In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a conditional gauge theorem for these diffusions in bounded Lipschitz domains. Informally the Schrödinger-type operators we consider are of the form L + μ · ∇ + ν where ...

Let T be the unit circle with an irrational rotation T : x 7→ x+α mod 1, F a real or circle valued cocycle (i.e. we consider cylinder flows and Anzai skew products). A0 and L0 are the Banach spaces of zero mean absolutely continuous, respectively Lipschitz (real or T-valued) cocycles. Two cocycles on T are said to be cohomologous if they differ in a coboundary, i.e. a function G − G ◦ T where G...

Nuances of truth represent a robust paradigm in the framework of many-valued logics [1]. The idea of nuancing states that a many-valued object is uniquely determined by some Boolean objects, its nuances, and it is called the determination principle. However, a many-valued object cannot be recovered only from its Boolean nuances. This idea goes back to Gr. C. Moisil [4] and it is mathematically ...

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (∈,∈ ∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investiga...

This paper deals with the determination of the absolute valued algebras with a nonzero idempotent commuting with the remaining idempotents and satisfying x2x = xx2 for every x. We prove that, in addition to the absolute valued algebras R, C, H, or O of the reals, complexes, division real quaternions or division real octonions, one such absolute valued algebra A can also be isometrically isomorp...

We introduce the notion of a C *-valued weight between two C *-algebras as a generalization of an ordinary weight on a C *-algebra and as a C *-version of operator valued weights on von Neumann algebras. Also, some form of lower semi-continuity will be discussed together with an extension to the Multiplier algebra. A strong but useful condition for C *-valued weights, the so-called regularity, ...

The aim of this paper is to introduce the notions of interval valued (∈,∈ ∨q)-fuzzy Boolean (implicative, positive implicative and fantastic) filters in BL-algebras and to investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, the relations among these generalized fuzzy filters are discussed. It is proved that an interval valued (∈,∈...

Based on a formula of Tseng, we show that the squared norm of the matrix-valued Fischer-Burmeister function has a Lipschitz continuous gradient.