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Search results for: EXISTENCE RESULTS
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Existence results to delay fractional differential equations with nonlinear boundary conditions
PublicationPraca dotyczy problemów brzegowych dla ułamkowych równań różniczkowych z opóźnionym argumentem. Podano warunki dostateczne na istnienie rozwiązań ekstremalnych takich zagadnień.
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Existence of solutions with an exponential growth for nonlinear differential-functional parabolic equations
PublicationWe consider the Cauchy problem for nonlinear parabolic equations with functional dependence.We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
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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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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublicationIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Systems of boundary value problems of advanced differential equations
PublicationThis paper considers the existence of extremal solutions to systems of advanced differential equations with corresponding nonlinear boundary conditions. The monotone iterative method is applied to obtain the existence results. An example is provided for illustration.
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe 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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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Positive solutions to Sturm–Liouville problems with non-local boundary conditions
PublicationIn this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ζ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.
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Functional delay fractional equations
PublicationIn 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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Tinnitus Therapy Based on High-Frequency Linearization Principles - Preliminary Results
PublicationThe 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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Quasi-solutions for generalized second order differential equations with deviating arguments
PublicationThis paper deal with boundary value problems for generalized second order differential equations with deviating arguments. Existence of quasi-solutions and solutions are proved by monotone iterative method. Examples with numerical results are added.
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Fractional problems with advanced arguments
PublicationThis paper concerns boundary fractional differential problems with advanced arguments. We investigate the existence of initial value problems when the initial point is given at the end point of an interval. Nonhomogeneous linear fractional differential equations are also studied. The existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using...
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Application of the numerical-analytic method for systems of differential equations with parameter
PublicationThe numerical-analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation. We also obtain several existence results for problems with deviations of an argument
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Boundary problems for fractional differential equations
PublicationIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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Fractional differential equations with causal operators
PublicationWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublicationIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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Systems of Nonlinear Fractional Differential Equations
PublicationUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.
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On neutral differential equations and the monotone iterative method
PublicationThe application of the monotone iterative method to neutral differential equations with deviating arguments is considered in this paper. We formulate existence results giving sufficient conditions which guarantee that such problems have solutions. This approach is new and to the Authors' knowledge, this is the first paper when the monotone iterative method is applied to neutral first-order differential equations with deviating...
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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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The Analysis of Cross-Polarisation Discrimination for Body Area Networks in Cylindrical Metallic Environment
PublicationThe analysis of cross-polarisation discrimination for Body Area Networks in an untypical environment of cylindrical metallic room has been performed in the paper. This analysis was done based on the measurements carried out for dynamic narrowband off-body channels operating at the frequency of 2.45 GHz. The results have shown that there is a strong dependence of the depolarisation effect on the existence of direct component in...
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Homoclinics for singular strong force Lagrangian systems in R^N
PublicationWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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Social convergence in Nordic countries at regional level
PublicationResearch background: Geographical proximity, common historical roots and collaboration within the Nordic Council cause the Nordic countries to be often wrongly treated as monoliths. However, in reality, Nordic regions differ in terms of broadly defined social and economic development. Issues concerning the standard of living are one of the priorities of the Helsinki Treaty signed by Nordic countries. Purpose of the article: The...
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Tinnitus Therapy Based on High-Frequency Linearization
PublicationThe 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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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublicationIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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First-order differential equations with nonlocal boundary conditions
PublicationWe study a first-order boundary value problem subject to some boundary conditions given by Riemann-Stieltjes integrals. Using a monotone iterative method, we formulate sufficient conditions which guarantee the existence of extremal or quasi-solutions in the corresponding region bounded by upper and lower solutions of our problems. The case when a unique solution exists is also investigated. Some examples are given to illustrate...
