Related papers: Projective center point and Tverberg theorems

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.

In 2009, Blagojevic, Matschke & Ziegler established the first tight colored Tverberg theorem, but no lower bounds for the number of colored Tverberg partitions. We develop a colored version of our previous results (2008), and we extend our…

Dual to Koldobsky's notion of j-intersection bodies, the class of j-projection bodies is introduced, generalizing Minkowski's classical notion of projection bodies of convex bodies. A Fourier analytic characterization of j-projection bodies…

A classical result asserts that the complex projective plane modulo complex conjugation is the 4-dimensional sphere. We generalize this result in two directions by considering the projective planes over the normed real division algebras and…

We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the…

We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton--Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.

We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…

We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra…

The topological Tverberg theorem claims that for any continuous map of the (q-1)(d+1)-simplex to R^d there are q disjoint faces such that their images have a non-empty intersection. This has been proved for affine maps, and if $q$ is a…

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…

Both the USA TST 2008 and the ELMO Shortlist 2013 suggested two issues that are connected to fixed points. These problems provide a strong linkage between the various attributes of specific points in a triangle. In this article, we will…

We establish two direct extensions to the Butterfly Theorem on the cyclic quadrilateral along with the proofs using the projective method and analytic geometry of the Cartesian coordinate system.

In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.

Recent progress building on the groundbreaking work of Mabillard and Wagner has shown that there are important differences between the affine and continuous theory for Tverberg-type results. These results aim to describe the intersection…

I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…

We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.

We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.

We consider a projection from the center of the unit sphere to a tangent space of it, the central projection, and study two area minimizing problems of the image of a closed subset in the sphere. One of the problems is the uniqueness of the…

We introduce a new type of mappings in metric space which are three-point analogue of the well-known Chatterjea type mappings, and call them generalized Chatterjea type mappings. It is shown that such mappings can be discontinuous as is the…