Dual Homogeneous Forms and Varieties of Power Sums

We review the classical definition of the dual homogeneous form of arbitrary even degree which generalizes the well-known notion of the dual quadratic form. Following the ideas of S. Mukai we apply this construction to the study of the varieties parametrizing representations of a homogeneous polynomial as a sum of powers of linear forms.Research supported in part by NSF Grant DMS 0245203.Lecture held in the Seminario Matematico e Fisico on October 15, 2003Received: April, 2004     

Microwave frequency shifting using photon acceleration

Using a Bostick Gun as a plasma source, we have been investigating the effects of a moving plasma front on the frequency of an incident R.F. signal. We have been able to measure frequency shifts of 10 MHz frequency with a 2.6 GHz signal. The density is such that the plasma frequency is well above the transmitter frequency 1.3 meters from the plasma source. No magnetic field is used.     

Graft polymerization of vinyl monomers inside macroporous polyacrylamide gel,cryogel, in aqueous and aqueous‐organic media initiated by diperiodatocuprate(III) complexes

Graft polymerization initiated by diperiodatocuprate(III) complex (Cu(III)) initiator was found to be an effective and convenient method for graft polymerization of vinyl monomers onto macroporous polyacrylamide gels, the so‐called cryogels (pAAm‐cryogels). The effect of time, temperature, monomer and initiator concentration during the graft polymerization in aqueous and aqueous‐organic media was studied. The graft polymerization of water‐soluble monomers as [2‐(methacryloyloxy)ethyl]‐trimethylammonium chloride, 2‐hydroxyethyl methacrylate, N‐isopropylacrylamide, and N,N‐dimethylacrylamide proceeds with higher grafting yield in aqueous medium, as compared with that in aqueous‐organic media. Graft polymerization in aqueous‐organic media such as water–DMSO solutions allows grafting of water‐insoluble monomers such as glycidyl methacrylate and N‐tert‐butylacrylamide with high grafting degrees of 100 and 410%, respectively. It was found that the deposition of initiator on the pore surface of cryogels promoted graft polymerization by facilitating the formation of the redox couple Cu(III)‐acrylamide group. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1952–1963, 2006     

Variation of geometric invariant theory quotients

Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parameterizing isomorphism classes of geometric objects (vector bundles, polarized varieties, etc.). The quotient depends on a choice of an ample linearized line bundle. Two choices are equivalent if they give rise to identical quotients. A priori, there are infinitely many choices since there are infinitely many isomorphism classes of linearized ample line bundles. Hence several natural questions arise. Is the set of equivalence classes, and hence the set of non-isomorphic quotients, finite? How does the quotient vary under change of the equivalence class? In this paper we give partial answers to these questions in the case of actions of reductive algebraic groups on nonsingular projective algebraic varieties. We shall show that among ample line bundles which give projective geometric quotients there are only finitely many equivalence classes. These classes span certain convex subsets (chambers) in a certain convex cone in Euclidean space, and when we cross a wall separating one chamber from another, the corresponding quotient undergoes a birational transformation which is similar to a Mori flip.     

Inhomogeneous two-fluid cosmologies

A new class of expanding cosmological solutions is derived. The matter content of these models is a mixture of two interacting simple fluids: the first one, homogeneous and isotropic with equation of statep = (-1), the dynamics of which is given by the FRW equation and the second one an inhomogenous dust. The limiting case of two dusts corresponds to the Szekeres' universes of class II. A large subclass of the models evolve to a FRW phase for all physically meaningful values of the polytropic index and the curvature parameterk. A gauge condition, under which the metric is invariant, is shown to exist for k0. In particular, it explains why the parabolic model is a peculiar solution in the class found by Szekeres.On leave from Departamento de Fisica Teórica e Experimental Universidade Federal do Rio Grande do Norte, Natal, RN, Brazil.     

Chimie des complexes de metaux de transition avec des hydrocarbures cyanes : III. Quelques observations sur la conformation et la reactivite de complexes dicyclopentadienyles du molybdene et du tungstene

A new class of cyclic telluronium salts has been prepared. All the salts are stable in solution in CHCl₃ or dimethylsulphoxide (DMSO). Conductivity measurements in DMSO and dimethylformamide (DMF) have shown that considerable ion pairing occurs in solution. Infrared, ¹H, ¹³C, ¹²⁵Te NMR, and mass spectra are reported and discussed.     

Nitroxides with two pK values--useful spin probes for pH monitoring within a broad range

A series of 4-dialkylamino-2,5-dihydroimidazole nitroxides with pyridine-4-yl, 4-dimethylaminophenyl or 4-hydroxyphenyl groups in position 2 of the imidazole ring were prepared using the reaction of RMgBr with corresponding 5-dialkylamino-4,4-dimethyl-4H-imidazole 3-oxides. The EPR spectra of the nitroxides were shown to be pH-sensitive due to consecutive protonation of the amidino moiety and the basic group(s) at position 2 of the imidazole ring. The 5,5-dimethyl-4-(dimethylamino)-2-ethyl-2-pyridine-4-yl-2,5-dihydro-1H-imidazol-1-oxyl showed a monotonic increase in the isotropic nitrogen hyperfine (hfi) coupling constant alpha(N) of 1 .4 G over a pH range from 2 to 6.5. Such a broad range of pH-sensitivity could be useful for many biophysical and biomedical applications, including pH-monitoring in the stomach.