An Investigation Into The Mathematical and Physical Origins of The Fine-Structure Constant

The fine-structure constant, α, unites fundamental aspects of electromagnetism, quantum physics, and relativity. As such, it is one of the most important constants in nature. However, why it has the value of approximately 1/137 has been a mystery since it was first identified more than 100 years ago. To date, it is an ad hoc feature of the Standard Model, as it does not appear to be derivable within that body of work — being determined solely by experimentation. This report presents a mathematical formula for α that results in an exact match with the currently accepted value of the constant. The formula requires that a simple corrective term be applied to the value of one of the factors in the suggested equation. Notably, this corrective term, at approximately 0.023, is similar in value to the electron anomalous magnetic moment value, at approximately 0.0023, which is the corrective term that needs to be applied to the g-factor in the equation for the electron spin magnetic moment. In addition, it is shown that the corrective term for the proposed equation for α can be derived from the anomalous magnetic moment values of the electron, muon, and tau particle — values that have been well established through theory and/or experimentation. This supports the notion that the corrective term for the α formula is also a real and natural quantity. The quantum mechanical origins of the lepton anomalous magnetic moment values suggest that there might be a quantum mechanical origin to the corrective term for α as well. This possibility, as well as a broader physical interpretation of the value of α, is explored.

On sub-Riemannian geodesic curvature in dimension three

We introduce a notion of geodesic curvature k ζ k_{\zeta} for a smooth horizontal curve 𝜁 in a three-dimensional contact sub-Riemannian manifold, measuring how much a horizontal curve is far from being a geodesic. We show that the geodesic curvature appears as the first corrective term in the Taylor expansion of the sub-Riemannian distance between two points on a unit speed horizontal curve d SR 2 ⁢ ( ζ ⁢ ( t ) , ζ ⁢ ( t + ε ) ) = ε 2 - k ζ 2 ⁢ ( t ) 720 ⁢ ε 6 + o ⁢ ( ε 6 ) . d_{\mathrm{SR}}^{2}(\zeta(t),\zeta(t+\varepsilon))=\varepsilon^{2}-\frac{k_{\zeta}^{2}(t)}{720}\varepsilon^{6}+o(\varepsilon^{6}). The sub-Riemannian distance is not smooth on the diagonal; hence the result contains the existence of such an asymptotics. This can be seen as a higher-order differentiability property of the sub-Riemannian distance along smooth horizontal curves. It generalizes the previously known results on the Heisenberg group.

The assessment of students’ achievements from the subject Basics of Accounting in the study program Accounting at FEM SUA in Nitra

The Faculty of Economics and Management is providing quality economic and managerial education within the accredited study programs. We analyzed the obtained students´ results of study program Accounting in the subject of Basics of Accounting. The analysis subject was the students’ success in the before mentioned subject and changes in the final assessment. We assessed reached results of 318 students for 4 academic years, this subject was obligatory for these students. The final assessment was analyzed as a whole, as well as the manner these students achieved. We were interested whether the student met the conditions in an ordinary term. According to our opinion the analysis considered the necessary factor, the type of graduated secondary school. The average grade in individual terms was calculated by the arithmetic mean from all grades “A - FX”, the total average grade was similarly calculated as the arithmetic mean of the final assessment recorded in the reports. In the analysis, the structure of students was also described through the mode, which is defined as the most common value of a statistical feature. We found out that the graduates of business academy prevail in the study program Accounting. We assumed that the graduates of business academies reach the best results in comparison with other students. However, the aggregated results of assessments did not confirm the existence of such an advantage. The worst average assessment is characteristic for the first corrective term, on the contrary, the best average grade is given in the second corrective term.

