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Search results for: DIFFERENCE FUNCTIONAL INEQUALITIES
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Difference functional inequalities and applications.
PublicationThe paper deals with the difference inequalities generated by initial boundary value problems for hyperbolic nonlinear differential functional systems. We apply this result to investigate the stability of constructed difference schemes. The proof of the convergence of the difference method is based on the comparison technique, and the result for difference functional inequalities is used. Numerical examples are presented.
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Implicit difference functional inequalities and applications
PublicationKlasyczne rozwiązania problemów początkowych przybliżane są rozwiązaniami uwikłanych metod różnicowych. Wykazana została zbieżność i stabilność uwikłanych schematów. Przy założeniu, że funkcje dane spełniają nieliniowe oszacowanie typu Perrona względem argumentu funkcyjnego, udowodniono stabilność metody uwikłanej, wykorzystując twierdzenie porównawcze dla funkcji spełniających uwikłane nierówności różnicowe typu Volterry.
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Differential difference inequalities related to hyperbolic functional differential systems and applications
PublicationZagadnienie początkowo brzegowe dla ukadów quasiliniowych równań różniczkowo funkcyjnych przeksztacane jest w układ równań różniczkowych zwyczajnych poprzez dyskretyzację względem zmiennej przestrzennej. Podane są warunki wystarczające dla zbieżności metody prostych. Otrzymany układ równań różniczkowo funkcyjnych zwyczajnych jest rozwiązywany uwikłaną metodą różnicową. Zbieżność schematu różnicowego jest dowodzona metodą porównawczą....
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Differential inequalities with initial time difference.
PublicationUzyskano pewne wyniki porównawcze pomiędzy rozwiązaniami nierówności różniczkowych startujących z różnych punktów początkowych. O nieliniowej funkcji f (związanej z zagadnieniem) zakładano jednostronny warunek Lipschitza. Podano pewne zastosowanie otrzymanych wyników. Sformułowano też pewne warunki dotyczące stabilności.
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Systems of differential inequalities with initial time difference.
PublicationPewne twierdzenia porównawcze są formułowane dla takich zagadnień.O funkcji F występującej po prawej stronie nierówności różniczkowej zakłada się, że spełnia własności kwasimonotoniczności. Sformułowanorównież twierdzenia o istnieniu ekstremalnych rozwiązań dla odpowiednich równań różniczkowych pierwszego rzędu z odchylonymi argumentami.
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Delay differential inequalities with initial time difference
PublicationPraca dotyczy nierówności różniczkowych z argumentami opóźnionymi przy różnych warunkach początkowych. Podano twierdzenia porównawcze dla takich nierówności. Podano też warunki dostateczne na istnienie ekstremalnych rozwiązań odpowiednich równań różniczkowych z argumentami opóźnionymi.
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Delay integro-differential inequalities with initial time difference and applications.
PublicationPraca dotyczy nierówności różniczko-całkowych z opóźnionymi argumentami przy różnych warunkach początkowych. Przy pewnych założeniach (m.in. monotoniczność, jednostronny warunek Lipschitza) sformułowano twierdzenia porównawcze dla rozwiązań w.w nierówności. Pokazano zastosowania w technice iteracji monotonicznych i sformułowano warunki dostateczne na istnienie rozwiązań ekstremalnych dla równań różniczkowo-całkowych z odchylonymi...
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Generalized solutions of first order partial differential functional inequalities
PublicationW pracy rozważa się zagadnienia początkowo brzegowe dla nieliniowych równań różniczkowo funkcyjnych cząstkowych pierwszego rzędu. Podano dowód jednoznaczności rozwiązań uogólnionych. Oparty jest on na twierdzeniu porównawczym dla nierówności różniczkowo funkcyjnych w sensie Caratheodory'ego. Prezentowane jest twierdzenie o uogólnionych rozwiązaniach nierówności różniczkowo funkcyjnych.
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Implicit difference methods for parabolic functional differential equations.
PublicationPraca dotyczy przybliżania rozwiązań quasiliniowych parabolicznych równań różniczkowo-funkcyjnych za pomocą schematów różnicowych, uwikłanych ze względu na zmienną czasową. Wykonano pełną analizę zbieżności metod i pokazano na przykładzie, że nowe metody są istotnie lepsze od schematów jawnych. Dowód stabilności oparty jest na metodzie porównawczej z nieliniowymi oszacowaniami typu Perrona. Otrzymane wyniki można zastosować do...
