiązaniami uwikłanych metod różnicowych. Wykazana została zbieżność i stabilność uwikłanych schematów. Dowód stabilności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perrona dla funkcji danych.
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Solution of coupled integral equations for quantum scattering in the presence of complex potentials
PublicationIn 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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Existence of unbounded solutions to parabolic equations with functional dependence
PublicationThe Cauchy problem for nonlinear parabolic differential-functional equations is considered. Under natural generalized Lipschitz-type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u(·); (ii) the functional dependence u(·) and ∂xu(·); (iii) the functional dependence u(·)and the pointwise dependence ∂xu(t,x).
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The passive operating mode of the linear optical gesture sensor
PublicationThe study evaluates the influence of natural light conditions on the effectiveness of the linear optical gesture sensor, working in the presence of ambient light only (passive mode). The orientations of the device in reference to the light source were modified in order to verify the sensitivity of the sensor. A criterion for the differentiation between two states - "possible gesture" and "no gesture" - was proposed. Additionally,...
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Independence in uniform linear triangle-free hypergraphs
PublicationThe independence number a(H) of a hypergraph H is the maximum cardinality of a set of vertices of H that does not contain an edge of H. Generalizing Shearer’s classical lower bound on the independence number of triangle-free graphs Shearer (1991), and considerably improving recent results of Li and Zang (2006) and Chishti et al. (2014), we show a new lower bound for a(H) for an r-uniform linear triangle-free hypergraph H with r>=2.
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On constitutive relations in the resultatnt non-linear theory of shells
PublicationThe authors summarize their current research in the field of constitutive modelling in the framework of non-linear 6-parameter shell theory. In particular the description of isotropic, multilayered composite and functionally graded shells is presented.
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On geometrically non-linear FEA of laminated FRP composite panels
PublicationThe paper presents a state-of-art review on Finite Element Analysis (FEA) of geometrically non-linear problems for laminated composite plates and shells made as fibre reinforced polymer (FRP) laminates. Besides a subjective overview of the historical development of geometrically non-linear FEA of laminated FRP composite panels, some remarks on possible future issues in this research area are given
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Application of the numerical-analytic method for systems of differential equations with parameter
PublicationThe numerical-analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation. We also obtain several existence results for problems with deviations of an argument
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks
PublicationIn this article, we formulate and solve the representation problem for diffusion equations: giving a discretization of the Laplace transform of a diffusion equation under a space discretization over a space scale determined by an increment h > 0, can we construct a continuous in h family of Cauer ladder networks whose constitutive equations match for all h > 0 the discretization. It is proved that for a finite differences discretization...
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Exact resultant equilibrium conditions in the non-linear theory of branching and self-intersecting shells
PublicationWe formulate the exact, resultant equilibrium conditions for the non-linear theory of branching and self-intersecting shells. The conditions are derived by performing direct through-the-thickness integration in the global equilibrium conditions of continuum mechanics. At each regular internal and boundary point of the base surface our exact, local equilibrium equations and dynamic boundary conditions are equivalent, as expected,...
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Parameter and delay estimation of linear continuous-time systems
PublicationIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous identification...
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Certain family of analytical solutions of nonlinear von Neumann equations
PublicationIn this paper we present a slight generalization of certain type of Darboux transformation, that may be used sub-sequently in a convenient way. This method allows to obtain families of solutions of nonlinear von Neumann equations, that are used in particular in DNA modeling.
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Parameter and delay estimation of linear continuous-time systems
PublicationIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is usually described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous...
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublicationIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Flood Routing by the Non-Linear Muskingum Model: Conservation of Mass and Momentum
PublicationIn this paper, the conservative properties of the Muskingum equation, commonly applied to solve river flood routing, are analysed. The aim of this analysis is to explain the causes ofthe mass balance error, which is observed in the numerical solutions of its non-linear form. The linear Muskingum model has been considered as a semi-discrete form of the kinematic wave equation and therefore it was possible to derive its two non-linear...
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Errors of a Linear Current Approximation in High-Speed PMSM Drives
PublicationCurrent sampling techniques and predictive algorithms used in the digital control of electric drives rely on a simple mathematical model that assumes linear current changes upon constant supplying voltages. This paper identifies rotor movement as a factor that makes this assumption invalid when the rotor covers an angular distance of a few tens of degrees during the control interval duration. The errors of the linear current approximation...
