Physical Mathematics

In this paper, we consider some geometric topological properties of the functor P- probabilistic measures and its subfunctors in the category of compacta and continuous mappings into itself.

In this paper we introduce Photodynamics and use it to resolve three outstanding problems in physics: in relativity, the motion of massive particles at the speed of light; in cosmology, how cooling CMB photons lose energy for 13.8 billion years without slowing down; in neutrino astrophysics, neutrino oscillation at light speed in response to the challenge posed by the 2015 Nobel Prize in Physics. These are all major unsolved problems in relativity, cosmology, and neutrino astrophysics, whose solutions have evaded our best efforts for decades. The common cause of these problems has been the erroneous application of Einstein's E = mc2 to particles that travel at the speed of light. We prove conclusively that E = mc2 applies only to particles that cannot travel at the speed of light, and in fact prevents them from attaining light speed. This reveals that an enormous problem has existed, over a century. Relativity, the foundation of modern physics, is woefully incomplete and inadequate. It does not contain a valid relativistic dynamics for the vast majority of particles in the Universe, the particles that travel at the speed of light. To resolve this problem we introduce Photodynamic, a previously unknown fundamental law of nature. Photodynamic is the only mechanism that allows particles to travel at the speed of light, and then, only if they have mass. This means that photons, gravitons, gluons, and neutrinos are all relativistic massive particles. So all theories describing the origin, characteristics, and interactions of fundamental particles as well as those of the origin, constitution, and evolution of the Universe, must be made compatible with photodynamics. Photodynamic is a change in relativity, a change in the very foundations of physics, and as such will impact all fields of physics involving particles that travel at the speed of light.

We present to the international scientific community a series of misprint and some mathematical mistake found in Stephen Hawking's doctoral thesis, titled \Properties of Expanding Universe". These errors have been found as a result of my translation work into Spanish of the aforementioned thesis.

The work investigates the effects of mixed convection and Navier slip parameters on a chemically reactive heat and mass MHD fluid flow over a permeable surface with convective boundary conditions. By transforming the system of coupled partial differential equations governing the flow into a system of coupled ordinary differential equations using similarity transformation, the resulting ordinary differential equations are solved using the Fourth order Runge – Kutta method with shooting technique. The effects of mixed convection and Navier parameters on the velocity, temperature and concentration profiles are quantitatively discussed graphically.

We have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a discrete space-time and shows that macroscopic space-time is a renormalization limiting form. Weaving together a number of our previous results we then prove that quantum states invariant under either an external group of local diffeomorphisms of space-time or, by contrast, quantum states invariant under the internal action of a compact Lie group are ‘common’, in a well-defined sense. These form the building blocks of invariant fields and Lagrangians. A form of N=1 Supersymmetry and noncumulative space – time naturally emerges, which predicts a spin-2 massless graviton and its companion graviton.