arxiv.org/abs/1001.2967v1
Comment on "Harold Jeffreys's Theory of Probability Revisited"
Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]...
arxiv.org/abs/2201.05665v1
Harold Widom's work in random matrix theory
This is a survey of Harold Widom's work in random matrices. We start with his pioneering papers on the sine-kernel determinant, continue with his and Craig Tracy's groundbreaking results concerning the distribution functions of random matrix theory,...
arxiv.org/abs/2301.04021v2
Need for "special" states in a deterministic theory of quantum mechanics
There are several theories or processes which may underlie quantum mechanics and make it deterministic. Some references are given in the main text. Any such theory, plus a number of reasonable assumptions, implies the existence of what I have called...
arxiv.org/abs/1407.5001v12
Vibrating Rays Theory
The present work is aimed to explain why we started to consider Vibrating Rays Theory (VRT) as a viable representation of nature, and to elaborate some of its consequences. In 1846 Faraday introduced the concept of vibrating rays, in which an atom is...
www.bing.com/ck/a?!&&p=32d166365f62effb9ababa993de8ac3d84d048a16ad6faa572231db404149c21JmltdHM9MTc3MjU4MjQwMA&ptn=3&ver=2&hsh=4&fclid=209578c6-e4a4-6037-3a8d-6fd4e54a616a&u=a1aHR0cHM6Ly9tYXRoLnN0YWNrZXhjaGFuZ2UuY29tL3F1ZXN0aW9ucy81NTY1OS9jb21iaW5hdG9yaWFsLWludGVycHJldGF0aW9uLW9mLWJpbm9taWFsLWludmVyc2lvbg&ntb=1
Combinatorial interpretation of Binomial Inversion
In discrete calculus it's the poset $\mathbb {Z}_ {\ge 0}$ under the usual order. This beautiful theory was first described by Gian-Carlo Rota in On the Foundations of Combinatorial Theory I, and elaborated …
arxiv.org/abs/math/0501315v2
Taming the wild in impartial combinatorial games
We introduce a misere quotient semigroup construction in impartial combinatorial game theory, and argue that it is the long-sought natural generalization of the normal-play Sprague-Grundy theory to misere play. Along the way, we illustrate how to u...
arxiv.org/abs/hep-th/9705117v2
Notes on Theories with 16 Supercharges
We survey the various field theories with 16 real supercharges. The most widely known theory in this class is the N=4 theory in four dimensions. The moduli space of vacua of these theories are described and the physics at the singularities of the m...
arxiv.org/abs/1710.05005v1
First Principles Free-Energy Theory of Solvation with Atomic Scale Liquid Struct…
Quantum-chemical processes in liquid environments impact broad areas of science, from molecular biology to geology to electrochemistry. While density-functional theory (DFT) has enabled efficient quantum-mechanical calculations which profoundly impac...
arxiv.org/abs/2106.04680v1
Ouroboros Functionals, Families of Ouroboros Functions, and Their Relationship t…
Previously, we have introduced a very small number of examples of what we call Ouroboros functions. Using our already established theory of Ouroboros spaces and their functions, we will provide a set of families of Ouroboros functions that bolster ou...
arxiv.org/abs/1604.01913v1
Valeurs multiples de fonctions L de formes modulaires
This doctoral thesis studies the overlap between two well-known collections of results in number theory: the theory of periods and period polynomials of modular forms as developed by Eichler, Shimura and Manin and its extensions by Köhnen and Zagier...
arxiv.org/abs/2106.01419v1
Assumption Digging in Euclidean Geometry
Theory Building has been largely ignored in Mathematics Education, especially at the Middle and High School Levels. This thesis focuses on Assumption Digging, a type of Theory Building similar to what Hilbert undertook in his Grundlagen with Euclidea...
arxiv.org/abs/0903.2064v1
Einstein's unpublished opening lecture for his course on relativity theory in Ar…
In 1922 the University of Buenos Aires (UBA) Council approved a motion to send an invitation to Albert Einstein to visit Argentina and give a course of lectures on his theory of relativity. The motion was proposed by Jorge Duclout (1856-1927), who...
arxiv.org/abs/1102.0596v1
A sneak preview of proof theory of ordinals
This talk is a sneak preview of the project, 'proof theory for theories of ordinals'. Background, aims, survey and furture works on the project are given. Subsystems of second order arithmetic are embedded in recursively large ordinals and then the l...
arxiv.org/abs/2303.09670v1
Slack Hopf Monads
Hopf monads generalise Hopf algebras. They clarify several aspects of the theory of Hopf algebras and capture several related structures such as weak Hopf algebras and Hopf algebroids. However, important parts of Hopf algebra theory are not reached b...
arxiv.org/abs/1502.04794v1
On a Final Theory of Mathematics and Physics
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is mounting...
arxiv.org/abs/physics/0003035v1
Will the Population of Humanity in the Future be Stabilized?
A phenomenological theory of growth of the population of humankind is proposed. The theory based on the assumption about a multifractal nature of the set of number of people in temporal axis and contains control parameters. In particular cases the...
arxiv.org/abs/2009.06370v2
Transparency and granularity in the SP Theory of Intelligence and its realisatio…
This chapter describes how the SP System, meaning the SP Theory of Intelligence, and its realisation as the SP Computer Model, may promote transparency and granularity in AI, and some other areas of application. The chapter describes how transparency...
arxiv.org/abs/1506.00380v3
Operational axioms for diagonalizing states
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum stat...
arxiv.org/abs/1003.3434v1
On the present state of the Andersen-Lempert theory
In this survey of the Andersen-Lempert theory we present the state of the art in the study of the density property (which means that the Lie algebra generated by completely integrable holomorphic vector fields on a given Stein manifold is dense in th...
arxiv.org/abs/1103.1343v2
Realization theory of discrete-time linear switched systems
The paper presents realization theory of discrete-time linear switched systems. A discrete-time linear switched system is a hybrid system, such that the continuous sub-system associated with each discrete state is linear. In this paper we present nec...