Related papers: A positive factorization for the balanced superell…
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
Any rational number can be factored into a product of several rationals whose sum vanishes. This simple but nontrivial fact was suggested as a problem on a maths olympiad for high-school students. We completely solve similar questions in…
First, we give a formula for the foci of an ellipse, $E_0$, as a function of the coefficients of an equation of $E_0$(see Theorem <ref>T2</ref>). To prove Theorem <ref>T2</ref>, we use two interesting formulas proven in <cite>B</cite> and…
Alternative canonical methods for defining canonical SO(3)-coupled bases for SU(3) irreps are considered and compared. It is shown that a basis that diagonalizes a particular linear combination of SO(3) invariants in the SU(3) universal…
It is shown that for a bounded weighted bilateral shift $T$ acting on $\ell_p(\Z)$ for $1\leq p\leq 2$ supercyclicity of $T$, weak supercyclicity of $T$, cyclicity of $T\oplus T$ and cyclicity of $T^2$ are equivalent. A new sufficient…
Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions. Factorizations of spinor polynomial corresponds to the…
By applying Berry-phase theory for the effective half-filled Hubbard model, we derive an analytical expression for the electronic polarization driven by the relativistic spin-orbit (SO) coupling. The model itself is constructed in the…
We propose a contact-topological approach to the spatial circular restricted three-body problem, for energies below and slightly above the first critical energy value. We prove the existence of a circle family of global hypersurfaces of…
Fix a positive integer k. In this paper, we give a formula in closed form for all k-polygonal numbers that are also centered k-polygonal.
The results of an extensive numerical study of the periodic orbits of planar, elliptic restricted three-body planetary systems consisting of a star, an inner massive planet and an outer mass-less body in the external 1:2 mean-motion…
Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that "most" functions are optimized by measures supported on a periodic orbit, and it has…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a…
A tiling (edge-to-edge) of the plane is a family of tiles that cover the plane without gaps or overlaps. Vertex figure of a vertex in a tiling to be the union of all edges incident to that vertex. A tiling is $k$-vertex-homogeneous if any…
A conformal map from a Riemann surface to the Euclidean four-space is explained in terms of its twistor lift. A local factorization of a differential of a conformal map is obtained. As an application, the factorization of a differential…
We show that every positive expansive flow on a compact metric space consists of a finite number of periodic orbits and fixed points.
We study the cone of completely positive (cp) matrices for the first interesting case $n = 5$. This is a semialgebraic set, which means that the polynomial equalities and inequlities that define its boundary can be derived. We characterize…
Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…
The existence of an equidimensional morphism f with etale local sections from a regular algebraic space X to a locally noetherian normal algebraic space S of characteristic zero with excellent local rings implies that S is regular and f…
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with…