Physical Mathematics

In this paper, we consider the elementary particles in the light of Astro-Theology. We see that these two branches of physics can be united using well known chemistry equations. A Pressure and a Temperature equation are derived, as well as spin and charge equation

In this paper, we take the first steps of simplifying particles into a linear function that organizes particles based on their particle number, similar to how atoms are arranged by atomic number. This repeats the method that was used to organize atomic elements and create the Periodic Table of Elements in the 1800s. The solution to linearize particles into a predictable function is not as simple as atomic elements, but it does exist. We will introduce an equation that fits known particles into a linear function and enables the prediction of future particles based on missing energy levels. It also predicts an exact mass of the neutrino. To accomplish this, particles are first organized by particle numbers, similar to atomic numbers in the Periodic Table of Elements and then charted against their known Particle Data Group energy levels. The results show similarities between particles and atomic elements – in both total numbers in formation and also in numbers where both are known to be more stable.

We consider a stabilization problem for a coupled wave equations on an exterior of bounded domain with interior stabilization. Under a geometrical control condition (BLR condition ), for any initial data in the energy space, we show a result of exponential stability in odd dimensional case and polynomial stability in the case of even dimension.

This paper addresses several topics in mathematics and in particular it aims to answer the following questions: Why is it that the π value cannot be π=3.1415. Why should this value be different? Where can one notice the wrong calculations and its effects? Based on the results obtained, we conclude that the value 3.1415 is a value that does not respond to reality and does not give correct results. The reasons for this conclusion are mentioned several times and appropriate arguments are presented. For the sake of truth this value should be different, and at the same time should no longer continue to be used. Contradictions in the 3.1415 value first began in the Geomechanical laboratory during calculations where this value always provided wrong results. In direct analysis where cutting cohesion and tangent are required, the surface of the sample which enters the apparatus for analysis is of the size d=71 mm r=35.5 mm. When this area is estimated according the principles of Archimedes a smaller surface is obtained, the result is 39.57 cm2 and when this area is calculated according to the 3.24 value then we obtain an area of 40.83 cm2 which is represented as 39.57 cm2 therefore cohesion and tangent are erroneous results in this analysis. The next error is the analysis of suppression (compression). Where the frame of the apparatus have the measure of sample size d=71 mm, r=35.5 mm which is compressed and one can later discover the degree of sample deformation. The mistake lies in that the real sample in the framework of the apparatus is 40.83 cm2 , while we calculate the value of the surface as 39.57 cm2 . Review of soil analysis is also mistaken. When the sample with the size Ø 50 mm and length 100 mm is subject to the vertical force until it breaks, the resulting resisting force does not belong to the sample that lies in the frame of the apparatus

Given a null hypersurface of a Lorentzian manifold, we induce a Riemannian metric on the null hypersurface using a normalizing field defined on some open set containing the null hypersurface. We establish links between the null geometry and basics invariants of the associated Riemannian metric. This allowed us, using some comparison theorems from Riemannian geometry, to get important results on the topology of the null hypersurface.

The paper shows how any number of (scalar) relative velocities due to external energies or forces can be added relativistically without the total velocity of the subject body or particle exceeding c. The result is based on the product of fields rather than addition. It is also shown that Fermat’s last theorem can be reduced from four variables to two and recast as the relativistic addition of real fractions of c. The only rational solutions to the reduction correspond to powers of no higher than N=2 in Fermat’s conjecture

This paper discusses ultra-low energy levels of the hydrogen atom which was not predictable with quantum mechanics. In the energy-momentum relationship applicable to the electron in a hydrogen atom, derived by the author, there is a negative energy solution, just like the Einstein relationship which holds in free space. The matter formed from a proton with positive mass, and an electron with negative mass that orbits near that proton, is smaller than an ordinary hydrogen atom to an extreme degree. When this unknown matter gathers in large amounts, it becomes a huge mass. This paper identifies such matter as the true nature of dark matter, the mysterious matter that physicists are currently searching for

We examine accidental symmetry of hydrogen-like atoms analytically in spherical coordinates. Some unfamiliar but notable functional relations of the radial eigenfunctions of system’s Hamiltonian are constructed, for both discrete and continuous energy eigenvalues. Analytical similarity of the symmetry between two-dimensional and threedimensional hydrogen atoms are therefore demonstrated.

This paper is bringing a better knowledge of associative triple systems and their related algebraic structures. We prove that any associative triple system is either a T*-extension of an associative triple system or an ideal of codimension one of a T*-extension of an associative triple system. Morover, we give several information about the structure of symmetric associative triple systems

In this article, we studied covariant functors are finite-valued at the categories Comp-compact spaces, metrizable spaces, S-stratifiable spaces, ℵ-spaces, paracompact p-spaces and its continuous maps

Unitary Representations corresponding to local shifts in reference frames are a key topic for progress in Quantum Gravity. The fibre bundle construct defined in our previous work in which quantum fields become liftings of; or sections through; a fibre bundle with base space curved space-time, continues to be the context for this paper. We investigate in more depth the subgroup T of the Poincare group consisting of translations of space-time as a gauge group of automorphisms. We define a representation of T as a group of automorphisms of the local fibre algebra A(x) which we assume to be isomorphic to a von Neumann algebra with trivial centre acting on a separable Hilbert space. Provided this group representation α is weakly measurable, then we have previously proved that it is also norm continuous, and is implemented by a norm, hence weakly and strongly, continuous unitary representation, by unitaries in the algebra. We discuss the dependence of this key result on the strange properties of Stonean spaces and extend our exploitation of Mackey Theory to give a more straightforward group theoretic proof. From such unitary representations a minimal form of Supersymmetry naturally emerges, which predicts the existence of both the mass zero graviton, and its gravitino partner.

This paper discusses a thought experiment whose result contradict the predictions of the special theory of relativity. The reason why this contradiction appears is a velocity vector attached to an inertial frame. Since this sort of inertial frame exists in the natural world, the “principle of relativity” that regards all inertial frames as equivalent, cannot be regarded as a true principle. This paper concludes that the special theory of relativity, which assumes the “principle of relativity” in its development, is a theory with a built-in contradiction.