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Modified linear viscoelastic model of earthquake-induced structural pounding
PublicationIn recent times, earthquake-induced structural pounding has been intensively studied through the use of different impact force models. The numerical results obtained from the previous studies indicate that the linear viscoelastic model is relatively simple and accurate in modeling pounding-involved behavior of structures during earthquakes. The only shortcoming of the model is a negative value of the pounding force occurring just...
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Method of lines for nonlinear first order partial functional differential equations.
PublicationClassical solutions of initial problems for nonlinear functional differential equations of Hamilton--Jacobi type are approximated by solutions of associated differential difference systems. A method of quasilinearization is adopted. Sufficient conditions for the convergence of the method of lines and error estimates for approximate solutions are given. Nonlinear estimates of the Perron type with respect to functional variables...
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A solution of non-linear differential problem with application to selected geotechnical problems
PublicationA certain non-linear differential equation containing a power of unknown function being the solution is considered with application to selected geotechnical problems. The equation can be derived to a linear differential equation by a proper substitution and properties of the operations G and S.
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Existence and uniqueness for neutral equations with state dependent delays
PublicationW pracy w celu wykazania istnienia i jednoznaczności rozwiązania równania została zaprezentowana metoda porównawcza.
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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublicationThe paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned `integrating filters' of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization...
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublicationIn 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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Application of Pierson-Moskowitz wave spectrum to solution differential equations of multihull vessel
PublicationMotion of a dynamic system can be generated by different external or internal factors. At mathematical modelling external excitation factors of the most significant effect on the system, are selected. Such external factors are usually called excitations. Response of the system to given excitations is mathematically characterized by a definite transformation called operator of a system. For a broad class of dynamic systems the...
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Monotone iterative method for first-order differential equations at resonance
PublicationThis paper concerns the application of the monotone iterative technique for first-order differential equations involving Stieltjes integrals conditions. We discuss such problems at resonance when the measure in the Stieltjes integral is positive and also when this measure changes the sign. Sufficient conditions which guarantee the existence of extremal, unique and quasi-solutions are given. Three examples illustrate the results.
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Stability of trusses with linear elastic side-supports
PublicationThe present research is devoted to study of a lateral buckling of truss with linear elastic side supports. The elastic support reaction in relation to force in compressed chord and coefficient of buckling length related to side support distance are also calculated. The effect of slope of side support on limit force is also considered. The nonlinear analysis of two roof trusses are carried out. The results are compared to design...
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Non-Linear Control of Electrical Machines Using Non-Linear Feedback
PublicationPrzedstawiono zasady nieliniowego sterowania oraz zastosowanie nielinowego sprzężenia zwrotnego do maszyn elektrycznych. Opisano nieliniowe sterowanie obcowzbudnym silnikiem prądu stałego. Zaprezentowano multiskalarne modele maszyn prądu przemiennego. Maszynę indukcyjną zamodelowano z wykorzystaniem strumienia wirnika oraz z wykorzystaniem strumienia stojana. MMultiskalarne modele maszyny indukcyjnej wykorzystano do nieliniowego...
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Neoclassical Navier–Stokes Equations Considering the Gyftopoulos–Beretta Exposition of Thermodynamics
PublicationThe seminal Navier-Stokes equations were stated even before the creation of the foundations of thermodynamics and its first and second laws. There is a widespread opinion in the literature on thermodynamic cycles that the Navier-Stokes equations cannot be taken as a thermodynamically correct model of a local "working fluid", which would be able to describe the conversion of "heating" into "working" (Carnot's type cycles) and vice...
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The shallow sea experiment with usage of linear hydrophone array
PublicationPurpose of this article is to present designed and made linear hydrophone array and the results obtained during in situ trails on Gulf of Gdańsk. The measuring system allowed to localize hydrophones in the selected points and perform measurements in both the horizontal antenna positioning and vertical. Made in this way recordings allow creating accurate 3D imaging of sound intensity/propagation. During research three floating objects...
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Quasi-solutions for generalized second order differential equations with deviating arguments
PublicationThis paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.
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Linear viscoelastic modelling of damage-involved structural pounding during earthquakes
PublicationDamage-involved structural pounding during earthquakes has been recently intensively studied using different impact force models. The results of the previous studies indicate that the linear viscoelastic model is relatively simple yet accurate in modelling pounding-involved behaviour of structures during earthquakes. The only shortcoming of the model is a negative value of the pounding force occurring just before separation, which...
