Physical Mathematics

In this paper, the theory of the Ricci flows for manifolds is elaborated with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometrical arena for nonholonomic Riemannian spaces, Lagrange mechanics, Finsler geometry, and various models of gravity (the Einstein theory and string, or gauge, generalizations). Nonhlonomic frames are considered with associated nonlinear connection structure and certain defined classes of nonholonomic constraints on Riemann manifolds for which various types of generalized Finsler geometries can be modelled by Ricci flows. We speculate upon possible applications of the nonholonomic flows in modern geometrical mechanics and physics.

The whole reality (Universe) represents the unity in its diversity. What is the basic mechanism that creates the unity of being? Many thinkers have expressed the Unity Principle by saying “everything is connected to everything else”, but nobody has detected its essence. On the base of dialectical logic, the Unity Principle is discovered which illustrate the exact mechanism how the physical Universe may work at its macro and micro levels. Fundamental discovery of the dialectical Unity Principle is a base on which new fundamentals of theoretical physics are built in the field of cosmology and particle physics

Direct Mathematical calculations for the absolute efficiency of well-type gamma ray scintillation crystals are described. Calculated detection efficiencies are drawn for two commonly used well crystals. Comparisons are made between present works and published Monte Carlo values. The present approach proved quite success in predicting the efficiency of well type detectors providing only the geometry and materials of the system formed of source, detector and shielding as well as the energy of the emitted photons.

The analysis is performed for the steady-state boundary layer flow with free convective heat transfer over a horizontal surface embedded in a fluid-saturated porous medium subject to variable wall heat flux (WHF) and variable wall temperature (VWT). In modeling the flow inertia, no slip boundary conditions and exponentially decaying internal heat generation (IHG) are taken into account. The similarity equations are solved numerically and their solutions are dependent on the problem parameters G, m, λ. The influence of such parameters on flow characteristics such as velocity, temperature profiles, the skin friction coefficient, and the Nusselt number are thoroughly discussed. It is found that the flow profiles along with physical parameters significantly altered the rate of heat transfer and induced more flow within the boundary layer than that of without IHG.

Currently, in the scientific literature there is the statement that 96% of the total amount of the matter in the universe is the so-called the dark matter. It is uniformly fills the entire universe and it cannot be identified with the any observable celestial bodies. It was called the dark matter because it is invisible. No one has not seen in order to it was involved in the gravitational interactions between stars and star clusters. Its existence the astrophysics explains by causes of the background radiation of radio waves. This radiation is detected by radio telescopes at wavelengths of about 7.35 cm. Actually, it is unknown nothing in addition. The share of the baryonic matter is not more than 4% of all matter in the universe (baryonic matter mainly consists of the heavy elementary particles, neutrons and protons). In connection with this in the science the assumption gaining strength, that in the universe there are two kinds of a matter. One of them is the ordinary baryonic matter, and the other, the so-called a dark matter. It is by primary kinds of a matter. There is the evidences and the objections to such a view of nature. To add the arguments in favor of evidence to the existence of a dark matter in the space between the baryon bodies, in this article we re-look at the experience of PA Cherenkov 1934 about the luminescence of very fast electrons due to D-rays of the radioactive elements as they pass through the liquid. In 1958, to Cherenkov, together with Tamm and Frank was awarded the Nobel Prize in Physics "for the discovery and interpretation of the Cherenkov effect."

A solution to this problem has been unknown for years and the fact that it hasn’t been solved yet leaves a lot of unanswered questions regarding Engineering and Pure Mathematics. Turbulence is a specific topic in fluid mechanics which is a vital part of the course when it comes to real life situations. In two and three dimensional systems of equations and some initial conditions, if the smooth solutions exist, they have bounded kinetic energy. In three space dimensions and time, given an initial velocity vector, there exists a velocity field and scalar pressure field which are both smooth and globally defined that solve the Navier-Stokes equations. There are difficulties in two-dimensions and three dimensions in a possible solution and which have been unsolved for a long time and our goal is to propose a solution in three-dimensions. Lets see if we can relate a couple of courses of pure mathematics to come up with an implication.

