Effect of hydrogenation on B/Si(0 0 1)-(1 × 2)

Ab initio calculations, based on pseudopotentials and density functional theory, have been performed to investigate the effect of hydrogenation on the atomic geometries and the energetics of substitutional boron on the generic Si(0 0 1)-(1 × 2) surface. For a single B atom substitution corresponding to 0.5 ML coverage, we have considered two different sites: (i) the mixed Si-B dimer structure and (ii) boron substituting for the second-layer Si to form Si-B back-bond structure, which is energetically more favorable than the mixed Si-B dimer by 0.1 eV/dimer. However, when both of these cases are passivated by hydrogen atoms, the situation is reversed and the Si-B back-bond case becomes 0.1 eV/dimer higher in energy than the mixed Si-B dimer case. For the B incorporation corresponding to 1 ML coverage, among the substitutional cases, 100% interdiffusion into the third layer of Si and 50% interdiffusion into the second layer of Si are energetically similar and more favorable than the other cases that are considered. However, when the surface is passivated with hydrogen, the B atoms energetically prefer to stay at the third layer of the Si substrate.     

FeCl3·6H2O-catalyzed selective conjugate reduction of alkylidene-β-keto esters and alkylidene-1,3-diketones

FeCl₃·6H₂O/triethylsilane composite catalyst system is successfully developed for the selective conjugate reduction of carbon-carbon double bond of Michael acceptor-alkylidene-β-keto esters and alkylidene-1,3-diketones under mild reaction conditions to afford the corresponding saturated β-keto esters and 1,3-diketones. The process involves the iron-catalyzed hydrosilylation, followed by in situ hydrolysis of silyl enol ether. The optimal reaction conditions include 20?mol% of FeCl₃·6H₂O and triethylsilane in dichloromethane at room temperature. A broad range of substrates undergoes the reduction in 1, 4-selective manner to afford the corresponding saturated compounds in excellent yields.     

Ginzburg-Landau equation and motion by mean curvature, II: Development of the initial interface

In this paper, we study the short time behavior of the solutions of a sequence of Ginzburg-Landau equations indexed by ∈. We prove that under appropriate assumptions on the initial data, solutions converge to ±1 in short time and behave like the one-dimensional traveling wave across the interface. In particular, energy remains uniformly bounded in ∈. Partially supported by the NSF Grant DMS-9200801 and by the Army Research Office through the Center for Nonlinear Analysis.     

Ginzburg-Landau equation and motion by mean curvature, I: Convergence

In this paper we study the asymptotic behavior (∈→0) of the Ginzburg-Landau equation: $$u_l^\varepsilon - \Delta u^\varepsilon + \frac{1}{{\varepsilon ^2 }}f(u^\varepsilon ) = 0.$$ . where the unknownu ^∈ is a real-valued function of [0. ∞)× ^Rd , and the given nonlinear functionf(u) = 2u(u ²?1) is the derivative of a potential W(u) = (u ²?l)²/2 with two minima of equal depth. We prove that there are a subsequence ∈_n and two disjoint, open subsetsP, N of (0, ∞) ×R ^d satisfying $$u^{\varepsilon _n } \to 1_\mathcal{P} - 1_\mathcal{N} , as n \to \infty . $$ uniformly inP andN (here 1 _A is the indicator of the setA). Furthermore, the Hausdorff dimension of the interface Γ = complement of (P∪N) ? (0, ∞)×R ^d is equal tod and it is a weak solution of the mean curvature flow as defined in [13,92]. If this weak solution is unique, or equivalently if the level-set solution of the mean curvature flow is “thin,” then the convergence is on the whole sequence. We also show thatu ^∈n has an expansion of the form $$u^{\varepsilon _n } (t,x) = q\left( {\frac{{d(t,x) + O(\varepsilon _n )}}{{\varepsilon _n }}} \right).$$ whereq(r) = tanh(r) is the traveling wave associated to the cubic nonlinearityf, O(∈) → 0 as ∈ → 0, andd(t, x) is the signed distance ofx to thet-section of Γ. We prove these results under fairly general assumptions on the initial data,u ⁰. In particular we donot assume thatu ^∈(0.x) = q(d(0,x)/∈), nor that we assume that the initial energy, ε^∈(u ^∈(0, .)), is uniformly bounded in ∈. Main tools of our analysis are viscosity solutions of parabolic equations, weak viscosity limit of Barles and Perthame, weak solutions of mean curvature flow and their properties obtained in [13] and Ilmanen’s generalization of Huisken’s monotonicity formula.     

