We prove two results about the local properties of generically one to one analytic mappings. Version: .76; Revised: 12–15–98; Run: March 23, 1999 §1: Introduction In this paper we consider two local properties of analytic maps which are generically one to one. First we consider holomorphic maps from open sets in C which behave locally like monoidal transformations: Let (z, w) denote coordinates...

We take a fresh look at the problem of removing occluders in an image using inpainting. We examine a geometric method that utilizes a second image of the scene from a different viewpoint, to identify the occluded objects. We recover the missing intensities by using the geometric relationship between corresponding points in the two images. The relationship is generally specified by the “epipolar...

Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)—to Klein. We will see that they are not rivalling but are tied (by Galois). We also examine their modern life as philosophies of non-commutative geometry. Connections between different objects (see keywords) are discussed. ∗Support...

Multiphase flow phenomena are ubiquitous. Common examples include coupled atmosphere and ocean system (air and water), oil reservoir (water, oil and gas), cloud and fog (water vapor, water and air). Multiphase flows also play an important role in many engineering and environmental science applications. In some applications such as flows in unconfined karst aquifers, karst oil reservoir, proton ...

One of the key properties of the length of a curve is its lower semicontinuity : if a sequence of curves γi converges to a curve γ, then length(γ) ≤ lim inf length(γi). Here the weakest type of pointwise convergence suffices. There are higher-dimensional analogs of this semicontinuity for Riemannian (and even Finsler) metrics. For instance, the Besicovitch inequality (see, e.g., [1] and [4]) im...

Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters, specific heats or susceptibilities. The relative entropy induces a metric, the so-called information or Fisher-Rao metric, on the space of parameters and the g...

Sample size calculations require specification of the treatment effect, but what if this is not known? Two-stage tests use the first stage to estimate the treatment effect and modify the sample size accordingly. The purpose of this paper is to unify the theory of two-stage testing based on treatment effect. The conditional error function approach of Proschan and Hunsberger (1995) is shown to be...

Modern physical theories tell us that space is not euclidean. Yet, to most people, euclidean geometry seems most natural. Furthermore, most mathematical theories of non-euclidean geometry refer back to euclidean geometry in one way or another. For example, in differential geometry, the differential areas are almost always approximately Euclidean. Why is this? I want to suggest here a reason roo...

We review entanglement in the context of two qubits. Equivalence under appropriate local operations leads to a representation of the notions of entangled and separable states and entanglement witnesses geometrically in 3 dimensions. The corresponding four dimensional description captures, in addition, the entanglement measure and en-tanglement distillation geometrically. We give a neat formula ...

The results of [1, 2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1, 2]. Secondly, these codes are used to define a dual two-weight code and strongly regular graph similar to the classical case of projective linear two-weight code...