On partial tilting modules and right bounded complexes

We construct rather short partial tilting complexes [(T)\dot]{\dot T} such that quite different indecomposable right bounded complexes [(C)\dot]{\dot C} have the property that any morphism from [(T)\dot]{\dot T} to a shift of [(C)\dot]{\dot C} is homotopic to zero. We also show that, for some [(T)\dot]{\dot T} , the strategy to obtain a bounded complex [(C)\dot]{\dot C} as a mutation of [(T)\dot]{\dot T} is not unique.     

Morphological and chemical characterization of weathering products on buried Sasanian glass from central Iraq

This paper discusses the morphological and chemical features of the weathering products on Sasanian glass finds excavated at the ancient Sasanian town of Veh Arda?īr, some 30 km south of Baghdad (Iraq), and dated from the third to the sixth century. All the considered fragments represent soda-lime glass, with MgO contents between 3% and 8%, resulting from the use of soda-rich plant ash as a flux; within this general frame, two productions can be distinguished due to their MgO to K₂O ratio. Four main alteration typologies were observed by visual examination of the excavated samples; these were studied by scanning electron microscopy, energy dispersive X-ray analysis, inductively coupled plasma-mass spectrometry, X-ray diffraction and thermal analysis. Different alteration features were generally observed for samples belonging to the two compositional groups. In particular, samples with higher MgO to K₂O ratios show definitely thinner crusts, associated with alteration plugs going down into the glass. Moreover, gray or black crusts are related to the presence of manganese at significant levels in the original glass.     

Synthesis and Biological Studies of O3-Aryl Galactosides as Galectin Inhibitors

β-Galactose derivatives have recently been reported to selectively inhibit galectin-3, and a library of O3-arylated galactosides with varying substitution patterns was designed to study such inhibitions further. The O3-arylated galactosides were synthesized using diaryliodonium salts under mild and transition metal free conditions, providing the target products in moderate to good yields. An O3-trifluoroethylated galactoside was also synthesized using iodonium salt chemistry. Azido-substituted products were subsequently transformed into the corresponding triazoles. After deprotection, a selection of galactoside derivatives were evaluated for inhibitory potencies against galectins-1, 3, 4 N (N-terminal domain), 4 C (C-terminal domain), 7, 8 N, 8 C, 9 N, and 9 C and one compound with promising affinity and selectivity for both the N- and C-terminal domain of galectin-9 was discovered.     

A coassociativeC *-quantum group with nonintegral dimensions

By weakening the counit and antipode axioms of aC ^*-Hopf algebra and allowing for the coassociative coproduct to be nonunital, we obtain a quantum group, that we call aweak C ^*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. Every finite-dimensional weakC ^*-Hopf algebra has a dual which is again a weakC ^*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We briefly discuss applications to amalgamated crossed products, doubles, and quantum chains.Supported by the Hungarian Scientific Research Fund, OTKA T 016 233.Supported by the Hungarian Scientific Research Fund, OTKA-1815.     

Propagation of Optical Beams in Active Media Inside Gaussian Cavities

The evolution of relevant beam parameters of a light beam propagating through an iterated sequence of spherical lenses and Gaussian apertures immersed in an active medium is investigated. This structure is a classical model for an optical resonator. The effective size of the field distribution, the beam quality factor and the radius of wave front curvature are calculated as functions of the number of transits. Steady-state values of these parameters are also determined and the dependence of the results on the gain of the medium, the aperture width and the focal length is illustrated. A comparison with the case without active medium is also discussed.     

Heterocyclic rearrangements. Phenylhydrazones and N-methyl-N-phenylhydrazones of 3-acylisoxazoles

The reaction of 3-benzoyl-5-phenylisoxazole ( 4 ) and 3-acetyl-5-methylisoxazole ( 5 ) with phenylhydrazine and N-methyl-N-phenylhydrazine has been investigated and the reactivity of (E)- and (Z)-phenylhydrazones and N-methyl-N-phenylhydrazones has been studied.     

On the relations between two types of convergence for convex functions

Theory and applications have shown that there are two important types of convergence for convex functions: pointwise convergence and convergence in a topology induced by the convergence of their epigraphs. We show that these two types of convergence are equivalent on the class of convex functions which are equi-lower semicontinuous. This turns out to be maximal classes of convex functions for which this equivalence can be obtained. We also indicate a number of implications of these results to the convergence of convex sets and the corresponding support functions and to the convergence of the infima of sequences of convex minimization problems.     

Catalytic enantioselective conjugate addition of dialkylzinc reagents to N-substituted-2,3-dehydro-4-piperidones

The first, highly enantioselective, copper/phosphoramidite-catalyzed conjugate addition of dialkylzinc reagents to N-substituted 2,3-dehydro-4-piperidones is described.