Enveloping subspaces and superposition of states

In the space of pure states of a generic physical system, a family ? of subsets is singled out and used to extend the quantum-mechanical notion of “superposition” of pure states. ? possesses a natural lattice structure and corresponds to the lattice of closed subspaces of Quantum Mechanics.     

Hydrogen Bonding Patterns in 2,6-diamino-4-oxopyrimidinium Sulfosalicylate Monohydrate

The title compound, [C₄H₇N₄O⁺, C₇H₅O₆S^? . H₂O] contains one 2, 6-diamino-4-oxopyrimidinium cation, one sulfosalicylate anion and a water molecule. The crystal structure was determined by single crystal X-ray diffraction. This compound crystallized in the orthorhombic system; space group Pna2₁ with the unit cell parameters a = 13.402(3) Å, b = 16. 221(3) Å, c = 6.714(2) Å, V = 1459.6(6), Z = 4. The sulfonic acid group has protonated the aminopyrimidine moiety. The protonated N1 atom and N4 amino group are hydrogen bonded to the keto group (O1) of the neighbouring pyrimidine forming a six-membered ring with graph-set notation R₂ ¹(6) and a supramolecular chain along the c-axis. This supramolecular chain is further strengthened by one of the sulfonate oxygen atoms (O3), bridging the pyrimidines via hydrogen bonded rings, R₃ ²(10) involving N(3)–H(3)···O(3) and N(2)–H(2B)···O(3) hydrogen bonds. The other two oxygen atoms of the sulfonate groups are bridged by water molecules via O-H···O hydrogen bonds constituting a supramolecular chain. The water molecule also acts as hydrogen bond acceptor with respect to the carboxyl group.     

Hydrogen evolution across nano-Schottky junctions at carbon supported MoS2 catalysts in biphasic liquid systems

The activities of a series of MoS(2)-based hydrogen evolution catalysts were studied by biphasic reactions monitored by UV/Vis spectroscopy. Carbon supported MoS(2) catalysts performed best due to an abundance of catalytic edge sites and strong electronic coupling of catalyst to support.     

The Chair–Envelope Conformation of Two Derivatives of Triethylammonium 3-Oxo-8,9-Dinitro-Bicyclo [3.3.1] Non-7-En-6-Nitronate [I] and [II]

Abstract  

The title compounds C₁₉H₁₈N₃O₉ ⁻·C₆H₁₆N⁺ (I) [triethylammonium 2-benzyl-2-ethoxycarbonyl-3-oxo-8,9-dinitro-bicyclo [3.3.1] non-7-en-6-nitronate] and C₁₉H₁₇N₄O₁₁ ⁻·C₆H₁₆N⁺ (II) [triethylammonium 2(4-nitrophenylmethyl)-2-ethoxycarbonyl-3-oxo-8,9-dinitro-bicyclo [3.3.1] non-7-en-6-nitronate] crystallize in monoclinic crystal system with P2 ₁ /c space group. In compounds I and II, the bicyclo [3.3.1] nonane has chair–envelope conformation. The crystal structure of compound (I) is stabilized by N–H⋯O, N–H⋯N hydrogen bonds. In both the crystal structures weak C–H⋯O hydrogen bond is observed. Both compounds adopt chair–envelope conformation. An examination of puckering parameters, torsion angles and model (Dreiding) of the title compounds clearly indicates that the ring A has slightly distorted chair conformation and ring B has slightly distorted envelope conformation.     

Synthesis and Crystal Structure of a New Schiff Base 4-[(2-hydroxy-benzylidene)-amino]-<Emphasis Type="Italic">N</Emphasis>-(5-methyl-isoxazol-3-yl)-benzenesulfonamide

Abstract  The structure of the title compound (C₁₇H₁₅N₃O₄S)₂ the schiff base, bis(N-(5-methyl-3-isoxazolyl)-4-[(2-hydroxy benzylidene)-amino]) benzene sulfonamide was elucidated by H¹, C¹³ NMR, UV–VIS and IR spectroscopic techniques. The X-ray structure was determined in order to establish the conformation of the molecule. The compound crystallizes in the triclinic space group P-1, with a = 11.419(1), b = 11.426(0), c = 13.316(1) ?, α = 71.94(2), β = 89.79(1), γ = 89.14(2)° and Z = 4. Two benzene rings and azomethine group are practically coplanar, as a result of intramolecular hydrogen bonds involving the hydroxy O atom and azomethine N atom. The component species further interact via N–H···N and C–H···O hydrogen bonds and π–π stacking interactions. Index Abstract  The title compound (C₁₇H₁₅N₃O₄S)₂, Schiff base, bis(N-(5-methyl-3-isoxazolyl)-4-[(2-hydroxy benzylidene)-amino]) benzene sulfonamide was synthesized by the condensation of 4-amino-N-(5-methyl-3-isoxazolyl) benzene sulfonamide (SMZ) and 2-hydroxy benzaldehyde (SA). Its structure was confirmed by single crystal X-ray diffraction analysis. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints

In this paper, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. The natural formulation leads to a nonconvex optimization problem. This problem is shown to be equivalent to a convex optimization problem with linear objective function, linear equality and inequality constraints and quadratic inequality constraints. Here, the indirect elimination method is applied to reduce the convex optimization problem into an equivalent convex optimization problem of lower dimension with only inequality constraints. The primal-dual interior point method is utilized to develop an effective algorithm (in terms of computational efficiency) via solving the modified KKT equations with Newton method. Numerical simulations are carried out. Compared to algorithms based on a trust region interior point method and sequential quadratic programming method, it is observed that the method proposed is much superior in terms of computational efficiency.     

Photon- and electron-induced surface voltage in electron spectroscopies on ZnSe(0 0 1)

The surface band bending in ZnSe(0 0 1), as a function of the temperature, is investigated both in the valence band (by photoemission) and in the conduction band (by inverse photoemission and absorbed current spectroscopies). Two different mechanisms are invoked for interpreting the experimental data: the band bending due to surface states, and the surface voltage induced by the incident beam. While the latter is well known in photoemission (surface photovoltage), we demonstrate the existence of a similar effect in inverse photoemission and absorbed current spectroscopies, induced by the incident electrons instead of photons. These results point to the importance of considering the surface voltage effect even in electron-in techniques for a correct evaluation of the band bending.