We present a declarative framework for updating views over indefinite databases, that is, databases with null values. The framework follows the standard database approach, which allows for a unique null constant. As the main contributions of the paper, we introduce the concept of an indefinite deductive database as a formal representation of a view over an indefinite database, propose a semanti...

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

Abstract We define generalised zeta functions associated with indefinite quadratic forms of signature $$(g-1,1)$$ (g-1,1) —and more generally, to complex symmetric matrices whose imaginary ...

<p style='text-indent:20px;'>This paper study nonstationary homoclinic-type solutions for a fractional reaction-diffusion system with asymptotically linear and local super nonlinearity. The resulting problem engages two major difficulties: one is that the associated functional strongly indefinite, second lies in verifying link geometry showing boundedness of Cerami sequences when nonlinea...

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a “definite totality” but rather is “indefinitely extensible”. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this pictur...

Efficient learning of a data analysis task strongly depends on the data representation. Many methods rely on symmetric similarity or dissimilarity representations by means of metric inner products or distances, providing easy access to powerful mathematical formalisms like kernel approaches. Similarities and dissimilarities are however often naturally obtained by non-metric proximity measures w...

Robotics researchers increasingly agree that ideas from biology and self-organization can strongly benefit the design of autonomous robots. Biological organisms have evolved to perform and survive in a world characterized by rapid changes, high uncertainty, indefinite richness, and limited availability of information. Industrial robots, in contrast, operate in highly controlled environments wit...

in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.