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     

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.     

Null-controllability of a Hyperbolic Equation as?Singular Limit of Parabolic Ones

This article considers a hyperbolic equation perturbed by a vanishing viscosity term depending on a small parameter ε>0. We show that the resulting parabolic equation is null-controllable. Moreover, we provide uniform estimates, with respect to ε, for the parabolic controls and we prove their convergence to a control of the limit hyperbolic equation. The method we use is based on Fourier expansion of solutions and the analysis of a biorthogonal sequence to a family of complex exponential functions.     

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.     

Bruhat Order in Full Symmetric Toda System

In this paper we discuss some geometrical and topological properties of the full symmetric Toda system. We show by a direct inspection that the phase transition diagram for the full symmetric Toda system in dimensions n = 3, 4 coincides with the Hasse diagram of the Bruhat order of symmetric groups S ₃ and S ₄. The method we use is based on the existence of a vast collection of invariant subvarieties of the Toda flow in orthogonal groups. We show how one can extend it to the case of general n. The resulting theorem identifies the set of singular points of dim = n Toda flow with the elements of the permutation group S _n , so that points will be connected by a trajectory, if and only if the corresponding elements are Bruhat comparable. We also show that the dimension of the submanifolds, spanned by the trajectories connecting two singular points, is equal to the length of the corresponding segment in the Hasse diagram. This is equivalent to the fact that the full symmetric Toda system is in fact a Morse–Smale system.     

Unique Cartan decomposition for II1 factors arising from arbitrary actions of free groups

We prove that for any free ergodic probability measure-preserving action ${\mathbb{F}_n \curvearrowright (X, \mu)}$ of a free group on n generators ${\mathbb{F}_n, 2\leq n \leq \infty}$ , the associated group measure space II₁ factor ${L^\infty (X)\rtimes \mathbb{F}_n}$ has L ^∞(X) as its unique Cartan subalgebra, up to unitary conjugacy. We deduce that group measure space II₁ factors arising from actions of free groups with different number of generators are never isomorphic. We actually prove unique Cartan decomposition results for II₁ factors arising from arbitrary actions of a much larger family of groups, including all free products of amenable groups and their direct products.     

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.     

Thermal stability evolution of carbon nanotubes caused by liquid oxidation

Carbon nanotubes (CNTs) grown by chemical vapor decomposition of ethylene on alumina- and silica-supported Fe–Co bimetallic catalysts were examined before and after purification encompassing chemical oxidation treatment in 3 M NaOH and 3 M HNO₃ solutions, sequentially. Thermal properties were investigated and correlated with structural changes followed by TEM, X-ray diffraction and Raman spectroscopy characterization. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TG) were employed simultaneously in the regime of TPO and TPH, in diluted flow of either O₂ or H₂. TG revealed almost complete burning of both refined CNT samples in diluted O₂, indicating the efficiency of the purification method used to remove the catalyst remains. However, different trends and significant magnitudes of changes in the heat of combustion demonstrate changes in CNTs stability after purification as a function of the catalyst support type. This is the consequence of changes in carbon type, CNTs order degree and morphology, as well as the degree of functionalization, which have their own effects on the CNTs thermal stability.