P Adic Analysis

Part I – Spirilla Theory and Cosmology
Stephen Hawking once proclaimed that String Theory may be able to unify the various forces although later he became disillusioned thinking that there may be no Theory of Everything. This very condensed book pulls together the various forces into the Spirilla Theory which supersedes String Theory and introduces the Relativity of Consciousness.

The foundation of the Spirilla Theory is based on the writings of H. P. Blavatsky, A. B. Bailey, and A. Besant. By overlaying the works of Einstein, Bohm, de Broglie, Dirac, Bell and other great scientific minds, on top of the foundation, the unification of the various forces and theories starts to appear; each field of study supplying a part of the puzzle but only a holistic view of ALL endeavors will solve the mystery. The book starts by laying the groundwork through the Introduction, a review of Bell’s Theorem and p-adic mathematics; following this, each major section begins with a quote from the foundational works followed by the quotes from scientific papers demonstrating the current known thinking on the various topics; no attempts are made to edit the works (except with a few exceptions for clarity and/or length) of the various authors and references to the scientists’ works are maintained. Each section is pulled together so that a picture can be seen.
This section;
1. Redefines the atom with the addition of a subquark;
2. Defines the Spirilla Theory which unifies Quantum Mechanics and General Relativity, and explains Quantum Entanglement;
3. Defines new particles;
4. Redefines time and space;
5. Defines and solves the mystery of Black Holes and links the cosmic and quantum black hole through the spirillae;
6. Delves into the mystery of the Macroverse;
7. Outlines the steps in the origins of the universe;
8. Adds an equation to Einstein’s original 1905 paper on relativity which sees the speed of light approaching infinity;
9. Gives the foundation for developing space travel; and, as an appendix,
10. Gives detailed information for the development of a new energy source – Quantum Energy.

Part II - Ontology, Epistemology & Manifestations
Part II is divided into three sections:
1. Ontology and the fundamental concepts of reality which discusses:
a. consciousness and delves into the mystery of human consciousness having cosmic origins;
b. reincarnation and gives the various laws affecting rebirth, with a discussion on the principle of mutation and the perfecting of form;
c. the work of form-building, transmutation of form and the building of a human form.
2. Epistemology which covers a great deal of topics however; for the purposes of NOE the subject is restricted to;
a. evolution including a definition of the Law of Evolution, the cyclic ebb and flow and the rhythmic work of creation, the process of substitution, the evolution of man and the genesis of the pithecoid stocks; and
b. death including the processes of death, two main reasons for cremation and the sequence of events at death.
3. Manifestations of the various religions including:
a. why Christians don’t believe in reincarnation;
b. the coming science of invocation and evocation;
c. Quantum Entanglement Over Time (QEoT) or The Law of Cause and Effect, and The Law of Karma with a discussion on The Golden Rule ; and
d. The New World Religion.

This is an introduction to p-adic geometry and p-adic analysis focusing on the theme of p-adic period mappings. We follow as closely as possible the development of the classical theory of complex period mappings, blending differential equations, group theory and geometry. The text ends with a detailed discussion of p-adic triangle groups.

The Moody pilot wave is a light wave. This light wave is the creation of all things. All answers we seek to the most profound answers of mathematics and physics are found in the reciprocal of the light wave. The reciprocal = 1/ light. This represents an explosion of information made from the light wave collapse yet the collapse is not chaotic it is harmonic decoherence. In this collapse, all information about our universe is revealed. It has now been discovered that this light wave has two forms. An isomorphism is two things that are considered the same.  There is the duality of light in which our reality dwells and there is the perfect light that has not collapsed and has not interfered with itself or any other thing. This creates another realm, a second dimension more fundamental than the reality or the light wave that we live in. It is perfect space, pure potential, and has no duality. It is one thing before it splits into three and creates our reality. It is a perfect paradise, a monopole, and I will prove that the realm exists, the only analogy that can be drawn is this other realm appears to be exactly as Heaven is described, the proof that God is light and we are children of the light. Proven by science and math.

This is an introduction to $p$-adic geometry and $p$-adic analysis focusing on the theme of $p$-adic period mappings. We follow as closely as possible the development of the classical theory of complex period mappings, blending differential equations, group theory and geometry. The text ends with a detailed discussion of $p$-adic triangle groups.

