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The generalized quasilinearization for integro-differential equations of Volterra type on time scales
PublikacjaBadano równania całkowo-różniczkowe on ''time scales'' i podano warunkidostateczne na zbieżność metody kwazilinearyzacji do jego rozwiązania. Podano warunki na to, aby zbieżność ta była kwadratową.
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Remarks on the convergence of an iterative method of solution of generalized least squares problem
PublikacjaW pracy przedstawiona jest metoda iteracyjna znajdowania regularyzowanego (w sensie Tichonowa) rozwiązania układu równań Ax=b z dowolną macierzą A. Dla danej liczby alfa i wektora g daje ona ciąg przybliżeń zbieżny do rozwiązania (w sensie najmniejszych kwadratów) tego układu. Rozwiązanie to minimalizuje odległość zbioru wszystkich rozwiązań średniokwadratowych układu Ax=b od wektora g. Podane zostało również oszacowanie szybkości...
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Generalized Euler method for nonlinear first order partial differential equations.
PublikacjaKlasyczne rozwiązania nieliniowych równań różniczkowych cząstkowych pierwszego rzędu są aproksymowane w tej pracy za pomocą rozwiązań quasiliniowych układów równań różnicowych. Podstawowa idea pracy jest oparta na teorii charakterystyk. Podane są warunki wystarczające dla zbieżności metody. Dowód stabilności schematu różnicowego wykorzystuje metodę porównawczą z nieliniowymi oszacowaniami typu Perrona dla danych funkcji.Podane...
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A Generalized Framework Towards Structural Mechanics of Three-layered Composite Structures
PublikacjaThree-layered composite structures find a broad application. Increasingly, composites are being used whose layer thicknesses and material properties diverge strongly. In the perspective of structural mechanics, classical approaches to analysis fail at such extraordinary composites. Therefore, emphasis of the present approach is on arbitrary transverse shear rigidities and structural thicknesses of the individual layers. Therewith...
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Single and Dual-GPU Generalized Sparse Eigenvalue Solvers for Finding a Few Low-Order Resonances of a Microwave Cavity Using the Finite-Element Method
PublikacjaThis paper presents two fast generalized eigenvalue solvers for sparse symmetric matrices that arise when electromagnetic cavity resonances are investigated using the higher-order finite element method (FEM). To find a few loworder resonances, the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm with null-space deflation is applied. The computations are expedited by using one or two graphical processing...
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Comparing Arbitrary Unrooted Phylogenetic Trees Using Generalized Matching Split Distance
PublikacjaIn the paper, we describe a method for comparing arbitrary, not necessary fully resolved, unrooted phylogenetic trees. Proposed method is based on finding a minimum weight matching in bipartite graphs and can be regarded as a generalization of well-known Robinson-Foulds distance. We present some properties and advantages of the new distance. We also investigate some properties of presented distance in a common biological problem...
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Generalized solutions of mixed problems for first-order partial functional differential equations
PublikacjaW pracy udowodniono twierdzenie o istnieniu rozwiązań i ich ciągłej zależności od warunków początkowo brzegowych. Do przekształcenia zagadnienia oryginalnego w układ równań całkowo funkcyjnych typu Volterry użyto metody bicharakterystyk. Istnienie rozwiązań udowodnione jest metodą kolejnych przybliżeń, przy użyciu twierdzeń o nierównościach całkowych. Rozwiązania klasyczne układów równań całkowo funkcyjnych prowadzą do rozwiązań...
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Generalized adaptive notch and comb filters for identification of quasi-periodically varying systems
PublikacjaW artykule wprowadzono pojęcie obiektów pseudookresowych o parametrach będących liczbami rzeczywistymi. Pokazanometody oparte na metodzie funkcji bazowych pozwalające na identyfikację takich obiektów. Przedstawiono związekpomiędzy zaprojektowanymi algorytmami a klasycznymi filtrami wycinającymi typu notch.
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Communication Model Order Reduction in Hybrid Methods Involving Generalized Impedance Matrix
PublikacjaA novel strategy for the efficient analysis of frequency-domain scattering electromagnetic problems in open and closed domains is presented. A fully automatic model-order reduction technique, called the enhanced reduced-basis method, is applied to increase the efficiency of the hybrid approach, which combines the finite-element and mode-matching methods. Numerical tests show that the proposed algorithm yields reliable and highly...
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Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublikacjaWe study far- and near-field magnetic and electric multipole moments induced in the ground state of the Dirac one-electron atom placed in a weak 2L-pole magnetostatic field. The analysis is carried out within the framework of the first-order Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E)...
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Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac–Coulomb Green function
PublikacjaWe present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Ze. Calculations are...
