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The main purpose of the present paper is to study the global behavior of solutions to the L2‐critical Schrodinger–Poisson system i∂tψ(t,x)+Δψ(t,x) = V(t,x)ψ(t,x), (t,x)∈R+×R3, δV(t,x) = −4π|ψ(t,x)|83, ψ(0,x) = ψ0(x). More precisely, we... more
The main purpose of the present paper is to study the global behavior of solutions to the L2‐critical Schrodinger–Poisson system i∂tψ(t,x)+Δψ(t,x) = V(t,x)ψ(t,x), (t,x)∈R+×R3, δV(t,x) = −4π|ψ(t,x)|83, ψ(0,x) = ψ0(x). More precisely, we shall establish the local existence of solutions for initial data ψ0 in L2(R3), as well as the existence of global solutions for small initial data. Finally, we shall prove the existence of scattering operator.
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We prove decay with respect to some Lebesgue norms for a class of Schrödinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space... more
We prove decay with respect to some Lebesgue norms for a class of Schrödinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space for the solutions to the systems of $N$ defocusing Choquard equations with mass-energy intercritical nonlinearities in any space dimension and of defocusing Hartree-Fock equations, for any dimension $d\geq3$.
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We present new extended Strichartz estimates for the solutions to the heat equation with inhomogeneous nonlinearity in the mass-energy intercritical framework in space dimension d ≥ 1. As an application we show local and global... more
We present new extended Strichartz estimates for the solutions to the heat equation with inhomogeneous nonlinearity in the mass-energy intercritical framework in space dimension d ≥ 1. As an application we show local and global well-posedness in the Strichartz space Lq((0,T); Lr(ℝd)), both in the focusing and the defocusing case, assuming the initial data are in the Sobolev space Hσ(ℝd)), with σ ∈ (0, 1].
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The paper deals with the formulation and approximation of a static thermoelasticity problem with bilateral frictional contact between a deformable body and rigid foundation. The friction is in the form of nonmonotone and multivalued law.... more
The paper deals with the formulation and approximation of a static thermoelasticity problem with bilateral frictional contact between a deformable body and rigid foundation. The friction is in the form of nonmonotone and multivalued law. The coupling effect in the problem is neglected, so the thermic part of the problem is considered independently of the elasticity problem. The formulated problem is approximated by finite element method as in [6].
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By means of the transmutation method we construct explicit solutions of some fractional order Volterra integral equations of second kind, with one or two different Erdelyi‐Kober operators, the latter involving hypergeometric integrals.... more
By means of the transmutation method we construct explicit solutions of some fractional order Volterra integral equations of second kind, with one or two different Erdelyi‐Kober operators, the latter involving hypergeometric integrals. The same method is applied to fractional differential and differ‐integral equations, involving simultaneously Erdelyi‐Kober fractional integrals and derivatives of different orders. The idea of this method is to use transmutation operators to reduce the solutions of the discussed problems to the known solutions of the simplest problems of the same type (in this case, with Riemann‐Lioville operators). Some illustrative examples are given.
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ABSTRACT In this paper, in the first part, we work on the solutions of one- dimensional Burgers-Sivashinsky Equation in the bounded domain [-L,L]. In the second part, we consider radially symmetric solutions of this equation in two and... more
ABSTRACT In this paper, in the first part, we work on the solutions of one- dimensional Burgers-Sivashinsky Equation in the bounded domain [-L,L]. In the second part, we consider radially symmetric solutions of this equation in two and higher dimension in a bounded domain [0, R]. In both cases, using Lyapunov function approach, we study the long time behavior of the solutions and prove that there exists a time independent bound for the L2 norm of the solutions. Thus in each case there exists an absorbing ball when time tends to infinity.
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A disadvantage of the existing bi-proportional system for the Bulgarian parliamentary elections is the large number of discordances (a party list with less votes gets more seats than a party list with more votes) in the seat... more
A disadvantage of the existing bi-proportional system for the Bulgarian parliamentary elections is the large number of discordances (a party list with less votes gets more seats than a party list with more votes) in the seat distributions. Different schemes has been proposed to deal with this phenomenon. In this paper we propose two new methods: 1) augmentation of the electoral regions and 2) introduction of a new electoral region for accounting the votes cast abroad. In this way the number of discordances may be vastly reduced.
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Given a function f(z), analytic on a regular compact set E in the complex plane, and a sequence of polynomials, orthogonal, with respect to a nonnegative and integrable weight ω)(z), on the boundary of E, we provide results about the... more
Given a function f(z), analytic on a regular compact set E in the complex plane, and a sequence of polynomials, orthogonal, with respect to a nonnegative and integrable weight ω)(z), on the boundary of E, we provide results about the behavior of the Fourier series of f(z) with respect to ω(z). The results are original.
