On superluminal fermions within the second derivative equation

We postulate the second-order derivative equation with four parameters for spin-1/2 fermions possessing two mass states. For some choice of parameters fermions propagate with the superluminal speed. Thus, the novel tachyonic equation is suggested. The relativistic 20-component first-order wave equation is formulated and projection operators extracting states with definite energy and spin projections are obtained. The Lagrangian formulation of the first-order equation is presented and the electric current and energy-momentum tensor are found. The minimal and non-minimal electromagnetic interactions of fermions are considered and Schr\"{o}dinger's form of the equation and the quantum-mechanical Hamiltonian are obtained. The canonical quantization of the field in the first-order formalism is performed and we find the vacuum expectation of chronological pairing of operators.Comment: 21 pages, minor corrections, journal version, accepted in IJMP

Note on Dirac--K\"ahler massless fields

We obtain the canonical and symmetrical Belinfante energy-momentum tensors of Dirac--K\"{a}hler's fields. It is shown that the traces of the energy-momentum tensors are not equal to zero. We find the canonical and Belinfante dilatation currents which are not conserved, but a new conserved dilatation current is obtained. It is pointed out that the conformal symmetry is broken. The canonical quantization is performed and the propagator of the massless fields in the first-order formalism is found.Comment: 16 pages, minor corrections in the text, published versio

Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance

Kalb-Ramond equations for massive and massless particles are considered in the framework of the Petiau-Duffin-Kemmer formalism. We obtain $10\times10$ matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy-momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.Comment: 9 pages, no figure

Maxwell - Chern - Simons topologically massive gauge fields in the first-order formalism

We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field. It was demonstrated that the gauge field possesses the `scale dimensionality' d=1/2. Maxwell - Chern - Simons topologically massive gauge field theory in 2+1 dimensions is formulated in the first-order formalism. It is shown that 6x6-matrices of the relativistic wave equation obey the Duffin - Kemmer - Petiau algebra. The Hermitianizing matrix of the relativistic wave equation is given. The projection operators extracting solutions of field equations for states with definite energy-momentum and spin are obtained. The 5x5-matrix Schrodinger form of the equation is derived after the exclusion of non-dynamical components, and the quantum-mechanical Hamiltonian is obtained. Projection operators extracting physical states in the Schrodinger picture are found.Comment: 18 pages, correction in Ref. [5

The multiplicity and the spectra of secondaries correlated with the leading particle energy

The spectra of leading particles of different nature in pp-collisions at E sub 0 = 33 GeV are obtained. The multiplicities and the spectra of secondaries, mesons, gamma-quanta, lambda and lambda-hyperons and protons for different leading particle energy ranges are determined

Comparative analysis of order allocation methods and intelligent systems for effective download of production capacities of manufacturing enterprise

The article compares the planning systems of the enterprise, determines their opportunities to use simulation for the process of distribution of production orders. A comparative review of the methods used in production planning systems and the multi-agent approach in solving the problem of the allocation of production orders is carried out. The possibility of approaches in cases when it is impossible to perform production tasks within the established time frame is considered, as well as to effectively load the available capacities of the units. In case it is not possible to produce the necessary quantity to distribute the part to another, similar to the type of equipment used, but different from it by the quantity and production capacity of the unit. Transmission must be carried out under the condition of sufficient capacity in the subdivision. The results of theoretical and experimental studies are presented. In the process of work, we used the BPsim. MAS dynamic modeling system. An automated system with the possibility of using simulation for the allocation of production orders is considered. © 2019 IOP Publishing Ltd. All rights reserved.The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006

Method for loading cargo trucks using two-dimensional packing algorithms

The paper describes the method for optimization of loading cargo trucks using two-dimensional packing algorithms. The point of this method is to reduce loading cargo problem to two-dimensional packing problem. This problem can be solved by using of various algorithms. There is analysis of several algorithms that are most often used in practical calculations of objects distribution in 2D space in this paper. The object of this study is transport of the metal processing company and its products (cargo). PHP programming language, MySQL database, and Apache web server are used to create client application. The interface developed using HTML5, CSS and javascript. © 2019 IOP Publishing Ltd. All rights reserved.The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006

On First-Order Generalized Maxwell Equations

The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the canonical and symmetrical Belinfante energy-momentum tensors. It is shown that the traces of the energy-momentum tensors are not equal to zero and the dilatation symmetry is broken in the theory considered. The matrix Hamiltonian form of equations is obtained after the exclusion of the nondynamical components. The canonical quantization is performed and the propagator of the fields is found in the first-order formalism.Comment: 14 pages, corrections in Eq.(38),(39),(59

Square vortex solitons with a large angular momentum

We show the existence of square shaped optical vortices with a large value of the angular momentum hosted in finite size laser beams which propagate in nonlinear media with a cubic-quintic nonlinearity. The light profiles take the form of rings with sharp boundaries and variable sizes depending on the power carried. Our stability analysis shows that these light distributions remain stable when propagate, probably for unlimited values of the angular momentum, provided the hosting beam is wide enough. This happens if the peak amplitude approaches a critical value which only depends on the nonlinear refractive index of the material. A variational approach allows us to calculate the main parameters involved. Our results add extra support to the concept of surface tension of light beams that can be considered as a trace of the existence of a liquid of light.Comment: 6 pages, 6 figures, submitted to Phys. Rev.