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Implementation of algebraic procedures on the GPU using CUDA architecture on the example of generalized eigenvalue problem
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Myeloperoxidase Modulates Inflammation in Generalized Pustular Psoriasis and Additional Rare Pustular Skin Diseases
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Generalized solution of mixed problems for first order partial differential equations with state dependent delays
PublikacjaW pracy zostało udowodnione twierdzenie o istnieniu i jednoznaczności rozwiązań dla zagadnień początkowo-brzegowych z cząstkowym równaniem różniczkowo-funkcyjnym z opóźnionym argumentem zależnym od funkcji niewiadomej. Użyto metody bicharakterystyk. Jednoznaczność rozwiązań wykazano metodą porównawczą, istnienie - metodą ciągów przybliżeń.
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Multilevel model order reduction with generalized compression of boundaries for 3-d FEM electromagnetic analysis
PublikacjaThis paper presents a multilevel Model Order Reduction technique for a 3-D electromagnetic Finite Element Method analysis. The reduction process is carried out in a hierarchical way and involves several steps which are repeated at each level. This approach brings about versatility and allows one to efficiently analyze complex electromagnetic structures. In the proposed multilevel reduction the entire computational domain is covered...
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Closed forms of the Green's function and the generalized Green's function for the Helmholtz operator on the N-dimensional unit sphere
PublikacjaPokazano, że funkcję Greena dla operatora Helmholtza na N-wymiarowej sferze jednostkowej można wyrazić przez funcję Gegenbauera pierwszego rodzaju. W tych przypadkach, w których funkcja Greena nie istnieje, skonstruowano uogólnioną funkcję Greena.
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Generalized Taylor formula and shell structures for the analysis of the interaction between geosythetics and engineering structures of transportation lines
PublikacjaThe analysis of the interaction between geosynthetics and engineering structures (e.g. railroad bed, soil foundation, pipeline) assumes that the geosynthetic form elastic membranes or shell laid on different types of foundations. The mathematical description of that problems in continuous domain employs Laplace operator Δ or d’Alembert operator □. In this paper we demonstrate the analysis based on generalize Taylor formula, and...
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Application of Generalized Regression Neural Network and Gaussian Process Regression for Modelling Hybrid Micro-Electric Discharge Machining: A Comparative Study
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Rating mathematical models for first-pass of tracer in pCT lung studies
PublikacjaThis paper presents a comparison of model based on the Gauss function and the most commonly used Gamma-variate model in perfusion computed tomography (pCT) lung studies. It also verifies whether used model affects value of blood volume parameter. Three mean concentration-time curves were created from actual pCT measurements: arterial input function, blood vessels in lungs and lung parenchyma. On the basis of these mean curves we...
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Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublikacjaZnaleziono magnetyczny moment anapolowy indukowany w stanie podstawowym relatywistycznego atomu jednoelektronowego przez zewnętrzne stałe, słabe, jednorodne pole elektryczne. Podano wyrażenie analityczne dla polaryzowalności anapolowej takiego atomu. Obliczenia wykonano, stosując rozwinięcie sturmowskie uogólnionej funkcji Greena-Diraca-Coulomba.
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GPU-Accelerated LOBPCG Method with Inexact Null-Space Filtering for Solving Generalized Eigenvalue Problems in Computational Electromagnetics Analysis with Higher-Order FEM
PublikacjaThis paper presents a GPU-accelerated implementation of the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method with an inexact nullspace filtering approach to find eigenvalues in electromagnetics analysis with higherorder FEM. The performance of the proposed approach is verified using the Kepler (Tesla K40c) graphics accelerator, and is compared to the performance of the implementation based on functions from...
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Electric-field-induced magnetic quadrupole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublikacjaStosując rozwinięcie sturmowskie uogólnionej funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla magnetycznego momentu kwadrupolowego, indukowanego przez zewnętrzne słabe, stałe, jednorodne pole elektryczne w stanie podstawowym relatywistycznego atomujednoelektronowego.
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Electric and magnetic dipole shielding constans for the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublikacjaStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla stałych ekranowania elektrycznego i magnetycznego relatywistycznego atomu wodoropodobnego w stanie podstawowym.
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Magnetic field-induced electric quadrupole moment in the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublikacjaStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla elektrycznego momentu kwadrupolowego, indukowanego przez zewnętrzne pole magnetyczne w relatywistycznym atomie wodoropodobnym w stanie podstawowym. Wykazano, że jest to efekt czysto relatywistyczny.