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We study the Cauchy problem for the Schrodinger equation with a mixed type nonlinear term. We analyze the local and global properties of solutions in dependence of the nonlinear power, the repulsive or attractive character of nonlinear... more
We study the Cauchy problem for the Schrodinger equation with a mixed type nonlinear term. We analyze the local and global properties of solutions in dependence of the nonlinear power, the repulsive or attractive character of nonlinear interaction and the size of the initial data.
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Learning strategy in an intelligent learning system is generally elaborated on the basis of assessment of the following factors: learner’s time for reaction, content of the learning object, amount of learning material in a learning... more
Learning strategy in an intelligent learning system is generally elaborated on the basis of assessment of the following factors: learner’s time for reaction, content of the learning object, amount of learning material in a learning object, learning object specification, e‐learning medium and performance control. Current work proposes architecture for dynamic learning strategy design by implementing multidimensional analysis model of learning factors. The analysis model concerns on‐line analytical processing (OLAP) of learner’s data structured as multidimensional cube. Main components of the architecture are analysis agent for performing the OLAP operations on learner data cube, adaptation generator and knowledge selection agent for performing adaptive navigation in the learning object repository. The output of the analysis agent is involved in dynamic elaboration of learning strategy that fits best to learners profile and behavior. As a result an adaptive learning path for individual learner and for learn...
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Pontryagin gives a well known example of a two-dimensional compact subspaces P and Q; P,Q⊂R5 for which dim(P×Q) = 3. In this note we investigate the conditions for existing of such ``exotic'' subspaces of an the class of some... more
Pontryagin gives a well known example of a two-dimensional compact subspaces P and Q; P,Q⊂R5 for which dim(P×Q) = 3. In this note we investigate the conditions for existing of such ``exotic'' subspaces of an the class of some compact metric spaces (also called often ``Polish spaces'') for example-the class of absolutely retracts or the products of continua.
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A plane acoustic wave is scattered by either a soft or a hard small torus. The incident wave has a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low-frequency approximation method is... more
A plane acoustic wave is scattered by either a soft or a hard small torus. The incident wave has a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low-frequency approximation method is applicable to the scattering problem. It is shown that there exists exactly one toroidal coordinate system that fits the given geometry. The R-separation of variables is utilized to obtain the series expansion of the fields in terms of toroidal harmonics (half-integer Legendre functions of first and second kind). The scattering problem for the soft torus is solved analytically for the near field, governing the leading two low-frequency coefficients, as well as for the far field, where both the amplitude and the cross-section are evaluated. The scattering problem for the hard torus appears to be much more complicated in calculations. The Neumann boundary condition on the surface of the torus leads to a three-term recurrence relation for the series coeffic...
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The mathematical model of a problem of minimization of a dose of an irradiation of the personnel which is carrying out dismantling of the completing block of a nuclear power plant is considered. Dismantling of elements of the block is... more
The mathematical model of a problem of minimization of a dose of an irradiation of the personnel which is carrying out dismantling of the completing block of a nuclear power plant is considered. Dismantling of elements of the block is carried out consistently. A brigade of workers having carried out dismantling of the next element of the block passes to
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ABSTRACT In this paper we consider the problem of differentiation of coquaternionic functions. Let us recall that coquaternions are elements of an associative non‐commutative real algebra with zero divisor, introduced by James Cockle... more
ABSTRACT In this paper we consider the problem of differentiation of coquaternionic functions. Let us recall that coquaternions are elements of an associative non‐commutative real algebra with zero divisor, introduced by James Cockle (1849) under the name of split‐quaternions or coquaternions. Developing two type complex representations for Cockle algebra (complex and paracomplex ones) we present the problem in a non‐commutative form of the δ̄‐type holomorphy. We prove that corresponding differentiable coquaternionic functions, smooth and analytic, satisfy PDE of complex, and respectively of real variables. Applications for coquaternionic polynomials are sketched.
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ABSTRACT In the present communication we develop a complete representation of whole multidimensional manifolds, with the Cantor diagonal type of algorithm [1, 2] replaced by a new and simpler type of Cartesian‐indexing basis‐matching... more
ABSTRACT In the present communication we develop a complete representation of whole multidimensional manifolds, with the Cantor diagonal type of algorithm [1, 2] replaced by a new and simpler type of Cartesian‐indexing basis‐matching algorithm [3]. We provide graphical comparison between the results obtained via the Cantor diagonal algorithm and the Cartesian‐indexing algorithm. For this purpose, we test the algorithms on several different types of ‘benchmark’ multidimensional manifolds: Green's functions for linear PDEs, Cartesian products of 3‐dimensional manifolds, intersections of multidimensional manifolds. One new type of intersection problems which can be solved invoking the new representation is computing the intersections of multidimensional manifolds in parametric form (rather than only in implicit form, as earlier [3]). This work is based on research conducted within two consecutive Strategic Projects of the Norwegian Research Council: ‘GPGPU—Graphics Hardware as a High‐end Computational Resource’ (2004‐2007) and ‘Heterogeneous Computing’ (2008‐2010).
