2‐branes with Arnold‐Beltrami fluxes from minimal supergravity

We describe this paper as a Sentimental Journey from Hydrodynamics to Supergravity. Beltrami equation in three dimensions that plays a key role in the hydrodynamics of incompressible fluids has an unsuspected relation with minimal supergravity in seven dimensions. We show that just supergravity and no other theory with the same field content but different coefficients in the lagrangian, admits exact two‐brane solutions where Arnold‐Beltrami fluxes in the transverse directions have been switched on. The rich variety of discrete groups that classify the solutions of Beltrami equation, namely the eigenfunctions of the operator on a three‐torus, are by this newly discovered token injected into the brane world. A new quite extensive playing ground opens up for supergravity and for its dual gauge theories in three dimensions, where all classical fields and all quantum composite operators will be assigned to irreducible representations of discrete crystallographic groups Γ.     

Phase separation in H2O:N2 mixture: molecular dynamics simulations using atomistic force fields

A class II atomistic force field with Lennard-Jones 6-9 nonbond interactions is used to investigate equations of state (EOS) for important high explosive detonation products N(2) and H(2)O in the temperature range of 700-2500 K and pressure range of 0.1-10 GPa. A standard sixth order parameter-mixing scheme is then employed to study a 2:1 (molar) H(2)O:N(2) mixture, to investigate, in particular, the possibility of phase separation under detonation conditions. The simulations demonstrate several important results, including (i) the accuracy of computed EOS for both N(2) and H(2)O over the entire range of temperature and pressure considered, (ii) accurate mixing-demixing phase boundary as compared to experimental data, and (iii) the departure of mixing free energy from that predicted by ideal mixing law. The results provide comparison and guidance to state-of-the-art chemical kinetic models.     

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.     

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.     

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.     

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.     

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.     

PLS-DA - Docking Optimized Combined Energetic Terms (PLSDA-DOCET) protocol: a brief evaluation

Docking studies have become popular approaches in drug design, where the binding energy of the ligand in the active site of the protein is estimated by a scoring function. Many promising techniques were developed to enhance the performance of scoring functions including the fusion of multiple scoring functions outcomes into a so-called consensus scoring function. Hereby, we evaluated the target oriented consensus technique using the energetic terms of several scoring functions. The approach was denoted PLSDA-DOCET. Optimization strategies for consensus energetic terms and scoring functions based on ROC metric were compared to classical rigid docking and to ligand-based similarity search methods comprising 2D fingerprints and ROCS. The ROCS results indicate large performance variations depending on the biological target. The AUC-based strategy of PLSDA-DOCET outperformed the other docking approaches regarding simple retrieval and scaffold-hopping. The superior performance of PLSDA-DOCET protocol relative to single and combined scoring functions was validated on an external test set. We found a relative low mean correlation of the ranks of the chemotypes retrieved by the PLSDA-DOCET protocol and all the other methods employed here.