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Siedmiokryterialny miernik oceny niepotokowych procesów produkcyjnych
PublikacjaGrowing expectations of clients, who demand products adapted to their individual needs is inducing the development of batch processes. The author developed a model of batch processes rating based on the following criterions: • Economical criterion applies to evaluation of the productions’ cost levels connected with the process subjected to analysis and necessary investment funds. • Ecological criterion is about means of natural...
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Aestheticization of Flowcharts
PublikacjaOne of the important issues of diagrams is their aesthetics. In this paper a method of its formalization for freehand drawn flowcharts is proposed. In order to formalize the evaluation of flowcharts' aesthetics a criterion consisting of several measures is proposed. Based on this criterion the algorithms for automatic optimization of flowcharts' appearance are proposed.
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Load capacity and serviceability conditions for footbridges made of fibre-reinforced polymer laminates = Warunki nośności i użytkowalności w odniesieniu do kładek z laminatów polimerowych
PublikacjaThe contribution is focused on derivation of the Ultimate Limit State (ULS) and Serviceability Limit State (SLS) design criteria for footbridges built of fibre-reinforced polymer matrix (FRP) laminates. The ULS design criterion is based on the design guidelines for above-ground, pressure, FRP composite tanks and the Tsai-Wu failure criterion, which is used to predict the onset of FRP laminates damage. The SLS criterion is based...
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Risk criteria for sea-going ships arising from the operation of the main engines' crankshaft - conecting rod - piston systems
PublikacjaIn the article the risk criterion for sea-going ships arising from the operation of the main engines' crankshaft - connecting rod - piston systems is proposed. These criterion is based on the procedures recommended in the Formal Safety Assessment method developed under the auspices of International Maritime Organization (IMO). First of all the collective risk criterion for ship has been proposed. In the next step, the share of...
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A more colorful hat problem
PublikacjaThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. We consider a generalized hat...
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Some Introductory and Historical Remarks on Mechanics of Microstructured Materials
PublikacjaHere we present few remarks on the development of the models of microstuctured media and the generalized continua.
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Examination of selected failure criteria with asymmetric shear stresses in the collapse analysis of laminated shells
PublikacjaThe paper is concerned with failure analysis of composite shells performed with the usage of the nonlinear 6‐parameter shell theory with drilling rotation degree of freedom. This special theory embodies naturally unlim-ited translations and rotations and is suitable for analysis of irregular shells for instance with various, partic-ularly orthogonal, intersections. The presence of the drilling rotation is inherently accompanied...
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Obserwatory prędkości dla bezczujnikowego sterowania maszynami prądu przemiennego
PublikacjaPrzedstawiono model matematyczny uogólnionej maszyny elektrycznej rozszerzony przez wprowadzenie dodatkowych zmiennych. Na podstawie modelu rozszerzonego opracowano strukturę obserwatora prędkości maszyny uogólnionej. Zaprezentowano struktury obserwatorów prędkości dla poszczególnych rodzajów maszyn prądu przemiennego. Pokazano, że prędkość kątową wirnika można odtwarzać dla różnych typów maszyn stosując odpowiednie zmienne stanu...
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Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra
PublikacjaIn this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized...
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Two-criteria optimisation problem for ventral hernia repair
PublikacjaTwo-criteria optimisation problem related to laparoscopic ventral hernia repair is formulated in this paper. An optimal implant from a given set and its orientation is sought. The implant is subjected to kinematic extortions due to a patient’s body movement and intra-abdominal pressure. The first criterion of the optimisation problem deals with the reaction force in the implant fastener, while the deflection of the implant constitutes...
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A multi-criteria decision model for the introduction of electric storage multiple units on the partially electrified Gdynia-Hel railway
Publikacja: In this article a multi-criteria study of the use of independently powered electric multiple units on the partially electrified Gdynia Główna - Hel line was carried out. The use of (currently used) diesel and, as an alternative, electric and electric multiple units with an electric energy storage was considered. The analysis was carried out on the basis of three criteria for assessing the route service options, i.e. environmental,...
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Identification of quasi-periodically varying systems with quasi-linear frequency changes
PublikacjaThe 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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Analog modelling in qualitative analysis of vibration propagation
PublikacjaThe theory of dynamic systems is usually used to model the real systems. The models are based on solving ordinary differential equations, partial or difference, which enable obtaining the relation between input signal and the system response (output signal). The analogy between those models and generalized dynamic systems or control systems can be practically used. Vibration propagation can be described in a similar way as the...
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Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogenlike atom in the ground state
PublikacjaThe second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green's function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_{2}$...
