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Search results for: NONLOCAL INTEGRAL THEORY
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An orthogonality relation for the Whittaker functions of the second kind of imaginary order
PublicationPrzeprowadzono dowód ortogonalności funkcji Whittakera drugiego rodzaju rzędu urojonego. Użyto metody analogicznej do tej, którą zaprezentowano we wcześniejszej pracy tych samych autorów [J. Math. Anal. Appl. 365 (2010) 195-197], poświęconej funkcjom Macdonalda rzędu urojonego.
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A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
PublicationThe orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices is evaluated in a closed form. It is found to be proportional to a sum of two terms, both depending on the second upper indices and containing the Dirac delta distribution.
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On the derivatives $\partial^{2}P_{\nu}(z)/\partial\nu^{2}$ and $\partial Q_{\nu}(z)/\partial\nu$ of the Legendre functions with respect to their degrees
PublicationWe provide closed-form expressions for the degree-derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$ and $[\partial Q_{\nu}(z)/\partial\nu]_{\nu=n}$, with $z\in\mathbb{C}$ and $n\in\mathbb{N}_{0}$, where $P_{\nu}(z)$ and $Q_{\nu}(z)$ are the Legendre functions of the first and the second kind, respectively. For $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$, we find that % \begin{displaymath} \frac{\partial^{2}P_{\nu}(z)}{\partial\nu^{2}}\bigg|_{\nu=n} =-2P_{n}(z)\Li_{2}\frac{1-z}{2}+B_{n}(z)\ln\frac{z+1}{2}+C_{n}(z), \end{displaymath} % where...
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Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
PublicationZaprezentowano metode obliczenia dwóch całek oznaczonych zawierających wielomiany Gegenbauera. Wynik wykorzystano do znalezienia sum czterech szeregów o wyrazach zawierających wielomiany Gegenbauera oraz funkcje Legendre'a (pierwszego lub drugiego rodzaju) na odcinku (-1,1).
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Orthogonality relations for the associated Legendre functions of imaginary order
PublicationOrthogonality relations for the associated Legendre functions of imaginary order are derived. They are expressed in terms of the Dirac delta function. The method is based on some known properties of the associated Legendre functions and the Dirac delta distribution. A special case of one of the relations has appeared in some recent applications.
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Existence and approximate solutions of Neumann problems
PublicationDyskutowany jest problem Neumanna dla równań różniczkowych drugiego rzędu.Praca dotyczy istnienia rozwiązań i zbieżnosci iteracji monotonicznych któresą przybliżonymi rozwiązaniami omawianych zagadnień. Określone zostały wa-runki zbieżności takich ciągów oraz określono rodzaj tej zbieżnosci.
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Remarks on the Subject of Back-Up Protection of Residual Current Devices
PublicationResidual current devices without integral overcurrent protection (RCCBs) are back-up protected by fuses or miniature circuit-breakers (MCBs). If the latter are used, special attention must be given to the coordination between an RCCB and an MCB. This paper indicates probable cases of the aforementioned devices coordination, in which back-up protection of the RCCB is not adequate. A laboratory test has shown that depending on the...
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Do positrons measure atomic and molecular diameters?
PublicationWe report on density functional calculations (DFT) of elastic integral scattering cross-sections for positron collisions with argon, krypton, nitrogen and methane. The long-range asymptotic polarization potential is described using higher-order terms going much beyond an induced dipole potential (−α / r 4) while the short-range interaction is modeled by two different forms of electron – positron correlation potential (Boroński-Nieminen...
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Laplace domain BEM for anisotropic transient elastodynamics
PublicationIn this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained....
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Bound on Bell inequalities by fraction of determinism and reverse triangle inequality
PublicationIt is an established fact that entanglement is a resource. Sharing an entangled state leads to nonlocal correlations and to violations of Bell inequalities. Such nonlocal correlations illustrate the advantage of quantum resources over classical resources. In this paper, we quantitatively study Bell inequalities with 2 × n inputs. As found in Gisin et al. [Int. J. Quantum. Inform. 05, 525 (2007)], quantum mechanical correlations...
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Total domination in versus paired-domination in regular graphs
PublicationA subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph induced by S contains a perfect matching, then S is a paired-dominating set. The domination number, denoted γ(G), is the minimum cardinality of a dominating set of G, while the...
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Types of Markov Fields and Tilings
PublicationThe method of types is one of the most popular techniques in information theory and combinatorics. However, thus far the method has been mostly applied to one-dimensional Markov processes, and it has not been thoroughly studied for general Markov fields. Markov fields over a finite alphabet of size m ≥ 2 can be viewed as models for multi-dimensional systems with local interactions. The locality of these interactions is represented...
