An L-spherical code is a set of Euclidean unit vectors whose pairwise inner products belong to the set L. We show, for a fixed α, β > 0, that the size of any [−1,−β] ∪ {α}-spherical code is at most linear in the dimension. In particular, this bound applies to sets of lines such that every two are at a fixed angle to each another.

In the context of the p-spin spherical model we show how saddle points of the

We present the results of an empirical study, which investigated the effects of the amount of information and the type of information refuted in refutation texts. The study compared the effects of three refutation texts on elementary school children’s understanding of the scientific concept of the Earth. One text refuted only the belief that the Earth is flat, the second refuted in addition the...

Light scattered from spherical bubbles in water manifests an enhancement in the backward direction analogous to the well-known optical glory of a drop. Unlike the glory for water drops, in which the rays travel partially on the drop's surface, the glory for bubbles is due to rays that are refracted and multiply reflected within the scatterer and is an example of a transmitted wave glory. Photog...

Let Uε(g) be the simply connected quantized enveloping algebra associated to an exceptional simple Lie algebra g at the roots of unity. The De Concini-Kac-Procesi conjecture on the dimension of the irreducible representations of Uε(g) is proved for representations corresponding to the spherical conjugacy classes of the simply connected group with Lie algebra g.

We construct piecewise constant wavelets on spherical triangulations, which are orthogonal with respect to a scalar product on L(S), defined in [3]. Our classes of wavelets include the wavelets obtained by Bonneau in [1] and by Nielson et all. in [2]. We also proved the Riesz stability and showed some numerical experiments.

A new anchor-based optimization method of defining energy density functionals (EDFs) is proposed. In this approach, the parameters EDFs carried out for a selected set spherical anchor nuclei, physical observables which are modified by correction function, takes into account global performance EDFs. It shown that use approach leads to substantial improvement in description binding energies sever...

A general analysis for characterizing and classifying ‘isolated horizons’ is presented in terms of null tetrads and spin coefficients. The freely specifiable spin coefficients corresponding to isolated horizons are identified and specific symmetry classes are enumerated. For isolated horizons admitting at least one spatial isometry, a standard set of spherical coordinates are introduced and ass...

In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to various types of asymptotic problems in the Kähler geometry of GIT quotients. We discuss several particular classes of examples, namely, toric varieties, spherical varieties and the symplectic version of quiver varieties.

A spherical approximation technique is presented that affords a mathematical characterization of a virtual space receptive field (VSRF) based on first-spike latency in the auditory cortex of cat. Parameterizing directional sensitivity in this fashion is much akin to the use of difference-of-Gaussian (DOG) functions for modeling neural responses in visual cortex. Artificial neural networks and a...