Improved synthesis of P(3HB-co-3HV-co-3HHx) terpolymers by mutant Cupriavidus necator using the PHA synthase gene of Chromobacterium sp. USM2 with high affinity towards 3HV

Unlike polyhydroxyalkanoates (PHAs) copolymers, the controlled and efficient synthesis of PHA terpolymers from triglycerides and fatty acids are yet to be established. This study demonstrates the production of P(3HB-co-3HV-co-3HHx) terpolymer with a wide range of 3HV monomer compositions from mixtures of crude palm kernel oil and 3HV precursors using a mutant Cupriavidus necator PHB⁻4 transformant harboring the PHA synthase gene (phaC) of a locally isolated Chromobacterium sp. USM2. The PHA synthase of Chromobacterium has an unusually high affinity towards 3HV monomer. P(3HB-co-3HV-co-3HHx) terpolymers with 3HV monomer composition ranging from 2 to 91 mol% were produced. Generation of 3HHx monomers was affected by the concentration and feeding time of 3HV precursor. P(3HB-co-24 mol% 3HV-co-7 mol% 3HHx) exhibited mechanical properties similar to that of common low-density polyethylene. P(3HB-co-3HV-co-3HHx) terpolymers with a wide range of 3HV molar fraction had been successfully synthesized by adding lower concentrations of 3HV precursors and using a PHA synthase with high affinity towards 3HV monomer.     

Biosynthesis and characterization of novel polyhydroxyalkanoate polymers with high elastic property by Cupriavidus necator PHB4 transformant

We attempted to synthesize novel polyhydroxyalkanoate (PHA) containing new 3-hydroxy-4-methylvalerate (3H4MV) monomer from the transformed strain of Cupriavidus necator PHB⁻4 harboring the PHA synthase gene of Chromobacterium sp. USM2 (phaC_Cs). Novel PHA containing SCL and MCL monomers were successfully synthesized from crude palm kernel oil (CPKO) and isocaproic acid. Results showed that P(3HB-co-1 mol% 3HV-co-3 mol% 3H4MV-co-18 mol% 3HHx) possessed higher thermal stability, higher elastomeric behavior at room temperature and higher ductility than the P(3HB-co-5 mol% 3HHx). The novel PHA film was found to possess an interesting rubber-like elasticity and flexibility property which has not been reported. The soil surface degradation study showed that the novel PHA film was degraded faster than the 3HB homopolymer and copolymer with 5 mol% of 3HHx.     

Classification with Gaussians and convex loss Ⅱ:improving error bounds by noise conditions

We continue our study on classification learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and general convex loss functions. Our main purpose of this paper is to improve error bounds by presenting a new comparison theorem associated with general convex loss functions and Tsybakov noise conditions. Some concrete examples are provided to illustrate the improved learning rates which demonstrate the effect of various loss functions for learning algorithms. In our ...     

Understanding how both the partitions of a bipartite network affect its one-mode projection

It is a well-known fact that the degree distribution (DD) of the nodes in a partition of a bipartite network influences the DD of its one-mode projection on that partition. However, there are no studies exploring the effect of the DD of the other partition on the one-mode projection. In this article, we show that the DD of the other partition, in fact, has a very strong influence on the DD of the one-mode projection. We establish this fact by deriving the exact or approximate closed-forms of the DD of the one-mode projection through the application of generating function formalism followed by the method of iterative convolution. The results are cross-validated through appropriate simulations.     

威布尔分布族刻度参数的经验Bayes检验函数的收敛速度

本文研究了在"加权线性损失"下,威布尔分布族刻度参数经验Bayes (EB)检验问题.利用概率密度函数的递归核估计,构造了刻度参数的经验Bayes检验函数,并获得了它的收敛速度,在适当的条件下,收敛速度的阶可任意接近O(n^-1),推广了文献的结果.最后给出一个有关本文主要结果的例子.     

An application of weighted Hardy spaces to the Navier–Stokes equations

In this article, we consider the mapping properties of convolution operators with smooth functions on weighted Hardy spaces H^p(w)$H^p(w)$ with w   belonging to Muckenhoupt class _A∞$A_{\infty }$. As a corollary, one obtains decay estimates of heat semigroup on weighted Hardy spaces. After a weighted version of the div–curl lemma is established, these estimates on weighted Hardy spaces are applied to the investigation of the decay property of global mild solutions to Navier–Stokes equations with the initial data belonging to weighted Hardy spaces.     

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.     

Separation dichotomy and wavefronts for a nonlinear convolution equation

This paper is concerned with a scalar nonlinear convolution equation, which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that, at each end of the real line, every bounded positive solution of the convolution equation should either be separated from zero or be exponentially converging to zero. This dichotomy principle is then used to establish a general theorem guaranteeing the uniform persistence and existence of semi-wavefront solutions to the convolution equation. Finally, we apply our theoretical results to several well-studied classes of evolution equations with asymmetric non-local and non-monotone response. We show that, contrary to the symmetric case, these equations can possess simultaneously stationary, expansion and extinction waves.