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Harmonic Vibrations of Nanosized Magnetoelectric Bodies with Coupled Surface and Interphase Effects: Mathematical Models and Finite Element Approaches
PublikacjaThe harmonic problems for piezomagnetoelectric nanosized bodies with taking into account the coupled damping and surface effects are considered on the base of the generalized Gurtin-Murdoch model. In the development of previous investigations, the coupled mechanical, electric and magnetic surface effects with surface inertial terms are introduced into the model. For a homogeneous model, the composite material is considered as homogeneous...
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Modelling, Simulation and Optimization of the Wavemaker in a Towing Tank
PublikacjaThe paper analyses the problem of experimental identification (frequency response), modelling and optimization of the towing tank wavemaker in the Scilab/Xcos environment. The experimental identification of the objects (the towing tank wavemaker placed in the hydrodynamic laboratory of the CTO S.A. Ship Design and Research Centre (CTO)) and the implementation of the models in the simulation environment, enable to perform: 1. tuning...
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Rozprzestrzenianie się w podtorzu skutków katastrof kolejowych z udziałem materiałów niebezpiecznych
PublikacjaDuża część przewozów materiałów niebezpiecznych prowadzona jest koleją. W związku z tym bezpieczeństwo tych przewozów nabiera coraz większego znaczenia. Każda katastrofa z udziałem materiałów niebezpiecznych ma negatywny wpływ na uczestników tego zdarzenia oraz na otaczające środowisko, bowiem jej zasięg na ogół nie jest lokalny. Z tego wynika, że w przypadku zaistnienia katastrofy należy minimalizować jej skutki oraz w dalszych...
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Variable-structure algorithm for identification of quasi-periodically varying systems
PublikacjaThe paper presents a variable-structure version of a generalized notchfiltering (GANF) algorithm. Generalized notch filters are used for identification of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The proposed algorithm is a cascade of two GANF filters: a multiple-frequency "precise" filter bank, used for precise system tracking, and a...
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Effect of power frequency on the stress state of disc actuator
PublikacjaThe paper presents the concept of determinig the optimum frequency of coil supply in inductive-dynamic drive. As a criterion to obtain the sought frequency, the smallest value of reduced stress in the disc was assumed while maintaining the desired dynamics.
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Three-objective antenna optimization by means of kriging surrogates and domain segmentation
PublikacjaIn this paper, an optimization framework for multi-objective design of antenna structures is discussed which exploits data-driven surrogates, a multi-objective evolutionary algorithm, response correction techniques for design refinement, as well as generalized domain segmentation. The last mechanism is introduced to constrain the design space region subjected to sampling, which permits reduction of the number of training data samples...
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Experimentally feasible semi-device-independent certification of four-outcome positive-operator-valued measurements
PublikacjaRecently the quantum information science community devoted a lot of attention to the theoretical and practical aspects of generalized measurements, the formalism of all possible quantum operations leading to acquisition of classical information. On the other hand, due to imperfections present in quantum devices, and limited thrust to them, a trend of formulating quantum information tasks in a semi-device-independent manner emerged....
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Synthesis of coupled lossy resonator filters.
PublikacjaA technique for fast synthesis of coupling matrix low-pass prototypes of generalized. Chebyshev bandpass filters with lossy resonators is presented in this letter. The coupling matrix is found by solving a nonlinear least squares problem based on zeros and poles of filter's transfer functions.
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Performance of isotropic constitutive laws in simulating failure mechanisms in scaled RC beams
PublikacjaResults of numerical calculations of reinforced concrete (RC) beams are presented. Based on experimental results on longitudinally reinforced specimens of different sizes and shapes are investigated. Four different continuum constitutive laws with isotropic softening are used: one defined within continuum damage mechanics, an elasto-plastic with the Rankine criterion in tension and the Drucker-Prager criterion in compression, a...
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Turning maneuver as a potential cause of the next stability failure mode for a ship in operation
PublikacjaThe only formal stability-related requirement referring to a turning maneuver of a ship results from the IS Codeand its application is limited to passenger ships only. The goal of the adopted criterion is to prevent an excessiveangle of heel in turn. Likewise, the remaining prescriptive criteria, this one is simply based on the concept ofa threshold that must not be exceeded. In this case, the angle of heel...
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Variational principles for bound states of Schrödinger and Dirac equations allowing the use of discontinuous trial functions
PublikacjaWe 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.
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Safety at railway level crossings and Vision Zero
PublikacjaIn this work, safety analysis at the railway level crossings is presented using advanced mathematical modelling. Resistivity of track subgrade panels is taken into account. The analysis does not refer to the assessment of the current regulations. Specific cases of generalized dynamic system are considered by introducing operations S=Δ, S=P defined in space C(N) of real sequences. In this model, generalized discrete exponential...