Related papers: On the universality of Somos' constant
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
We calculate the particle spectrum of the SSM which follows from the assumption that the commonly assumed universal form of the soft supersymmetry --breaking terms is invariant under renormalisation. It is argued that this ``strong''…
A classical solution is called universal if the quantum correction is a multiple of the metric. Universal solutions consequently play an important role in the quantum theory. We show that in a spacetime which is universal all of the scalar…
We give a complete proof of the generalized Khavinson conjecture which states that, for bounded harmonic functions on the unit ball of $\mathbb{R}^n$, the sharp constants in the estimates for their radial derivatives and for their gradients…
The issue of the cosmological constant is discussed in details and a solution to the problem is suggested.
In this appendix to our paper with the same title posted on arxiv we give a quick proof of an inequality that can be substituted to Hastings's result, quoted as Lemma 1.9 in our previous paper. Our inequality is less sharp but also appears…
The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between…
We study the possible interpretation of the "universal constants" by the classification of J.~M.~L\'evy-Leblond. $\hbar$ and $c$ are the most common example of constants of this type. Using Fock's principle of the relativity w.r.t.…
We define the generalized-Euler-constant function $\gamma(z)=\sum_{n=1}^{\infty} z^{n-1} (\frac{1}{n}-\log \frac{n+1}{n})$ when $|z|\leq 1$. Its values include both Euler's constant $\gamma=\gamma(1)$ and the "alternating Euler constant"…
Scaling relations for the mass, angular momentum and other properties of a wide range of self-similar structures in the universe are seen to have universal features. As a consequence of the ideas elaborated in earlier papers these relations…
In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of an even-dimensional neighborly polytope. This in particular provides the final step for Mn\"ev's proof of the…
This paper collects results and open problems concerning several classes of functions that generalize uniform continuity in various ways, including those metric spaces (generalizing Atsuji spaces) where all continuous functions have the…
We prove a general multidimensional invariance principle for a family of U-statistics based on freely independent non-commutative random variables of the type $U_n(S)$, where $U_n(x)$ is the $n$-th Chebyshev polynomial and $S$ is a standard…
We provide a consistency relation between cosmological observables in general relativity with the cosmological constant. Breaking of this relation at any redshift would imply the breakdown of the hypothesis of the cosmological constant as…
Various contributions to the cosmological constant are discussed and confronted with its recent measurement. We briefly review different scenarious -- and their difficulties -- for a solution of the cosmological constant problem.
We here consider a generalization of the Klein-Gordon scalar wave equation which involves a single arbitrary function. The quantization may be viewed as allowing $\hbar$ to be a function of the momentum or wave vector rather than a…
We study the properties of fundamental physical constants using the threefold classification of dimensional constants proposed by J.-M. L{\'e}vy-Leblond: constants of objects (masses, etc.), constants of phenomena (coupling constants), and…
A generalization of the law of total covariance is presented and proved.
In this paper, we consider representations of integers as sums of generalized heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such…
We connect a possible solution for the ``cosmological constant problem'' to the existence of a (postulated) conformal fixed point in a fundamental theory. The resulting cosmology leads to quintessence, where the present acceleration of the…