The formula Yoshio Koide, shows a pretty compelling link between the masses of leptons: electron, muon, tauon. We offer a clear improvement in accuracy in expressing this formula electron unit. This opens the way for the assumption of heavy leptons type of composite. Under discussion is then referred to the cause, beyond the standard model, the neutrino flavor mixture, treated with PMNS matrix.

Quantum and relativistic phenomena can be explained by the hypothesis that both the universe and the elementary particles are formed by atoms’ four spatial dimensions. It is also possible to deduce and calculate properties of elementary particles, such as mass, electric charge, spin, radio, etc. Based on this hypothesis, the fundamental constants can be calculated depending only on the speed of light c. Moreover, the Schrodinger equation can be deduced and the equality of inertial and gravitational mass can be demonstrated. The aim of this article is to establish a relationship between electron mass and electron charge, and thereby calculate the electrical charge depending on the mass of the electron, Planck's constant h and the speed of light c. Through this relationship, extended to the gravitational and magnetic fields, it is possible to establish a relationship between the constants of both fields.

This study suggests grouping of numbers that do not divide the number 3 and/or 5 in eight columns. Allocation results obtained from multiplication of numbers is based on column belonging to him. If in the Sieve of Eratosthenes the majority of multiplication of prime numbers result in a results devoid of practical benefit (numbers divisible by 2, 3 and/or 5), in the sieve of prime numbers using algorithms, each multiplication of prime number gives a result in a number not divisible to 2, 3 and/or 5.

Here is the solution to the Yang-Mills Mass Gap Problem as described below. The Mass in the material universe is a balance between the resistance to mass formation (cuz=Pi-base e), squeezing Energy, and Gravity pulling it apart. There is an explanation as to why there are 116 sable elements in the material universe. The calculations are verified by predicting the size of the universe within experimental error.

This paper presents the solution to the Birch Swimmerton problem. It entails the use of critical damping of a Mass-Spring-Dash Pod system which, when modelled mathematically, provide the equation that allows the solution of the zeta problem to be solved.

This paper deals with linear ill-posed problems relating to Hilbert Systems using comparisons of methods (Matlab Backslash, SVD, GMRES, QR, and PCG) including their regularizations. Hilbert systems of varying sizes were investigated and several results on these methods were presented in tabular form based on error and relative error norm. From our numerical results ran on Matlab version 7.01 only QR regularization method is recommended for the solution of Hilbert linear system.

This paper presents a new revolutionary theory on how the universe came to be and is sustained. It shows, through the use of Mathematical Physics, how the so-called “Superforce is” determined. The Superforce is that single force that overrides all other forces of Physics, namely, Gravity, Electromagnetic, and Nuclear Forces. The theory presented here is in harmony with other field that touch on it, including Quantum Mechanic, Chemistry, Physics, Theology, Sacred Scripture, and Philosophy. Newtonian Mechanics is useful here. There is absolute time and space contrary to Einsteinian Mechanics. Our universe is just one wavelength of a spectrum. Shown is the irreducible gravitational constant and how the 11 dimension universe is built up from there. The paper provides a solution to these 11 simultaneous equations. This paper is a brief summary of the blog Astrotheology-Cusack’s Universe and the series of books by the same title. That blog is over 4300 pages posts long, and thus difficult to summarize in less than 20 pages. However, the attempt is made here. The reader is referred to those sources to glean the detail. This paper bring physics into harmony with Quantum Mechanics and also with the account of Genesis account version of Creation, which the Egyptians knew and the Hebrews learned The ancients knew much more about our universe than we previously thought.

This paper provides the solution to the Navier-Stokes Clay Institute Problem. The Golden Mean parabola is a solution to this equation. The solution shows that the Navier Stokes Equation is smooth.

