We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most applications, hence the need for delaying the exact computations at run time until they are actually needed. Our approach is generic and extensible in the sen...

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two or more copulas. Similarly, one might consider weighted geometric means. Consider, for instance, the...

Practical solid modeling systems are plagued by numerical problems that arise from using oating-point arithmetic. For example, polyhedral solids are often represented by a combination of geometric and combinatorial information. The geometric information might consist of explicit plane equations, with oating-point coeecients; the combinatorial information might consist of face, edge, and vertex ...

particulate matters commonly found dispersed in the atmosphere are composed of a large variety of substances. dustfall is the usual index of particles in the size range greater than 10 m. two semi automated so2 sampling units were installed in tehran university campus (from 21 january 1973 to 22 dec. 1974) and gheitarieh area (from 23 august to 23 oct. 1974) hydrogen peroxide method was used fo...

For a prime p, we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These groups correspond to sublattices of index p of the transcendental lattice TS of S; we classify these lattices up to isomorphism using Nikulin’s discriminant form technique. We then study geometric realizations of p-torsion ...

For a prime p, we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These groups correspond to sublattices of index p of the transcendental lattice TS of S; we classify these lattices up to isomorphism using Nikulin’s discriminant form technique. We then study geometric realizations of p-torsion ...

This thesis investigates computational methods for pricing complex path-dependent derivative securities, especially geometricand arithmetic-moving-average-lookback options. The latter security was rst issued by Polaris Securities in 1999. Our methodology can be easily modi ed to price similarly structured options issued by other securities rms. The moving-average-lookback option is a call optio...

Optimal inequalities involving the p-Yang means are established. Bounding quantities are either the arithmetic or geometric or the harmonic combinations of the p-geometric and the p-quadratic means.

Debate continues on the proper approach for forecasting rates of return. Generally, past performance of similar risk-class asset returns serves as the determinant for expected future returns. These forecasts inform strategies applicable to endowments, retirement and trust funds, and generally to any investment. Traditionally, arithmetic averages (means) have served as the historical metric. Arg...