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Implicit difference methods for Hamilton-Jacobi differential functional equations
PublicationKlasyczne rozwiązania problemów początkowych przybliżane są rozwiązaniami odpowiedniego układu quasiliniowego równań różniczkowo funkcyjnych. Rozpatrywana metoda numeryczna jest uwikłana względem zmiennej przestrzennej. Wykazana została zbieżność i stabilność uwikłanych schematów. Dowód stabilności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perrona dla funkcji danych.
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Implicit difference methods for first order partial differential functional equations
PublicationKlasyczne rozwiązania problemów początkowo brzegowych przybliżane są rozwiązaniami uwikłanych metod różnicowych. Wykazana została zbieżność i stabilność uwikłanych schematów. Dowód stabilności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perrona dla funkcji danych.
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Implicit difference methods for infinite systems of hyperbolic functional differential equations
PublicationPraca dotyczy klasycznych rozwiązań problemów początkowo brzegowych dla nieskończonych układów nieliniowych równań rózniczkowo funkcyjnych. Skonstruowane są dwa typy schematów różnicowych. Pokazujemy, ze rozwiązania rozważanego zagadnienia różniczkowego można przybliżyć przy pomocy rozwiązań nieskończonych układów równań różnicowych. W drugiej części pracy udowadniamy, że również rozwiązania skończonych układów równań różnicowych...
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First-order functional difference equations with nonlinear boundary value problems
PublicationDyskutowano problem brzegowy dla równań różnicowych z opóźnionym argumentem. Nierówności różnicowe związane z w/w problem też były przedmiotem badań. Stosując metodę iteracji monotonicznych, sformułowano warunki dostateczne na istnienie ekstremalnych rozwiązań problemów brzegowych z opóźnionymi argumentami. Podano dwa przykłady ilustrujące otrzymane wyniki.
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Implicit difference methods for first order partial differential functional equations
PublicationW pracy prezentowana jest nowa klasa metod numerycznych dla quasiliniowych równań różniczkowo funkcyjnych pierwszego rzędu. Są to schematy różnicowe uwikłane względem zmiennej czasowej. Podana jest pełna analiza zbieżności rozważanych metod uwikłanych oraz przykład numeryczny pokazujący, że klasa tych metod jest szersza niż klasa schematów jawnych. Dowód stabilności opiera się na technice porównawczej z nieliniowym oszacowaniem...
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Implicit difference methods for quasilinear differential functional equations on the Haar pyramid
PublicationW pracy prezentowana jest klasa metod numerycznych dla quasiliniowych równań różniczkowo funkcyjnych pierwszego rzędu. Metody numeryczne są uwikłane względem zmiennej czasowej. Istnienie rozwiązania przybliżonego wykazane zostało przy użyciu nierówności różnicowych. Dowód stabilności bazuje na technice porównawczej z nieliniowym oszacowaniem typu Perona dla funkcji danych. Przedstawione zostały również przykłady numeryczne.
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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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Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients - convergence analysis
PublicationW pracy wykazano zbieżność metody różnicowej dla zagadnienia początkowego dla równania parabolicznego bez pochodnych mieszanych, ze współczynnikami zależnymi od czasu, z nieliniową i nielokalną prawą stroną równania.
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Digital divide - inequalities in level of implementation of new information and telecommunication technologies. Cross country study
PublicationTekst stanowi analizę nierówności stopnia wdrożenia oraz implementacji ICTs w różnych krajach świata. Autor szacuje wskaźnik GINI dla możliwych krajów świata.In the paper presented, the author considers few aspects of the so-called "digital divide". It is easily noticeable worldwide, that new information and communication technologies (ICTs) "possess" a great ability to spread, at high pace, among countries from all around the...
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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...
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Explicit and implicit difefrence methods for quasilinear first order partial functional differential equations.
PublicationInitial boundary value problems of the Dirichlet type for quasilinear functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. Suffcient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both classes...
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Method of lines for Hamilton-Jacobi functional differential equations.
PublicationInitial boundary value problems for nonlinear first order partial functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A method of quasi linearization is adopted. Suffcient conditions for the convergence of the method of lines and error estimates for approximate solutions are presented. The proof of the stability of the diffrential difference...
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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublicationA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...
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Visual Traffic Noise Monitoring in Urban Areas
PublicationThe paper presents an advanced system for railway and road traffic noise monitoring in metropolitan areas. This system is a functional part of a more complex solution designed for environmental monitoring in cities utilizing analyses of sound, vision and air pollution, based on a ubiquitous computing approach. The system consists of many autonomous, universal measuring units and a multimedia server, which gathers, processes and...
