The inflaton necessary to implement the mechanism of inflationary cosmology has natural candidates in quiver gauge theory. We discuss the dimensionless coefficients of quartic couplings and enumerate scalars which are singlet under the low-energy gauge group. The inflaton mass is generally predicted to be in the TeV region, close to 4 TeV for one specific unified model. A quartic inflaton poten...

We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the number of lines is at most 60 in both cases. We also give a complete classification of large configurations of lines.

This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate polynomials of degree four. Conditions are given for the convex hull of a plane quartic to be exactly semidefinite representable with at most 12 lifting variables. If the quartic is rationally parametrizable, an exact se...

We calculate both the cubic and the quartic self-couplings of the lighter scalar Higgs boson without assuming the decoupling limit in the two-Higgs-doublet model (THDM). In some regions of parameter space of the THDM where the electroweak phase transition is strongly first order, it is possible that the quartic self-coupling of the lighter scalar Higgs boson might be deviated by at least 40 % f...

This paper shows that many of elliptic curve cryptosystems over quartic extension fields of odd characteristics are reduced to genus two hyperelliptic curve cryptosystems over quadratic extension fields. Moreover, it shows that almost all of the genus two hyperelliptic curve cryptosystems over quadratic extension fields of odd characteristics come under Weil descent attack. This means that many...

In fact, [Eisenstein 1850] evaluated cubes and fourth powers of Gauss sums attached to cubic and quartic characters to prove the corresponding reciprocity laws. One essential point is the p-adic approximation of Gauss sums by [Kummer 1847], generalized in [Stickelberger 1890]. Since the rings of algebraic integers generated by third or fourth roots of unity have class number one and finitely-ma...

We consider deformations of a toroidal orbifold T 4/Z2 and an orbifold of quartic in CP . In the T 4/Z2 case, we construct a family of noncommutative K3 surfaces obtained via both complex and noncommutative deformations. We do this following the line of algebraic deformation done by Berenstein and Leigh for the Calabi-Yau threefold. We obtain 18 as the dimension of the moduli space both in the ...

We study new physics eeects to the quartic gauge boson couplings formulated by the electroweak chiral Lagrangian. Five next-to-leading order operators characterize the anomalous quartic gauge interactions which involve pure Goldstone boson dynamics for the electroweak symmetry breaking. We estimate the typical size of these couplings in diierent strongly-interacting models and examine the sensi...

We argue that topological compactons (solitons with compact support) may be quite common objects if k-fields, i.e., fields with nonstandard kinetic term, are considered, by showing that even for models with well-behaved potentials the unusual kinetic part may lead to a power-like approach to the vacuum, which is a typical signal for the existence of compactons. The related approximate scaling s...

We establish a complete set of invariants for ternary quartic forms. Further, we express four classical invariants in terms of these generators.