Volume 78, Issue 6

Core parts of the Standard Model are derived from B. Heim’s quantum field theory, whose poly-metric describes spacetime and matter in a unified formalism. Its non-linear eigenvalue equation transforms into the Einstein field equation in the macroscopic limit. The 6-dimensional Heim space can be determined as locally isomorphic to a SU (2) ⊗ SU (2) ⊗ U (1) ⊗ U (1) symmetry and thus to the SU (3), which allows to connect to the local gauge symmetries and boson fields of the Standard Model. The Fermion and Higgs field and their coupling are deduced from Heim’s basic equations, providing new insight into possible correlations of these fields. Furthermore, the derivation yields an additional imaginary coupling term which seems to account for quantum mechanical state reduction in the non-relativistic limit. The recently performed calculation of the mass spectrum of elementary particles in a new approach based on Heim’s theory (with average error to the data < 1 % ${< } 1\%$ ) appears as even more relevant, having now shown that the theory can connect to the achievements of the Standard Model.

A discrete predator–prey model with square root functional response describing prey herd behavior and nonlinear predator harvesting has been considered in the present work. Three equilibria of the system have been found and observed that two equilibrium points always exist and are feasible, but the interior equilibrium point is feasible under a parametric condition. The local stability of the three equilibria has been analyzed. The interior equilibrium point is locally asymptotically stable under a parametric condition. It is examined that a flip and Neimark–Sacker bifurcations have occurred in the system at the axial equilibrium point. The flip and Neimark–Sacker bifurcations have been analyzed by the center manifold theorem and bifurcation theory, considering the harvesting coefficient as the bifurcation parameter. The proposed discrete model with a nonlinear Michaelis–Menten type harvesting effect on the predator population exhibits rich dynamics; for instance, bifurcations, chaos, and more complex dynamical behaviors. The discrete-time model also produced few numerical simulation results that are more accurate than the continuous model. The proposed discrete model will be performed better than the continuous model in populations with non-overlapping generations or smaller densities. The harvesting coefficient’s optimal value has finally been identified, and an optimal harvesting policy has been introduced. To verify the results, further numerical simulations have been performed.

In this letter, we derived a new generalized Boussinesq-type equation on the basis of the generalized bilinear derivative with the prime number p = 3. By searching for a general form of rational solution to the new generalized Boussinesq-type equation, we found that this new model only contains a form of solution of the degree of F = F ( x , t ) with respect to x must be less than or equal to 1. Immediately after, a conjecture related to this result was put forward. Besides, we analyzed this obtained rational solution evolutionary processes by 3D-and 2D-graphs.

Lie group theory is applied to the curve equation which maintains constant normal accelerations for a vehicle with constant deceleration. The curve equation is a third order nonlinear ordinary differential equation for which the symmetries are calculated. It is shown that the equation possesses four-parameter Lie group of transformations including scaling, rotation and translational symmetries. In the case of constant velocity, the algebra increases to a six-parameter Lie group of transformations. Using the symmetries of the differential equation, the group invariant solutions are determined first. The conditions for group invariant solutions to exist are given. By employment of the symmetries, a solution is obtained by reduction of order also. It is found that the nontrivial solutions are of implicit complex forms.

The evidence in favor of a Universe expanding at a constant rate, in contrast to the various episodes of deceleration and acceleration expected in the standard model, has been accumulating for over a decade now. In recent years, this inference has been strengthened by a study of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric in relation to Einstein’s principle of equivalence. This earlier work concluded that the choice of lapse function g tt = 1 characterizing the FLRW solution to Einstein’s equations is inconsistent with any kind of accelerated cosmic expansion. In this paper, we demonstrate and confirm this important result by directly testing the self-consistency of four well-known FLRW cosmologies. These include the Milne universe, de Sitter space, the Lanczos universe, and the R h = ct model. We show that only the constantly expanding models (Milne and R h = ct ) are consistent with the principle of equivalence, while de Sitter and Lanczos fail the test. We discuss some of the many consequences of this conclusion.

