Starting with Planck scale it is developed the Relativistic Radial Density Theory (<i>RRDT</i>). In this theory, the Planck and gravitational parameters can be described as the functions of the radial mass (energy) density value. This density is maximal at the minimal radius and minimal at the maximal radius. This conclusion is based on the fact that the ratio of Planck mass and Planck length (radius) is constant. These radiuses can be described as the function of the energy conservation constant <i>κ</i>. Using <i>RRD</i><i>T</i>, it is possible to develop the connections between Planck’s and gravitational parameters as function of the maximal and minimal radial mass (energy) density values. In that sense, the gravitational length, time, energy and temperature can be presented as the function of the Planck length, time, energy and temperature, respectively. This opens possibility to merge of Quantum Field Theory (<i>QFT</i>) and the General Theory of Relativity (<i>GTR</i>) at the quantum scale in gravitational field. The existence of the maximal radial mass (energy) density value at the minimal radius in gravitational field means that no singularity in that field. Further, the existence of the minimal radial mass (energy) density value at the maximal radius in gravitational field means that no infinity in that field. It follows the postulation: the most minimal radius in a gravitational field belongs to the minimal mass (energy). Since the Planck mass is not the minimal mass in space-time, the Planck length/radius is not the minimal length/radius in the space-time. If the calculated minimal (or maximal) radius is the bigger than the related official radius it means that there exists a dark matter in this object. In that sense, the black holes are presenting the state of the matter at the minimal radius where we have the maximal radial mass (energy) density value. Further, the maximal possible radius of the matter is presenting the state with the minimal radial mass (energy) density value. Thus, the maximal and minimal radial mass (energy) density values are constants and conserved items. Now the question is: do motion of the Universe follows the <i>RRD</i><i>T</i>?

The c-equivalence principle, commonly accepted as true by most physicists, is the unstated assumption that equals the kinematic speed of light. Should someone prove the principle false, it would render the composition of two Lorentz transformations meaningless. The second hypothesis of the Special Theory of Relativity in its strong form would also be invalidated. This paper examined some of the consequences for physics, should this principle be proven false and outline some experiments to determine light speed, which could falsify the principle and provide evidence for the ether.

A three-level laser with an open cavity and a two-mode vacuum reservoir is explored for its quantum properties. Our investigation begins with a normalized order of the noise operators associated with the vacuum reservoir. The master equation and linear operators' equations of motion are used to determine the equations of evolution of the atomic operators' expectation values. The equation of motion answers are then used to calculate the mean photon number, photon number variance, and quadrature variance for single–mode cavity light and two–mode cavity light. As a result, for γ=0, the quadrature variance of light mode <b>a</b> is greater than the mean photon number for two-mode cavity light. As a result, for the two-mode cavity light, the maximum quadrature squeezing is 43.42 percent.

Skew-symmetric differential forms possess properties that enable one to carry out a qualitative investigation of the equations of mathematical physics and the foundations of field theories. In the paper we call attention to a unique role in field theory of closed exterior skew-symmetric differential forms, which correspond to conservation laws for physical fields (to conservative quantities). At the same time, it was shown that such closed exterior forms can be derived from skew-symmetric differential forms, which follow from the mathematical physics equations describing material media such as thermodynamic, gas-dynamic, cosmic media. This points a connection the field theory equations with the mathematical physics equations. Such connection discloses the properties and specific features of field theory.

In this paper we present a new classes of solutions for the Einstein-Maxwell system of field equations in a spherically symmetric spacetime under the influence of an electric field considering the MIT bag model equation of state with a particular form the metric potential that depends on an adjustable parameter. The obtained solutions can be written in terms of elementary functions, namely polynomials and algebraic functions. The obtained models satisfy all physical properties expected in a realistic star. The results of this research can be useful in the development and description of new models of compact structures.

With respect to the exciton moving in the two-dimensional quantum well, the paper presents a scheme which can rigorously calculate out the binding energy of the exciton in the two-dimensional semiconductor quantum well by simply using the relation <math><semantics> <mrow> <mrow><mo>|</mo> <mrow> <msub> <mi>z</mi> <mi>e</mi> </msub> <mo>&#x2212;</mo><msub> <mi>z</mi> <mi>h</mi> </msub> </mrow> <mo>|</mo></mrow><mo>=</mo><mi>&#x03C1;</mi><mi>tan</mi><mi>&#x03B1;</mi></mrow></semantics></math>, which is much simpler than the complex calculation of Ref.[1-2]. Concerning the calculation result eq.(13), the paper discusses the results for two significant cases of <math><semantics> <mrow> <mrow><mo>|</mo> <mrow> <msub> <mi>z</mi> <mi>e</mi> </msub> <mo>&#x2212;</mo><msub> <mi>z</mi> <mi>h</mi> </msub> </mrow> <mo>|</mo></mrow></mrow></semantics></math><<<math><semantics> <mi>&#x03C1;</mi></semantics></math>and <math><semantics> <mrow> <mrow><mo>|</mo> <mrow> <msub> <mi>z</mi> <mi>e</mi> </msub> <mo>&#x2212;</mo><msub> <mi>z</mi> <mi>h</mi> </msub> </mrow> <mo>|</mo></mrow><mo>&#x2192;</mo><mi>&#x221E;</mi></mrow></semantics></math>.

The aim of this note is to remind and explain that authors have an obligation to make sure their manuscript is based on original research, which means it is never before published. Intentionally submitting or re-submitting a manuscript for more than publication is considered a violation of publishing ethics.

The convection-diffusion equation is of primary importance in understanding transport phenom-ena within a physical system. However, the currently available methods for solving unsteady convection-diffusion problems are generally not able to offer excellent accuracy in both time and space variables. A procedure was given in detail to solve the one-dimensional unsteady convec-tion-diffusion equation through a combination of Runge-Kutta methods and compact difference schemes. The combination method has fourth-order accuracy in both time and space variables. Numerical experiments were conducted and the results were compared with those obtained by the Crank-Nicolson method in order to check the accuracy of the combination method. The anal-ysis results indicated that the combination method is numerically stable at low wave numbers and small CFL numbers. The combination method has higher accuracy than the Crank-Nicolson method.