We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli spaces of stable varieties to the moduli space of a product of stable varieties; (b) this map is always finite étale; and (c) this map very often is an isomorphis...

We present a geometric interpretation of a product form stationary distribution for a d-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The d-dimensional SRBM data can be equivalently specified by d + 1 geometric objects: an ellipse and d rays. Using these geometric objects, we establish necessary and sufficient conditions for characterizing p...

In this paper, we explore the geometric objects of conformal geometric algebra based on their IPNS (inner product null space) representation in some detail. Spheres of dimension 1 , 2 and three are objects of conformal geometric algebra. Usually, points in conformal geometric algebra are represented as ordinary spheres with zero radius, but what about circles with zero radius? We expect many pr...

high congestion of returned product at remanufacturing facility causes substantial delays and consequently remarketing value losses for time-sensitive and high-tech products with short life cycles, such as electronic equipments. at the remanufacturing site the returned product are inspected and classified according to their quality and processing time in one of the two classes: class 1 being ad...

Features are important to maintain geometric and non-geometric relations across product models. The generic feature model provides flexibility and finer-level of granularity for an integrated feature-based modelling framework between CAD/CAM applications. Unfortunately, often during data translation some useful geometric and non-geometric information such as features and their associated semant...

A Clifford algebra has three major multiplications: inner product, outer product and geometric product. Accordingly, the same Clifford algebra has three versions: Clifford vector algebra, which features on inner products and outer products of multivectors; Clifford bracket algebra, which features on pseudoscalars and inner products of vectors; Clifford geometric algebra, which features on geome...

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used...

This paper describes a geometric query model for dynamic exploring multidimensional data. An application of the model for solving the problem of materials selection in product design is discussed. Data from database are interpreted geometrically as multidimensional points. A query window is a query solid of any shape specified by its location. The queries are formulated with geometric objects a...