Wyniki wyszukiwania dla: mathematical models
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A comprehensive approach to double inverted pendulum modelling
PublikacjaThe problem of mathematical modelling and indication of properties of a DIP has been investigated in this paper. The aim of this work is to aggregate the knowledge on a DIP modelling using the Euler-Lagrange formalism in the presence of external forces and friction. To indicate the main properties important for simulation, model parameters identification and control system synthesis, analytical and numerical tools have been used....
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The impact of methods the stochastic analysis on swimming safety of multihull floating units (Part 2)
PublikacjaIn part 2 the equations of the catamaran motion were divided into the system of two groups not conjugated with themselves containing the mutually conjugated equations. The feedback is obtained by the linear and nonlinear coefficients of dampening and coefficients of hydrostatic elasticity. The first group includes the symmetric movements (longitudinal movements), and the second group includes the antisymmetric movements (transverse)....
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Control of induction machine supplied by a current source inverter using the multi-scalar transformation and backstepping approach
PublikacjaThe paper describes the voltage control technique of squire-cage induction machines supplied by a current source inverter. The control system is based on new transformation of the electric drive system (machine and inverter) state variables to the multi-scalar variables form. The backstepping approach is used to obtain the feedback control law. The control system contains the structure of the observer...
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Numerical Characterization of Thresholds for the Focusing 1d Nonlinear Schrödinger Equation
PublikacjaThe focusing nonlinear Schrödinger equation arises in various physical phenomena and it is therefore of interest to determine mathematical conditions on the initial data that guarantee whether the corresponding solution will blow up in finite time or exist globally in time. We focus on solutions to the mass‐supercritical nonlinear Schrödinger equation (1) in 1D case. In particular, we investigate numerical thresholds between blow...
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Comparison of hydrogen bonds and diverse weak interactions of the nitro group in 2-methyl-4-nitroanilinium nitrate, bisulfate and two hexafluoridosilicates: elementary graph-set approach
PublikacjaCrystal structures of (H2m4na)NO3 (1), (H2m4na)HSO4 (2), (H2m4na)2SiF6 (3) and (H2m4na)2SiF6*2H2O (4), where 2m4na = 2-methyl-4-nitroaniline, are presented. Two layers of interactions occur in the structures, N—H...O/F hydrogen bonds and interactions with the nitro group. Although diverse, hydrogen-bonding patterns are compared with each other by means of interrelations among elementary graph-set descriptors and descriptors of hydrogen-bonding...
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Action-reaction based synthesis of acoustic wavefield equations
PublikacjaThe analysis of acoustic fields is usually based on the well-known mathematics of second order partial differential equations called wave equations. The author explores the duality and symmetry of linear fluid mechanics and develops two distinct equations of acoustics on the basis of a causal approach to local small-scale phenomena. Wavefields that are solutions of these equations have different composition, the spherical pressure...
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Modelling and analysis of medium frequency transformers for power converters
PublikacjaThe evolutions in power systems and electric vehicles, related to the economic opportunities and the environmental issues, bring the need of high power galvanically isolated DC-DC converter. The medium frequency transformer (MFT) is one of its key components, enabled by the increasing switching frequency of modern power semiconductors like silicon carbide transistors or diodes. The increased operating frequency offers small...
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Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublikacjaThis paper presents results concerning numerical solutions to a fractional neutron point kinetics model for a nuclear reactor. The paper discusses and expands on results presented in (Espinosa-Paredes et al., 2011). The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and a numerical solution using the Edwards’ method was proposed (Edwards et al., 2002). The mathematical model...
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Platform Supporting the Esophageal Impedance Analysis
PublikacjaThe esophageal pH-impedance examination is one of the most popular diagnostic methods for identifying the upper gastrointestinal tract’s diseases. Inconclusive test evaluation criteria makes it difficult to state the definite diagnosis. In this paper, the computer platform supporting the research and teaching process in the area of pH-impedance analysis is presented. Users, having a variety of mathematical and statistical methods...
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Endoscopy video analysis algorithms and their independence of rotation , brightness , contrast , color and blur
PublikacjaThe article presents selected image analysis algorithms for endoscopy videos. Mathematical methods that are part of these algorithms are described, and authors’ claims about the characteristics of these algorithms, such as the independence of rotation, brightness, contrast, etc. are mentioned. Using the common test on the real endoscopic image database and a set of image transformations, the validity of these claims was checked...
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Neurocontrolled Car Speed System
PublikacjaThe features of the synthesis of neural controllers for the car speed control system are considered in this article. The task of synthesis is to determine the weight coefficients of neural networks that provide the implementation of proportional and proportional-integralderivative control laws. The synthesis of controllers is based on an approach that uses a reversed model of the standard. A model of the car speed control system with...
