About the synthesis of N-1-substituted 3-aminopyrroles. A comparison

A general method for the preparation of 3-amino-1-methylpyrroles in excellent yields is reported. The key step involves the N-methylation of the nitro derivatives 2 , under phase transfer catalysis conditions.     

Realization ofU q (so(N)) within the differential algebra onR q N

We realize the Hopf algebraU _q–1 (so(N)) as an algebra of differential operators on the quantum Euclidean spaceR _q ^N . The generators are suitableq-deformed analogs of the angular momentum components on ordinaryR ^N . The algebra Fun(R _q ^N ) of functions onR _q ^N splits into a direct sum of irreducible vector representations ofU _q–1 (so(N)); the latter are explicitly constructed as highest weight representations.     

Numerical calculation of cutoff frequencies of optical fibers by a variational technique

A numerical method for calculating cutoff frequencies of modes of weakly guiding optical fibers is described. Starting from a properly constructed field representation, the method follows a variational approach to obtain an eigenvalue problem for the cutoff frequencies which can be easily solved by a standard numerical routine. The field representation uses an expansion in terms of the Laguerre–Gauss functions in the fiber core and limiting form for small arguments of modified Bessel functions in the fiber cladding. Fibers with power-law refractive index profiles and fibers with a profile showing a dip on the axis are analyzed. Results obtained for modes of arbitrary order (both azimuthal and radial) show that our method is very efficient and accurate.     

Minimum embedding of P3‐designs into (K4—e)‐designs

A (K₄ ? e)‐design on v + w points embeds a P₃‐design on v points if there is a subset of v points on which the K₄ ? e blocks induce the blocks of a P₃‐design. It is shown that w ≥ ¾(v ? 1). When equality holds, the embedding design is easily constructed. In this paper, the next case, when w = ¾v, is settled with finitely many exceptions. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 352–366, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10044     

The hidden geometry of the quantum Euclidean space

We briefly describe how to introduce the basic notions of noncommutative differential geometry on the 3-dim quantum space covariant under the quantum group of rotations SO _q(3).     

On cubic-linear polynomial mappings

In the field of the Jacobian conjecture it is well-known after Dru?kowski that from a polynomial ‘cubic-homogeneous’ mapping we can build a higher-dimensional ‘cubic-linear’ mapping and the other way round, so that one of them is invertible if and only if the other one is. We make this point clearer through the concept of ‘pairing’ and apply it to the related conjugability problem: one of the two maps is conjugable if and only if the other one is; moreover, we find simple formulas expressing the inverse or the conjugations of one in terms of the inverse or conjugations of the other. Two nontrivial examples of conjugable cubic-linear mappings are provided as an application.     

H,C, Pt NMR study on platinum(II) interaction with sulphur containing Amadori compounds

The NMR study on the interaction of Pt(II) with Amadori compounds is performed. The Amadori compounds are derived from the reaction of β-d-glucose with l-cystine leading to N,N′-di-(1-deoxy-β-fructos-1-yl)-l-cystine [FruCyscys], and with l-methionine leading to N-(1-deoxy-β-fructos-1-yl)-l-methionine [FruMet].     

Chloroform sorption in nanoporous crystalline and amorphous phases of syndiotactic polystyrene

The transport of chloroform in films of atactic polystyrene and of semicrystalline syndiotactic polystyrene in its nanoporous form (δ‐form) has been investigated by gravimetric analysis. Experimental tests have been performed at 35, 49, and 56 °C and at several vapor pressures ranging from 0.5 to 100 Torr. Nonequilibrium lattice fluid prediction of the amorphous sorption behavior was used to enucleate the sorption contribution of the crystalline nanoporous phase from semicrystalline samples. Sorption behavior of the crystalline phase has been interpreted on the basis of Langmuir equation. Moreover, the chloroform sorption at low activities in the crystalline nanoporous phase has been predicted by using Grand Canonical Monte Carlo molecular simulations. Isosteric heats of sorption were also experimentally evaluated for the crystalline phase, and compared with the corresponding prediction of molecular simulation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 8–15, 2008