Related papers: Constructing and Understanding New and Old Scales …
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
We discuss the general theory of realizing two-variable fuctions on slide rules (based on our paper 1977) and offer some new scales for practical use.
For each type of number, structures that differ by arbitrary scaling factors and are isomorphic to one another are described. The scaling of number values in one structure, relative to the values in another structure, must be compensated…
Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship…
The biggest question in beyond the standard model physics is what are the scales of new physics. Ideas about scales, as well as experimental evidence and constraints, are surveyed for a variety of possible forms of new physics:…
We review the status of low-scale string theories and large extra-dimensions. After an overview on different string realizations, we discuss some of the main important problems and we summarize present bounds on the size of possible…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful…
We present an overview of both older and recent developments concerning scale separation in string theory. We focus on parametric scale separation obtained at the classical level in flux compactifications down to AdS vacua. We review the…
There are compelling historical and mathematical reasons why we ended up, among others in Physics, with using the scalars given by the real or the complex numbers. Recently, however, infinitely many easy to construct and use other algebras…
This article is Part I in a series of three papers devoted to determining the minimal complexity of scales in the inner model $K(\mathbb{R})$. Here, in Part I, we shall complete our development of a fine structure theory for $K(\mathbb{R})$…
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…
These lectures contain an introduction to the theory and practice of weak-scale supersymmetry. They begin with a discussion of the hierarchy problem and the motivation for weak-scale supersymmetry. They continue by developing the coset…
After summarizing the status of the Standard Model, we focus on the Hierarchy Problem and why we believe this strongly suggests the need for new physics at the TeV scale. We then concentrate on theories with extra dimensions and their…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…
Ages are key to truly understand a large plethora of astrophysical phenomena. On the other hand, stellar clusters are open windows to understand stellar evolution, specifically, the change with time and mass of different stellar properties.…
We describe here our perception of complex systems, of how we feel the different layers of description are important part of a correct complex system simulation. We describe a rough models categorization between rules based and law based,…
This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few…