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Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing
PublikacjaThe grazing bifurcation is considered for the Newtonian model of vibro-impact systems. A brief review on the conditions, sufficient for the existence of a grazing family of periodic solutions, is given. The properties of these periodic solutions are discussed. A plenty of results on the topological structure of attractors of vibro-impact systems is known. However, since the considered system is strongly nonlinear, these attractors...
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Hopf bifurcation in time‐delayed gene expression model with dimers
PublikacjaWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the formation of dimers (i.e., complex formed by two protein monomers), the way in which dimers bind to DNA and time delay in translation process. For the model consisting of three ordinary differential equations with time delay, we derive conditions for stability of the positive...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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Shielded coupled strip and slot guides with a thin omega pseudochiral medium layer
PublikacjaA method of moments combined with mode matching technique is applied to analyze the shielded coupled strip and slot line structures containing a thin plate of Omega pseudochiral medium. The boundary problems are simplified by introducing for omega medium the approximate continuity conditions. Such mathematical model allows to examine the field displacement effect appearing in the considered guide resulting from the coupling between...
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Five-phase squirrel-cage motor. Construction and drive properties
PublikacjaThis paper presents the simulation and experimental results of a five-phase squirrel-cage induction motor. The new machine has been designed to operate in a drive system with third harmonic rotor flux injection in order to improve the motor torque utilization. The motor structure, the mathematical model as well as the laboratory prototype have been described. The motor speed-torque characteristics and transients are elaborated...
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Pantographic metamaterials: an example of mathematically driven design and of its technological challenges
PublikacjaIn this paper, we account for the research efforts that have been started, for some among us, already since 2003, and aimed to the design of a class of exotic architectured, optimized (meta) materials. At the first stage of these efforts, as it often happens, the research was based on the results of mathematical investigations. The problem to be solved was stated as follows: determine the material (micro)structure governed by those...
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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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Non-linear circuit model of a single doubly-fed induction machine formulated in natural axes for drive systems simulation purposes
PublikacjaMathematical 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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Assesment of operation of ship main diesel engine using the theory of semi-markovian and markov processes.
PublikacjaTo precisely determine the task it is necessary to specify also its duration time, apart from conditions in which it will be realized. When considering propulsion engine, i.e. the main element of ship propulsion system, especially important becomes not only the problem which amount of energy could be at one's disposal but also within which time interval it could be delivered. Therefore apart from applying the commonly used reliability...
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Control design for slow speed positioning
PublikacjaThe problem under study is a synthesis of position and heading control system for low frequency model of surface vessel described by 3 DOF mathematical model. The recursive vectorial backstepping control design was used to keep fixed position and heading in presence of wave disturbances. The controller has been simulated on computer model of scaled supply vessel. It has been assumed that the actuators produce generalized forces...
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Asynchronous Method of Simultaneous Object Position and Orientation Estimation with Two Transmitters
PublikacjaThis paper proposes an object location method for all types of applications, including the Internet of Things. The proposed method enables estimations of the position and orientation of an object on a plane or in space, especially during motion, by means of location signals transmitted simultaneously from two transmitters placed on the object at a known distance from each other. A mathematical analysis of the proposed method and...
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Dynamic variables limitation for backstepping control of induction machine and voltage source converter
PublikacjaDynamic variables limitation for backstepping control of induction machine and voltage source converter The paper presents the method of control of an induction squirrel-cage machine supplied by a voltage source converter. The presented idea is based on an innovative method of the voltage source converter control, consisting in direct joining of the motor control system with the voltage source rectifier control system. The combined...
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High-accuracy computation of hard X-ray focusing and imaging for refractive optics
PublikacjaA mathematical apparatus for solving problems of X-ray wave propagation through complex optical systems, when the lens thickness can change with jumps, is developed and presented. The developed method is based on the use of the superposition of oriented Gaussian beams, which satisfy the Helmholtz equation with high accuracy. The wave propagation in air and through kinoform and ordinary lenses is considered. Focusing and imaging...
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CFGFRPT Piles with a Circular Cross-Section and their Application in Offshore Structures
PublikacjaThe possibilities of using concrete piles in a polymer composite reinforced with glass fibres in offshore facilities were shown. Laboratory tests of CFGFRPT type piles compressed axially and in eccentric compression for the analysis of CFGFRPT piles were used. Methods of analysis of dynamic systems for mathematical modelling of the displacement of the hammer in the pile driving process were applied. The possibilities of combining...
