Search results for "Variable"
showing 10 items of 1674 documents
Probabilistic foundations of contextuality
2017
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint, contextuality is mathematically impossible even if one generally allows (as one must) for random variables not to be jointly distributed. To avoid contradictions one has to adopt the Contextuality-by-Default approach: measurements made in different contexts are always distinct and stochastically unrelated to each other. Contextuality is reformulated then in terms of the (im)possibility of imposing on all the measurements in a system a joint distribution of a particul…
Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview
2012
Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent, response variables), and in quantum mechanics (QM), to deal with the EPR entanglement phenomena (deciding whether an EPR experiment allows for a "classical" account). The parallels between these problems are established by observing that any two noncommuting measurements in QM are mutually exclusive and can therefore be treated as analogs of different values of one and the same input. Both problems reduce to that of the existence of a jointly distributed syst…
Quantifier Elimination and Rectilinearisation Theorem for Generalised Quasianalytic Algebras
2013
International audience; An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation result for generalised quasianalytic algebras.
Virtual and arrow Temperley–Lieb algebras, Markov traces, and virtual link invariants
2021
Let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and let [Formula: see text] be the algebra of Laurent polynomials in the variable [Formula: see text] and standard polynomials in the variables [Formula: see text] For [Formula: see text] we denote by [Formula: see text] the virtual braid group on [Formula: see text] strands. We define two towers of algebras [Formula: see text] and [Formula: see text] in terms of diagrams. For each [Formula: see text] we determine presentations for both, [Formula: see text] and [Formula: see text]. We determine sequences of homomorphisms [Formula: see text] and [Formula: see text], we determine Markov traces […
Envelopes of open sets and extending holomorphic functions on dual Banach spaces
2010
We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.
Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator
2017
We prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the $p(x)$-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and three weak solutions, by using variational methods and critical point theory.
Multiple solutions for a Neumann-type differential inclusion problem involving the p(.)-Laplacian
2012
Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a Neumann-type differential inclusion problem involving the $p(\cdot)$-Laplacian.
Partial inner product spaces: Some categorical aspects
2012
We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.
On the problem of regularity in the Sobolev space Wloc1,n
2009
Abstract We prove that a variant of the Hencl's notion of A C λ n -mapping (see [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189]), in which λ is not a constant, produces a new solution to the problem of regularity in the Sobolev space W loc 1 , n .
Total curvatures of compact complex submanifolds in $$C/P^n$$
1995
LetM be a complex submanifold in\(C/P^n\). We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in\(C/P^n\).