Facile access to redox-active C2-bridged complexes with half-sandwich manganese end groups

The dinuclear mixed-valent complex [(MeC5H4)(dmpe)MnC(2)Mn(dmpe)(C5H4Me)](+)[(eta2-MeC5H4)3Mn](-)[1](+)[2]- (dmpe=1,2-bis(dimethylphosphanyl)ethane) was prepared by the reaction of [Mn(MeC5H4)2] with dmpe and Me(3)SnC[triple chemical bond]CSnMe3. The reactions of [1](+)[2]- with K[PF6] and Na[BPh4] yielded the corresponding anion metathesis products [(MeC5H4)(dmpe)MnC2Mn(dmpe)(C5H4Me)][PF6] ([1][PF6]) and [(MeC5H4)(dmpe)MnC2Mn(dmpe)(C5H4Me)][BPh4] ([1][BPh4]). These mixed-valent species can be reduced to the neutral form by reaction with Na/Hg. The obtained complex [(MeC5H4)(dmpe)MnC2Mn(dmpe)(C5H4Me)] (1) displays a triplet/singlet spin equilibrium in solution and in the solid state, which was additionally studied by DFT calculations. The diamagnetic dicationic species [(MeC5H4)(dmpe)MnC2Mn(dmpe)(C5H4Me)][PF6]2 ([1][PF6]2) was obtained by oxidizing the mixed-valent complex [1][PF6] with one equivalent of [Fe(C5H5)2][PF6]. Both redox processes are fully reversible. The dinuclear compounds were characterized by NMR, IR, UV-visible, and Raman spectroscopy, cyclic voltammetry, and magnetic susceptibility measurements. X-ray diffraction studies were performed on [1][2], [1][PF6], [1][BPh4], and [1][PF6]2.     

Neutron forward diffraction by single crystal prisms

We have derived analytic expressions for the deflection as well as transmitted fraction of monochromatic neutrons forward diffracted by a single crystal prism. In the vicinity of a Bragg reflection, the neutron deflection deviates sharply from that for an amorphous prism, exhibiting three orders of magnitude greater sensitivity to the incidence angle. We have measured the variation of neutron deflection and transmission across a Bragg reflection, for several single crystal prisms. The results agree well with theory.      

Modeling undesirable factors in data envelopment analysis

Data envelopment analysis is a mathematical programming technique for identifying efficient frontiers for peer decision making units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. In the current paper, we present a data envelopment analysis (DEA) model in which can be used to improve the relative performance via increasing undesirable inputs and decreasing undesirable outputs.     

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 10⁴ to 6.08 × 10⁴. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.     

A novel neural network based on NCP function for solving constrained nonconvex optimization problems

This article presents a novel neural network (NN) based on NCP function for solving nonconvex nonlinear optimization (NCNO) problem subject to nonlinear inequality constraints. We first apply the p‐power convexification of the Lagrangian function in the NCNO problem. The proposed NN is a gradient model which is constructed by an NCP function and an unconstrained minimization problem. The main feature of this NN is that its equilibrium point coincides with the optimal solution of the original problem. Under a proper assumption and utilizing a suitable Lyapunov function, it is shown that the proposed NN is Lyapunov stable and convergent to an exact optimal solution of the original problem. Finally, simulation results on two numerical examples and two practical examples are given to show the effectiveness and applicability of the proposed NN. © 2015 Wiley Periodicals, Inc. Complexity 21: 130–141, 2016     

Optically transparent Au{111} substrates: flat gold nanoparticle platforms for high-resolution scanning tunneling microscopy

We demonstrate a new type of Au{111} substrate that is both atomically flat and optically transparent, which consists of solution-grown flat gold nanoparticles (FGNPs) deposited on indium tin oxide (ITO)-coated glass. We show that FGNPs are atomically flat single-crystal plates with large {111} faces that expose only 2-4 atomic layers. These FGNPs are excellent platforms for alkanethiol self-assembled monolayers (SAMs) and for high-resolution scanning tunneling microscopy (STM). Our supported FGNPs are also low-cost Au{111} substrates, employing only basic wet chemical techniques in preparation. This approach should be broadly applicable to other types of substrates for scanning probe microscopies.     

A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

Asymptotic Stability of Harmonic Maps on the Hyperbolic Plane under the Schrödinger Maps Evolution

We consider the Cauchy problem for the Schrödinger maps evolution when the domain is the hyperbolic plane. An interesting feature of this problem compared to the more widely studied case on the Euclidean plane is the existence of a rich new family of finite energy harmonic maps. These are stationary solutions, and thus play an important role in the dynamics of Schrödinger maps. The main result of this article is the asymptotic stability of (some of) such harmonic maps under the Schrödinger maps evolution. More precisely, we prove the nonlinear asymptotic stability of a finite energy equivariant harmonic map under the Schrödinger maps evolution with respect to non-equivariant perturbations, provided obeys a suitable linearized stability condition. This condition is known to hold for all equivariant harmonic maps with values in the hyperbolic plane and for a subset of those maps taking values in the sphere. One of the main technical ingredients in the paper is a global-in-time local smoothing and Strichartz estimate for the operator obtained by linearization around a harmonic map, proved in the companion paper [36]. © 2021 Wiley Periodicals LLC.