Search

The authors consider the optimization problem related to the integral representation of the deviation of positive linear operators on the classes of (ψ, β )-differentiable functions in the integral metric. The Poisson integral is taken as a positive linear operator, being the solution of the Laplace equation in polar coordinates with the corresponding initial conditions given on the boundary of the unit disc. The Poisson integral refers to operators with a delta-like kernel; therefore, it is the best apparatus for solving many problems of applied mathematics, namely: optimization methods and calculus of variations, mathematical control theory, theory of dynamical systems and game problems of dynamics, applied nonlinear analysis and moving objects search. The classes of (ψ, β )-differentiable functions are generalizations of the well-known Sobolev, Weyl–Nagy, etc. classes in optimization problems, on which the asymptotic properties of solutions of Laplace equations in the unit disc are analyzed. The problem solved in the paper will make it possible to generate high-quality mathematical models of many natural and social processes. [ABSTRACT FROM AUTHOR]

Container shipment has promoted the development of intermodal connections with the use of different vehicles. The activity of freight forwarding companies (FFC) is aimed at improving container transportation of export and import cargoes to the clients, which is possible due to improving motor transportation of goods in containers. The major limitation of FFC activity is their specializing in one direction only - export or import. In import, container delivery expenses of the client depend upon the time of container shipping from the port. The average penalty makes up $10 to $25 per TEU daily. The paper suggests an export and import scheme of container deliveries by linear operators to FFC clients. The scheme allows shortening the term of container equipment exploitation and reducing linear operators' demurrage and detention expenses due to the suggested algorithm of FFC search of export freight for their returning auto transport. The economic indicator of improving the export and import scheme of container shipment was received while arranging cargo delivery from Kyiv at a price of $ 650 to $ 750 per vehicle. Every day Odessa port ships 10 to 20 containers with import goods, and 5 to 10 of them can be shipped with export goods on their way back so that the average profit beyond the driver's wages could make up approximately $ 1500 to $ 2500 per day. [ABSTRACT FROM AUTHOR]

The extended stochastic integral with respect to a Lévy process and the corresponding Hida stochastic derivative have many applications in the stochastic analysis, in particular, in the theory of stochastic differential and integral equations. One of main lacks of these operators, if one considers them as linear operators on the space of square integrable random variables (L²), consists in their unboundedness. Moreover, the domain of the extended stochastic integral (and of the conjugated to this integral operator -- the stochastic derivative) depends on an interval of integration. As a result, there are problems with some applications of the above-mentioned operators. Therefore an important problem is a modification of definitions of the extended stochastic integral and the Hida stochastic derivative that gives us the possibility to define these operators as linear bounded (i.e., continuous) ones. In this paper, using the theory of Hilbert equipments, we introduce and study the extended stochastic integral with respect to a Lévy process and the Hida stochastic derivative as linear continuous operators on a suitable rigging of (L²). This gives a possibility to extend an area of applications of these operators. [ABSTRACT FROM AUTHOR]

In advance digital systems, implemented using various VLSI circuits, an important issue remains to reduce the area of the circuit, which is occupied by the control device, and, consequently, reduce the delay time and the amount of power consumption. As a rule, reducing the area of the circuit of the control device allows improving its other characteristics. Methods for solving this problem to some extent depend on the features of the implemented control algorithm and element basis. The article proposes a method for reducing the number of LUT (Look-Up-Table) elements in the scheme of a composition microprogram control unit (CMCU), based on converting the addresses of the outputs of linear operator circuits (LOC) into output codes. This transformation reduces the number of inputs of the addressing scheme of microinstructions, which is especially important when implementing the circuit of the control device on the FPGA basis due to the small number of inputs of elements of the tabular type LUT. The outputs of the LOC are encoded as elements of some classes of partitioning the set of outputs. This approach allows you to move from a multi-level microinstruction addressing scheme to a two-level one. The control memory and the address conversion block are implemented on embedded memory blocks. The proposed method is an adaptation of the method of double coding of states of Miles automata to the features of CMCU. The method is advisable to use if the microinstruction addressing unit is represented by a multi-level scheme. This is possible if the number of arguments in the memory excitation functions exceeds the number of LUT inputs. If the bit width of the microinstruction address exceeds the number of LUT inputs, then the address converter block circuit is also multilevel. Analysis of standard automata from the library and the Virtex 7 basis showed that this method can be applied to 68% of the library elements. The article considers an example of the synthesis of a CMCU circuit using the proposed method. [ABSTRACT FROM AUTHOR]