Related papers: Generalized Ray Spaces for Paraparticles
Recently it turned out that the paraproduct plays the key role in some highly singular partial differential equations. In this note the counterparts for Besov--Morrey spaces are obtained. This note is organized in a self-contained manner.
In recent years, unprecedented progress in observational cosmology has revealed a great deal of information about the formation and evolution of structures in the universe. This, in turn, has raised many challenging issues for the…
Assuming existence of (very) heavy fourth generation of quarks and antiquarks we argue that antibaryon composed of the three heavy antiquarks can be light, stable and invisible, hence a good candidate for the Dark matter particle. Such…
An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V(p), with a…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
Motivated by the observed ratio of dark matter to baryon mass densities, $\rho_D/\rho_B \simeq 5$, we propose a theory of dark-color unification. In this theory, the dark to visible baryon masses are fixed by the ratio of dark to visible…
The primordial black hole (PBH) comprising full dark matter (DM) abundance is currently allowed if its mass lies between $10^{-16}M_{\odot} \lesssim M \lesssim 10^{-11} M_{\odot}$. This lightest mass range is hard to be probed by ongoing…
The algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons, satisfying the mutual parafermion relations, is known to be the Lie superalgebra osp(2m+1|2n). The Fock spaces of…
P-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $Sp(2,R)\otimes Sp(2,R)$ locally invariant. Although this special…
Let $P$ be a set of points in $\mathbb{R}^d$, $B$ a bicoloring of $P$ and $\Oo$ a family of geometric objects (that is, intervals, boxes, balls, etc). An object from $\Oo$ is called balanced with respect to $B$ if it contains the same…
We mainly discuss the cardinal invariants and generalized metric properties on paratopological groups or rectifiable spaces, and show that: (1) If $A$ and $B$ are $\omega$-narrow subsets of a paratopological group $G$, then $AB$ is…
We prove sharp upper bounds for sums of eigenvalues (and other spectral functionals) of Laplace-like operators, including bi-Laplacian and fractional Laplacian. We show that among linear images of a highly symmetric domain, our spectral…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
Gamma-ray bursts (GRBs) are believed to originate from ultra-relativistic winds/fireballs to avoid the "compactness problem". However, the most energetic photons in GRBs may still suffer from $\gamma-\gamma$ absorption leading to…
A new infinite family of examples of finite non-bicolorable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and Kochen-Specker theorem and…
We revisit the field content and consistency of the New General Relativity family of theories. These theories are constructed in a geometrical framework with a flat and metric-compatible connection, so the affine structure is entirely…
A $Z_2\times Z_2$-graded Lie superalgebra $g$ is a $Z_2\times Z_2$-graded algebra with a bracket $[.,.]$ that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology, $g$ is not a…
For any prime number p and any positive real number {\alpha}, we construct a finitely generated group {\Gamma} with p-gradient equal to {\alpha}. This construction is used to show that there exist uncountably many pairwise non-commensurable…
One of the most compelling candidates for Dark Matter (DM) are light pseudo-scalar particles (axions), motivated by the strong CP problem and axiverse scenario in string theory. Depending on their mass and type of self-interaction, these…
We ask whether the universe can be a patchwork consisting of distinct regions of matter and antimatter. In previous work we demonstrated that post-recombination matter-antimatter contact near regional boundaries leads to an observable (but…