Browsing by Author "Dishliev A."
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Item Asymptotic properties of solutions of a class of impulsive differential equations of second order with a retarded argument(1997-01-01) Bainov D.; Dimitrova M.; Dishliev A.Some asymptotic properties are studied for the solutions of a class of impulsive differential equations of second order with retarded argument and fixed moments of impulse effect. Sufficient conditions are found for oscillation of all bounded solutions. © 1997, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.Item Asymptotic properties of solutions of a class of impulsive differential equations of second order with a retarded argument(1997-01-01) Bainov D.; Dimitrova M.; Dishliev A.Some asymptotic properties are studied for the solutions of a class of impulsive differential equations of second order with retarded argument and fixed moments of impulse effect. Sufficient conditions are found for oscillation of all bounded solutions. © 1997, Department of Mathematics, Tokyo Institute of Technology. All rights reserved.Item Characterization of anodized Al 1050 with electrochemically deposited Cu, Ni and Cu/Ni and their behavior in a model corrosive medium(2021-01-01) Girginov C.; Kozhukharov S.; Tsanev A.; Dishliev A.The specific benefits of the modified films formed on preliminary anodized aluminum, including the versatility of their potential applications impose the need for evaluation of the exploitation reliability of these films. In this aspect, the dura-bility of Cu and Ni modified anodized aluminum oxide (AAO) films on the low-doped AA1050 alloy was assessed through extended exposure to a 3.5% NaCl model corrosive medium. The electrochemical measurements by means of electrochemical impedance spectroscopy (EIS) and potentiodynamic scanning (PDS) after 24 and 720 hours of exposure have revealed that the obtained films do not change their obvious barrier properties. In addition, supplemental analyses of the coatings were performed, in order to elucidate the impact of the AC-deposition of Cu and Ni inside the pores. The scanning electron microscopy (SEM) images have shown that the surface topology is not affected and resembles the typical surface of an etched metal. The subsequent energy dispersive X-ray spectroscopy (EDX) tests have revealed a predominance of Cu in the combined AAO-Cu/Ni layers, whereas additional X-ray photoelectron (XPS) analyses showed that both metals form oxides with different oxidation states due to alterations in the deposition conditions, promoted by the application of AC-polarization of the samples.Item Characterization of anodized Al 1050 with electrochemically deposited Cu, Ni and Cu/Ni and their behavior in a model corrosive medium(2021-01-01) Girginov C.; Kozhukharov S.; Tsanev A.; Dishliev A.The specific benefits of the modified films formed on preliminary anodized aluminum, including the versatility of their potential applications impose the need for evaluation of the exploitation reliability of these films. In this aspect, the dura-bility of Cu and Ni modified anodized aluminum oxide (AAO) films on the low-doped AA1050 alloy was assessed through extended exposure to a 3.5% NaCl model corrosive medium. The electrochemical measurements by means of electrochemical impedance spectroscopy (EIS) and potentiodynamic scanning (PDS) after 24 and 720 hours of exposure have revealed that the obtained films do not change their obvious barrier properties. In addition, supplemental analyses of the coatings were performed, in order to elucidate the impact of the AC-deposition of Cu and Ni inside the pores. The scanning electron microscopy (SEM) images have shown that the surface topology is not affected and resembles the typical surface of an etched metal. The subsequent energy dispersive X-ray spectroscopy (EDX) tests have revealed a predominance of Cu in the combined AAO-Cu/Ni layers, whereas additional X-ray photoelectron (XPS) analyses showed that both metals form oxides with different oxidation states due to alterations in the deposition conditions, promoted by the application of AC-polarization of the samples.Item Continuous dependence of the solution of a system of differential equations with impulses on the impulse hypersurfaces(1988-11-01) Dishliev A.; Bainov D.In the present paper the initial value problem is considered for systems of ordinary differential equations with impulses where the impulses are realized in the moments when the integral curve of the system meets some of previously given hypersurfaces called impulse hypersurfaces. Sufficient conditions for the continuous dependence of the solution on the impulse hypersurfaces are found. © 1988.Item Continuous dependence of the solution of a system of differential equations with impulses on the impulse hypersurfaces(1988-11-01) Dishliev A.; Bainov D.In the present paper the initial value problem is considered for systems of ordinary differential equations with impulses where the impulses are realized in the moments when the integral curve of the system meets some of previously given hypersurfaces called impulse hypersurfaces. Sufficient conditions for the continuous dependence of the solution on the impulse hypersurfaces are found. © 1988.Item Continuous Dependence on the Initial Condition of the Solution of a System of Differential Equations with Variable Structure and with Impulses(1987-01-01) Dishliev A.; Bainov D.Item Continuous Dependence on the Initial Condition of the Solution of a System of Differential Equations with Variable Structure and with Impulses(1987-01-01) Dishliev A.; Bainov D.Item I-optimal curve for impulsive Lotka-Volterra predator-prey model(2002-05-01) Angelova J.; Dishliev A.; Nenov S.For the classical Lotka-Volterra predator-prey system, new notion I-optimal curve ξI is introduced. This curve is disposed in the phase space of the system. The curve ξI intersects each trajectory γc of Lotka-Volterra system at least once. The points of ξI possess the following optimal property: if (m, M) ∈ ξI ∩ γc(0), then after a ``jump`` with magnitude I to the origin of coordinates, it hits a trajectory γc(1) and c1 is minimal; i.e., γc(1) is the ``nearest`` to the stable centre. The minimality concerns the rest points of initial trajectory γc(0), from which the ``impulsive jumps`` (subtractings) with magnitude I to (0, 0) are realized. The monotonicity, continuity, and linear asymptotical behaviour of ξI curve are proved. © 2002 Elsevier Science Ltd. All rights reserved.Item Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations(1996-06-28) Bainov D.; Dishliev A.; Stamova I.In the present paper, by means of a suitable comparison lemma sufficient conditions for uniform Lipschitz stability of an arbitrary solution of an impulsive system of differential-difference equations