Lebesgue constants for periodic Hermite spline interpolation operators on uniform lattices

We derive a complex line integral representation for the ebyshev norm of periodic spline interpolation operators of odd degree on uniform lattices. Several generalizations are indicated.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Space tilings and local isomorphism

We prove for a large class of tilings that, given a finite tile set, if it is possible to tile Euclideann-space with isometric copies of this set, then there is a tiling with the ‘local isomorphism property’. Research supported in part by NSF Grant No. DMS-9001475.     

Influence of trans-cis photoisomerizations of solubilized compounds on transition temperatures in the system cetyltrimethylammonium bromide-water: Light-induced phase transitions

Transition temperatures (TN1) from the nematic lyotropic liquid-crystalline phase to the isotropic phase were measured for the system cetyltrimethylammonium bromide (CTAB) water in the presence of small amounts of 3-stilbene carboxylic acid (3SC), 4-stilbene carboxylic acid (4SC) and Δ2/2'-bi-(2H-l,4-benzothiazine) (BT). TNI, increases as a function of trans-3SC or trans-4SC concentration, ranging from 01 to 08 wt %, by up to 12°C. A further increase in TNI between 2 and 5°C can be achieved by photochemically converting the solubilized trans stilbene derivatives to the cis isomers. Irradiation of a trans-3SC containing sample at a temperature just above TNl leads to a light-induced phase transition to the lyotropic liquid-crystalline phase. Solubilization of trans-BT causes a slight decrease of TNI while photoisomerization to cis-BT increases T_NI by 1°C.