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Thermodynamic modeling of combustion process of the internal combustion engines – an overview
PublikacjaThe mathematical description of combustion process in the internal combustion engines is a very difficult task, due to the variety of phenomena that occurring in the engine from the moment when the fuel-air mixture ignites up to the moment when intake and exhaust valves beginning open. Modeling of the combustion process plays an important role in the engine simulation, which allows to predict incylinder pressure during the combustion,...
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A bound on the number of middle-stage crossbars in f-cast rearrangeable Clos networks
PublikacjaIn 2006 Chen and Hwang gave a necessary and sufficient condition under which a three-stage Clos network is rearrangeable for broadcast connections. Assuming that only crossbars of the first stage have no fan-out property, we give similar conditions for f-cast Clos networks, where f is an arbitrary but fixed invariant of the network. Such assumptions are valid for some practical switching systems, e.g. high-speed crossconnects....
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Application of Multivariate Analysis Methods in Welding Engineering
PublikacjaPhenomena and processes taking place during welding are usually very complex and, for this reason, should be described using multivariate methods. The article discusses the methodological basis and selected application areas as regards the solving of welding problems using statistical multivariate methods. In addition, the article presents exemplary applications of the design of experiment, multiple regression analysis, cluster...
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COMPUTER ANALYSIS OF HYDRAULIC CONDITIONS IN A SANITARY CHAMBER
PublikacjaThis paper presents analysis of hydraulic conditions of sewage flow down the slipway (ramp) in the collecting sanitary chamber connecting 3 collectors on the inlet: ⌀600, ⌀800 and ⌀1400 and one on the outlet ⌀1600 mm, with a maximum difference of elevation 5 m. The mathematical model has been made and hydraulic calculations were carried out in steady flow conditions. Then wastewater surface elevation, energy grade line elevation,...
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Magnetic and capacitive couplings influence on power losses in double circuit high voltage overhead transmission line
PublikacjaPurpose – The paper aims to discuss problems of power and energy losses in a double-circuit overhead transmission line. It was observed from energymeters’ readings, that in such a line, active power losses can be measured as “negative”. The “negative” active power losses appear when the active power injected to the circuit is lower than the active power received at the circuit end. The purpose of this paper is to explain this phenomenon. Theoretical...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublikacjaDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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Parametric method for evaluating optimal ship deadweight
PublikacjaThe paper presents a method of choosing the optimal value of the cargo ships deadweight. The method may be useful at the stage of establishing the main owners requirements concerning the ship design parameters as well as for choosing a proper ship for a given transportation task. The deadweight is determined on the basis of a selected economic measure of the transport effectiveness of ship – the Required Freight Rate (RFR). The...
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Representation of magnetic hysteresis in single-phase transformer for circuit simulations
PublikacjaThe paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. In the circuit transformer model, it is assumed that there is a flux common Φ to all windings as nonlinear and hysteretic function of the total currents Θ (Ampere turns) of all windings. To simulate magnetic behaviour of the iron core the feedback scalar Preisach model of hysteresis is developed. The Preisach...
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The Use of Cluster Analysis to Evaluate the Impact of COVID-19 Pandemic on Daily Water Demand Patterns
PublikacjaProper determination of unitary water demand and diurnal distribution of water consumption (water consumption histogram) provides the basis for designing, dimensioning, and all analyses of water supply networks. It is important in the case of mathematical modelling of flows in the water supply network, particularly during the determination of nodal water demands in the context of Extended Period Simulation (EPS). Considering the...
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Application of sliding switching functions in backstepping based speed observer of induction machine
PublikacjaThe paper presents an analysis of the speed observer which is based on the backstepping and sliding mode approach. The speed observer structure is based on the extended mathematical model of an induction machine. The observer structure is based on the measured phase stator currents and transformed to ( αβ ) coordinate system. The stator voltage vector components are treated as known values. Additionally, such an observer structure...
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Analytical method of determining dynamic properties of thermocouples used in measurements of quick – changing temperatures of exhaust gases in marine diesel engines
PublikacjaThe article presents selected issues of mathematical modeling of heat exchange between the thermocouple and the exhaust gas flowing them, in unsteady conditions. On the way of energy balancing consideration of thermodynamic processes developed differential equations describing the dynamic properties for three versions of the design sheathed thermocouples: with weld isolated from the sheath, with weld welded the sheath and with...
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Observation Value Analysis – Integral Part of Bayesian Diagnostics
PublikacjaThe decision making process, in general, is understood as a process of selecting one of the available solutions to the problem. One of possible approaches supporting the process is Bayesian statistical decision theory providing a mathematical model to make decisions of a technical nature in conditions of uncertainty. Regarding above, a detailed subject of the research is to analyze the value of the observation, which is a part...
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How to choose drive’s rated power in electrified urban transport?
