An enumerative formula for the spherical cap discrepancy

An extension of the exponential formula in enumerative combinatorics

Let α be a formal variable and Fw be a weighted species of structures (class of structures closed under weight-preserving isomorphisms) of the form Fw = E(F c w), where E and F c w respectively denote the species of sets and of connected Fw-structures. Multiplying by α the weight of each F c wstructure yields the species Fw(α) = E(F c αw). We introduce a “universal” virtual weighted species, Λ,...

The Impending Demise of the Discrepancy Formula

Spherical Designs, Discrepancy and Numerical Integration

A spherical design is a point configuration on the sphere, which yields exact equal-weight quadrature formulae for polynomials up to a given degree. Until now only very specific constructions for spherical designs are known. We establish connections to spherical cap discrepancy and show some general discrepancy bounds. Furthermore, we reformulate the problem of constructing designs as an optimi...

Combining spherical-cap and Taylor bubble fluid

Basaltic activity is the most common class of volcanism on Earth, characterized by magmas 12 of sufficiently low viscosities such that bubbles can move independently of the melt. Following 13 exsolution, spherical bubbles can then expand and/or coalesce to generate larger bubbles of 14 spherical-cap or Taylor bubble (slug) morphologies. Puffing and strombolian explosive activity are 15 driven b...

an investigation about the appropriate stochastic modeling framework for agricultural insurance pricing

با توجه به اینکه بیمه محصولات کشاورزی در ایران بیشتر جنبه ای حمایتی دارد و خسارات گزارش شده عموما بیش از حق بیمه های دریافت شده است، در این پایان نامه به جهت تعیین قیمت بیمه محصولات کشاورزی (گندم دیم) از فرآیندهای نوفه شلیک به عنوان مدلی مناسب استفاده شده است. بر اساس داده های صندوق بیمه کشاورزی از خسارات اعلام شده در سال زراعی 1388-1389 گندم دیم، در این پایان نامه حق بیمه خالص و ناخالص این محص...