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Search results for: LINEAR DIOPHANTIE EQUATIONS
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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....
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Energy Technologies - Linear algebra 2018/2019 (M.Łapińska)
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WZiE - BiM - Linear Algebra 2024-25 (M.Łapińska)
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Gesture Recognition With the Linear Optical Sensor and Recurrent Neural Networks
PublicationIn this paper, the optical linear sensor, a representative of low-resolution sensors, was investigated in the multiclass recognition of near-field hand gestures. The recurrent neural network (RNN) with a gated recurrent unit (GRU) memory cell was utilized as a gestures classifier. A set of 27 gestures was collected from a group of volunteers. The 27 000 sequences obtained were divided into training, validation, and test subsets....
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On the instantaneous frequency smoothing for signals with quasi-linear frequency changes
PublicationThe problem of estimation of the slowly-varying instantaneous frequency of a nonstationary complex sinusoidal signal buried in noise is considered. This problem is usually solved using frequency tracking algorithms. It is shown that the accuracy of frequency estimates can be considerably increased if the results yielded by the frequency tracker are further processed using the appropriately designed filters. The resulting frequency...
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Physics-guided neural networks (PGNNs) to solve differential equations for spatial analysis
PublicationNumerous examples of physically unjustified neural networks, despite satisfactory performance, generate contradictions with logic and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already at the training stage and lead to many inaccuracies in the final applications. One of the methods to justify the typical black-box model already at the training stage involves extending...
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Novel fast non-linear electrochemical impedance method for corrosion investigations
PublicationThe paper presents a novel approach to corrosion rate monitoring using non-linear electrochemical impedance spectroscopy. The authors propose a new variant of non-linear impedance measurement using amplitude-modulated multi-frequency ac perturbation signal. It allows shortening of measurement duration so it is possible to monitor corrosion rate of the systems experiencing rapid changes. In this way a limitation resulting from lack...
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ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING
PublicationThe paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection-diffusion equations. For the numerical solution of the 1D advection-diffusion equation a method, originally proposed for solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and consequently, to reduce...
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Use of a Least Squares with Conditional Equations Method in Positioning a Tramway Track in the Gdansk Agglomeration
PublicationSatellite measurement techniques have been used for many years in different types of human activity, including work related to staking out and making use of rail infrastructure. First and foremost, satellite techniques are applied to determine the tramway track course and to analyse the changes of its position during its operation. This paper proposes using the least squares with conditional equations method, known in geodesy (LSce)....
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Non-linear circuit model of a single doubly-fed induction machine formulated in natural axes for drive systems simulation purposes
PublicationMathematical modelling and a circuit model formulated in natural axes of a single doubly-fed induction machine, with the account of magnetic circuit nonlinearity are presented in the paper. Derivation of the model differential equations was based on Lagrange's energy method. State functions of magnetic elements in the model are non-linear and depend on all currents flowing in the machine windings and on the angle of rotor position....
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Positivity and job burnout in emergency personnel: examining linear and curvilinear relationship
PublicationThe aim of this study was to examine whether the relationship between the ratio of job-related positive to negative emotions (positivity ratio) and job burnout is best described as linear or curvilinear. Participants were 89 police officers (12% women) and 86 firefighters. The positivity ratio was evaluated using the Job-related Affective Wellbeing Scale (Van Katwyk, Fox, Spector, & Kelloway, 2000). Exhaustion and disengagement,...
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Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads
PublicationWe discuss the finite element modeling of porous materials such as bones using the linear micropolar elasticity. In order to solve static boundary-value problems, we developed new finite elements, which capture the micropolar behavior of the material. Developed elements were implemented in the commercial software ABAQUS. The modeling of a femur bone with and without implant under various stages of healing is discussed in details
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Analysis of Crash Computation on a Basis of the Pronciple of Linear Momentum and Kinetic Energy
PublicationThe article shows the calculation of a vehicle crash with a fixed pile, modelled by the finite element method. There were compared during the crash simulations changes in kinetic energy, as well as – changes in linear momentum and its derivative, with respect to time. Calculations were made in the HyperWorks CAE software environment. The obtained results show influence of various body parts and devices of the deceleration on...
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On dynamic equations with deviating arguments
PublicationPraca dotyczy istnienia rozwiązań równań dynamicznych z odchylonymi argumentami. Podane zostały warunki dostateczne na istnienie rozwiązania. Dwa przykłady ilustrują otrzymane wyniki.
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Simplified Dirac--Coulomb Equations
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Differential equations with delayed arguments
PublicationPraca dotyczy problemów brzegowych dla równań różniczkowych z opóźnionymi argumentami. Podane zostały warunki dostateczne na istnienie jednego rozwiązania bądź rozwiązań ekstremalnych. Dyskusja dotyczy również nierówności różniczkowych. Przykłady ilustrują otrzymane wyniki.
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Advances in Differential Equations
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Differential Equations & Applications
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JOURNAL OF EVOLUTION EQUATIONS
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Application of Galvanostatic Non-Linear Impedance Spectroscopy to the Analysis of Metallic Material Degradation
PublicationThis study presents a novel application of Non-Linear Electrochemical Impedance Spectroscopy (NLEIS) in galvanostatic mode for the rapid, non-destructive assessment of metal degradation. By using galvanostatic mode instead of traditional potentiostatic methods, polarization-related challenges are mitigated, enabling more accurate and reliable analysis. The technique allows for the determination of corrosion rates (corrosion current)...
