Identifying the projective group for patterns by developing the camera model, the projective Fourier transform and its inverse are obtained in analogy with the classical, that is, Euclidean Fourier analysis. Projectively adapted properties are demonstrated in a numerical test. Using the expression of the projective Fourier integral by a standard Fourier integral in the coordinates given by the ...

Let us be more precise. Of course, it is tautological that any projective curve can be embedded into some projective space. However, once we begin making demands on the embedding, we start to get some interesting answers. For instance, can we make sure target projective space “small”? It is easy to show that not every curve can be embedded in P2. Conversely, every smooth projective curve can be...

A fake projective plane is a compact complex surface (a compact complex manifold of dimension 2) with the same Betti numbers as the complex projective plane, but not isomorphic to the complex projective plane. As was shown by Mumford, there exists at least one such surface. In this paper we prove the existence of a fake projective plane which is birational to a cyclic cover of degree 7 of a Dol...

Is this really evidence (as is often cited) that the Continuum Hypothesis has no answer? Another prominent problem from the early 20th century concerns the projective sets, [8]; these are the subsets of Rn which are generated from the closed sets in finitely many steps taking images by continuous functions, f : Rn → Rn, and complements. A function, f : R→ R, is projective if the graph of f is a...

The interaction of various algebraic structures, describing fusion, braiding and group symmetries in quantum projective field theory, is an object of an investigation in the paper. Structures of projective Zamolodchikov algebras, their representations, spherical correlation functions, correlation characters and envelopping QPFT–operator algebras, projective Ẅ–algebras, shift algebras, infinite ...

2. Projective Tensors. Theorems of the projective geometry of paths appear to have their statement in terms of what may be called projective tensors, i. e. tensors which are independent of the particular set of functions T\^ defining the paths. We shall show how a set of projective tensors may be derived by covariant differentiation from an w-uple of mutually independent vectors. Let h(a)i deno...

inspired by a recent work of buchweitz and flenner, we show that, for a semidualizing bimodule $c$, $c$--perfect complexes have the ability to detect when a ring is strongly regular.it is shown that there exists a class of modules which admit minimal resolutions of $c$--projective modules.

It is a continuing task of psychoanalytic thinking to attempt to generate concepts and consistent language that are helpful in understanding the interplay between phenomena in an intrapsychic sphere (e.g. thoughts and feelings) and phenomena in the sphere of external reality and interpersonal relations (e.g. the reality of the other person in an object relationship as opposed to the psychologic...

We introduce the notion of the projective linking number LinkP(Γ, Z) of a compact oriented real submanifold Γ of dimension 2p − 1 in complex projective n-space P with an algebraic subvariety Z ⊂ P − Γ of codimension p. This notion is related to projective winding numbers and quasi-plurisubharmonic functions, and it is generalized to any projective manifold X . It is shown that a basic conjectur...

In this paper an unusual taxonomy for optical mappings is introduced based on their geometric characteristics: 1. type of projection center (single viewpoint, non single viewpoint) and 2. type of transformation (projective, non projective). Under this background we survey the multi media geometry (refraction resulting from different optical media). Strict physical models of non projective mappi...