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Shadow Economy in Poland Recent Evidence Based on Survey Data
PublicationThe book provides an estimate of the size of the shadow economy in Poland. Using analogous data, it traces core determinants of the existence of the shadow economy in Poland. It compares results with neighbouring countries, and if possible, the remaining Central-Eastern economies. The book tells why the problem of the unreported economic activity matters; it presents the problem from different angles―economic, social and institutional....
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn 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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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Open Research DataThe 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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Analysis of a gene expression model
PublicationWe study a mathematical model of gene transcription and protein synthesis with negative feedback. We consider a system of equations taking into account the number of active binding sites, the way in which dimers bind to DNA and time delay in translation process. For a simplified model that consist of three ordinary differential equations with time delay we derive conditions for stability of the positive steady state and for the...
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Euro 2012 in Gdańsk, Poland. Is it worth using public funds?
PublicationThe aim of this study is to estimate the willingness - to - pay (WTP) among the community of the Pomeranian region, Poland in connection with intangible benefits and costs st emming from hosting the Euro 2012 in Gdansk. A survey conducted among 407 respondents was the source of information. The results of the study show that the average value of WTP benefit for the whole sample was 45,72 PLN2012 and WTP cost...
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Can Inflation Forecast and Monetary Policy Path be Really Useful? The Case of the Czech Republic
PublicationProducing and revealing inflation forecast is belie ved to be the best way of implementing a forward-looking monetary policy. The article focuses on inflation forecast targeting (IFT) at the Czech National Bank (CNB) in terms of its efficiency in shaping consumers’ inflation expectations. The goal of the study is to verify the accuracy of the inflation forecasts, and their influence on inflation...
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Detection of defects in PMMA beam using shear waves - numerical simulation and experiment
PublicationTest doświadczalny falami sprężystymi jest częścią systemu diagnostycznego belek. Autorzy badają pole przyspieszeń wywołane przepływem fal ultradźwiękowych i jego modyfikacje wynikające z wprowadzonych uszkodzeń belki. Artykuł porównuje wyniki eksperymentalne z symulacjami numerycznymi MES. The experimental test introduced in the paper is the part of the diagnostic system utilizing the elastic waves. The authors investigate the...
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Social Convergence in Nordic NUTS-3 Regions
PublicationGeographical proximity, common historical roots and collaboration within the Nordic Council make the Nordic countries, often wrongly treated as monoliths. However, in reality, Nordic regions differ in terms of broadly defined social and economic development. Issues concerning the standard of living are one of the priorities of the Helsinki Treaty signed by Nordic countries. The main goal of this paper is to analyze the existence...
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Poszukiwanie dobrych odpowiedzi na źle postawione pytania, rzecz o przedsiębiorczości kobiet
PublicationWomen entrepreneurship has been the subject of research for many years and its results are often compared against the men entrepreneurship results. The conducted research has often been aimed at identification/recognition of the differences between the entrepreneurs of opposite gender. The lack of satisfactory proof for the existence of the differences has been attributed by some determined researchers to inappropriate research...
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The cohomological span of LS-Conley index
PublicationIn this paper we introduce a new homotopy invariant – the cohomological span of LS-Conley index. We prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form Lx+K(x), where L is bounded linear and K is completely continuous. We give examples of Hamiltonian systems for which our methods give better results than the Morse inequalities. We also give a formula...
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TRAVELLING WAVES FOR LOW–GRADE GLIOMA GROWTH AND RESPONSE TO A CHEMOTHERAPY MODEL
PublicationLow-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the...
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Imaging of morphological and physicochemical changes occuring in the structure of austenitic steel due to the thermal sensitization
Open Research DataIn polycrystalline materials, grain boundaries are always where phenomena such as surface diffusion, sedimentation and corrosion occur. They have a significant impact on the macroscopic properties of the construction material [1]. In addition to inhomogeneities such as manganese sulphide inclusions formed during the metallurgical process, interfacial...
