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Wyniki wyszukiwania dla: EXISTENCE, UNIQUENESS, CHARACTERISTICS, RENEWAL
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Existence and uniqueness of solutions for single-population McKendrick-von Foerster models with renewal
PublikacjaWe study a McKendrick-von Foerster type equation with renewal. This model is represented by a single equation which describes one species which produces young individuals. The renewal condition is linear but takes into account some history of the population. This model addresses nonlocal interactions between individuals structured by age. The vast majority of size-structured models are also treatable. Our model generalizes a number...
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Straightened characteristics of McKendrick-von Foerster equation
PublikacjaWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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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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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publikacjawe 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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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Dane BadawczeThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublikacjaIn this paper, we discuss well-posedness of the boundary-value problems arising in some “gradientincomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy...
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Functional delay fractional equations
PublikacjaIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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Existence of unbounded solutions to parabolic equations with functional dependence
PublikacjaThe Cauchy problem for nonlinear parabolic differential-functional equations is considered. Under natural generalized Lipschitz-type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u(·); (ii) the functional dependence u(·) and ∂xu(·); (iii) the functional dependence u(·)and the pointwise dependence ∂xu(t,x).
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On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions
PublikacjaIn the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the...
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublikacjaThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli
PublikacjaWithin the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order...
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublikacjaIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublikacjaVarious equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublikacjaA 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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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublikacjaThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
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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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Rotating rod and ball
PublikacjaWe consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time...
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On a comparison principle and the uniqueness of spectral flow
PublikacjaThe spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply...
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Billiard in a rotating half-plane
PublikacjaThe main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic...
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Existence and uniqueness for neutral equations with state dependent delays
PublikacjaW pracy w celu wykazania istnienia i jednoznaczności rozwiązania równania została zaprezentowana metoda porównawcza.
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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
PublikacjaWe provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of...
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Man in Early Islamic Philosophy: Al-Kindi and Al-Farabi
PublikacjaMan was, neither for Al-Kindi, nor for Al-Farabi, a clearly isolated object of philosophical reflection. This does not mean, however, that both Islamic philosophers were not at all concerned with the uniqueness of man, his nature or the purpose of his existence. In order to understand and analyze in depth the philosophies of man voiced by Al-Kindi and Al-Farabi, one must focus primarily on their epistemologies, on their philosophical...
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Existence and uniqueness for neutral equations with delay dependant on a solution and its derivative
PublikacjaDla wykazania istnienia i jednoznaczności w pracy została zaprezentowana metoda porównawcza.
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Caffeine Inhibits Differentiation Of Lung Cancer Stem Cells By Modulating Their Respiratory Metabolism
PublikacjaIt is ell established that many tumor types contain a fraction of cells, with stem cell-like properties, called cancer stem cells (CSCs), that are resistant to apoptosis induced by therapeutic agents. The presence of CSCs may explain why a standard anticancer treatment, that eliminates only differentiated cancer cells, does not lead to cancer cure.We previously showed the existence of caffeine-sensitive mechanism that controls...
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On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity
PublikacjaIn this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class...
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Tinnitus Therapy Based on High-Frequency Linearization
PublikacjaThe aim of this work was to present problems related to tinnitus symptoms, its pathogenesis, hypotheses on tinnitus causes, and therapy treatments to reduce or mask the phantom noise. In addition, the hypothesis on the existence of parasitic quantization that accompanies hearing loss was recalled. The paper contains a description of experiments carried out with the application of high-frequency dither having specially formed spectral...
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Recurrent bowel-blood translocations of Escherichia coli with the unique virulence characteristics over three-year period in the patient with acute myeloid leukaemia – case report
PublikacjaIn patients with haematological malignancies, the bowel remains the main source of Escherichia coli bloodstream infections. We present the clinical example of recurrent bowel-blood translocations of E. coli with the unique virulence characteristics in a 55-year-old male with the diagnosis of acute myeloid leukaemia. The virulent factors profile of examined strains confirmed that the co-existence of genes papC, sfa, usp and cnf1,...
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The Laboratory Stand for the Evaluation of Heat Dissipation from the Power Cable in a Casing Pipe
PublikacjaThe current carrying capacity of a power cable determines its efficiency, which depends on its capability to dissipate heat produced inside the cable, as a result of current flow, into the surrounding. The studies were conducted to determine how the characteristics of the medium around the cable affected its temperature and, as a result, its ability to transport electricity. The experimentation in the lab and real measurements...
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Timber - material of the future. Examples of small wooden architecture structures.
PublikacjaThe aim of this article is to present various types of wood-based products, classified as engineered timber, while specifying the implications of their structural properties for their forms. Timber is used as a construction material due to its fire resistance, good structural characteristics and insulating properties. The advent of new technologies of wood processing and wood-based materials production has converted timber into...
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FINITE GROUND CPW-FED UWB ANTENNA OVER THE METALLIC CYLINDRICAL SURFACES
PublikacjaThe investigation of finite ground coplanar fed ultra-wideband (UWB) antenna and the influence of its curvature and the proximity of circular metallic screen on the reflection coefficients and radiation characteristics is presented. The antenna is composed of two circular coplanar strips which enclose slot aperture of similar shape and is designed on a thin and flexible substrate which allows its bending. The antenna configuration...
