Quasisymmetric homeomorphisms of the circle, that arise in the Teichmüller theory of Riemann surfaces as boundary values of quasiconfomal diffeomorphisms of the disk, have fractal graphs in general and are consequently not so amenable to usual analytical or calculus procedures. In this paper we make use of the remarkable fact this group QS(S) acts by substitution (i.e., pre-composition) as a fa...

R. Thomas proved that the Hodge conjecture is essentially equivalent to the existence of a Thomas hyperplane section having only ordinary double points as singularities and such that the restriction of a given primitive Hodge class to it does not vanish. We show that the relations between the vanishing cycles associated to the ordinary double points of a Thomas hyperplane section have the same ...

Using a Hilbert space framework inspired by the methods of orthogonal projections and Hodge decompositions, we study general class problems (called Z-problems) that arise in effective media theory, especially within theory composites, for defining operator. A new unified approach is developed, based on block operator methods, obtaining solutions Z-problem, formulas terms Schur complement, assoc...

This paper [1] has been retracted as it is essentially identical in content with the published article " Determination of Sturm-Liouville operator on a three-star graph from four spectra, " by Dehghani Tazehkand and Akbarfam, published in Acta

background and objectives : resistance among bacterial isolates is the leading cause of increased mortality and morbidity worldwide. carbapenems once thought to be effective are becoming ineffective mostly due to the emergence of carbapenemase. this study was designed to determine in vitro efficacy of modified hodge test for detection of carbapenemase production in gram negative rods. material ...

Stringy Hodge numbers are introduced by Batyrev for a mathematical formulation of mirror symmetry. However, since the stringy Hodge numbers of an algebraic variety are defined by choosing a resolution of singularities, the well-definedness is not clear from the definition. Batyrev proved the well-definedness by using the theory of motivic integration developed by Kontsevich, Denef-Loeser. The a...

Recall first that a weight k Hodge structure (L,L) has coniveau c ≤ k2 if the Hodge decomposition of LC takes the form LC = Lk−c,c ⊕ Lk−c−1,c+1 ⊕ . . .⊕ Lc,k−c with Lk−c,c 6= 0. If X is a smooth complex projective variety and Y ⊂ X is a closed algebraic subset of codimension c, then Ker (H(X,Q) → H(X \ Y,Q)) is a sub-Hodge structure of coniveau ≥ c of H(X,Q) (cf. [32, Theorem 7]). The generaliz...

In despair, as Deligne (2000) put it, of proving the Hodge and Tate conjectures, we can try to find substitutes. For abelian varieties in characteristic zero, Deligne (1982) constructed a theory of Hodge classes having many of the properties that the algebraic classes would have if the Hodge conjecture were known. In this article I investigate whether there exists a theory of " rational Tate cl...