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Topological Behaviour of Solutions of Vibro-Impact Systems in the Neighborhood of Grazing
PublicationThe 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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DIAGNOSIS OF MALIGNANT MELANOMA BY NEURAL NETWORK ENSEMBLE-BASED SYSTEM UTILISING HAND-CRAFTED SKIN LESION FEATURES
PublicationMalignant melanomas are the most deadly type of skin cancer but detected early have high chances for successful treatment. In the last twenty years, the interest of automated melanoma recognition detection and classification dynamically increased partially because of public datasets appearing with dermatoscopic images of skin lesions. Automated computer-aided skin cancer detection in dermatoscopic images is a very challenging task...
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublicationVarious 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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ESTIMATION OF THE WILLINGNESS-TO-PAY FOR PRESERVING THE FOOTBALL ARENA IN GDANSK
PublicationThe European Football Championship (Euro 2012) organized in Poland became the pretext for a number of infrastructural changes. A high level of expenditure makes the Polish event the most expensive among events of this magnitude. The fact that these changes were 100% financed by public funds raises the question of whether these funds were used in a substantiated way. Therefore, the aim of this study is...
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Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions
PublicationIn this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments α and also in the case when α(t)=t, t∈[0,1]....
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The use of Markov chains in the social convergence analysis
PublicationThe main goal of this article is to analyze the social convergence process using Markov chains. In this research, term social convergence refers to the reduction of dispersion in the standard of living among countries. The use of Markov chains in the social convergence analysis allowed describing movements of observational units within the distribution and providing more details about the mechanism of the convergence process. A...
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GPS-derived height changes in diurnal and sub-diurnal timescales
PublicationThis paper describes the research concerning precise short-time GPS solutions conducted in the Centre of Applied Geomatics, Military University of Technology, Warsaw, Poland. The data from ASG-EUPOS (Polish Active Geodetic Network) was processed using Bernese 5.0 software and EPN (EUREF Permanent Network) standards and models. In this study, the adapted 3-hour observation window is shifted every hour for obtaining hourly geocentric...
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Anticarcinogenic and antioxidant activities of leaves and flowers hydroalcoholic extracts of Nerium oleander L.: PCA analysis and phytochemical content by FTIR spectroscopy
PublicationAims: The aim of this work is the evaluation the anticarcinogenic effect on HT29 cancer cells lines and antioxidant effect of three extracts from different morphological parts (leaves (LE), pink flowers (PFE) and white flowers (WFE)) of Nerium oleander lin. Methods: This research provides the anticarcinogenic activity of extracts from N. oleander white flowers. Principal Component Analysis (PCA) was applied to estimate the relationship...
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A Canonical Switched Capacitor DC-DC Converter. A look at how the historical SC synthesis problem is getting solved
PublicationWe reconsider a solution to the historical problem in switched capacitor (SC) DC-DC converter synthesis. Specifically, we retackle the problem of constructing an SC twophase network realizing arbitrary voltage conversion ratio within rational bounds defined. Theoretical foundations are available in our earlier research [3] where a nonconstructive proof of existence was given. We briefly review and comment on known circuit solutions...
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The potential of Web-GIS and geovisual analytics in the context of marine cadastre
PublicationThe importance of the marine environment to human existence makes it imperative that information models represent the multidimensional nature of reality as closely as possible in order to facilitate good governance. Information regarding jurisdiction, as well as the effects of formal law and community interests on the marine environment (e.g. nature and spatial extents as well as rights, responsibilities, restrictions etc.) would...
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Seasonal variability and morphological structure of bacteria in the Admiralty Bay (King George Island, Antarctic).
PublicationIntroduction: The aim of investigations was to state whether melting glaciers cause mass mortality of the sea stenohalyne organisms, what in consequence can lead to an increase of accumulation and growth of psychrophilic bacteria. It may be also that fresh melting water is unfavourable to the sea bacteria and front glacier's regions are not the areas of their intensive development. Methods: Field investigations were done in Admiralty...