Infrared phonon spectra of 3d-metal doped YBa2(Cu1-x M x )3O7-δ

Infrared (IR) absorption spectra of doped YBa₂(Cu_1–x M _x )₃O_7–, with M representing Co, Fe, Ni, and Zn were observed as a function of concentrationx. TheB _1u IR mode at 580 cm^–1 was observed for all samples which were in the orthorhombic phase, which includes all the Ni and Zn doped samples and the lower concentrations (x<2.5%) for Fe and Co samples. The tetragonal phase of Co and Fe systems (x%>2.5%) shows three new IR modes at 655 cm^–1, 340 cm^–1, and 175 cm^–1. The frequency of the B_1u mode at 580 cm^–1 remains unchanged for all the Ni and Zn concentrations. In contrast, this mode shows a strong monotonic frequency softening with increase in Co substitution, while in the Fe-system it shows a comparable monotonic mode softening for 3%x%0%, and then remains unchanged for 12%x%3%. These observations indicate that Fe and Co substitute on the Cu(1) sites, whereas Ni and Zn most likely substitute on Cu(2) sites. We attribute the difference in the mode softening for Co and Fe to different Cu(1) local environments for these two elements. Indication for a chain-plane charge transfer based on our results is also discussed.     

Ortho effects in organic molecules on electron impact. 14—Concerted and stepwise ejections of SO2 and N2 from N-arylidene 2-nitrobenzenesulphenamides

Unexpected ortho interaction of the nitro group has been noticed during the mass spectral fragmentations of N-arylidene 2-nitrobenzenesulphenamides, where the molecular ions expel SO₂ and N₂ both in concerted and stepwise processes. Loss of a hydrogen or the substituent from this fragment leads to a very abundant ion in all the compounds studied. Based on chemical evidence and linked-scan studies, a 1,2-phenylenetropylium cation structure has been postulated for the [M–SO₂–N₂–H/substituent]⁺ ion.     

Extraction of cations as salts of fatty acids : Beryllium as Butyrate

The extraction of beryllium has been carried out in the presence of butyric acid. Of the solvents tried, viz., ether, benzene, chloroform, amyl acetate, ethyl acetate and carbon tetrachloride, chloroform is found to be the best, ethyl acetate being the next. 30.7 mg of BeO in solution as chloride is raised to a pH of 9.3 to 9.5 to which 10-15 ml of butyric acid is added. Four extractions with chloroform extract 99% of beryllium.     

The Homology of Partitions with an Even Number of Blocks

Let denote the subposet obtained by selecting even ranks in the partition lattice . We show that the homology of has dimension , where is the tangent number. It is thus an integral multiple of both the Genocchi number and an André or simsun number. Using the general theory of rank-selected homology representations developed in [22], we show that, for the special case of , the character of the symmetric group S _2n on the homology is supported on the set of involutions. Our proof techniques lead to the discovery of a family of integers b _i(n), 2 i n, defined recursively. We conjecture that, for the full automorphism group S _2n, the homology is a sum of permutation modules induced from Young subgroups of the form , with nonnegative integer multiplicity b _i(n). The nonnegativity of the integers b _i(n) would imply the existence of new refinements, into sums of powers of 2, of the tangent number and the André or simsun number a _n(2n).Similarly, the restriction of this homology module to S _2n–1 yields a family of integers d _i(n), 1 i n – 1, such that the numbers 2^–i d _i(n) refine the Genocchi number G _2n . We conjecture that 2^–i d _i(n) is a positive integer for all i.Finally, we present a recursive algorithm to generate a family of polynomials which encode the homology representations of the subposets obtained by selecting the top k ranks of , 1 k n – 1. We conjecture that these are all permutation modules for S _2n .     

A Decomposition of a Weaker Form of Continuity

The aim of this paper is to give a decomposition of a weaker form of continuity, namely gα^**-continuity by providing the concepts of K-sets and K-continuity. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analytical solutions for inherently incremental,similar elastic contact problems with bulk stress

Analytical solutions are obtained for a class of inherently incremental, similar elastic half-plane frictional contact problems which involve simultaneous application of a changing, remote bulk-stress during oblique loading. The method is based on Abel Integral Equations. The spatial gradient of the slip function is obtained uniquely by the conditions determining the existence of a bounded solution to the shear traction Cauchy SIE and global shear equilibrium, provided there is stick at all points in the contact throughout the loading. Solutions are obtained for both the cylindrical indenter and the flat punch with rounded edges. The method also lends itself easily to generalization to non-linear load paths and a number of such problems are considered. Problems involving the development of slip zones within the contact may be solved in some special cases.