with variable impulsive perturbations are obtained.Item Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations(1996-06-28) Bainov D.; Dishliev A.; Stamova I.In the present paper, by means of a suitable comparison lemma sufficient conditions for uniform Lipschitz stability of an arbitrary solution of an impulsive system of differential-difference equations with variable impulsive perturbations are obtained.Item Oscillation of the solutions of a class of impulsive differential equations with a deviating argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions are found for oscillation of all solutions of a class of impulsive differential equations with deviating argument. ©1998 by North Atlantic Science Publishing Company.Item Oscillation of the solutions of a class of impulsive differential equations with a deviating argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions are found for oscillation of all solutions of a class of impulsive differential equations with deviating argument. ©1998 by North Atlantic Science Publishing Company.Item Oscillation of the solutions of impulsive differential equations and inequalities with a retarded argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions for oscillation of all solutions of a class of impulsive differential equations and inequalities with a retarded argument and fixed moments of impulse effect are found. © 1998 Rocky Mountain Journal of Mathematics. © 1998 Applied Probability Trust.Item Oscillation of the solutions of impulsive differential equations and inequalities with a retarded argument(1998-01-01) Bainov D.; Dimitrova M.; Dishliev A.Sufficient conditions for oscillation of all solutions of a class of impulsive differential equations and inequalities with a retarded argument and fixed moments of impulse effect are found. © 1998 Rocky Mountain Journal of Mathematics. © 1998 Applied Probability Trust.Item Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population(1990-01-01) Bainov D.; Dishliev A.The dynamics of a population whose mathematical model is the equation of Verhulst is considered. From the population, by discrete external effects (in the form of impulses), a certain quantity of biomass is taken away (or added). This process is described by means of differential equations with impulses at fixed moments. The moments and the magnitudes of the impulses are determined so that the time of regeneration of the quantity of biomass taken away from the population be minimal. © 1990.Item REPRODUCIBILITY OF THE SURFACE CHARACTERISTICS OF ANODIZED AA2024-T3 AIRCRAFT ALLOY WITH DEPOSITED Ce-CONVERSION COATING(2022-01-01) Kozhukharov S.; Dishliev A.; Girginov C.The establishment of any technology requires data verification regarding the repeatability and reproducibility of the obtained products. It includes the capability to repeat the properties of the respective products, in order to ensure quality reproduction. Namely, the ability of reproducing the characteristics of the final products determines the reliability of the used technological regime. In the present study a large amount of data was collected and analyzed. The data contain information for the color characteristics and the hydrophobicity of 28 samples of the AA2024-T3 aircraft alloy, coated with combined oxide layers. The coating primers were formed by means of anodization and subsequent sealing with cerium oxide layers. The combination of these methods results in the formation of hybrid layers, composed of Anodic Aluminum Oxide (AAO) and Cerium Conversion Coating (CeCC). Finally, the combined AAO-CeCC protective coatings were submitted to a total of 56 measurements and the obtained results underwent statistical data treatment. As a main result, the acquired statistical data have revealed a high level of repeatability, and can be used as a standard for the further production of similar coating systemsItem Stability on a cone in terms of two measures for differential equations with “maxima”(2010-01-01) Dishliev A.; Hristova S.Stability in terms of two measures for nonlinear differential equations with “maxima” is studied. A special type of stability in terms of two measures is defined. The new type of stability generalizes some of the known in the literature. Sufficient conditions for the defined stability are obtained. Cone-valued continuous Lyapunov functions are applied. Method of Razumikhin as well as comparison method for scalar ordinary differential equations have been employed. The usefulness of the introduced definition and the obtained sufficient conditions is illustrated through an example. © 2010, Duke University Press. All rights reserved.Item Stability on a cone in terms of two measures for differential equations with “maxima”(2010-01-01) Dishliev A.; Hristova S.Stability in terms of two measures for nonlinear differential equations with “maxima” is studied. A special type of stability in terms of two measures is defined. The new type of stability generalizes some of the known in the literature. Sufficient conditions for the defined stability are obtained. Cone-valued continuous Lyapunov functions are applied. Method of Razumikhin as well as comparison method for scalar ordinary differential equations have been employed. The usefulness of the introduced definition and the obtained sufficient conditions is illustrated through an example. © 2010, Duke University Press. All rights reserved.Item Uniform Stability with Respect to the Impulse Hypersurfaces of the Solutions of Differential Equations with Impulses(1993-01-05) Bainov D.; Dishliev A.The systems of differential equations with impulses are divided into several classes according to the way in which the moments of the impulses are determined. In the present paper the initial value problem is considered for systems of differential equations for which the impulses are realized at the moments when the integral curve of the problem meets certain hypersurfaces, called impulse hypersurfaces, of the extended phase space. The notions of strong uniform stability of the solutions of systems without impulses and uniform stability with respect to the impulse hypersurfaces of the solutions of systems with impulses are introduced. The main results are given in two theorems. The first one contains sufficient conditions under which strong uniform stability of the zero solution of the respective system without impulses implies uniform stability with respect to the impulse hypersurfaces of the zero solution of the initial system with impulses. In the second theorem sufficient conditions are given under which uniform Lipschitz stability of the zero solution of the corresponding system without impulses implies uniform stability with respect to the impulse hypersurfaces of the zero solution of the initial system with impulses. © 1993 Academic Press, Inc.