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ANALIZA AERODYNAMICZNA ŁOPAT NA PRZYKŁADZIE PROJEKTU DWUWIRNIKOWEJ TURBINY WIATROWEJ MAŁEJ MOCY
PublicationW artykule przedstawiono proces projektowania oraz analizy aerodynamicznej łopat turbiny wiatrowej z wykorzystaniem metody BEMT (ang. Blade Element Momentum Theory). Dokonano doboru profili aerodynamicznych oraz opisano procedurę wyznaczania optymalnego rozkładu kątów zwichrowania i długości cięciw profili w funkcji długości łopaty dla założonych parametrów wejściowych. Dokonano obliczenia działających sił oraz generowanej mocy...
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Flexomagneticity in buckled shear deformable hard-magnetic soft structures
PublicationThis research work performs the first time exploring and addressing the flexomagnetic property in a shear deformable piezomagnetic structure. The strain gradient reveals flexomagneticity in a magnetization phenomenon of structures regardless of their atomic lattice is symmetrical or asymmetrical. It is assumed that a synchronous converse magnetization couples both piezomagnetic and flexomagnetic features into the material structure....
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A Note on Shannon Capacity for Invariant and Evolving Channels
PublicationIn the paper we discuss the notion of Shannon capacity for invariant and evolving channels. We show how this notion is involved in information theory, graph theory and Ramsey theory.
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A Generalized Version of the Lions-Type Lemma
PublicationIn this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space
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Inverse Nonlinear Eigenvalue Problem Framework for the Synthesis of Coupled-Resonator Filters With Nonresonant Nodes and Arbitrary Frequency-Variant Reactive Couplings
PublicationA novel, general circuit-level description of coupledresonator microwave filters is introduced in this article. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary reactive frequencyvariant coupling (AFVC) networks is proposed. The engineered formulation is more general than prior-art ones—with the only restriction that the coupling...
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Compact Quasi-Elliptic-Type Inline Waveguide Bandpass Filters With Nonlinear Frequency-Variant Couplings
PublicationThis work presents the design techniques to synthesize a class of compact inline quasi-elliptic-type waveguide cavity bandpass filters based on novel nonlinear frequency-variant couplings (NFVCs). These highly dispersive frequency-variant couplings (FVCs) are realized by means of a pair of partial-height posts that are placed at the junctions between every two cavity resonators. Each NFVC produces a transmission pole in between...
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Road Safety Observatories within the Structure of Integrated Transport Safety Systems
PublicationAccurate knowledge about the causes, circumstances and place of transport accidents is the prerequisite to take the correct action to improve transport safety. Developing appropriate organizational structures, forms and methods of management and implementation of safety measures in the sectoral approach condition the success. Therefore the Safety Information System is one of the integral areas of the Integrated Transport Safety...
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The role of observatories in the integrated transport safety systems
PublicationAccurate knowledge about the causes, circumstances and place of transport accidents is the prerequisite to take the correct action to improve transport safety. Developing appropriate organizational structures, forms and methods of management and implementation of safety measures in the sectoral approach condition the success. Therefore, the Safety Information System is one of the integral areas of the Integrated Transport Safety...
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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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Thermal and Electrodynamic Risk of Residual Current Devices in the Case of Back-Up Protection by Overcurrent Circuit Breakers
PublicationResidual current operated circuit breakers without integral overcurrent protection should be back-up protected. As back-up protection devices, overcurrent circuit breakers are used. The maximum let-through energy and let-through current of the overcurrent devices were evaluated under laboratory conditions. The thermal and electrodynamic risk of residual current devices was analyzed.
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Usability of Mobile Applications: A Consolidated Model
PublicationMobile devices have become an integral part of the digital ecosystem, connecting people, businesses, and information around the world in ways never before possible. In particular, smartphones, tablets and other handheld devices equipped with mobile applications have changed every aspect of our lives. Today, a user can choose from nearly five million applications available for both Android and iOS operating systems. However, only...
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Prospects of ionic liquids application in electronic and bioelectronic nose instruments
PublicationThis paper addresses the problem of application of ionic liquids to chemical sensors and biosensors being an integral part of the electronic and bioelectronic-type instruments. The design and principle of operation of the electronic and bioelectronic noses are compared. Both the benefits and shortcomings of the application of ionic liquids in these type of instruments are described. The prospects of the development and application...
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Homoclinics for singular strong force Lagrangian systems
PublicationWe study the existence of homoclinic solutions for a class of generalized Lagrangian systems in the plane, with a C1-smooth potential with a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin.Under a strong force condition around the singular point ξ, via minimization of an action integral, we will prove the existence of at least two geometrically distinct homoclinic solutions.
