Related papers: Alpha magnitude
Galactic systems, and the Universe at large, exhibit large dynamical anomalies: The observed matter in them falls very short of providing enough gravity to account for their dynamics. The mainstream response to this conundrum is to invoke…
On basis of modification of Einstein's gravitational equations by adding the term $f(R)\propto \beta R^n$, a geometric model of quintessence is proposed. The evolution equation for the scale factor $a$ of the Universe is analyzed for the…
"An invariant of metric spaces under bornologous equivalences" gives an invariant and "A coarse invariant" extends the invariant to coarse equivalences. In both papers the invariant is defined for a class of metric spaces called sigma…
To explain the recently reported large-scale spatial variations of the fine structure constant $\alpha$, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
The notion of a homogeneous standard filtration of $\sigma$-algebras was introduced by the author in 1970. The main theorem asserted that a homogeneous filtration is standard, i.e., generated by a sequence of independent random variables,…
Idempotent analogues of convexity are introduced. It is proved that the category of algebras for the capacity monad in the category of compacta is isomorphic to the category of $(\max,\min)$-idempotent biconvex compacta and their biaffine…
In this paper we consider a special class of polymorphisms with invariant measure, - (cf.[1])- the algebraic polymorphisms of compact groups. A general polymorphism is -- by definition -- a many-valued map with invariant measure, and the…
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chru\'sciel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change…
In the present paper, the notion of $\mathbb{R}$-complex Finsler space with Infinite Series ($\alpha, \beta$)- metric $\dfrac{\beta^2}{\beta - \alpha}$ is defined. The Fundamental metric fields $g_{ij}$, $g_{i\bar{j}}$, their determinants…
Consider a polynomial $f$ defined over a field $k$, the multiplicity is perhaps the most naive measurement of the singularities of $f$. This paper describes the first steps toward understanding a much more subtle measure of singularities…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
Robustness is a property of system analyses, namely monotonic maps from the complete lattice of subsets of a (system's state) space to the two-point lattice. The definition of robustness requires the space to be a metric space. Robust…
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product(STP) of matrices are…
The idea that General Relativity could be an effective model, of a yet unknown theory of gravity, has gained momentum among theoretical physicists. The polynomial affine model of gravity is an alternative model of affine gravity that…
In this paper, we study various factorization invariants of arithmetical congruence monoids. The invariants we investigate are the catenary degree, a measure of the maximum distance between any two factorizations of the same element, the…
In this paper, a new class of Finsler metrics which are included $(\alpha,\beta)$-metrics are introduced. They are defined by a Riemannian metric and two 1-forms $\beta=b_i(x)y^i$ and $\gamma= \gamma_i(x)y^i$. This class of metrics are a…
This work extends the recently introduced Alpha-Procrustes family of Riemannian metrics for symmetric positive definite (SPD) matrices by incorporating generalized versions of the Bures-Wasserstein (GBW), Log-Euclidean, and Wasserstein…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…