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On Von Karman Equations and the Buckling of a Thin Circular Elastic Plate
PublicationWe shall be concerned with the buckling of a thin circular elastic plate simply supported along a boundary, subjected to a radial compressive load uniformly distributed along its boundary. One of the main engineering concerns is to reduce deformations of plate structures. It is well known that von Karman equations provide an established model that describes nonlinear deformations of elastic plates. Our approach to study plate deformations...
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Direct estimation of linear and nonlinear functionals of quantum state
PublicationWe present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of...
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Functional differential equations
PublicationSformułowano dość ogólne warunki dostateczne na to, aby odpowiednio zdefiniowane ciągi monotoniczne były zbieżne do jedynego, w pewnym segmencie, rozwiązania zagadnienia początkowego dla funkcyjnych równań różniczkowych. Omawiane równanie jest ogólne, a np. zwyczajne równania różniczkowe czy równania różniczkowo-całkowe są jego szczególnymi przypadkami.
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Optimization of Data Assignment for Parallel Processing in a Hybrid Heterogeneous Environment Using Integer Linear Programming
PublicationIn the paper we investigate a practical approach to application of integer linear programming for optimization of data assignment to compute units in a multi-level heterogeneous environment with various compute devices, including CPUs, GPUs and Intel Xeon Phis. The model considers an application that processes a large number of data chunks in parallel on various compute units and takes into account computations, communication including...
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Stability of truss with side - supports. The case of linear and rotational elastic supports
PublicationThe research is devoted to study lateral buckling of truss with linear and rotational elastic side-supports. Geometrically nonlinear analysis of example truss with linear and rotational elastic sidesupports is carried out. The limit normal force in compressed chord of the truss due to stiffness of side supports is calculated. The elastic support reaction in relation to force in compressed chordand coefficient of buckling length...
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A robust sliding mode observer for non-linear uncertain biochemical systems
PublicationA problem of state estimation for a certain class of non-linear uncertain systems has been addressed in this paper. In particular, a sliding mode observer has been derived to produce robust and stable estimates of the state variables. The stability and robustness of the proposed sliding mode observer have been investigated under parametric and unstructured uncertainty in the system dynamics. In order to ensure an unambiguous non-linear...
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Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling
PublicationIn order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix ρ, all the kinetic constants are encoded in a matrix H; (2) find a Darboux–Bäcklund dressing transformation for the Lax representation iρ˙=[H,f(ρ)], where f models a time-dependent environment; (3) find...
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Research on Linear Actuators for Active Foil Bearings
PublicationActive foil bearings are a kind of gas foil bearing. They contain actuators which allow for modification of the bearing sleeve size and the shape of the lubrication gap. Rotor vibrations can be actively controlled by these changes. It is possible, among other things, to reduce the starting torque, control the vibration amplitude at different speeds and improve operational safety. Prototypes of active foil bearings are being developed...
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Identification of quasi-periodically varying systems with quasi-linear frequency changes
PublicationThe problem of identification of linear quasi-periodically varying systems is considered. This problem can be solved using generalized adaptive notch filtering (GANF) algorithms. It is shown that accuracy of system parameter estimation can be increased if the results obtained from GANF are further processed using a cascade of appropriately designed filters. The resulting generalized adaptive notch smoothing (GANS) algorithms can...
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The Linear Array 2x1 of Slot Monopoles for 6-8.5 GHZ UWB Standard
PublicationThe results of numerical simulations and measurements of 2x1 linear array of slot monopoles are presented in the paper. At the begining a single slot monopole was designed. Next the 2x1 linear array of these monopoles was numerically tested for various configurations of the feeding network. The single monopole and the array were fabricated and the results of the measurements of the reflection coefficients and the radiationpatterns...
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations
PublicationThe light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo (MC) algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present implementation...
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Weighted difference schemes for systems of quasilinear first order partial functional differential equations
PublicationThe paper deals with initial boundary value problems of the Dirichlet type for system of quasilinear functional differential equations. We investigate weighted difference methods for these problems. A complete convergence analysis of the considered difference methods is given. Nonlinear estimates of the Perron type with respect to functional variables for given functions are assumed. The proof of the stability of difference problems...
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A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations
PublicationThe article describes how to identify the boundary and yield surface for hypoplastic constitutive equations proposed by Wu, Gudehus and Bauer. It is shown how to identify and plot the surfaces for any equation in this class. Calculation errors are analyzed characteristic for appleid set of numerical formulas. In the paper there are computer links to the source code prepared in the MATLAB system, based on istructions in the article....