The assessment of students’ achievements from the subject Basics of Accounting in the study program Accounting at FEM SUA in Nitra

The Faculty of Economics and Management is providing quality economic and managerial education within the accredited study programs. We analyzed the obtained students´ results of study program Accounting in the subject of Basics of Accounting. The analysis subject was the students’ success in the before mentioned subject and changes in the final assessment. We assessed reached results of 318 students for 4 academic years, this subject was obligatory for these students. The final assessment was analyzed as a whole, as well as the manner these students achieved. We were interested whether the student met the conditions in an ordinary term. According to our opinion the analysis considered the necessary factor, the type of graduated secondary school. The average grade in individual terms was calculated by the arithmetic mean from all grades “A - FX”, the total average grade was similarly calculated as the arithmetic mean of the final assessment recorded in the reports. In the analysis, the structure of students was also described through the mode, which is defined as the most common value of a statistical feature. We found out that the graduates of business academy prevail in the study program Accounting. We assumed that the graduates of business academies reach the best results in comparison with other students. However, the aggregated results of assessments did not confirm the existence of such an advantage. The worst average assessment is characteristic for the first corrective term, on the contrary, the best average grade is given in the second corrective term.

A Novel Uniform-Flux Solution Based on the Green's Function Method for Modeling the Pressure-Transient Behavior of a Restricted-Entry Well in Anisotropic Gas Reservoirs

Summary Applied gas-well-testing data analysis considers that the nonlinear diffusivity equation becomes linearized by the pseudopressure function and by assuming the gas viscosity-compressibility product constant throughout the test history. This approach is justified for small pressure drawdowns only. This condition is seldom met in low-permeability gas reservoirs, whether the wellbore is fully perforated or not. This paper considers a restricted-entry vertical well in a homogeneous anisotropic infinite reservoir producing at constant-gas-flow rate, which, surprisingly, has not been the object of much research, either by numerical simulation or by analytical means. In this work, the Green's function (GF) method is used to rewrite the usual partial-differential formulation as a multidimensional integro-differential equation for the pseudopressure function that rigorously accounts the gas viscosity-compressibility product change. From there, an approximate explicit solution for a uniform-flux boundary condition is derived, which shows that the pseudopressure solution is given by the correspondent restricted-entry well slightly compressible (i.e., liquid) solution, plus a corrective term that handles the gas viscosity-compressibility product variation with pressure. Comparison with a commercial numerical simulator shows that the uniform-flux approximate solution is very accurate. Results are presented for a few perforation lengths and positions, with and without vertical anisotropy. It is shown that during the perforation-radial (early-time) and final-radial (late-time) flow regimes, the corrective term becomes constant. Their magnitudes, however, are quite different; during the perforation-radial flow regime, the corrective term is quite large compared with the one seen at long times. Thus, the pseudopressure derivative with respect to the natural log of time exhibits the same restricted-entry behavior observed in oil reservoirs. By averaging the uniform-flux solution over the open interval, an infinite-conductivity approximate solution for the wellbore pseudopressure is presented, which shows a very-good agreement with results obtained from a finite-difference simulator.

GRAVITATIONAL LENSING IN AN ENERGY-DEPENDENT SPACETIME METRIC

In this article, we explore the consequences in the calculation of deflection angle of photons, caused by a gravitational source of mass M, for the case of an energy dependent metric. We analyze the corrections to the standard Schwarzschild case for the weak and strong limits. In both cases, the corrections to the deflection angle are of the order ϵ/E Pl , where E Pl is the Planck energy and ϵ, the energy of the photon at spatial infinite. The corrections to the angular separation image is also of order ϵ/E Pl , for the weak limit, while in the strong case there is a corrective term with the shape ϵ/E Pl n e2nπ for the relativistic image of order n. The amplification of the image is also discussed. Even if corrections are tiny, in both limits, we discuss the qualitative effects for different types of Lorentz invariance deformations.

Exponential Observer Design for State Estimation in a Class of Anaerobic Sulfate Reducing Bioreactor

The objective of this work is to infer the biomass and product concentrations in a class of bioreactor, under the assumption of substrate measurements. This is done by employing a mathematical model of a continuous stirred bioreactor where the corresponding kinetic term is experimentally corroborated. The observer's structure contains, as usual, a predictive term given for nominal model plus a corrective term, which is proposed as adaptive one, where the corresponding observer's gain obey a specific dynamic equation, which provides an exponential convergence characteristic, under the Lipschitz assumption of the system. Numerical simulations show an adequate performance of the proposed observer and a comparison with a finite-time observer is done.