An improved Hardy-Sobolev inequality and its application

For , a bounded domain, and for , we improve the Hardy-Sobolev inequality by adding a term with a singular weight of the type . We show that this weight function is optimal in the sense that the inequality fails for any other weight function more singular than this one. Moreover, we show that a series of finite terms can be added to improve the Hardy-Sobolev inequality, which answers a question of Brezis-Vazquez. Finally, we use this result to analyze the behaviour of the first eigenvalue of the operator as increases to for .

     

Triple minima in the free energy of semiflexible polymers

We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness lambda for finite chains of length L. We find that the polymer properties obtained in this ensemble are qualitatively different from those obtained using constant-force ensembles. In particular, we find that as we change the stiffness parameter, t=L/lambda, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.     

Axially symmetric solutions generated by the complexification technique

Banerjee and Andrade generated axially symmetric electrovac solutions from the spherically symmetric Reissner-Nordström solution by giving a complex translation along theZ axis. We use the same method for generating new more complicated axially symmetric solutions from known solutions. Several such examples are given.     

Spectrophotometric determination of uranium(VI) with benzoylacetanilide

Ohne Zusammenfassung

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Use of complex forming substitution reactions for the selective enthalpiometric determination of cations and anions

     

Amperometric determination of 2-benzothiazole sulphenamide accelerators

A simple method for the amperometric estimation of N-cyclohexyl-2-benzothiazole sulphenamide, N-dicyclohexyl-2-benzothiazole sulphenamide, 2-(morpholinothio)benzothiazole and N-tert.-butyl-2-benzothiazole sulphenamide is reported. The results are obtained within 5 min and are correct within +/- 2.0%.     

Comparative studies of the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of 25Mg+

We have employed the relativistic coupled cluster theory to calculate the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of singly ionized magnesium. Comparison with experimental and the other theoretical results are done and predictions are also made for a few low lying excited states which could be of interest. We have made comparative studies of the important many body effects contributing to the hyperfine constants for the different states of the ion.     

Theoretical studies of electric quadrupole transition probabilities in Mg II

The relativistic coupled cluster theory is employed to calculate electric quadrupole (E2) transition probabilities among the doublet states of Mg II which are of interest in astrophysical problems. This is the first time a highly correlated fully ab initio method has been used to compute these quantities for this particular ion. The line strengths and transition probabilities of a number of different transitions are reported and compared with those available in the literature.Received: 4 June 2003, Published online: 30 September 2003PACS: 31.10. + z Theory of electronic structure, electronic transitions, and chemical bindingSonjoy Majumder: Present address: Institut für Theoretische Chemie, Technische Universität München, 85747 Garching, Germany.     

Enhanced intravenous transgene expression in mouse lung using cyclic-head cationic lipids

Herein, we report enhanced intravenous mouse lung transfection using novel cyclic-head-group analogs of usually open-head cationic transfection lipids. Design and synthesis of the new cyclic-head lipid N,N-di-n-tetradecyl-3,4-dihydroxy-pyrrolidinium chloride (lipid 1) and its higher alkyl-chain analogs (lipids 2-4) and relative in vitro and in vivo gene transfer efficacies of cyclic-head lipids 1-4 to their corresponding open-head analogs [lipid 5, namely N,N-di-n-tetradecyl-N,N-(2-hydroxyethyl)ammonium chloride and its higher alkyl-chain analogs, lipids 6-8] have been described. In stark contrast to comparable in vitro transfection efficacies of both the cyclic- and open-head lipids, lipids 1-4 with cyclic heads were found to be significantly more efficient (by 5- to 11-fold) in transfecting mouse lung than their corresponding open-head analogs (5-8) upon intravenous administration. The cyclic-head lipid 3 with di-stearyl hydrophobic tail was found to be the most promising for future applications.     

A unique series of dinuclear transition metal-polyradical complexes with a m-phenylenediamine spacer and their catalytic reactivity

A series of dinuclear transition metal complexes with either six or four iminosemiquinone radicals, in which the metal centres are separated by a distance of approximately 6.8 A, together with their catalytic reactivity is reported.     

Syntheses,structural analyses,and magneto-structural correlations of three polymeric Fe(II) complexes with azide ligand

Three new metal-organic polymeric complexes, [Fe(N(3))(2)(bpp)(2)] (1), [Fe(N(3))(2)(bpe)] (2), and [Fe(N(3))(2)(phen)] (3) [bpp = (1,3-bis(4-pyridyl)-propane), bpe = (1,2-bis(4-pyridyl)-ethane), phen = 1,10-phenanthroline], have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature magnetic measurements in the range 300-2 K. Complexes 1 and 2 crystallize in the monoclinic system, space group C2/c, with the following cell parameters: a = 19.355(4) A, b = 7.076(2) A, c = 22.549(4) A, beta = 119.50(3) degrees, Z = 4, and a = 10.007(14) A, b = 13.789(18) A, c = 10.377(14) A, beta = 103.50(1) degrees, Z = 4, respectively. Complex 3 crystallizes in the triclinic system, space group P(-)1, with a = 7.155(12) A, b = 10.066(14) A, c = 10.508(14) A, alpha = 109.57(1) degrees, beta = 104.57(1) degrees, gamma = 105.10(1) degrees, and Z = 2. All coordination polymers exhibit octahedral Fe(II) nodes. The structural determination of 1 reveals a parallel interpenetrated structure of 2D layers of (4,4) topology, formed by Fe(II) nodes linked through bpp ligands, while mono-coordinated azide anions are pendant from the corrugated sheet. Complex 2 has a 2D arrangement constructed through 1D double end-to-end azide bridged iron(II) chains interconnected through bpe ligands. Complex 3 shows a polymeric arrangement where the metal ions are interlinked through pairs of end-on and end-to-end azide ligands exhibiting a zigzag arrangement of metals (Fe-Fe-Fe angle of 111.18 degrees) and an intermetallic separation of 3.347 A (through the EO azide) and of 5.229 A (EE azide). Variable-temperature magnetic susceptibility data suggest that there is no magnetic interaction between the metal centers in 1, whereas in 2 there is an antiferromagnetic interaction through the end-to-end azide bridge. Complex 3 shows ferro- as well as anti-ferromagnetic interactions between the metal centers generated through the alternating end-on and end-to-end azide bridges. Complex 1 has been modeled using the D parameter (considering distorted octahedral Fe(II) geometry and with any possible J value equal to zero) and complex 2 has been modeled as a one-dimensional system with classical and/or quantum spin where we have used two possible full diagonalization processes: without and with the D parameter, considering the important distortions of the Fe(II) ions. For complex 3, the alternating coupling model impedes a mathematical solution for the modeling as classical spins. With quantum spin, the modeling has been made as in 2.