Analysis of adiabatic processes at the elementary particle level and of the manner in which they correlate with the principle of conservation of energy, the principle of least action and entropy. Analysis of the initial and irreversible adiabatic acceleration sequence of newly created elementary particles and its relation to these principles. Exploration of the consequences if this first initial acceleration sequence is not subject to the principle of conservation

The numerous internal symmetries are found in N-dimensional integer lattices (ZN). The relation of these symmetries with the new mathematical category named the Masks (or Neighborhoods) is shown. A set of definitions for the Correct Masks and Perfect Masks is presented; the identity between the Correct and Perfect Masks is hypothesized. The relationship between the Perfection of the Mask and the new category named “Mathematical String” is shown. The Correctness of the several Masks in ZN (N=1,2) is proven and a simple method to find the Correctness for all other N is outlined. The hypothesis of high population density of Perfect Masks in integer lattices ZN with large N is stated.

The wavelet envisioned by Huygen’s in diffraction phenomenon is re-interpreted as being polarized after passing through slit/hole which removed the electric field component from the Electromagnetic Radiation (EM-R), the remained wave consist of the Circular Magnetic Field (CMF), this CMF lost the speed of light and the electric field, hence it’s a short distance travel field, originated from the CMF produced by accelerated electrons, integrated with the Electric Field (EF) during the Flip-Flop (F-F) mechanism producing EM-R; hence the passing of light through a single hole/slit resulted in a CMF which reproduced as rings on the monitor screen in single wave diffraction, while the interference of two such CMF in double slits experiment, produced constructive or destructive interference forming patches on the monitor screen; and the perceived electron diffraction is an enter of two CMF from a single electron into a slit then emerged to produce constructive or destructive interference, in addition to the electron which entered and emerged from the slit with the stronger CMF, the paper finally derived the origin of Planck ‘constant (h) for the second time; the logical interpretation of double slits diffraction will restore the common sense in the physical world, distorted by the pilot wave.

We introduce and examine quantum states of a special kind, referred to as E-states, whose properties are both structurally and functionally analogous to the sieve of Eratosthenes. More broadly, the concept of an E-state is related to a certain noncommutative extension of the Dirichlet ring, also discussed here for the first time. Furthermore, we demonstrate that E-states can be implemented on a universal quantum computer and, as a particular application, we construct an algorithm which implements the Dirichlet multiplication of sequences on a quantum computer. We also discuss the potential applicability of E-states to the problem of integer factorization although, we haste to add, we are not aware at present of the possibility of using this approach to obtain algorithms of sub-exponential complexity

This survey reviews the recent development of mesh deformation methods. During the past two decades a vast number of researches have been concerned with developing an efficient and robust mesh deformation technique. This has been achieved either by proposing a novel approach, improving an existing one, or by combining two existing approaches together resulting in a new hybrid approach. It is important to keep track of the most up to date developments in the field of mesh deformation, in order to allow the researchers to adopt the most efficient and application compatible scheme as well as to propose new methods of improvements. In this survey the mesh deformation techniques have been classified into two main categories, 1) physical analogy based techniques and 2) interpolation based techniques. The most significant techniques under these two classes are reviewed and the aspects of strength and weaknesses are highlighted.

The initial process for introducing the respective input variables to the mathematical models depends on the flight mission to define; keeping in mind the simplifications that are taking place are also established; as well as input data relevant to mention such as for example are the speed, the height, the cut-off, data concerning the orbit perigee, apogee, period and flat trajectory of the orbit. It is defined in the same simplified manner, the orbital elements and the inclination to consider. Additionally, the energy requirement is established and a specific impulse not defined, specific current pulses propellants either solid or liquid. Specific impulses of current propellants either solid or liquid must not exceed the limits established in technologically optimum mass distribution and the number of stages. At that point the main problem to observe will be associated with the number one phase in which we must find the path from the launch point to the injection of the payload, minimizing the loss of thrust required for acceleration, gravitational effects and drag. This requires a path to minimize these losses and minimize the overall fuel consumption of the vehicle. as part of the origin of the proposed research problem, was noted the work developed in the research hotbed SE-AST (Hotbed of astronautically studies) that have been developed academic work order relating to conceptual designs rocket dimensioning of motors and calculating orbits within the projects undertaken there labor and courses, but has been developed from work pending that address the dynamic of powered flight path.