Automatic processing system for shadowgraph and interference patterns

The design and operation of an automatic system for the processing of shadowgraph and interference images are described. The system includes a two-coordinate processing table with an optical system for the projection of transparent images onto the photodetector, an image filter in the photodetector field, and a device for controlling the movement of the table and transmitting information to the minicomputer

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.Comment: 11 pages, LaTe

Current Concept of Revascularization in STEMI Patients with Multivessel Coronary Artery Disease: Evidence Base and Our Own Randomized Trial Results

The use of personalized approach for the optimal revascularization strategy in patients with ST‐segment elevation myocardial infarction (STEMI) and multivessel coronary artery disease (MVCAD) is based on complete revascularization by using latest generation drug‐eluting stents, with the choice between multivessel primary stenting and staged stenting strategy. The chapter includes theoretical rationale, original single‐center study, an original calculator for choosing optimal revascularization strategy, and a clinical case example

Weyl Quantization of Fractional Derivatives

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for analytic functions. To define a quantum analog of the fractional Liouville derivative, which is defined on the real axis, we can use the representation of the Weyl quantization by the Fourier transformation.Comment: 9 pages, LaTe

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.Comment: latex2e, 11pt, 40 pages with table of conten

The Role of Plastic Flow in Processes of High-speed Sintering of Ceramic Materials under Pressure

A model to describe the kinetics of the compaction of conductive nitride ceramics using electropulse technologies is developed. The relationship between density and pressure is established on the basis of three components of the geometric, plastic and stressed state, which is affects the contact area between the particles. The model takes into account the change in the relative area of the interpartial contacts under the action oftwo mechanisms of mass transfer-diffusion and plastic flow. It is shown that a decrease in the particle size of the powder leads to an in-crease in the diffusion contribution and a decrease in the plastic flow, at all other conditions being equal. And for the case of nano-sized particles, diffusion mass transfer is predominant.Increasing in the heating rate leads to a decrease in the contribution of dif-fusion mass transfer at equal temperatures, as well as to an increase in the temperature of the beginning of shrinkage.The processes of plasma-plasma sintering, high-voltage electro-pulsed consolidation and hot pressing control the same mechanisms, plastic flow and diffusion mass transfer, which do not require, in the first approximation, the influence of the electric current on the properties of materials. Keywords: spark-plasma sintering, high-voltage electrodischarge consolidation, sintering kinetic

Fractional Liouville and BBGKI Equations

We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case.The interpretation of fractional analog of phase space as a space with fractal dimension and as a space with fractional measure are discussed. The fractional analogs of the Hamiltonian systems are considered as a special class of non-Hamiltonian systems. The fractional generalization of the reduced distribution functions are suggested. The fractional analogs of the BBGKI equations are derived from the fractional Liouville equation.Comment: 20 page

Nonholonomic Constraints with Fractional Derivatives

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.Comment: 18 page