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Experimental bases for the rail track surface damage detection system
PublicationA diagnosis of rail surface is generally based on the classical method of direct assessment and track geometry measurements. Identification and qualification of inequality and damage on the surface rails is depend on the skills and experience person who conducting inspection. In times of increasing exploitation of railways, infrastructure managers decide to use systems supporting the assessment of technical condition of the railways....
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Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media
PublicationThis article deals with the stochastic Gross–Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation...
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Structural studies of a cold-adapted dimeric Beta-D-galactosidase from Paracoccus sp. 32d
PublicationThe crystal structure of a novel dimeric [beta]-D-galactosidase from Paracoccus sp. 32d (Par[beta]DG) was solved in space group P212121 at a resolution of 2.4 Å by molecular replacement with multiple models using the BALBES software. This enzyme belongs to glycoside hydrolase family 2 (GH2), similar to the tetrameric and hexameric [beta]-D-galactosidases from Escherichia coli and Arthrobacter sp. C2-2, respectively. It is the second...
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Successive cytotoxicity control by evolutionary surface decorated electronic push-pull green ZnCr-LDH nanostructures: Drug delivery enlargement for targeted breast cancer chemotherapy
PublicationThe reason for the increasing bioavailability and biocompatibility of the porous nanomaterials in the presence of different (bio)molecules is still unknown. The role of difference functional groups and their interactions with the potential bioavailability and biocompatibility is of great importance. To investigate the potential contribution of the electronic effects (especially on the surface of the porous nanomaterials) on their...
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Removal of diphenols using pine biochar. Kinetics, equilibrium, thermodynamics, and mechanism of uptake
PublicationThermal pyrolysis synthesized activated biochar from the Pinus elliottii sawdust (PS) at 600° C. The obtained activated biochar (PB600) was used for the removal of three diphenols, catechol (CAT), resorcinol (RES), and hydroquinone (HYD), which are utilized mainly in different industries. The PB600 was characterized by several analytical techniques. The BET surface area of 1473 m2.g−1 and a total pore volume of 0.707 cm3 g−1 was...
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Functional Materials
e-Learning CoursesPrerequisites: The course is primarily open to all PhD students at Gdansk University of Technology. This course is compulsory for PhD students assigned to Automation, Electronics, Electrical Engineering and Space Technologies tracks at Doctoral School at Gdańsk University of Technology Content During the course students will learn about different classes of intelligent materials and a strong emphasis will be placed on their practical...
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Density functional theory-based simulations of sum frequency generation spectra involving methyl stretching vibrations: effect of the molecular model on the deduced molecular orientation and comparison with an analytical approach
PublicationThe knowledge of the first hyperpolarizability tensor elements of molecular groups is crucial for a quantitative interpretation of the sum frequency generation (SFG) activity of thin organic films at interfaces. Here, the SFG response of the terminal methyl group of a dodecanethiol (DDT) monolayer has been interpreted on the basis of calculations performed at the density functional theory (DFT) level of approximation. In particular,...
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Optoelectronic properties of curved carbon systems
PublicationSystematic investigation of optoelectronic properties of curved carbon systems has been performed and the results have been compared with the representatives of flat carbon systems. Moreover, the application of third order dispersion corrected density functional tight binding method (with third order corrections of self-consistent charges) including Becke-Johnson dumping (DFTB3-D3(BJ)) has been validated in order to obtain reliable...
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Morse inequalities via Conley index theory
PublicationThe relation known as the Morse inequalities can be extended to a more general setting of flows on a locally compact metric spaces (Conley index) as well as dynamical systems on Hilbert spaces (LS-index). This paper is a discourse around this extension. Except the part concerning the LS-index the material is self-contained and has a character of a survey.
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Digital Gaps and Economic Inequalities in MENA Countries: An Empirical Investigation
PublicationThis research contributes to the present state of the art by examining changes in cross-country inequalities in digital technologies deployment and economic performance. Our empirical target builds on the hypothesis that rapid global diffusion of digital technologies unequivocally leads to gradual eradication of cross-country digital gaps and cross-country inequalities in terms of deployment of ICT; the technology convergence occurs....
