Related papers: A measure for the chirality of triangles
Molecular chirality has traditionally been viewed as a binary property where a molecule is classified as either chiral or achiral, yet in the recent decades mathematical methods for quantifying chirality have been explored. Here we use toy…
We consider an asymptotically flat Riemannian spin manifold of positive scalar curvature. An inequality is derived which bounds the Riemann tensor in terms of the total mass and quantifies in which sense curvature must become small when the…
In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…
In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, $(p,q)$-earth map tilings and their flip modifications, and quadrilateral…
As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.
The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the best-understood mirror statements relate certain small corners of the moduli spaces of X…
Recent work by J.Prades and myself on $K\to\pi\pi$ is described. The method we use to consistently connect long and short distances is described and numerical results for the $\Delta I=1/2$ rule and on $B_6$, the parameter relevant for the…
The triangular ratio metric is studied in subdomains of the complex plane and Euclidean $n$-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the…
We determine a positive real number (weight), which corresponds to a vertex of a tetrahedron and it depends on the three weights which correspond to the other three vertices and an infinitesimal number $\epsilon.$ As a limiting case, for…
Chiral tetrahedral molecules can be dealt under the standard of quaternionic algebra. Specifically, non-commutativity of quaternions is a feature directly related to the chirality of molecules. It is shown that a quaternionic representation…
Chirality, or handedness, is a topic that is common in biology and chemistry, yet is rarely discussed in physics courses. We provide a way of introducing the topic in classical physics, and demonstrate the merits of its inclusion - such as…
Finding necessary conditions for the geometry of flexible polyhedra is a classical problem that has received attention also in recent times. For flexible polyhedra with triangular faces, we showed in a previous work the existence of cycles…
We propose a method to perform a configuration determination for chiral and/or polar crystals by utilizing anisotropy of NMR shift. The chirality (handedness) or polarity of a crystal, that is characterized by its sign, can be extracted…
On a compact Riemannian manifold with boundary, we study the set of conformal metrics of negative constant scalar curvature in the interior and positive constant mean curvature on the boundary. Working in the case of positive Yamabe…
Chirality is at the origin of life and is ubiquitous in nature. An object is deemed chiral if it is non-superimposable with its own mirror image. This relates to how circularly polarized light interacts with such object, a circular…
Within the Standard Model, a review of the current determination of the sides and angles of the CKM unitarity triangle is presented, using experimental constraints from the measurements of |\epsilon_K|, |V_{ub}/V_{cb}|, \Delta m_d and from…
A Boolean $\sigma$-algebra $B$ is a measure algebra if and only if it is weakly distributive and uniformly concentrated.
We consider tilings of a triangle $ABC$ by congruent copies of a triangle that has one angle equal to $120^\circ$, has non-commensurable angles (that is, not all angles are rational multiples of $\pi$), and is not similar to $ABC$. We prove…
A uniaxial chiral metamaterial is constructed by double-layered four "U" split ring resonators mutually twisted by 90 degrees. It shows a giant optical activity and circular dichroism. The retrieval results reveal that a negative refractive…
The precise measurements of the Bd oscillation frequency and the limit on the Bs one one as well as the determination of the Cabibbo-Kobayashi-Maskawa matrix element Vub improve the constraints on the other elements of this matrix. A fit to…