Current practice defines the front velocity of a signal as the limit of the phase velocity for infinitely high frequency. However, the present article provides evidence that the propagation velocities of signal fronts for input signals of nonzero temporal duration result from the phase velocities in the low-frequency range. In conclusion, although the impulse response propagates at the phase velocity for infinitely high frequency, this is shown not to be true for the step response. The article further clarifies that the front or information velocity should be defined as the fastest phase velocity of a transmission medium.
My research began with the distribution of primes and composite numbers, I believe I have identified the mechanism. In this article I deal with the factorization of composite numbers or the search for prime numbers that multiplied together give the composite number under examination as a result. From the very beginning of the research I came across those sequences of prime numbers and composite numbers that I called combined sequences, continuing the research I believe I have revealed all the main characteristics. In this article I propose a table that derives strictly from the combined sequence that I had already called [Sc<=11], for this reason I have identified it with the same name.
Star light deflection near the sun of 1.75 arcseconds during a solar eclipse has been attributed to post-Newtonian physics for over a century; however, this can alternatively be shown as a geometric resultant of the Sun-Galaxy interface very near the Sun, and specifically conforming exactly to the curvature of the Sun’s orbit in the galaxy. It is clearly demonstrable through basic geometry that the post-Newtonian light deflection is simply due to the Sun-Milky Way Galaxy EquiPotential (EP) interface, and that a simple ratio exists to explain the galactic origin of the deflection effect. This report examines data and reviews solar eclipse deflection tests for their geometry as evidence for this alternative explanation, which we now add as a component model to Diffusion Gravity(DG) theory; moreover, we present a corresponding mechanism for deflection of light near the Sun due to virtual particle behaviors for photons. This effect of gravitational equipotential surfaces on the propagation of light occurs at the interface between gravitational scale regimes, i.e., the Sun-Galaxy interface where virtual particle (VP) streams from the Sun and galaxy form a boundary interface depletion zone, where a proportional diffusion “pressure” causes the attraction of the masses toward the depleted zone, while also manifesting light deflection-refraction effects near the Sun.
In this research, the author attempts to make a fundamental revision on the Newtonian mechanics to provide a new theory having a more diverse range of phenomena explained. It is proposed that the first and second laws are reformed and the third one is held while the general law of gravity has been removed. The basic concepts of Newtonian mechanics are location, mass and absolute time. The absolute time being held, mass is included as a more general concept and location is not an original concept, but a second order one. Motion in 3D frame is considered to be an inherent property for 3D objects and location is its integration. On the other hand, location for light as a 4D object is not sensible. The free fall phenomenon is described without using Newton’s general law of gravity. The well-known experimentally verified results of relativity theories (special and general) are covered by three postulations of the new theory. The gravity is a result of Ether’s motion as a fluid among cosmological masses and the accelerating expansions of galaxies as well as the fast motion of objects in the galaxies margin are shown to be explainable without needing some unknowns such as dark energy and dark matter. The philosophical aspects of new theory are analyzed at the end.
CAT4 is proposed as a general method for representing information, enabling a powerful programming method for large-scale information systems. It enables generalised machine learning, software automation and novel AI capabilities. It is based on a special type of relation called CAT4, which is interpreted to provide a semantic representation. This is Part 1 of a five-part introduction. The focus here is on defining the key mathematical structures first, and presenting the semantic-database application in subsequent Parts. We focus in Part 1 on general axioms for the structures, and introduce key concepts. Part 2 analyses the CAT2 sub-relation of CAT4 in more detail. The interpretation of fact networks is introduced in Part 3, where we turn to interpreting semantics. We start with examples of relational and graph databases, with methods to translate them into CAT3 networks, with the aim of retaining the meaning of information. The full application to semantic theory comes in Part 4, where we introduce general functions, including the language interpretation or linguistic functions. The representation of linear symbolic languages, including natural languages and formal symbolic languages, is a function that CAT4 is uniquely suited to. In Part 5, we turn to software design considerations, to show how files, indexes, functions and screens can be defined to implement a CAT4 system efficiently.