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Comparison of tuning procedures based on evolutionary algorithm for multi-region fuzzy-logic PID controller for non-linear plant
PublicationThe paper presents a comparison of tuning procedures for a multi-region fuzzy-logic controller used for nonlinear process control. This controller is composed of local PID controllers and fuzzy-logic mechanism that aggregates local control signals. Three off-line tuning procedures are presented. The first one focuses on separate tuning of local PID controllers gains in the case when the parameters of membership functions of fuzzy-logic...
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Theoretical and experimental study on scattering of low-energy electrons by dimethyl and diethyl ethers
PublicationWe report a joint theoretical and experimental investigation on low-energy electron scattering by dimethyl and diethyl ethers. The experimental elastic differential cross sections were measured at impact energies from 1 eV up to 30 eV and scattering angle range of 10◦ to 130◦. Theoretical elastic differential, integral and momentum-transfer cross sections are calculated at impact energies up to 30 eV, employing the Schwinger multichannel...
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Electron Scattering from Methyl Formate (HCOOCH3): A Joint Theoretical and Experimental Study
PublicationElastic low-energy electron collisions with methyl formate have been studied theoretically at the level of various theories. The elastic integral cross section was calculated using Schwinger multichannel and R-matrix methods, in the static-exchange and static-exchange plus polarization levels of approximations for energies up to 15 eV. The absolute total cross section for electron scattering from methyl formate has been measured...
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Colorings of the Strong Product of Circulant Graphs
PublicationGraph coloring is one of the famous problems in graph theory and it has many applications to information theory. In the paper we present colorings of the strong product of several circulant graphs.
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Fractional-order Systems and Synchronous Generator Voltage Regulator
PublicationModern regulators of synchronous generators, including voltage regulators, are digital systems, in their vast majority with standard structures contained in the IEEE standard. These are systems described with stationary differential equations of integral order. Differential equations of fractional order are not employed in regulators for synchronous generator control. This paper presents an analysis of the possibilities of using...
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Modelling of cutting by means of fracture mechanics
PublicationThe suitability of modern fracture mechanic theory was proved for the estimation of the cutting force and the cutting specific resistance. This paper shows modification of Ernst-Merchant theory and its application for determination some other properties of wood sample. This theory is acceptable for evaluation of shear yield stresses and shear plane angle. Sawing by gang saw machine was used as a process similar to the orthogonal...
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MODELLING OF CUTTING BY MEANS OF FRACTURE MECHANICS
PublicationThe suitability of modern fracture mechanic theory was proved for the estimation of the cutting force and the cutting specific resistance. This paper shows modification of Ernst-Merchant theory and its application for determination some other properties of wood sample. This theory is acceptable for evaluation of shear yield stresses and shear plane angle. Sawing by gang saw machine was used as a process similar to the orthogonal...
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TEORIA DECYZYJNYCH PROCESÓW SEMI-MARKOWA I JEJ ZASTOSOWANIE W PROJEKTOWANIU I EKSPLOATACJI OKRĘTOWYCH SILNIKÓW GŁÓWNYCH I INNYCH URZĄDZEŃ SIŁOWNI OKRĘTOWYCH
PublicationW referacie zaprezentowano znaczenie teorii procesów semi-Markowa w naukach technicznych, zwłaszcza w teorii niezawodności urządzeń technicznych, teorii bezpieczeństwa ich działania oraz statystycznej teorii podejmowania decyzji eksploatacyjnych. W referacie wyeksponowano także przydatność teorii procesów semi-Markowa w teorii i praktyce eksploatacji wspomnianych urządzeń technicznych na przykładzie tak istotnych urządzeń w transporcie...
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Characterizing the Performance of <span class="sc">xor</span> Games and the Shannon Capacity of Graphs
PublicationIn this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party xor game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games...
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Buckling analysis of a non-concentric double-walled carbon nanotube
PublicationOn the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient and the van der Waals interaction...
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KOLMOGOROV EQUATION SOLUTION: MULTIPLE SCATTERING EXPANSION AND PHOTON STATISTICS EVOLUTION MODELING
PublicationWe consider a formulation of the Cauchy problem for the Kolmogorov equation which corresponds to a localized source of particles to be scattered by a medium with a given scattering amplitude density. The multiple scattering amplitudes are introduced and the corresponding series solution of the equation is constructed. We investigate the integral representation for the first series terms, its estimations and values of the photon...
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Low energy elastic scattering of electrons from hexafluoropropene (C3F6)
PublicationWe present cross sections from a joint experimental and theoretical study on elastic electron scattering from hexafluoropropene (C3F6) in the gas phase. The experimental results, using low energy electron spectroscopy, were obtained at incident electron energies of 0.5, 1, 1.5, 2, 3, 4, 5, 6, 10, 12, 15 and 20 eV, for scattering angles ranging from 10°to 130°. The theoretical method used in the computation of the integral, momentum...
