Rotational symmetry and properties of the ancient solutions of Ricci flow on surfaces

We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of Daskalopoulos, Hamilton and Sesum on the a priori estimates for the ancient solutions of Ricci flow on surfaces. We also give a simple proof for the solution to be a Rosenau solution under some mild conditions on the solutions of Ricci flow on surfaces.     

Single-machine scheduling with effects of exponential learning and general deterioration

The purpose of this study is to explore the single-machine scheduling with the effects of exponential learning and general deterioration. By the effects of exponential learning and general deterioration, we meant that job processing time is decided by the functions of their starting time and positions in the sequence. Results showed that with the introduction of learning effect and deteriorating jobs to job processing time, single-machine makespan, and sum of completion time (square) minimization problems remained polynomially solvable, respectively. But for the following objective functions: the weighted sum of completion time and the maximum lateness, this paper proved that the weighted smallest basic processing time first (WSPT) rule and the earliest due date first (EDD) rule constructed the optimal sequence under some special cases, respectively.     

A further investigation of a pair of series transformation formulas with applications

As a theoretical completion or a substantial supplement to a recent joint paper by He et al. [Discrete Math. 308 (2008), pp. 3427–3440] containing a pair of series transformation formulas with a variety of illustrative examples, we provide some convergence theorems for the transformation formulas under certain general conditions. We also show that these two transformation formulas subject to the convergence conditions can be further utilized to produce more than 30 special power series sums and combinatorial identities (in a wider sense) mostly not given previously.     

Global attractors for the discrete Klein–Gordon–Schrödinger type equations

The purpose of this work is to investigate the asymptotic behaviours of solutions for the discrete Klein–Gordon–Schrödinger type equations in one-dimensional lattice. We first establish the global existence and uniqueness of solutions for the corresponding Cauchy problem. According to the solution's estimate, it is shown that the semi-group generated by the solution is continuous and possesses an absorbing set. Using truncation technique, we show that there exists a global attractor for the semi-group. Finally, we extend the criteria of Zhou et al. [S. Zhou, C. Zhao, and Y. Wang, Finite dimensionality and upper semicontinuity of compact kernel sections of non-autonomous lattice systems, Discrete Contin. Dyn. Syst. A 21 (2008), pp. 1259–1277.] for finite fractal dimension of a family of compact subsets in a Hilbert space to obtain an upper bound of fractal dimension for the global attractor.     

Competitive activity-based protein profiling identifies aza-β-lactams as a versatile chemotype for serine hydrolase inhibition

Serine hydrolases are one of the largest and most diverse enzyme classes in Nature. Most serine hydrolases lack selective inhibitors, which are valuable probes for assigning functions to these enzymes. We recently discovered a set of aza-β-lactams (ABLs) that act as potent and selective inhibitors of the mammalian serine hydrolase protein-phosphatase methylesterase-1 (PME-1). The ABLs inactivate PME-1 by covalent acylation of the enzyme's serine nucleophile, suggesting that they could offer a general scaffold for serine hydrolase inhibitor discovery. Here, we have tested this hypothesis by screening ABLs more broadly against cell and tissue proteomes by competitive activity-based protein profiling (ABPP), leading to the discovery of lead inhibitors for several serine hydrolases, including the uncharacterized enzyme α,β-hydrolase domain-containing 10 (ABHD10). ABPP-guided medicinal chemistry yielded a compound ABL303 that potently (IC(50) ≈ 30 nM) and selectively inactivated ABHD10 in vitro and in living cells. A comparison of optimized inhibitors for PME-1 and ABHD10 indicates that modest structural changes that alter steric bulk can tailor the ABL to selectively react with distinct, distantly related serine hydrolases. Our findings, taken together, designate the ABL as a versatile reactive group for creating first-in-class serine hydrolase inhibitors.     

Size-controllable synthesis of surface-enhanced Raman scattering-active gold nanoparticles coated on TiO2

As shown in the literature, gold nanoparticles (NPs) were popularly used in the fields of catalyst and surface-enhanced Raman scattering (SERS). In this work, size-controllable Au NPs coated on TiO(2) are synthesized by adjusting the pH of solutions based on sonoelectrochemical methods. The size-controlled Au NPs on TiO(2), ranging from 2 to 80 nm in diameter, can be obtained by varying the pH of solutions from 3 to 7 and placing the sample for 3 h before sonoelectrochemical reductions. The optimal particle sizes of Au NPs on TiO(2) to obtain the strongest SERS effects under an irradiation of 785 nm for probe molecules of adsorbed Rhodamine 6G (R6G) and deposited polypyrrole (PPy) are all ca. 60 nm.     

Experimental observation of chaotic phase synchronization of a periodically pump-modulated multimode microchip Nd:YVO4 laser

In this Letter we demonstrate the experimental observation of chaotic phase synchronization (CPS) in a periodically pump-modulated multimode microchip Nd:YVO₄ laser. PS transition is displayed via the stroboscopic technique. We apply the recurrence probability and correlation probability of recurrence to estimate the degree of PS. The degree of PS is studied taking into account the modulation amplitude and modulation frequency. We also propose an experimental compatible numerical simulation to reflect the fact that the Arnold tongues are experimentally and numerically exhibited in the periodically pump-modulated multimode microchip Nd:YVO₄ laser.     

Existence and uniqueness of generalized stationary waves for viscous gas flow through a nozzle with discontinuous cross section

In this paper we study the existence and uniqueness of the generalized stationary waves for one-dimensional viscous isentropic compressible flows through a nozzle with discontinuous cross section. Following the geometric singular perturbation technique, we establish the existence and uniqueness of inviscid and viscous stationary waves for the regularized systems with mollified cross section. Then, the generalized inviscid stationary waves are classified for discontinuous and expanding or contracting nozzles by the limiting argument. Moreover, we obtain the generalized viscous stationary waves by using Helly?s selection principle. However, due to the choices of mollified cross section functions, there may exist multiple transonic standing shocks in the generalized stationary waves. A new entropy condition is imposed to select a unique admissible standing shock in generalized stationary wave. We show that, such admissible solution selected by the entropy condition, admits minimal total variation and has minimal enthalpy loss across the standing shock in the limiting process.