Subelliptic Biharmonic Maps

We study subelliptic biharmonic maps, i.e., smooth maps ?:M→N from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of the energy functional $E_{2,b} (\phi ) = \frac{1}{2} \int_{M} \| \tau_{b} (\phi ) \|^{2} \theta \wedge (d \theta)^{n}$ . We show that ?:M→N is a subelliptic biharmonic map if and only if its vertical lift ?°π:C(M)→N to the (total space of the) canonical circle bundle $S^{1} \to C(M) \stackrel{\pi}{\longrightarrow} M$ is a biharmonic map with respect to the Fefferman metric F _θ on C(M).     

Some New Orders of Hadamard and Skew‐Hadamard Matrices

We construct Hadamard matrices of orders and , and skew‐Hadamard matrices of orders and . As far as we know, such matrices have not been constructed previously. The constructions use the Goethals–Seidel array, suitable supplementary difference sets on a cyclic group and a new efficient matching algorithm based on hashing techniques.     

The Interaction of Collinear Gaps of Arbitrary Charge in a Two Dimensional Dimer System

The correlation of gaps in dimer systems was introduced by Fisher and Stephenson (Phys Rev 132:1411–1431, 1963), who looked at the interaction of two monomers generated by the rigid exclusion of dimers on the closely packed square lattice. In previous work we considered the analogous problem on the hexagonal lattice, and we extended the set-up to include the correlation of any finite number of monomer clusters. For fairly general classes of monomer clusters we proved that the asymptotics of their correlation is given, for large separations between the clusters, by a multiplicative version of Coulomb’s law for 2D electrostatics. However, our previous results required that the monomer clusters consist (with possibly one exception) of an even number of monomers. In this paper we determine the asymptotics of general defect clusters along a lattice diagonal in the square lattice (involving an arbitrary, even or odd number of monomers), and find that it is given by the same Coulomb law. We also obtain a conceptual interpretation for the multiplicative constant as the product of the correlations of the individual clusters.     

Plasmonic Airy beam manipulation in linear optical potentials

We demonstrate, both theoretically and numerically, the efficient manipulation of plasmonic Airy beams in linear optical potentials produced by a wedged metal-dielectric-metal structure. By varying the angle between the metallic plates, we can accelerate, compensate, or reverse the self-deflection of the plasmonic Airy beams without compromising the self-healing properties. We also show that in the linear potentials the Airy plasmons of different wavelengths could be routed into different directions, creating new opportunities for optical steering and manipulation.     

Cyclic (v; r, s; ��) Difference Families with Two Base Blocks and v �� 50

We construct many new cyclic (v; r, s; λ) difference families with v ≥ 2r ≥ 2s ≥ 4 and v ≤ 50. In particular, we construct the difference families with parameters (45; 18, 10; 9), (45; 22, 22; 21), (47; 21, 12; 12), (47; 19, 15; 12), (47; 22, 14; 14), (48; 20, 10; 10), (48; 24, 4; 12), (50; 25, 20; 20), for which the existence question was an open problem. We point out that the (45; 22, 22; 21) difference family gives a balanced incomplete block design (BIBD) with parameters v = 45, b = 90, r = 44, k = 22, and λ = 21, and that the one with parameters (50; 25, 20; 20) gives a pair of binary sequences of length 50 with zero periodic autocorrelation function (the periodic analog of a Golay pair). The new SDSs include nine new D-optimal designs. A normal form for cyclic difference families (with base blocks of arbitrary sizes) is proposed and used effectively in compiling our selective listings in Tables 3–6 of known and new difference families in the above range.     

Strongly anisotropic diffusion problems; asymptotic analysis

The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrices have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them and establish convergence results. The analysis relies on averaging techniques, which have been used previously for studying transport equations whose advection fields have disparate components.     

Electrophilicity kernel and its hierarchy through softness in conceptual density functional theory

In the context of long‐range density functional theory of softness kernel, the concepts of local and kernel electrophilicity are developed to obtain the local to global hierarchical criteria such as bilocal symmetry, asymptotic behavior, and integral local to global relationships. Further development into potential‐density dependence is also provided while considering the local plus nonlocal specification of softness kernel and the associated atomic scales for the derived kernel; local and global electrophilicity are provided whose reliability is judged through the periodical features along the periodic table especially for the alkali metal atoms and the halogen atoms. © 2013 Wiley Periodicals, Inc.     

Thermal Degradation of Trioxane-Dioxqlane Copolymers Obtained with Boron Trifluoride-Acrylonitrile Complex as Initiator

The thermal degradation of certain trioxane-dioxolane copolymers obtained with boron trifluoride-acrylonitrile complex as initiator has been investigated. The thermal stability of samples, discussed in terms of topoenergetic values, was related both to copolymer composition and conversion. The most thermostable copolymers (～5% weight loss at 300°C in air), having 5–8% dioxolane units, had the highest intrinsic viscosity in the series and were isolated at 35–50% conversion. The results obtained were compared with similar data for a commercial tri-oxane-ethylene oxide copolymer containing 95% formal units.     

The checkerboard family of entangled states of two qutrits

By modifying the method of Bruß and Peres, we construct two new families of entangled two qutrit states. For all density matrices ρ in these families we have ρ _ij = 0 for i + j odd. The first family depends on 27 independent real parameters and includes both PPT and NPT states. The second family consists of PPT entangled states. The number of independent real parameters of this family is ≥ 11     

Crystallization study of sol-gel un-doped and Pd-doped TiO2 materials

Sol-gel nanostructured titania materials have been reported to have applications in areas ranging from optics via solar energy to gas sensors. In order to enhance the photocatalytic activity, there are many studies regarding the doping of titanium dioxide (TiO₂) material with either non-metals (S, C, N, P) or metals (Ag, Pt, Nd, Fe). The present work has studied some un-doped and Pd-doped sol-gel TiO₂ materials (films and gels), with various surface morphologies and structures, obtained by simultaneous gelation of both precursors Ti(OEt)₄ and Pd(acac)₂. Their structural evaluation and crystallization behavior with thermal treatment were followed by DTA/TG analysis, infrared (IR) spectroscopy, Fourier transform infrared (FTIR), spectroellipsometry (SE), X-ray diffraction (XRD) and atomic force microscope (AFM). The influence of Pd on TiO₂ crystallization for both supported and un-supported materials was studied (lattice parameters, crystallite sizes, internal microstrains). The changes in the optical properties of the TiO₂-based vitreous materials were correlated with the changes of the structure. The hydrophilic properties of the films were also connected with their structure, composition and surface morphology.