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Tinnitus Therapy Based on High-Frequency Linearization Principles - Preliminary Results
PublikacjaThe aim of this work is to present problems related to tinnitus symptoms, its pathogenesis, hypotheses on tinnitus causes, and therapy treatment to reduce or mask the phantom noise. In addition, the hypothesis on the existence of parasitic quantization that accompanies hearing loss has been recalled. Moreover, the paper describes a study carried out by the Authors with the application of high-frequency dither having specially formed...
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Curved Surface Minijet Impingement Phenomena Analysed with ζ-f Turbulence Model
PublikacjaThe jet impingement phenomenon plays an important role among the heat transfer intensification methods. Very often its application and analyses refer to simple flat surfaces, while there is a lack of information in the literature for cases addressing curved surfaces. In the present work, the single jet impingement on the non-flat (concave and convex) surface is studied for a wide range of geometries, which originate from the mini-jet...
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Electromodulation of photoluminescence in vacuum-evaporated films of bathocuproine
PublikacjaElectric field-modulated photoluminescence (EML) was measured in vacuum-evaporated films of bathocuproine (BCP), electron-transporting material commonly used in organic light-emitting diodes (OLEDs). The external electric field of 106 V/cm strength decreases long-wavelength photoluminescence (PL) up to 10% but the same effect on short-wavelength PL is above one order of magnitude smaller. The distinctive difference between the...
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Heat Dissipation from the Power Cable in the Casing Pipe
PublikacjaThe current carrying capacity of a power cable determines its ability to carry a specific current and is related to the efficiency of dissipation of heat generated in the cable laid in a specific environment. The studies were conducted in order to determine how the characteristics of the medium around the cable affected its temperature, and thus the ability of the cable to transmit electricity. The experimentation in the lab and...
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Istota chmury wartości - założenia podstawowe
PublikacjaObserwacje efektów działań gospodarczych przedsiębiorstw wsparte badaniami literatury pozwoliły na zdiagnozowanie niedostatku w zakresie ogólnych modeli tworzenia wartości. Punktem wyjścia było określenie celu działania przedsiębiorstwa, który wykazuje immanentną dychotomię. Dążenie do realizacja tak ujętego celu jest podstawą do konfigurowania wartości generowanych przez przedsiębiorstwo. W tym zakresie wykorzystujące wyniki prac...
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Al-Kindi’s “The Real One”: Considerations of a mathematician or of a metaphysician?
PublikacjaThe aim of the article is to analyze Al-Kindi’s concept of the True (Essential) One and certain additional issues, also taking into account the influence on his position from both classical philosophy and source texts of Islam. In the opening part of the article, Al-Kindi’s innovative approach to the application of mathematics in research in other areas of knowledge is discussed. In the next part,...
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The atlas of inequality aversion: theory and empirical evidence on 55 countries from the Luxembourg Income Study database
PublikacjaResearch background: In the distributive analysis, the constant relative inequality aversion utility function is a standard tool for ethical judgements of income distributions. The sole parameter ε of this function expresses a society’s aversion to inequality. However, the profession has not committed to the range of ε. When assessing inequality and other welfare characteristics, analysts assume an arbitrary level of ε, common...
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Spectral Finite Element Method in Condition Monitoring and Damage Detection
PublikacjaIt is well known that the dynamic behaviour of engineering structures may carry very important and crucial information that can be further used for the assessment of their condition as well as detection of any damage induced. The current interest in monitoring techniques based on the propagation of guided elastic waves requires that numerical techniques used for modelling the phenomena associated must shift into the realm of high...
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Reverberation divergence in VR applications
PublikacjaThe aim of this project was to investigate the correlation between virtual reality (VR) imagery and ambisonic sound. With the increasing popularity of VR applications, understanding how sound is perceived in virtual environments is crucial for enhancing the immersiveness of the experience. By examining the relationship between visual scenes and sound scenes, this research attempts to explore how the interaction between vision and...
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Seaweed utilization issues in biogas production
PublikacjaMacroalgae can be seen as a renewable feedstock for the production of biofuels in many coastal areas around the World and especially in Baltic Sea region where the eutrophication is particularly troublesome. The investigation of anaerobic digestion technologies for extracting inexhaustible bioenergy from seaweed was conducted in many research institutions mainly in laboratory scale. Although seaweeds seem to have a great potential...
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Daytime Acute Non-Visual Alerting Response in Brain Activity Occurs as a Result of Short- and Long-Wavelengths of Light
PublikacjaVery recent preliminary findings concerning the alerting capacities of light stimulus with long-wavelengths suggest the existence of neural pathways other than melatonin suppression that trigger the nonvisual response. Though the nonvisual effects of light during the daytime have not been investigated thoroughly, they are definitely worth investigating. The purpose of the present study is to enrich existing evidence by describing...
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Nitrogen-Incorporated Boron-Doped Nanocrystalline Diamond Nanowires for Microplasma Illumination
PublikacjaThe origin of nitrogen-incorporated boron-doped nanocrystalline diamond (NB-NCD) nanowires as a function of substrate temperature (Ts) in H2/CH4/B2H6/N2 reactant gases is systematically addressed. Because of Ts, there is a drastic modification in the dimensional structure and microstructure and hence in the several properties of the NB-NCD films. The NB-NCD films grown at low Ts (400 °C) contain faceted diamond grains. The morphology...
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Architektura a dekonstrukcja. Przypadek Petera Eisenmana i Bernarda Tschumiego
PublikacjaArchitecture and Deconstruction Case of Peter Eisenman and Bernard Tschumi Introduction Towards deconstruction in architecture Intensive relations between philosophical deconstruction and architecture, which were present in the late 1980s and early 1990s, belong to the past and therefore may be described from a greater than...