Approximation by complex szász-durrmeyer operators in compact disks

In the present paper, we deal with the complex Szász-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Control of the Electronic Ground State on an Electron‐Transfer Copper Site by Second‐Sphere Perturbations

The Cu_A center is a dinuclear copper site that serves as an optimized hub for long‐range electron transfer in heme–copper terminal oxidases. Its electronic structure can be described in terms of a σ_u* ground‐state wavefunction with an alternative, less populated ground state of π_u symmetry, which is thermally accessible. It is now shown that second‐sphere mutations in the Cu_A containing subunit of Thermus thermophilus ba₃ oxidase perturb the electronic structure, which leads to a substantial increase in the population of the π_u state, as shown by different spectroscopic methods. This perturbation does not affect the redox potential of the metal site, and despite an increase in the reorganization energy, it is not detrimental to the electron‐transfer kinetics. The mutations were achieved by replacing the loops that are involved in protein–protein interactions with cytochrome c, suggesting that transient protein binding could also elicit ground‐state switching in the oxidase, which enables alternative electron‐transfer pathways.     

On‐Line Monitoring of Chemical Reactions by using Bench‐Top Nuclear Magnetic Resonance Spectroscopy

Real‐time nuclear magnetic resonance (NMR) spectroscopy measurements carried out with a bench‐top system installed next to the reactor inside the fume hood of the chemistry laboratory are presented. To test the system for on‐line monitoring, a transfer hydrogenation reaction was studied by continuously pumping the reaction mixture from the reactor to the magnet and back in a closed loop. In addition to improving the time resolution provided by standard sampling methods, the use of such a flow setup eliminates the need for sample preparation. Owing to the progress in terms of field homogeneity and sensitivity now available with compact NMR spectrometers, small molecules dissolved at concentrations on the order of 1 mmol L^?1 can be characterized in single‐scan measurements with 1 Hz resolution. Owing to the reduced field strength of compact low‐field systems compared to that of conventional high‐field magnets, the overlap in the spectrum of different NMR signals is a typical situation. The data processing required to obtain concentrations in the presence of signal overlap are discussed in detail, methods such as plain integration and line‐fitting approaches are compared, and the accuracy of each method is determined. The kinetic rates measured for different catalytic concentrations show good agreement with those obtained with gas chromatography as a reference analytical method. Finally, as the measurements are performed under continuous flow conditions, the experimental setup and the flow parameters are optimized to maximize time resolution and signal‐to‐noise ratio.     

A study of the effect of step excrescences and free‐stream disturbances on boundary layer stability

In this work, a study of the mechanism by which free‐stream acoustic and vorticity disturbances interact with a boundary layer flow developing over a flat plate featuring a step excrescence located at a certain distance from a blunt leading edge is included. The numerical tool is a high‐fidelity implicit numerical algorithm solving for the unsteady, compressible form of the Navier–Stokes equations in a body‐fitted curvilinear coordinates and employing high‐accurate compact differencing schemes with Pade‐type filters. Acoustic and vorticity waves are generated using a source term in the momentum and energy equations, as opposed to using inflow boundary conditions, to avoid spurious waves that may propagate from boundaries. The results show that the receptivity to surface step excrescences is largely the result of an overall adverse pressure gradient posed by the step, and that the free‐stream disturbances accelerate the generation of instabilities in the downstream. As expected, it is found that the acoustic disturbance interacting with the surface imperfection is more efficient in exciting the Tollmien–Schlichting waves than the vorticity disturbance. The latter generates Tollmien–Schlichting waves that are grouped in wave packets consistent with the wavelength of the free‐stream disturbance. Copyright © 2015 John Wiley & Sons, Ltd.     

求解Schrdinger方程的高阶紧致差分格式

基于Richardson外推法提出了一种求解Schrdinger方程的高阶紧致差分方法.该方法首先利用二阶微商的四阶精度紧致差分逼近公式对原方程进行求解,然后利用Richardson外推技术外推一次,得到了Schrdinger方程具有O(r~4+h~4)精度的数值解.通过Fourier分析方法证明了该格式是无条件稳定的.数值实验验证了该方法的高阶精度及有效性.     

Connected signed graphs of fixed order,size, and number of negative edges with maximal index

In this paper we focus on connected signed graphs of fixed number of vertices, positive edges and negative edges that maximize the largest eigenvalue (also called the index) of their adjacency matrix. In the first step we determine these signed graphs in the set of signed generalized theta graphs. Concerning the general case, we use the eigenvector techniques for getting some structural properties of resulting signed graphs. In particular, we prove that positive edges induce nested split subgraphs, while negative edges induce double nested signed subgraphs. We observe that our concept can be applied when considering balancedness of signed graphs (the property that is extensively studied in both mathematical and non-mathematical context).     

Soliton squeezing generated in an all-fiber contiguration

We experimentally demonstrate amplitude squeezed soliton utilizing intensity-dependent self-phase modulation in an asymmetric Sagnac interferometer.The system.whose components are connected via ferrule connector/physical connection(FC/PC)fiber connectors,constitutes all-fiber configuration to generate squeezed soliton.Soliton amplitude reduction measured by homodyne detection is near 4.0 dB below the shot-noise level.Optimal squeezing fields in both simple and compact all-fiber configuration are obtained.     

Propagation of light in(2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The(2 1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.