The relevance of the research results presented in this article lies in the general concept of elasticity theory, which integrates the bases of theoretical-empirical physics, practical mathematics and the natural implementation of modelling results in the fields of industrial (to a large extent in the design and manufacture of aircraft and naval aircraft shells and fuselages), construction (more so in the design and formation of multi-layer building structures), electronics and other areas of the science and industry complex. The aim of the study is to form a mathematical model of thin plate vibration based on a system of differential equations for the computational case of point bonding. The method of scientific search (Multilocal Literature Review) is used to achieve the set goal, which made it possible to establish the actual scientific-theoretical basis of the investigated problem, the method of mathematical modelling allowing to systematize the systems of differential equations developed earlier and formed in the framework of the present study, both for the general concept of the theory of elasticity of thin plates and for a selected calculation situation with partial constraints in the form of point bond imposing. As a result of the investigations conducted in the framework of this study, a mathematical model of the oscillations of thin plates bounded by special point-coupling conditions has been obtained, consisting of a system of differential equations obtained by successive iterations of mathematical transformations for the generated local boundary conditions. The mathematical model obtained is of practical scientific interest. The developed model environment forms a complete mathematical theory of elasticity for the formulated problem of the oscillatory process of thin plates with bounding point couplings. This problem has not received a satisfactory mathematical apparatus because of the complexity and cumbersomeness of analytical methods to describe the investigated elastic object.

In this work, composite nanostructures (CNs) of SnO 2 –ZnO–g–C 3 N 4 have been prepared by a soft chemical method and investigated for their potential application in photocatalytic remediation of organics in water and antibacterial agents. Structural study revealed the presence of three phases related to hexagonal wurtzite phase of ZnO, tetragonal phase of SnO 2 and monoclinic phase of g–C 3 N 4 having nanocrystalline nature which confirms the formation of CNs. Formation of nanoscale morphology along with elemental composition of the CNs have been validated through scanning electron microscopy (SEM) coupled with energy dispersive X-ray (EDX) spectroscopy. The presence of only A 1g mode of SnO 2 in Raman spectrum of ternary CNs suggested that SnO 2 nanoparticles have been coated on the surfaces of ZnO and g–C 3 N 4 which is also evident from SEM results. SnO 2 –ZnO–g–C 3 N 4 CNs have shown much higher photocatalytic degradation efficiency and produced 7 mm greater zone of inhibition (ZOI) against Gram-positive S. Aureus bacteria as compared to pure ZnO which is quite significant result when compared to previously reported results for SnO 2 –ZnO CNs. These synthesized CNs may have potential uses in healthcare technology and treatment of organics in water.

In this special work, two types of material, which are undoped and Mn doped TiO 2 thin films, have been produced by spin coating technique, and then their structural, morphological and optical properties have been measured at different Mn doping rates. Four different doping ratios, undoped, 1, 3 and 5% Mn doped TiO 2 have been both experimentally and theoretically investigated and some significant enhancements have been reported. The results of X-ray diffraction (XRD) such as dislocation density, strain, and crystallite size have indicated that undoped, 1, 3 and 5% Mn doped TiO 2 thin films had the phase of anatase at 450 °C. It has been observed that the peak intensity of 3% Mn doped TiO 2 films has decreased compared to undoped and 1% Mn doped TiO 2 while the peak intensity has increased for 5% Mn doped TiO 2 . The refractive indices and dielectric coefficients of the undoped and Mn doped TiO 2 thin films have also been calculated. The undoped and Mn doped TiO 2 /p-Si heterojunction diodes has exhibited photosensitive behaviour in the illuminated environment. 1% Mn doped TiO 2 /p-Si heterojunction diode indicated the highest photocurrent. The electrical parameters of all diodes have been calculated and compared to the conventional J – V and Norde methods. Additionally, 1% Mn doped TiO 2 /p-Si heterojunction diode has been modelled by using the SCAPS-1D program, and J ph values have also been calculated based on the shallow donor density ( N D ). The experimental and theoretical J ph values of this diode were found to be compatible with each other.