Synthesis and Optical Properties of Novel Red-Emitting PbNb<Subscript>2</Subscript>O<Subscript>6</Subscript>: Eu<Superscript>3+</Superscript> Phosphors

Undoped and PbNb₂O_6:Eu³⁺ (1.0 ≤ x ≤ 6.0 mol%) phosphors were synthesized at 1100 °C for 3.5 h by the conventional solid state reaction method. Synthesized PbNb₂O₆:Eu³⁺ phosphors were characterized by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Energy dispersive spectroscopy (EDS) and Photoluminescence (PL) analyses. The PL spectra showed series of excitation peaks between 350 and 430 nm due to the 4f–4f transitions of Eu³⁺. For 395.0 nm excitation, emission spectra of Eu³⁺ doped samples were observed at 591 nm (orange) and 614 nm (red) due to the ⁵D₀ → ⁷F₁ transitions and ⁵D₀ → ⁷F₂ transitions, respectively. PL analysis results also showed that the emission intensity increased by increasing Eu³⁺ ion content. No concentration quenching effect was observed. The CIE chromaticity color coordinates (x,y) of the PbNb₂O₆:Eu³⁺ phosphors were found to be in the red region of the chromaticity diagram.     

Structural and Near-Infrared Properties of Nd<Superscript>3+</Superscript> Activated Lu<Subscript>3</Subscript>NbO<Subscript>7</Subscript> Phosphor

Undoped and Nd³⁺ doped lutetium niobate phases have been prepared by a conventional solid state reaction method using lutetium acetate and niobium oxide at 1250 °C for 6 h. X-ray diffraction patterns of the 6 mol% Lu₃NbO₇ sample exhibited a cubic fluorite single phase. Phase structure exhibited interesting crystallization behaviour depending on increasing Nd³⁺ concentration which led to a Lu₃NbO₇ single phase formation during the heat treatment process. SEM investigations were also in agreement with the XRD results. Morphologies of Nd³⁺ doped lutetium niobate powders exhibited oval like shapes and grain sizes varied between 0.3 and 5 μm. Near-infrared luminescence properties of Nd³⁺ doped Lu₃NbO₇ were also studied. 1.06 μm laser transition characteristics of Nd³⁺ doped lutetium niobate have been observed. Concentration quenching phenomenon was not detected depending on increasing Nd³⁺ doping concentrations at room temperature.     

Glass transition broadening via nanofiller-contiguous polymer network in aromatic thermosetting copolyester nanocomposites

The glass transition is a genuine imprint of temperature-dependent structural relaxation dynamics of backbone chains in amorphous polymers, which can also reflect features of chemical transformations induced in macromolecular architectures. Optimization of thermophysical properties of polymer nanocomposites beyond the state of the art is contingent on strong interfacial bonding between nanofiller particles and host polymer matrix chains that accordingly modifies glass transition characteristics. Contemporary polymer nanocomposite configurations have demonstrated only marginal glass transition temperature shifts utilizing conventional polymer matrix and functionalized nanofiller combinations. We present nanofiller-contiguous polymer network with aromatic thermosetting copolyester nanocomposites in which carbon nanofillers covalently conjugate with cure advancing crosslinked backbone chains through functional end-groups of constituent precursor oligomers upon an in situ polymerization reaction. Via thoroughly transformed backbone chain configuration, the polymer nanocomposites demonstrate unprecedented glass transition peak broadening by about 100 °C along with significant temperature upshift of around 80 °C. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1595–1603     

Martingale optimal transport and robust hedging in continuous time

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge–Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.     

Einstein-Rosen Universe with Wet Dark Fluid in General Relativity

Field equations in the presence of wet dark fluid distribution are obtained in general relativity with the aid of Einstein-Rosen cylindrically symmetric metric.