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Non-Linear Analysis of Structures Utilizing Load-Discretization of Stiffness Matrix Method with Coordinate Update
PublicationThis paper proposes a stiffness method based structural analysis algorithm for geometrically non-linear structures. In this study, the applied load on the joints has been discretized to a sequence of a few loadings applied. Each loading step produces incremental external nodal displacements, which are added to the corresponding coordinates to get a new geometrical shape of the structure. This process is iteratively repeated until...
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On modelling and non-linear elasto-plastic analysis of thin shells with deformable junctions
PublicationThe undeformed base surface of the irregular thin shell is modelled by the union of a finite number of regular smooth surface elements joined together along spatial curvilinear surface edges. The equilibrium conditions are formulated by postulating an appropriate form of the principle of virtual work, where also deformability of shell junctions is taken into account. The PVW is then discretised by C1 finite elements and the incremental-iterative...
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A Linear Phase Filter in Quadruplet Topology With Frequency-Dependent Couplings
PublicationThis letter presents a design of a linear phase microwave bandpass filter. The filter is composed of four resonators arranged in the quadruplet topology. Making the cross and one direct coupling dispersive gives additional design flexibility. The first advantage of using frequency-dependent couplings is the possibility to chose an arbitrary location of a pair of complex transmission zeros (TZs) in the s-domain. The second one is...
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Bearing estimation using double frequency reassignment for a linear passive array
PublicationThe paper demonstrates the use of frequency reassignment for bearing estimation. For this task, signals derived from a linear equispaced passive array are used. The presented method makes use of Fourier transformation based spatial spectrum estimation. It is further developed through the application of two-dimensional reassignment, which leads to obtaining highly concentrated energy distributions in the joint frequency-angle domain...
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Nonlinear and linear impedance of bismuth vanadate ceramics and its relation to structural properties
PublicationThe nonlinear and linear electrical properties, topography, and microstructure of bismuth-vanadate ceramics, were studied. The structurewas observed with the use of X-ray diffraction (XRD), scanning electronmicroscopy (SEM), atomic force microscopy (AFM) and confocal microscopy methods. The obtained results showed that ceramic is porous. Two phase transitionswere determinedwith the use of DSC measurements. The linear and nonlinear ac...
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The equations for interactions of polarization modes in optical fibres including the kerr effect
PublicationWe have derived coupled nonlinear Schro¨ dinger equations (CNLSE) for arbitrary polarized light propagation in a single-mode fibre employing electromagnetic field complete description. We used a basis of transverse eigenmodes with appropriate projecting; hence, the nonlinear constants depend on the waveguide geometry. Accounting for a weak nonlinearity, which is connected to the Kerr effect, we have given explicit expressions for...
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Linear viscoelastic transversely isotropic model based on the spectral decomposition of elasticity tensors
PublicationThe linear viscoelasticity is still a useful model in the engineering for studying the behavior of materials loaded with different loading rates (frequencies). Certain types of materials reveal also an anisotropic behavior: fiber reinforced composites, asphalt concrete mixtures, or wood, to name a few. In general, researchers try to identify experimentally the dependence of engineering constants like: directional Young’s moduli...
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Artur Gańcza dr inż.
PeopleI received the M.Sc. degree from the Gdańsk University of Technology (GUT), Gdańsk, Poland, in 2019. I am currently a Ph.D. student at GUT, with the Department of Automatic Control, Faculty of Electronics, Telecommunications and Informatics. My professional interests include speech recognition, system identification, adaptive signal processing and linear algebra.
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Multiple Solutions to Third-Order Differential Equations with Derivative Dependence and Deviating Arguments
PublicationIn this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J ⊂ [0,1] and advanced...
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The ONETEP linear-scaling density functional theory program
PublicationWe present an overview of the ONETEP program for linear-scaling density functional theory (DFT) calculations with large basis set (planewave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the...
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Pose classification in the gesture recognition using the linear optical sensor
PublicationGesture sensors for mobile devices, which have a capability of distinguishing hand poses, require efficient and accurate classifiers in order to recognize gestures based on the sequences of primitives. Two methods of poses recognition for the optical linear sensor were proposed and validated. The Gaussian distribution fitting and Artificial Neural Network based methods represent two kinds of classification approaches. Three types...
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Path integrals formulations leading to propagator evaluation for coupled linear physics in large geometric models
PublicationReformulating linear physics using second kind Fredholm equations is very standard practice. One of the straightforward consequences is that the resulting integrals can be expanded (when the Neumann expansion converges) and probabilized, leading to path statistics and Monte Carlo estimations. An essential feature of these algorithms is that they also allow to estimate propagators for all types of sources, including initial conditions....
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WCh - GT II - Linear algebra 2021/2022 (H.Guze)
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Respiration rate estimation using non-linear observers in application to wastewater treatment plant
PublicationA problem of respiration rate estimation using two new non-linear observers for a wastewater treatment plant is addressed in this paper. In particular, a non-linear adaptive Luenberger-like observer and a super twisting sliding mode observer have been derived to produce stable and bounded estimates of the respiration rate. During the synthesis of the particular observer, an appropriate mathematical utility model was used. The observability...
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Variational principles for bound states of Schrödinger and Dirac equations allowing the use of discontinuous trial functions
PublicationWe present systematic constructions of variational principles for energies of bound states of the Schroedinger and Dirac equations. The principles allow the use of discontinuous trial functions. The method employed is based on a generalized Lagrange procedure. Relationships between our variational principles and those available in the literature are established.