We give a method for constructing maps from a non-commutative scheme to a commutative projective curve. With the aid of Artin-Zhang’s abstract Hilbert schemes, this is used to construct analogues of the extremal contraction of a K-negative curve with self-intersection zero on a smooth projective surface. This result will hopefully be useful in studying Artin’s conjecture on the birational class...

Girard described two translations of intuitionistic logic into linear logic, one where A ! B maps to (!A) ? B, and another where it maps to !(A ? B). We detail the action of these translations on terms, and show that the rst corresponds to a call-by-name calculus, while the second corresponds to call-by-value. We further show that if the target of the translation is taken to be an aane calculus...

We develop a categorical compositional distributional semantics for Lambek Calculus with Relevant Modality !L*, which has limited edition of the contraction and permutation rules. The part is monoidal biclosed category coalgebra modality, very similar to structure Differential Category. instantiate this finite dimensional vector spaces linear maps via "quantisation" functors work three concrete...

Hierarchies of plane graphs, called graph pyramids, can be used for collecting, storing, and analyzing geographical information based on images or other input data. The visualization of graph pyramids facilitates studies about their structure, such as their vertex distribution or height in relation of a specific input image. Thus, a researcher can debug contraction processes and ask for statist...

Graph pyramids are often used for representing irregular image pyramids. For the 2D case, combinatorial pyramids have been recently defined in order to explicitly represent more topological information than graph pyramids. The main contribution of this work is the definition of pyramids of n-dimensional generalized maps. This extends the previous works to any dimension, and generalizes them in ...

Objectives: In this paper, we have to establish a generalized common fixed point theorem in cone rectangular metric spaces. Methods: use the Banach contraction principle technique theorem. Findings: The paper presents unique for two weakly compatible self-maps satisfying expansive type mapping space without assuming normality condition of cone. Our result extends and supplements some well-known...

In this thesis, we have proposed ACTOM, a Topic Map building approach based on an automated processtaking into account multilingual documents and Topic Map evolution according to content and usage changes.To enrich the Topic Map, we are based on a domain thesaurus and we propose to explore all potentialquestions related to source documents on order to represent usage in the Topic Ma...

In this paper, we present a new concept of random contraction and prove a coupled random fixed point theorem under this condition which generalizes stochastic Banach contraction principle. Finally, we apply our contraction to obtain a solution of random nonlinear integral equations and we present a numerical example.

Many documents and more generally many resources are produced or used in an e-learning application. In order to capitalize these resources and to facilitate their access, we propose to organise them in a “learning organisational memory” (MEMORAe project). In this paper, we present the context of use, the needs and the contents of this memory. We describe the ontologies and the Topic Maps formal...