PublikacjaSelection of drive's rated power influences not only vehicle's dynamics, but also its energy efficiency. Mentioned above approach requires a multiphysical model, which covers both mechanical and electrical phenomena. This paper discusses how selection of traction drive's rated power influences vehicle energy consumption on example of a trolleybus. A complex mathematical model was developed in Matlab/Simulink to describe the multiphisical...
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Firing map of an almost periodic input function
PublikacjaIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...
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Book review: Simulation-Driven Design Optimisation and Modelling for Microwave Engineering
PublikacjaCelem książki jest przedstawienie aktualnego stanu badań dotyczących projektowania układów mikrofalowych poprzez modelowanie i optymalizacje wspomagane symulacjami elektromagnetycznymi. Grupa międzynarodowych ekspertów zajmujących się rożnymi aspektami komputerowo wspomaganego projektowania układów mikrofalowych, podsumowuje i dokonuje przeglądu ostatnich osiągnięć w tej dziedzinie oraz przedstawia szereg praktycznych zastosowań....
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Symmetry-Breaking Bifurcation for Free Elastic Shell of Biological Cluster, Part 2
PublikacjaWe will be concerned with a two-dimensional mathematical model for a free elastic shell of biological cluster. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of the shell of biological cluster may be found as solutions of a certain nonlinear functional-differential equation with several physical parameters. For each multiparameter this...
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Determination of Sodium Ion Diffusion Coefficient in Tin Sulfide@Carbon Anode Material Using GITT and EIS Techniques
PublikacjaThe electroanalytical behavior of SnSx (x = 1, 2) encapsulated into a carbon phase was studied using the galvanostatic intermittent titration technique (GITT) and electrochemical impedance spectroscopy (EIS). These techniques are widely utilized in battery systems to investigate the diffusion of alkali metal cations in anode and cathode materials depending on the concentration of ions in the host material. Here, we report different...
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PARAMETRIC ANALYSIS OF THE EFFICIENCY OF THE COMBINED GAS-STEAM TURBINE UNIT OF A HYBRID CYCLE FOR THE FPSO VESSEL
PublikacjaA thermal diagram of the combined gas‒steam turbine unit of a hybrid cycle, which is an energy complex consisting of a base gas turbine engine with a steam turbine heat recovery circuit and a steam-injected gas turbine operating with overexpansion, is proposed. A mathematical model of a power plant has been developed, taking into consideration the features of thermodynamic processes of simple, binary, and steam-injected...
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Finite element modeling of plastic hinges based on ductility demand-capacity method using nonlinear material for dynamic analysis
PublikacjaThe article discusses modeling plastic hinges in reinforced concrete interme-diate supports using finite elements methods. The ductility demand-capacitymethod was used to determine the geometrical parameters of cross-section plas-ticization zones, their ability to move and rotate, as well as their ductility. Dueto the varied geometry and stiffness of the supports and their nonlinear behav-ior under dynamic load, this method was...
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Impact of Climate Change on a Runoff Formation in Seaside Catchment Area on the Example of the Babica River Catchment
PublikacjaThe paper presents the impact of taking into account climate change in the perspective of 2050 on the results of hydrological calculations of characteristic flows in the hydrographically diverse seaside catchment area on the example of the Babica river catchment. A mathematical model of the Babica river catchment was made in the HEC-HMS program. The SCS method was used. The outflow from the basin was analysed for waters with...
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Simulation of the remanence influence on the transient states in a single-phase multiwinding transformer
PublikacjaThis paper presents the mathematical model of a single-phase multi-winding core type transformer taking into account magnetic hysteresis phenomenon based on the feedback Preisach model (FPM). The set of loop differential equations was developed for a K-th winding transformer model where the flux linkages of each winding includes flux Φ common to all windings as a function of magneto motive force Θ of all windings. The first purpose...
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Representation of magnetic hysteresis in tape wound core using feedback Preisach model
PublikacjaThis paper presents a mathematical model for the hysteresis phenomenon in ferromagnetic tape wound core. The feedback scalar Preisach model of hysteresis is used to simulate magnetic behavior of the grain oriented silicon strip of ET114-27 type. Determination of B-H hysteretic curve is based on measurement of the initial magnetization curve and the main hysteresis loop. The Preisach distribution function (PDF) of ET114-27 material...
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublikacjaIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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Swarm Algorithms in Modern Engineering Optimization Problems
PublikacjaComplexity of today engineering problems is constantly increasing. Scientists no longer are facing issues, for which simple, mathematical programming methods are sufficient. Issues like autonomic vehicle navigation or classification are considered to be challenging, and although there exist valid means to solve them, in some cases there still is some place for improvement. With emergence of a new type of optimization techniques...
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Semi-definite programming and quantum information
PublikacjaThis paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations,...