Familien komplexer räume zu gegebenen infinitesimalen deformationen

Let M be a domain in the complex plane, :XM a flat family of reduced complex spaces, (X_o, _o) the fibre over a point OM, and x_o the sheaf of (1,O)-forms over X_o. The family defines an element (Ext¹ (_Xo, _o))_x for every point xX. We prove: If (X_o, _o) is a normal complex space, x a point in X_o such that (Ext² (_Xo, _o))_x=O, then for each infinitesimal deformation (Ext¹ (_Xo, _o))_x there exists a flat reduced family with =. This statement is analogous to a result of KODAIRA-NIRENBERG-SPENCER in the theory of deformations of compact complex manifolds.     

Impact of surface defects on a condensate of electron pairs in a quantum wire

Theoretical and Mathematical Physics - We study the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results, we formulate a simple mathematical...     

New oxacalix[4]arene carboxylate detects viologen in protic media

ABSTRACT

We demonstrate that Ullman fragment-coupling can be used to synthesise an oxacalix[4]arene monocarboxylic acid, which provides easy access to its water-soluble carboxylato derivatives. Crystallographic and computational data suggest that the new carboxyl-substituted oxacalix[4]arene adopts a 1,3-alternate conformation both in the solid-state and in methanol solution. Its water-soluble tetrabutylammonium derivate can detect the herbicide paraquat at neutral pH in aqueous media (K _a = 111 ± 3 M^–1) and in methanol (K _a = 2020 ± 70 M^–1).     

Constructing tilting modules

We investigate the structure of (infinite dimensional) tilting modules over hereditary artin algebras. For connected algebras of infinite representation type with Grothendieck group of rank , we prove that for each , there is an infinite dimensional tilting module with exactly pairwise non-isomorphic indecomposable finite dimensional direct summands. We also show that any stone is a direct summand in a tilting module. In the final section, we give explicit constructions of infinite dimensional tilting modules over iterated one-point extensions.

     

Ternary generalization of Pauli’s principle and the <Emphasis Type="Italic">Z</Emphasis><Subscript>6</Subscript>-graded algebras

We show how the discrete symmetries Z ₂ and Z ₃ combined with the superposition principle result in the SL(2,C) symmetry of quantum states. The role of Pauli’s exclusion principle in the derivation of the SL(2,C) symmetry is put forward as the source of the macroscopically observed Lorentz symmetry; then it is generalized for the case of the Z ₃ grading replacing the usual Z ₂ grading, leading to ternary commutation relations. We discuss the cubic and ternary generalizations of Grassmann algebra. Invariant cubic forms on such algebras are introduced, and it is shown how the SL(2,C) group arises naturally in the case of two generators only, as the symmetry group preserving these forms. The wave equation generalizing the Dirac operator to the Z ₃-graded case is introduced, whose diagonalization leads to a sixthorder equation. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry.     

Preprojective components of wild tilted algebras

If A is a finite dimensional, connected, hereditary wild k-algebra, k algebraically closed and T a tilting module without preinjective direct summands, then the preprojective componentP of the tilted algebra B=End_A (T) is the preprojective component of a concealed wild factoralgebra C of B. Our first result is, that the growth number (C) of C is always bigger or equal to the growth number (A). Moreover the growth number (C) can be arbitrarily large; more precise: if A has at least 3 simple modules and N is any positive integer, then there exists a natural number n>N such that C is the Kronecker-algebraK _n, that is the path-algebra of the quiver (n arrows).