相关论文: Is G a conversion factor or a fundamental unit?
In this article, we give a geometric description for any invertible operator on a finite dimensional inner--product space. With the aid of such a description, we are able to decompose any given conformal transformation as a product of…
The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI,…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
We consider fundamental physical constants which are among a few of the most important pieces of information we have learned about Nature after its intensive centuries-long studies. We discuss their multifunctional role in modern physics…
The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…
We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…
Our collective views regarding the question "what is fundamental?" are continually evolving. These ontological shifts in what we regard as fundamental are largely driven by theoretical advances ("what can we calculate?"), and experimental…
The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing…
It is difficult to identify a G-C fullerene directly from its dimensions as its lattice is not proportional to that of its archetype in general, although they have the same three-dimensional shape. In this paper, the area scale factor of a…
We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with identity. Those invertible under formal composition form a group $\mathcal{G}$. We consider the centraliser $C_g$ of an element…
The four types of homogeneity -- additive, multiplicative, exponential, and logarithmic -- are generalized as transformations describing how a function $f$ changes under scaling or shifting of its arguments. These generalized homogeneity…
Recently, a general tool called a holographic transformation, which transforms an expression of the partition function to another form, has been used for polynomial-time algorithms and for improvement and understanding of the belief…
The essential dimension is a numerical invariant of an algebraic group G which may be thought of as a measure of complexity of G-torsors over fields. A recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the essential…
It is shown that a trace invariant projection map, i.e. a positive unital idempotent map, of a finite dimensional C*-algebra into itself is non-decomposable if and only if it is atomic, or equivalently not the sum of a 2-positive and a…
An element $g$ of a group is called {\em reversible} if it is conjugate in the group to its inverse. This paper is about reversibles in the group $G$ of formally-invertible pairs of formal power series in two variables, with complex…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential…
In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…