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ABSTRACT In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black‐Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek)... more
ABSTRACT In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black‐Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard‐Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non‐differentiable functions. Results of numerical simulations are given.
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This article deals with the indoor thermal control problem in HVAC (heating, ventilation and air conditioning) systems. Important outdoor and indoor variables in these systems are: air temperature, global and diffuse radiations, wind... more
This article deals with the indoor thermal control problem in HVAC (heating, ventilation and air conditioning) systems. Important outdoor and indoor variables in these systems are: air temperature, global and diffuse radiations, wind speed and direction, temperature, relative humidity, mean radiant temperature, and so on. The aim of this article is to obtain the thermal comfort optimisation by model based predictive control algorithms (MBPC) of an integrated building system. The control law is given by a quadratic programming problem and the obtained control action is applied to the process. The derived models and model based predictive control algorithms are investigated based on real—live data. All researches are derived in MATLAB environment. The further research will focus on synthesis of robust energy saving control algorithms.
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This paper deals with numerical solution of nonlinear evolution systems modelling reaction-diffusion-convection processes in the natural and engineering sciences. Using Rothe method, we concentrate on construction of effective solution of... more
This paper deals with numerical solution of nonlinear evolution systems modelling reaction-diffusion-convection processes in the natural and engineering sciences. Using Rothe method, we concentrate on construction of effective solution of the corresponding nonlinear stationary problems on each time level. First we discuss the solution by Newton-Bellman & Kalaba quasilinearization. Then, on this base high order and cheaper (with respect to computational cost) algorithms are proposed. Numerical results for a parabolic-hyperbolic system of two equations from the filtration are discussed.
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Massive influx of information technology in municipal administrations increases their efficiency in delivering public services but increased the risk of theft of confidential information electronically. The report proposed an approach for... more
Massive influx of information technology in municipal administrations increases their efficiency in delivering public services but increased the risk of theft of confidential information electronically. The report proposed an approach for improving information security for small municipal governments in Bulgaria through enhanced intrusion detection and prevention system.
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The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the... more
The weakly perturbed nonlinear boundary value problems (BVP) for almost linear systems of ordinary differential equations (ODE) are considered. We assume that the nonlinear part contain an additional function, which defines the perturbation as singular. Then the Poincare method is not applicable. The problem of existence, uniqueness and construction of a solution of the posed BVP with integral condition is studied.
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In the present article we study the minimizers of the action functional, corresponding to the repulsive Hartree equation in the presence of external Coulomb potential. Using a modified reflection method and Pohozaev integral identities we... more
In the present article we study the minimizers of the action functional, corresponding to the repulsive Hartree equation in the presence of external Coulomb potential. Using a modified reflection method and Pohozaev integral identities we prove that the action minimizer is radially symmetric and unique.
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Loop Shaping Design of Distributed Parameter System. [AIP Conference Proceedings 1184, 39 (2009)]. Bogdan Gilev, Petko Petkov. Keywords. Electrostatics; Poisson and Laplace equations, boundary-value problems. Analytical and numerical... more
Loop Shaping Design of Distributed Parameter System. [AIP Conference Proceedings 1184, 39 (2009)]. Bogdan Gilev, Petko Petkov. Keywords. Electrostatics; Poisson and Laplace equations, boundary-value problems. Analytical and numerical techniques (heat transfer). ...
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The paper presents method, algorithm and software in Java for solving fuzzy linear systems of equations or fuzzy linear systems of inequalities. We implement software for calculating all minimum and maximum solutions of fuzzy linear... more
The paper presents method, algorithm and software in Java for solving fuzzy linear systems of equations or fuzzy linear systems of inequalities. We implement software for calculating all minimum and maximum solutions of fuzzy linear systems when the composition is max‐ ...
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In this work we prove the existence of solitary wave solutions and give conditions for formation of singularities for the focusing time‐dependent Schrodinger‐Hartree equation in Rn.
Research Interests: Mathematics and Soliton
The hybrid system in the paper means a mechanical system which consists of two parts with different structure—a part with distributed parameters and a part with discrete parameters. The most simple type of these systems is discussed in... more
The hybrid system in the paper means a mechanical system which consists of two parts with different structure—a part with distributed parameters and a part with discrete parameters. The most simple type of these systems is discussed in [1] and [2], where the free oscillations and the forced oscillations of a rod with a linear oscillator are studied. In [3] a more complicated example—the bending oscillations of a beam connected with a simple oscillator is considered and it is shown how the approach proposed in [1] could be extended in this case. In all these papers there was no resistance (proportional to the velocity) attached on the system with distributed parameters. In the present paper just this case will be considered. It turned out that in this case the approach developed in the previous papers does not work. To obtain an analytical solution of the problem another approach is developed. More concrete the investigated hybrid system is a rod (whose longitudinal oscillations are considered) connected w...