In this paper we analyse the construction of p−adic numbers, which we expand to the new combinatorial p − q−adic numbers. Thus, introducing combinatorics into algebraic number theory. After we validate the made progress, the topology and the algebra, we construct new functions, which are embedded infinite (combinatorial − and or periodic tower of) fields. Before we come to categories and functors, we also introduce briefly p−q−adic m−nomial combinatorial functions, respectively − series and give an example of a distribution function for it. Further, we show how a p−q−adic distribution function might be constructed.

The Black Hole is where sound, matter and energy come together in a beautifully synchronous fashion. It should be noted that the root is not a principle and only responds to the other two. It is the cosmic gene pool from which form is made but only when energy and sound act upon it. It remains even when the other two have ceased. The root contains the code for differentiation and replication. The actual black hole is a vortex of inconceivable rapidity of sound which carries the three forms of electricity.

References [1] G. Bachman, Introduction to p-adic numbers and valuation theory, Academic press, 1964. [2] G. Bachman, L. Narici, Functional Analysis, Academic Press, New York and London. [3] AJ Baker, An introduction to p-adic numbers and p-adic analysis, URL: http:// www.maths.gla.ac.uk/∼ ajb. [4] Y. Cho, P. Lin, SS Kim, A. Misiak, Theory of 2-Inner Product Spaces, Nova Science Publishers, 2001. [5] B. Dragovich, p-adic approach to the genetic code and genome, Institute of Physics, Belgrade, Serbia, TAG, 20-24 Oct, 2008, Annecy. [6] R. ...

In this research thesis, we describe various formulas concerning Yang-Mills equations, p-Adic, Adelic and Zeta Strings and Supersymmetry. We obtain several possible mathematical connections with various expressions regarding the Ramanujan mathematics


REVISITED AND DEFINITIVE VERSION 12.11.2020

If ~v1, : : : , ~vm are lexicographically positive elements in Z^n, a general recurrence is a computation rule a(~x) = f(a(~x - 􀀀 ~v1); : : : ; a(~x 􀀀-  ~vm)). Let H be a finite abelian p-group,
h : H^m ---> H a homomorphism of groups, t in H and f : H^m ---> H given by f = h + t. Suppose that one has an initial condition which is sucient for the recurrence rule to uniquely define a n-dimensional sequence a : N^n ---> H and this initial condition is given by p-automatic functions. Then the recurrent n-dimensional sequence (a(~x)) is p-automatic. This
is a consequence of a result by Denef and Lipschitz connecting p-automatic sequences with formal series over

In this paper, some classes much more general than the one in [NM Chuong, Yu. V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (Eds.), Harmonic, Wavelet and p-Adic Analysis, World Scientific, Singapore, 2007] of Cauchy problems for an interesting class of ...

A p-adic Schrödinger-type operator D[alpha]+VY is studied. D[alpha] ([alpha]>0) is the operator of fractional differentiation and is a singular potential containing the Dirac delta functions [delta]x concentrated on a set of points Y={x1,...,xn} of the field of p-adic numbers . It is shown that such a problem is well posed for [alpha]>1/2 and the singular perturbation VY is form-bounded for [alpha]>1. In the latter case, the spectral analysis of [eta]-self-adjoint operator realizations of D[alpha]+VY in is carried out.

Constants with formulae of the form treated by D. Bailey, P. Borwein, and S. Plouffe (BBP formulae to a given base b) have interesting computational properties, such as allowing single dig- its in their base b expansion to be independently computed, and there are hints that they should be normal numbers, i.e., that their base b digits are randomly distributed.

Examination of topological geometrodynamics in the matter of possible synthetic (engineered) topological condensation of photons in deep space or the collection of such from natural processes.  The focus is upon harnessing of useful energy for such applications as deep space transport.

For a prime p and a matrix A ∈ Z
n×n
, write A as A = p(A quo p)+
(A rem p) where the remainder and quotient operations are applied
element-wise. Write the p-adic expansion of A as A = A[0] + pA[1] +
p
2A[2] + · · · where each A[i] ∈ Z
n×n has entries between [0, p − 1].
Upper bounds are proven for the Z-ranks of A rem p, and A quo p.
Also, upper bounds are proven for the Z/pZ-rank of A[i]
for all i ≥ 0
when p = 2, and a conjecture is presented for odd primes.

The paper is the continuation of the previous paper on this topic. We first review some of the recent developments on 3x+1 problem. In the remaining part of the paper we prove the result announced at the end of the first paper. The proof uses the finite version of the method of mathematical induction. Index Terms-3x+1 problem, Collatz problem, p-adic numbers, 3-adic numbers, periods.