Related papers: Quartic double solids with icosahedral symmetry
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…
Symmetry implications for the decoherence of quantum oscillations of a two-state system in a solid are studied. When the oscillation frequency is small compared to the Debye frequency, the universal lower bound on the decoherence due to the…
In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable…
In this paper we prove some new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities, in any dimension larger or equal than two.
Supersymmetry is studied in 2+1 dimensions. In addition to the multiplets corresponding to those in 3+1 dimensions the Clifford algebra allows an extra set. When the extra chiral multiplet is included, formulating supersymmetric QED3 in the…
We estimate $\delta$-invariants of some singular del Pezzo surfaces with quotient singularities, which we studied ten years ago. As a result, we show that each of these surfaces admits an orbifold K\"ahler--Einstein metric.
The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.
We present an ultraviolet extension of the Twin Higgs in which the radial mode of twin symmetry breaking is itself a pseudo-goldstone boson. This "turtle" structure raises the scale of new colored particles in exchange for additional states…
The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line,…
A radiative model of quark and lepton masses utilizing the binary tetrahedral ($T^{\prime}$) flavor symmetry, or horizontal symmetry, is proposed which produces the first two generation of quark masses through their interactions with…
We define two conformal structures on $S^1$ which give rise to a different view of the affine curvature flow and a new curvature flow, the ``$Q$-curvature flow". The steady state of these flows are studied. More specifically, we prove four…
We will look for stable structures in four situations and discuss what is known and unknown.
The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.
In a series of three lectures, I review the theory and phenomenology of heavy quark masses and mixing angles and the status of their determination. In addition, I give an introduction to heavy quark symmetry, with the main emphasis on the…
This article reports the spherical coordinate form of three-dimensional generalized dynamics of soft-matter quasicrystals with 12-fold symmetry which provides a basis for solving initial-boundary value problems of the equations under some…
The aim of this short note is to give a simple proof of the non-rationality of the double cover of the three-dimensional projective space branched over a sufficiently general quartic.
Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously…
We study the thermodynamic properties of QCD at nonzero isospin chemical potential using improved staggered quarks at physical quark masses. In particular, we discuss the determination of the equation of state at zero and nonzero…
The q-deformed coherent states for a quantum particle on a circle are introduced and their properties investigated.
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.