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Given a sequence of events, how does one recognize that a change has occurred? We explore potential definitions of the concept of change in a sequence and propose that words in relativized solid codes might serve as indicators of change.
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A partial differential operator L:C∞(Rn)→C∞(Rn) is by definition transitive if one can find a function f∈C∞(Rn) for which the forward orbit OL(f) = {Lp(f)|f∞C∞(Rn)} is a dense subset of C∞Rn). Here the orbit OL(f) consists as usual of the... more
A partial differential operator L:C∞(Rn)→C∞(Rn) is by definition transitive if one can find a function f∈C∞(Rn) for which the forward orbit OL(f) = {Lp(f)|f∞C∞(Rn)} is a dense subset of C∞Rn). Here the orbit OL(f) consists as usual of the iterations of L:Lp(f) = L∘L∘L∘⋯L∘(f) (p times.) It was shown [1] that if L(u) = bu+ ∑ 0<|α|≤paα∂αu is a partial differential operator with constant coefficients then L is transitive if it does not contains a term of the type bu; in other words if b = 0. In this note we show that it is possible to omit the condition b = 0 for operators of first order as well for some operators of a Dirac type.
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Software for simulations with generalized nets is created. The program code has three parts. In the kernel the code for the structure and the transfer algorithms is implemented. The visual representation of the elements of the net is... more
Software for simulations with generalized nets is created. The program code has three parts. In the kernel the code for the structure and the transfer algorithms is implemented. The visual representation of the elements of the net is realized in the classes of the second part. The third part of the code consists of all the forms of the application.
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Let X be a normal space with finite positive dimension. In this note we investigate some reciprocity between connectedness and positive dimensionality. Some consequences are discussed.
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In this paper, our main task is to provide the mathematical characterization for the non-negativity of a given homogeneous real Weierstrass canonical pencil. Following the work of Uhlig [14] and Pantelous et al. [10], we determine... more
In this paper, our main task is to provide the mathematical characterization for the non-negativity of a given homogeneous real Weierstrass canonical pencil. Following the work of Uhlig [14] and Pantelous et al. [10], we determine analytically the family into a relevant set of indeterminates S, S. This new approach might be easily transferred into a standard computational routine by
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In this paper, is presented one software development and implementation of an algebraic method for XML data processing, which accelerates XML parsing process. Therefore, the proposed in this article nontraditional approach for fast XML... more
In this paper, is presented one software development and implementation of an algebraic method for XML data processing, which accelerates XML parsing process. Therefore, the proposed in this article nontraditional approach for fast XML navigation with algebraic tools contributes to advanced efforts in the making of an easier user‐friendly API for XML transformations. Here the proposed software for XML documents processing (parser) is easy to use and can manage files with strictly defined data structure. The purpose of the presented algorithm is to offer a new approach for search and restructuring hierarchical XML data. This approach permits fast XML documents processing, using algebraic model developed in details in previous works of the same authors. So proposed parsing mechanism is easy accessible to the web consumer who is able to control XML file processing, to search different elements (tags) in it, to delete and to add a new XML content as well. The presented various tests show higher rapidity and l...
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In this paper, we consider a mixed market in which a state-owned welfare-maximizing public (domestic) firm competes against a profit-maximizing private (foreign) firm. We suppose that the domestic firm is less efficient than the foreign... more
In this paper, we consider a mixed market in which a state-owned welfare-maximizing public (domestic) firm competes against a profit-maximizing private (foreign) firm. We suppose that the domestic firm is less efficient than the foreign firm. However, the domestic firm can lower its marginal costs by conducting cost-reducing R&amp;D investment. We examine the impacts of entry of a foreign firm
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ABSTRACT In this paper we consider the mathematical aspects of the Bulgarian proportional electoral systems used since 1990. They are variants of a proportional system at a nationwide level with 4-percent barrier such that the party seats... more
ABSTRACT In this paper we consider the mathematical aspects of the Bulgarian proportional electoral systems used since 1990. They are variants of a proportional system at a nationwide level with 4-percent barrier such that the party seats are personified from a number of regional party lists. This system is unique in the world electoral practice and may lead to severe inter-party distortions. These distortions although formally correct are hardly accepted by the public and by local party activists in particular. Methods to overcome these difficulties as well as the status-quo of the problem are considered. Finally new paradoxes are studied which are generalizations of the well known paradoxes for the plain proportional systems.