In this paper we describe an algorithm and a Fortran 90 module (Conical) for the computation of the conical function P −1 2+iτ (x) for x > −1, m ≥ 0, τ > 0. These functions appear in the solution of Dirichlet problems for domains bounded by cones; because of this, they are involved in a large number of applications in Engineering and Physics. In the Fortran 90 module, the admissible parameter r...

UNLABELLED To better characterize the assembly of the HIV-1 core, we have used electron cryotomography (ECT) to image infected cells and the viral particles cryopreserved next to them. We observed progressive stages of virus assembly and egress, including flower-like flat Gag lattice assemblies, hemispherical budding profiles, and virus buds linked to the plasma membrane via a thin membrane nec...

We explore a specific discretization of isothermic nets in the plane which can also be interpreted as a discrete holomorphic map. The discrete orthogonality of the quadrilateral net is achieved by the so called conical condition imposed on vertex stars. That is, the sums of opposite angles between edges around all vertices are equal. This conical condition makes it possible to define a family o...

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dyn...

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with ...

Many mammals forage and burrow in dark constrained spaces. Touch through facial whiskers is important during these activities, but the close quarters makes whisker deployment challenging. The diverse shapes of facial whiskers reflect distinct ecological niches. Rodent whiskers are conical, often with a remarkably linear taper. Here we use theoretical and experimental methods to analyze interact...

We have studied the large-scale beam breakup and filamentation of femtosecond pulses in a Kerr medium. We have experimentally monitored the formation of stable light filaments, conical emission, and interactions between filaments. Three major stages lead to the formation of stable light filaments: First the beam breaks up into a pattern of connected lines sconstellationd, then filaments form on...

Estimating the intrinsic dimension of a high-dimensional data set is a very challenging problem in manifold learning and several other application areas in data mining. In this paper we introduce a novel local intrinsic dimension estimator, conical dimension, for estimating the intrinsic dimension of a data set consisting of points lying in the proximity of a manifold. Under minimal sampling as...

A dilatation structure encodes the approximate self-similarity of a metric space. A metric space (X, d) which admits a strong dilatation structure (definition 2.2) has a metric tangent space at any point x ∈ X (theorem 4.1), and any such metric tangent space has an algebraic structure of a conical group (theorem 4.2). Particular examples of conical groups are Carnot groups: these are simply con...

A number of commonly available density functionals have been tested for their ability to describe the energetics and the geometry at conical intersections in connection with the spin-restricted ensemble referenced Kohn-Sham (REKS) method. The minimum energy conical intersections have been optimized for several molecular systems, which are widely used as paradigmatic models of photochemical rear...