On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative

Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study.     

Solid phase synthesis of two muramyl pentapeptide derivatives

Solid phase peptide synthesis (SPPS) of two selected muramyl pentapeptide derivatives is described. The simplicity of removing the protecting groups via one-step deprotection and cleavage from the resin is the biggest advantage of SPPS. Using this method, two muramyl pentapeptide derivatives, D-MurN₃-L-Ala-D-iGlu-L-Lys-D-Ala-D-Ser (5) and D-MurN₃-L-Ala-D-iGlu-L-Lys-D-Ala-D-Ala (6), were obtained. Their chemical structures were confirmed by high-resolution mass spectrometry (HRMS) and nuclear magnetic resonance (NMR) spectroscopy. To determine the absolute configuration of the carbon atom in the side chain of the muramic acid derivative, single-crystal X-ray diffraction measurements were recorded.     

Synthesis of 3-aminoindan-1-one derivatives from 2-acetylbenzaldehydes and secondary amines by Mannich annulation

An acid-promoted 2-component Mannich annulation reaction of readily available acetylbenzaldehydes and secondary amines has been reported. The approach provides a simple and efficient method under mild conditions to synthesize 3-aminoindan-1-one derivatives in moderate to good yields.     

Swendsen‐Wang dynamics for general graphs in the tree uniqueness region

The Swendsen‐Wang (SW) dynamics is a popular Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph G = (V,E). The dynamics is conjectured to converge to equilibrium in O(|V|^1/4) steps at any (inverse) temperature β, yet there are few results providing o(|V|) upper bounds. We prove fast convergence of the SW dynamics on general graphs in the tree uniqueness region. In particular, when β < β_c(d) where β_c(d) denotes the uniqueness/nonuniqueness threshold on infinite d‐regular trees, we prove that the relaxation time (i.e., the inverse spectral gap) of the SW dynamics is Θ(1) on any graph of maximum degree d ≥ 3. Our proof utilizes a monotone version of the SW dynamics which only updates isolated vertices. We establish that this variant of the SW dynamics has mixing time and relaxation time Θ(1) on any graph of maximum degree d for all β < β_c(d). Our proof technology can be applied to general monotone Markov chains, including for example the heat‐bath block dynamics, for which we obtain new tight mixing time bounds.     

Solid-Phase Organic Synthesis of Methyl Isoxazole-5-carboxylates Based on Wang Resin–Bound 1-Phenylselenoacrylate

A novel Wang resin–bound 1-phenylselenoacrylate reagent has been developed and used as dipolarophile for the 1,3-dipolar cycloaddition with nitrile oxides to the regioselective synthesis of methyl 3-substituted isoxazole-5-carboxylates in good yields and purities.     

γ-Valerolactone (GVL): An eco-friendly anchoring solvent for solid-phase peptide synthesis

Due to the hazardous nature of CH₂Cl₂, regulatory authorities have imposed restrictions to minimize or even stop its use. It has therefore become imperative to identify environmentally benign solvents to replace it. Here we report on a bio derived solvent, γ-valerolactone, for the incorporation of the first amino acid onto p-alkoxybenzyl alcohol resin in solid-phase peptide synthesis. Satisfactory loading values (by a spectrophotometric method) were achieved. Furthermore, racemization and dipeptide formation were also checked and found to be acceptable.     

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

Surface‐initiated ring‐opening polymerization of p‐dioxanone on Wang resin bead

Biodegradable poly(p‐dioxanone) (PPDO) was formed on Wang resin surface by surface‐initiated ring‐opening polymerization (SI‐ROP). The SI‐ROP of p‐dioxanone (PDO) was achieved by heating a mixture of Tin(II) bis(2‐ethylhexanoate) [Sn(Oct)₂], hydroxyl functionalized Wang resin, and PDO in anhydrous toluene at 80 °C. The resultant polymer‐grafted Wang resin (Wang‐g‐PPDO) was characterized by fourier transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), optical microscopy (OM), and field‐emission scanning electron microscopy (FE‐SEM). The FTIR spectra of Wang‐g‐PPDO show peak characteristic of PPDO at 2943 cm^?1 (? C? H stretch), at 1741 cm^?1 (? C?O stretch), and 1136 cm^?1 (C? O? C stretch) indicating the formation of ester linkage between PPDO and hydroxyl terminated Wang resin. The DSC thermogram show melting peak corresponding to PPDO polymer on Wang resin surface. Thermogravimetric investigation shows increase in PPDO content on the Wang resin surface in terms of percentage of weight loss with increase in reaction time. The OM and SEM photographs clearly show the formation of PPDO polymer on the Wang resin surface without altering the spherical nature of Wang resin bead. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1178–1184, 2008     

Incomplete financial markets and contingent claim pricing in a dual expected utility theory framework

This paper investigates the price for contingent claims in a dual expected utility theory framework, the dual price, considering arbitrage-free financial markets. A pricing formula is obtained for contingent claims written on n underlying assets following a general diffusion process. The formula holds in both complete and incomplete markets as well as in constrained markets. An application is also considered assuming a geometric Brownian motion for the underlying assets and the Wang transform as the distortion function.     

条件愈苦,意志愈坚 --记王淦昌早年的科研活动

文章介绍了中国物理学家王淦昌早期的科研工作，特别是在抗日战争时期的科研成绩．王淦昌早期的科研贡献并不是在先进的实验仪器上，在条件优裕的实验室内完成的，而是在实验设备缺乏，科学文献不足等极端困难的环境中完成的．从王淦昌身上，可以看到那个时代中国优秀科学家脚踏实地、执志若金的奋斗精神．