Higher order duality in multiobjective fractional programming with support functions

In this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond-Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases.     

DNS study on the formation of Lambda rotational core and the role of TS wave in boundary layer transition

Λ-vortex plays a pivotal role in the boundary layer transition process. In this paper, the generation of Lambda rotational core (Λ-vortex) in boundary layer transition and the role of TS (Tollmien–Schlichting) waves performed are studied by direct numerical simulation (DNS) in detail. It shows that the growth of TS wave under non-linear NS equations differs from the one under linearised NS (Navier–Stokes) equations at very early stage. With the evolution of TS waves, a newly found evolution procedure under non-linear NS equations helps to form the perturbation structures and lead them to evolve to Λ-vortices. The transition process undergoing the non-linear stage is also found to be much earlier than the previous studies had suggested.     

Continued fractions with multiple limits

For integers m2, we study divergent continued fractions whose numerators and denominators in each of the m arithmetic progressions modulo m converge. Special cases give, among other things, an infinite sequence of divergence theorems, the first of which is the classical Stern–Stolz theorem.We give a theorem on a class of Poincaré-type recurrences which shows that they tend to limits when the limits are taken in residue classes and the roots of their characteristic polynomials are distinct roots of unity.We also generalize a curious q-continued fraction of Ramanujan's with three limits to a continued fraction with k distinct limit points, k2. The k limits are evaluated in terms of ratios of certain q-series.Finally, we show how to use Daniel Bernoulli's continued fraction in an elementary way to create analytic continued fractions with m limit points, for any positive integer m2.     

XPS Study of the Oxygen on A_2BO_4-type Compounds-A New Discovery of O_(1S) Peaks

AzBO.-typecompoundsareakindofcatalyticmaterialwhichhasdemonstratedoutstandingperformance,especiallyincatalyticoxidationandreductionreactions"2.Forthistypeofcompounds,theexistingreportssuggestthattheexistenceofoxygenintheoxidestructureplaysaveryimpoytantroleinitscatalyticperformance,andstUdyonthedistributionofoxygenisnecessary.Theanalysismethod,XPS,isaquiteeffectivemeansforthispurpose.UPtonow,moststudiessuggestthattherearetWomajortypesofoxygenonthesurfaceofthistypeofcompounds,thatis,theadsor…     

Rational approximation to harmonic functions

Padé-type approximation is the rational function analogue of Taylor’s polynomial approximation to a power series. A general method for obtaining Padé-type approximants to Fourier series expansions of harmonic functions is defined. This method is based on the Newton-Cotes and Gauss quadrature formulas. Several concrete examples are given and the convergence behavior of a sequence of such approximants is studied. This revised version was published online in June 2006 with corrections to the Cover Date.     

Krylov subspace methods, biorthogonal polynomials and Padé-type approximants

It is shown that Krylov subspace methods for solving systems of linear equations can be based on formal biorthogonal polynomials and on Padé-type and Padé approximants. New algorithms for their implementation are derived. This revised version was published online in June 2006 with corrections to the Cover Date.     

Phase coexistence in NaZn13-type LaFe11.4Al1.6C0.02 compound

In NaZn₁₃-type LaFe_11.4Al_1.6C_0.02 compound, a signature of weak ferromagnetism is observed at ∼100 K under a low field by ac magnetic-susceptibility and electrical-resistivity measurements, implying the coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) phases. The hysteresis in isofield magnetization curves and large magnetic relaxation demonstrate the metastability of the magnetic state in the AFM-FM transition region. The variations of magnetization with temperature, time and field show distinct step-like behaviors, which is probably attributed to the discontinuous growth of ferromagnetic cluster in antiferromagnetic matrix.     

Boundedness of higher order commutators of generalized fractional integral operators on Hardy spaces

Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.     

[Ni(H2O)4]3[U(OH,H2O)(UO2)8O12(OH)3], crystal structure and comparison with uranium minerals with U3O8-type sheets

The new U(VI) compound, [Ni(H₂O)₄]₃[U(OH,H₂O)(UO₂)₈O₁₂(OH)₃], was synthesized by mild hydrothermal reaction of uranyl and nickel nitrates. The crystal-structure was solved in the P-1 space group, a=8.627(2), b=10.566(2), c=12.091(4) Å and α=110.59(1), β=102.96(2), γ=105.50(1)°, R=0.0539 and wR=0.0464 from 3441 unique observed reflections and 151 parameters. The structure of the title compound is built from sheets of uranium polyhedra closely related to that in β-U₃O₈. Within the sheets [(UO₂)(OH)O₄] pentagonal bipyramids share equatorial edges to form chains, which are cross-linked by [(UO₂)O₄] and [UO₄(H₂O)(OH)] square bipyramids and through hydroxyl groups shared between [(UO₂)(OH)O₄] pentagonal bipyramids. The sheets are pillared by sharing the apical oxygen atoms of the [(UO₂)(OH)O₄] pentagonal bipyramids with the oxygen atoms of [NiO₂(H₂O)₄] octahedral units. That builds a three-dimensional framework with water molecules pointing towards the channels. On heating [Ni(H₂O)₄]₃[U(OH,H₂O)(UO₂)₈O₁₂(OH)₃] decomposes into NiU₃O₁₀.     

Enantiopure inherently chiral calix[4]arene derivatives containing quinolin-2-yl-methanol moiety:Synthesis and application in the catalytic asymmetric addition of diethylzinc to benzaldehyde

A series of novel N,O-type chiral ligands derived from enantiopure inherently chiral calix[4]arenes containing quinolin-2-yl-methanol moiety in the cone or partial-cone conformation have been synthesized and characterized. Moreover, they have been applied to the catalytic asymmetric addition of diethylzinc to benzaldehyde, which represents the first example that the inherently chiral calixarene can be used as the chiral ligands for the catalytic asymmetric synthesis. Supported by the National Natural Science Foundation of China (Grant Nos. 20625206 & 20372064), the National Basic Research Project (Grant Nos. 2007CB808000 & 2008CB617501), and the Chinese Academy of Sciences