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Generalized Fibonacci Numbers and Music
Get PDFMathematics and music have well documented historical connections. Just as the ordinary Fibonacci numbers have links with the golden ratio, this paper considers generalized Fibonacci numbers developed from generalizations of the golden ratio. It is well known that the Fibonacci sequence of numbers underlie certain musical intervals and compositions but to what extent are these connections accidental or structural, coincidental or natural and do generalized Fibonacci numbers share any of these connections
Estimates of Solutions to Nonlinear Evolution Equations
Get PDFConsider the equation
u’(t) = A (t, u (t)), u(0)= U0 ; u' := du/dt (1).
Under some assumptions on the nonlinear operator A(t,u) it is proved that problem (1) has a unique global solution and this solution satisfies the following estimate
||u (t)|| < µ (t) -1 for every t belongs to R+ = [0,infinity).
Here µ(t) > 0, µ belongs to C1 (R+), is a suitable function and the norm ||u || is the norm in a Banach space X with the property ||u (t) ||’ <= ||u’ (t) ||
Cycles Cohomology and Geometrical Correspondences of Derived Categories to Field Equations
Get PDFThe integral geometry methods are the techniques could be the more naturally applied to study of the characterization of the moduli stacks and solution classes (represented cohomologically) obtained under the study of the kernels of the differential operators of the corresponding field theory equations to the space-time. Then through a functorial process a classification of differential operators is obtained through of the co-cycles spaces that are generalized Verma modules to the space-time, characterizing the solutions of the field equations. This extension can be given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic bundles category with a special connection (Deligne connection). Using the classification theorem given by geometrical Langlands correspondences are given various examples on the information that the geometrical invariants and dualities give through moduli problems and Lie groups acting
About the Dirichlet Boundary Value Problem using Clifford Algebras
Get PDFThis paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre
Measuring Time
Get PDFThe speed of light is an absolute, the measurement of the speed of light is not an absolute.
According to Special Relativity, the rate at which a clock ticks is a function of the speed at which it is travelling through space; the faster the speed, the slower the rate. This is called time dilation.
Time dilation is a function of the speed of an object through space. The faster an object is travelling the greater the time dilation.
Because of time dilation, we are unable to measure the absolute speed of an object through space.
We do not actually measure time. Instead we have instruments which measure the physical characteristics of instruments which are affected by time. We then interpret these physical characteristics and this interpretation becomes our measurement of time.
Our body is one of the instruments we use to measure time, but we also use various clocks.
Time is not a characteristic of the universe; it is a construct which can be defined to have any value we choose.
If we could establish a stationary point in space, it would be possible to:
measure the absolute speed of light.
measure the absolute speed through space of any moving object.
establish a clock for absolute time.
It might be theoretically possible to establish such a point, as follows:
Assume a space station, located at a Lagrange point.
Modify the speed of the space station through space for the x, y and z axes to maximize the speed of light.
The location of the space station when the speed of light was maximized would be at a stationary point in space
Can Quantum Mechanics and Relativity be Considered Per se Complete? - A discussion on Quantum Mechanics and Relativity in Full Space-Time Domain
Get PDFThis paper points out the incompleteness of the traditional quantum mechanics and relativity, which is embodied in space-time domains of definition, not in physical quantities for description. The real time and space are not continuous. The phenomena called “ghost-like long-range action†by Einstein in fact occur in the time discontinuity points, that is, Time Quantum Worm Holes put forward by Hawking. This paper also gives an essential difference between the macroscopic random motion and the microscopic random motion, which is critical for understanding wave-particle duality
Gravity – An Intrinsic Property of Matter! A Qualitative Graviton-Orbital-Band Theory
Get PDFAll profound theories of nature, life, and society have some philosophical underpinning; the theories of gravity are no exceptions. The theories of gravitation of Isaac Newton and Louis Le Sage were based on mechanical materialism and British empiricism. Albert Einstein developed his geometrical theory of gravity based on idealist Neo-Berkeleyan “positivism” of Ernst Mach. But none of these theories provide, among other things, any tangible intuition into the development of discrete, quantized and the shell like structure of matter from the subatomic to the cosmic, that modern physics, astrophysics and astronomy are revealing in increasing details. A dialectical and qualitative quantum mechanical approach to gravity based on a concept of quantized graviton-orbitals provides an explanation for the cellular structure in the universe
The Theory of The Nuclear Universe and The Secret of The Supernova
No full textThis article is a deep, logical and rational analysis of the three original nuclear and chemical elements of the architecture of the nuclear universe, and which give superconducting motion to the solar system and galaxies of the universe.
After the so-called Big Bang of the universe came the space, a new time count and the nuclear universe, governed by the attractions and repulsions of the physical properties of the nuclear superconductivity mass.
Then, three new superconductive materials emerged in space consisting of three new nuclear chemical elements.
The first liquid superconductive mass of gravity appeared.
Liquid superconductive masses of orbital attraction and the superconductive mass of orbital repulsion were formed.
The mass of gravity by means of a gravitational turmoil and centrifuged the three nuclear masses.
So in this way the solar system was created.
Then, the natural moons were created from the volumetric rest of the matter that formed the planet.
At this early time the moons had the rotational motion on their axis, similar to the planet.
At this early time the planets already had the rotation movement.
In "old age," the moon stopped the rotation and began the revolution movement.
In the 21st century, the Earth's core is solid or pasty
Constructing and Characterizing TiAlN Thin Film by DC. Pulsed Magnetron Sputtering at Different Nitrogen/Argon Gas Ratios
Get PDFIn this survey, the magnetron sputtering with Dc. Pulsed mode was embroiled to deposit TiAlN thin film on AISI 316 as a substrate. All the plasma magnetron parameters were fixed excluding the nitrogen gas ratio which was varied from 10% to 50% with step interval of 10% with respect to argon. The structure, mechanical, tribological and electrochemical peculiarities of TiAlN films were studied. The TiAlN deposition rate is decreased in regard with increasing the nitrogen gas ratio where, the film thickness recorded a maximum value of 3 µm at nitrogen gas ratio of 10 %. X-ray configurations demonstrated the formation of solid solution phase of TiAlN with different orientations. The TiAlN coating has (111) preferred orientation at 10 and 20% nitrogen gas ratios while has (200) preferred orientation at 30- 50% nitrogen gas ratios. The crystallite size is decreased with increasing the nitrogen gas ratio. The results depicted that, the microhardness of TiAlN film is increased with decreasing the nitrogen gas ratio and recorded a maximum value of approximately 850 HV0.015 at 10% N2. Additionally, the tribological properties of the coated AISI 316 with TiAlN are enhanced compared with the uncoated sample. The wear volume loss of the coated sample at 10% N2 has a value of nearly 9X104 µm3 which is low in comparison with AISI 316 substrate that has a value of 4.5X106 µm3. The corrosion resistance of all TiAlN coatings was better than the uncoated sample. It was demonstrated; the change in nitrogen gas ratio affected the physicochemical characteristics of the TiAlN coating
Optical Absorption in Incoherent and Coherent States of a Quantum Hall System
Get PDFIn connection with recent studies of extremely long-living spin-cyclotron excitations (actually magneto-excitons) in a quantum Hall electron gas, we discuss contribution to the light-absorption related to the presence of a magneto-exciton ensemble in this purely electronic system. Since the weakly interacting excitations have to obey the Bose-Einstein statistics, one can expect appearance of a coherent state in the ensemble. A comparative analysis of both incoherent and coherent cases is done. Conditions for a phase transition from the incoherent state to the coherent one are discussed