We show that the ring of modular forms with characters for even unimodular lattice signature (2,10) is generated by weights 4, 10, 12, 16, 18, 22, 24, 28, 30, 36, 42, and 252 one relation weight 504. The proof based on comparison orbifold quotient symmetric domain root stack coarse moduli space.

We study a scenario to derive four-dimensional modular flavor symmetric models from higher dimensional theory by assuming the compactification consistent with symmetry. In our scenario, wavefunctions in extra compact space are forms. That leads constraints on combinations between weights and $\Gamma_N$ ($\Gamma_N')$ representations of matter fields. also present illustrating examples.

It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value of the parameter (corresponding to half-densities) the star product is symmetric, and specializes in the projectively flat case to the one constructed previ...

The eigenvectors of a symmetric matrix can be chosen to form a biorthogonal set with respect to the identity and to the matrix itself. Similarly, the eigenvectors of a symmetric de nite linear pencil can be chosen to be biorthogonal with respect to the pair.This paper presents the three sets of matrix weights, with respect to which the eigenvectors of the symmetric de nite quadratic pencil are ...

In the recently developed algebraic attacks applying to block and stream ciphers([1-5]), the concept of algebraic immunity (AI) is introduced in [6] and studied in [6-14]. High algebraic immunity is a necessary condition for resisting algebraic attacks. In this paper, we give some lower bounds on algebraic immunity of Boolean functions. The results are applied to give lower bounds on AI of symm...

BACKGROUND Digital self-monitoring, particularly of weight, is increasingly prevalent. The associated data could be reused for clinical and research purposes. OBJECTIVE The aim was to compare participants who use connected smart scale technologies with the general population and explore how use of smart scale technology affects, or is affected by, weight change. METHODS This was a retrospec...

Recently I.Macdonald defined a family of systems of orthogonal symmetric polynomials depending of two parameters q, k which interpolate between Schur’s symmetric functions and certain spherical functions on SL(n) over the real and p-adic fields [M]. These polynomials are labeled by dominant integral weights of SL(n), and (as was shown by I.Macdonald) are uniquely defined by two conditions: 1) t...

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

We give a definition of the notion spherical varieties in world complex supervarieties with actions algebraic supergroups. A characterization affine is given which generalizes classical case. also explain some general properties monoid highest weights. Several examples are discussed that interesting their own right and highlight differences case, including regular representation, symmetric supe...