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Low energy elastic electron scattering from benzonitrile (C6H5CN)
PublicationWe present experimental differential elastic scattering cross sections (DCSs) for low energy electron scattering from benzonitrile along with integral and momentum-transfer cross sections that are determined from these DCSs. The measurements of DCSs are obtained using the relative flow method with helium as the standard gas, in a crossed electron-molecular gas beam arrangement. Our measurements are made at incident electron energies...
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Anomalous decay of quantum correlations of quantum-dot qubits
PublicationWe study the evolution of quantum correlations, quantified by the geometric discord, of two excitonic quantum-dot qubits under the influence of the phonon environment. We show that the decay of these correlations differs substantially from the decay of entanglement. Instead of displaying sudden-death-type behavior, the geometric discord shows a tendency to undergo transitions between different types of decay, is sensitive to nonlocal...
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Konkurencyjność międzynarodowa z uwzględnieniem mechanizmu autokonkurencji – aspekty teoretyczne i praktyczne
PublicationW licznych publikacjach na temat konkurencyjności międzynarodowej nie został, mimo ich mnogości, jednoznacznie określony obszar badawczy, a w wypadku pomiaru jej poziomu - opracowane metodologie są często krytykowane przez ekonomistów. Powszechnie utożsamia się konkurencyjność międzynarodową z produktywnością, co budzi wątpliwości licznych adwersarzy, podważających zasadność prowadzenia jakichkolwiek badań w tym obszarze. W artykule...
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ANALYSIS OF IMPACT of SHIP model parameters on changes of control quality index in ship dynamic positioning system
PublicationIn this work there is presented an analysis of impact of ship model parameters on changes of control quality index in a ship dynamic positioning system designed with the use of a backstepping adaptive controller. Assessment of the impact of ship model parameters was performed on the basis of Pareto-Lorentz curves and ABC method in order to determine sets of the parameters which have either crucial, moderate or low impact on objective...
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Investigation of the Aerodynamics of an Innovative Vertical-Axis Wind Turbine
PublicationThe paper presents the results of an experimental investigation and a three dimensional numerical analysis of the transient aerodynamic phenomena occurring in the innovative modification of classic Savonius wind turbine. An attempt to explain the increased efficiency of the innovative design a comparison with the traditional solution is undertaken. A vorticity measure based on the integral of the velocity gradient tensor second...
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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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Design of weighted PID controllers for control of the Stewart-Gough platform
PublicationStewart-Gough platform (SGP) is a popular parallel type manipulator that involves a 6 degrees of freedom (DOF) motion. In this paper, the process of mathematical modelling of SGP is presented. Two selected control algorithms that use PID controllers and weighted PID controllers are designed. Both control systems using these algorithms are implemented in MATLAB environment as well as on the actual SGP. Parameters of the controllers...
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Recent Applications of 1D GC-MS and 2D GC-MS in Foodomics Studies
PublicationGas chromatography coupled with mass spectrometry and food chemistry have been tightly linked since the 1960s. This setup is also an integral part of the omics studies when it comes to low mass metabolites. Therefore, the marriage of GC-MS and foodomics is obvious. Two-dimensional gas chromatography coupled with mass spectrometry fits perfectly within the latest trends in foodomics, since it is tailored for holistic food analysis....
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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Flexomagneticity in Functionally Graded Nanostructures
PublicationFunctionally graded structures have shown the perspective of materials in a higher efficient and consistent manner. This study reports a short investigation by concentrating on the flexomagnetic response of a functionally graded piezomagnetic nano-actuator, keeping in mind that the converse magnetic effect is only taken into evaluation. The rule of mixture assuming exponential composition of properties along with the thickness...
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USEFULNESS OF SEMI-MARKOV PROCESSES AS MODELS OF THE OPERATION PROCESSES FOR MARINE MAIN ENGINES AND OTHER MACHINES OF SHIP POWER PLANTS
PublicationThe paper describes the properties of semi-Markov processes and the opportunities and benefits from their use as models of the operation processes for marine combustion engines and other machines of ship power plants. The emphasis is put on the importance of the theory of semi-Markov processes for development of the theory of marine combustion engines and other machines of ship power plants, as well as for development of the operational...
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Paradygmat jakościowy w analizie interakcji międzykulturowych – interpretacja na bazie wybranych teorii psychologicznych
PublicationIntercultural interactions in a multicultural work environment are a peculiar type of social interactions. The results of prior research on the effects of interactions in such environment are inconclusive. The majority of the previous studies have emphasized problems, applied a quantitative methodology and interpreted the results with regard to social identity and categorization theory, information-processing theory and intergroup contact...
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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...