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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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Intrinsic asymmetry with respect to adversary: a new feature of Bell inequalities
PublicationIt is known that the local bound of a Bell inequality is sensitive to the knowledge of the external observer about the settings statistics. Here we ask how that sensitivity depends on the structure of that knowledge. It turns out that in some cases it may happen that the local bound is much more sensitive to the adversaryʼs knowledge about the settings of one party than the other. Remarkably, there are Bell inequalities which are...
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Strong Monogamies of No-Signaling Violations for Bipartite Correlation Bell Inequalities
PublicationThe phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as...
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Computational analysis of substituent effects on proton affinity and gas-phase basicity of TEMPO derivatives and their hydrogen bonding interactions with water molecules
PublicationThe study investigates the molecular structure of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and its derivatives in the gas phase using B3LYP and M06-2X functional methods. Intermolecular interactions are analyzed using natural bond orbital (NBO) and atoms in molecules (AIM) techniques. NO2-substituted TEMPO displays high reactivity, less stability, and softer properties. The study reveals that the stability of TEMPO derivatives...
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn 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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Advances in Functional Materials 2024
e-Learning CoursesOur summer school on Advances in Functional Materials 2024 aims to bring together young scientists (Ph.D. and MSc students) with specialists in materials engineering. You will be able to follow our lectures, and laboratory classes so you can practice what you have learned. This course consists of 40 hours of direct contact classes - 30 hours of lectures and 10 hours of laboratory classes delivered by our specialists from the Advanced...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublicationIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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Properties of Oxygen Vacancy and Hydrogen Interstitial Defects in Strontium Titanate: DFT + Ud,p Calculations
PublicationThis work presents extensive theoretical studies focused on the mixed ion-electron transport in cubic strontium titanate (STO). A new approach to the description of this difficult system was developed within the framework of linear-scaling Kohn–Sham density functional theory, as realized in the ONETEP program. The description we present is free of any empirical parameters and relies on the Hubbard U and Hund’s J corrections applied...
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Comprehensive evaluation of the carbon footprint components of wastewater treatment plants located in the Baltic Sea region
PublicationFinland and Poland share similar environmental interests with regard to their wastewater effluents eventually being discharged to the Baltic Sea. However, differences in the influent wastewater characteristics, treatment processes, operational conditions, and carbon intensities of energy mixes in both countries make these two countries interesting for carbon footprint (CF) comparison. This study aimed at proposing a functional...
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Phase-difference positioning in asynchronous system
PublicationThis paper presents concept and implementation of digital positioning system based on phase difference measurements, designed as a navigational aid for marine applications. Main feature of proposed system is the ability to work in both synchronous mode, with one master station and set of slave stations synchronized with master, and in asynchronous mode with independent clocking of all stations.
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Asynchronous time difference of arrival (ATDOA) method
PublicationA new method for a location service in the asynchronous wireless sensor networks is outlined. This method, which is called asynchronous time difference of arrival (ATDOA), enables calculation of the position of a mobile node without knowledge of relative time differences (RTDs) between measuring sensors. The ATDOA method is based on the measurement of time difference of arrival between the node and the same sensor at the discrete...
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Linear game non-contextuality and Bell inequalities—a graph-theoretic approach
PublicationWe study the classical and quantum values of a class of one-and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR(XOR-d) games we study are a subclass of the well-known linear games. We introduce a 'constraint graph' associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the...
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Elective seminar: Designing Urban Lighting for the Built Environment – from Theory to Practice
e-Learning CoursesGoal of the course: Understanding the basic design issues related to illumination of the exterior spaces in the built environment Course content / class schedule: 1.Student will learn the difference between Functional versus Decorative lighting in exterior spaces 2. Student will learn how artificial lighting can shape the appearance of an urban space 3. Student will learn necessary tools (luminaires, light sources,...
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On the Peano Theorem for Some Functional Differential Equations on Time Scale
PublicationThe Peano Theorem for some functional differential equations on time scale is proved. Assumptions are of Caratheodory type. Two counter examples for false Peano theorems in the literature are presented.
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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.
PublicationDeparting 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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Advances in Functional Materials Summer School 2023
e-Learning CoursesOur summer school on “Advances in Functional Materials” aims to bring together young scientists (Ph.D. and MSc students) with renowned specialists in materials engineering. Experts from academia, research units, and industry will deliver lectures, tutorials, and laboratory classes so that you can practice what you have learned. We divided the program into five main thematic topics: 1) Superconducting materials, 2) Additive manufacturing, 3)...
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Parabolic Equations with Functional Dependence
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence and prove theorems on the existence of solutions to parabolic differential-functional equations.