Composite Julia sets generated by infinite polynomial arrays

A definition of a generalized filled-in Julia set generated by an infinite array of proper polynomial mappings in  is introduced. It is shown that such Julia sets depend analytically on the defining polynomial mappings.     

Bounded point evaluations and cyclic polynomials on the spaces $$\hat F$$

LetF be aBK space withAK and denote the set of all formal power series with such that ε F for the sequence of coefficients of . We give a necessary and sufficient condition for a point to be a bounded point evaluation on , and for a polynomial to be cyclic in . As special cases, we obtain the results for the space ℓ _p (β) in [7]. Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and, in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8.     

Synthesis,Spectral Properties,and Crystal Structure of {Methoxo[4-phenylbutane-2,4-dione(p-nitrobenzoyl) hydrazonato(2-)]oxovanadium(V)}

The hydrazino complex {methoxo[4-phenylbutane-2,4-dione(p-nitrobenzoyl)hydrazonato(2-)]oxovanadium(V)}, VO(p-NO₂bhbzac)OCH₃, (1), has been prepared by the direct reaction of bis(benzoylacetonato) oxovanadium(IV), VO(bza)₂, with p-NO₂-C₆H₄C(O)NHNH₂, p-NO₂bh, in CH₃OH. The resulting compound contains benzoylacetone-(p-NO₂)benzoyl hydrazone as tridentate Schiff base-type ligand and OCH₃ group as Lewis base, both ligated to vanadium. The crystals are orthorhombic, with Z = 8, space group Pbca, a = 11.699(5) Å, b = 14.035(5) Å, c = 22.564(5) Å, R1 = 0.0756 and wR2 = 0.1302. The crystal structure demonstrated the square-pyramidal geometry of the VO_oxo(ONO)O coordination sphere with the oxo ligand at the apical position. The electronic absorption spectra revealed a ligand-to-metal charge-transfer (LMCT) band in the near UV region at _max = 23,700 cm^–1 (B = 5640 dm³ mol^–1 cm^–1) in CH₃CN, _max = 23,420 cm^–1 (B = 5550 dm³ mol^–1 cm^–1) in DMSO, and _max near 26,950 (sh) cm^–1 (B = 10,550 dm³ mol^–1 cm^–1) in CH₂Cl₂. The FT-IR spectra of (1) show the characteristic strong (V = O) stretching vibration at 993 cm^–1 and support the view that the oxovanadium complex is pentacoordinated and monomeric.     

An elementary construction of tilting complexes

Let A be an artin algebra and e∈A an idempotent with add(eA_A)=add(D(_AAe)). Then a projective resolution of Ae_eAe gives rise to tilting complexes for A, where P(l)^• is of term length l+1. In particular, if A is self-injective, then is self-injective and has the same Nakayama permutation as A. In case A is a finite dimensional algebra over a field and eAe is a Nakayama algebra, a projective resolution of eAe over the enveloping algebra of eAe gives rise to two-sided tilting complexes {T(2l)^•}_l?1 for A, where T(2l)^• is of term length 2l+1. In particular, if eAe is of Loewy length two, then we get tilting complexes {T(l)^•}_l?1 for A, where T(l)^• is of term length l+1.     

Computation of blowing up centers

Given a birational projective morphism of quasi-projective varieties . We want to find the ideal sheaf over X such that the blowing up of X along corresponds to f. In this paper we approach the problem from two directions, solving two subcases. First we present a method that determines when f is the composition of blowing ups along known centers, then by another method, we compute directly from .     

Spectral triangles of Schrödinger operators with complex potentials

Consider the Schrödinger operator with a complex-valued potential v of period Let and be the eigenvalues of L that are close to respectively, with periodic (for n even), antiperiodic (for n odd), and Dirichelet boundary conditions on [0,1], and let be the diameter of the spectral triangle with vertices We prove the following statement: If then v(x) is a Gevrey function, and moreover      

Nonlinear Liouville theorems for Grushin and Tricomi operators

The aim of this paper is to study necessary conditions for existence of weak solutions of the inequality