Path properties of l_p-valued Gaussian random fields

General limit theorems are established for l~p-valued Gaussian random fields indexed by a multidimensional parameter,which contain both almost sure moduli of continuity and limits of large increments for the l~p-valued Gaussian random fields under(?)explicit conditions.     

Heterologous Co-expression of accA, fabD, and Thioesterase Genes for Improving Long-Chain Fatty Acid Production in Pseudomonas aeruginosa and Escherichia coli

The goal of the present study was to increase the content of intracellular long-chain fatty acids in two bacterial strains, Pseudomonas aeruginosa PA14 and Escherichia coli K-12 MG1655, by co-overexpressing essential enzymes that are involved in the fatty acid synthesis metabolic pathway. Recently, microbial fatty acids and their derivatives have been receiving increasing attention as an alternative source of fuel. By introducing two genes (accA and fabD) of P. aeruginosa into the two bacterial strains and by co-expressing with them the fatty acyl?Cacyl carrier protein thioesterase gene of Streptococcus pyogenes (strain MGAS10270), we have engineered recombinant strains that are efficient producers of long-chain fatty acids (C16 and C18). The recombinant strains exhibit a 1.3?C1.7-fold increase in the production of long-chain fatty acids over the wild-type strains. To enhance the production of total long-chain fatty acids, we researched the carbon sources for optimized culture conditions and results were used for post-culture incubation period. E. coli SGJS17 (containing the accA, fabD, and thioesterase genes) produced the highest content of intracellular total fatty acids; in particular, the unsaturated fatty acid content was about 20-fold higher than that in the wild-type E. coli.     

Correlations Between FAS Elongation Cycle Genes Expression and Fatty Acid Production for Improvement of Long-Chain Fatty Acids in Escherichia coli

Microorganisms have been used for biodiesel (fatty acid methyl ester) production due to their significant environmental and economic benefits. The aim of the present research was to develop new strains of Escherichia coli K-12 MG1655 and to increase the content of long-chain fatty acids by overexpressing essential enzymes that are involved in the fatty acid synthase elongation cycle. In addition, the relationship of β-ketoacyl-acyl carrier protein (ACP) synthase (fabH), β-ketoacyl-ACP reductase (fabG), β-hydroxyacyl-ACP dehydrase (fabZ), and β-enoyl-ACP reductase (fabI) with respect to fatty acid production was investigated. The four enzymes play a unique role in fatty acid biosynthesis and elongation processes. We report the generation of recombinant E. coli strains that produced long-chain fatty acids to amounts twofold over wild type. To verify the results, NAD⁺/NADH ratios and glucose analyses were performed. We also confirmed that FabZ plays an important role in producing unsaturated fatty acids (UFAs) as E. coli SGJS25 (overexpressing the fabZ gene) produced the highest percentage of UFAs (35 % of total long-chain fatty acids), over wild type and other recombinants. Indeed, cis-9-hexadecenoic acid, a major UFA in E. coli SGJS25, was produced at levels 20-fold higher than in wild type after 20 h in culture. The biochemically engineered E. coli presented in this study is expected to be more economical for producing long-chain fatty acids in quality biodiesel production processes.     

Visible-Light-Induced ortho-Selective Migration on Pyridyl Ring: Trifluoromethylative Pyridylation of Unactivated Alkenes

The photocatalyzed ortho-selective migration on a pyridyl ring has been achieved for the site-selective trifluoromethylative pyridylation of unactivated alkenes. The overall process is initiated by the selective addition of a CF₃ radical to the alkene to provide a nucleophilic alkyl radical intermediate, which enables an intramolecular endo addition exclusively to the ortho-position of the pyridinium salt. Both secondary and tertiary alkyl radicals are well-suited for addition to the C2-position of pyridinium salts to ultimately provide synthetically valuable C2-fluoroalkyl functionalized pyridines. Moreover, the method was successfully applied to the reaction with P-centered radicals. The utility of this transformation was further demonstrated by the late-stage functionalization of complex bioactive molecules.     

Iwasawa Theory of Quadratic Twists of X_0(49)

The field K=Q((-7)(1/2)) is the only imaginary quadratic field with class number 1, in which the prime 2 splits, and we fix one of the primes p of K lying above 2. The modular elliptic curve X_0(49) has complex multiplication by the maximal order O of K, and we let E be the twist of X_0(49)by the quadratic extension K(M1/2)/K, where M is any square free element of O with M ≡1 mod 4 and(M, 7) = 1. In the present note, we use surprisingly simple algebraic arguments to prove a sharp estimate for the rank of the Mordell-Weil group modulo torsion of E over the field F_∞ = K(E_(p∞)),where E_(p∞) denotes the group of p~∞-division points on E. Moreover, writing B for the twist of X_0(49)by K((-7)(1/4))/K, our Iwasawa-theoretic arguments also show that the weak form of the conjecture of Birch and Swinnerton-Dyer implies the non-vanishing at s = 1 of the complex L-series of B over every finite layer of the unique Z_2-extension of K unramified outside p. We hope to give a proof of this last non-vanishing assertion in a subsequent paper.     

Preparation of interpenetrating polymer network composed of poly(ethylene glycol) and poly(acrylamide) hydrogels as a support of enzyme immobilization

Poly(ethylene glycol)(PEG)‐based interpenetrating polymeric network (IPN) hydrogels were prepared for the application of enzyme immobilization. Poly(acrylamide)(PAAm) was chosen as the other network of IPN hydrogel and different concentration of PAAm networks were incorporated inside the PEG hydrogel to improve the mechanical strength and provide functional groups that covalently bind the enzyme. Formation of IPN hydrogels was confirmed by observing the weight per cent gain of hydrogel after incorporation of PAAm network and by attenuated total reflectance/Fourier transform infrared (ATR/FTIR) analysis. Synthesis of IPN hydrogels with higher PAAm content produced more crosslinked hydrogels with lower water content (WC), smaller M_c and mesh size, which resulted in enhanced mechanical properties compared to the PEG hydrogel. The IPN hydrogels exhibited tensile strength between 0.2 and 1.2 MPa while retaining high levels of hydration (70–81% water). For enzyme immobilization, glucose oxidase (GOX) was immobilized to PEG and IPN hydrogel beads. Enzyme activity studies revealed that although all the hydrogels initially had similar enzymatic activity, enzyme‐immobilizing PEG hydrogels lost most of the enzymatic activity within 2 days due to enzyme leaching while IPN hydrogels maintained a maximum 80% of the initial enzymatic activity over a week due to the covalent linkage between the enzyme and amine groups of PAAm. Copyright © 2008 John Wiley & Sons, Ltd.     

Periodic solutions of Wick-type stochastic Korteweg–de Vries equations

Nonlinear stochastic partial differential equations have a wide range of applications in science and engineering. Finding exact solutions of the Wick-type stochastic equation will be helpful in the theories and numerical studies of such equations. In this paper, Kudrayshov method together with Hermite transform is implemented to obtain exact solutions of Wick-type stochastic Korteweg–de Vries equation. Further, graphical illustrations in two- and three-dimensional plots of the obtained solutions depending on time and space are also given with white noise functionals.     

Synthesis of Pure <Emphasis Type="Italic">meso</Emphasis>-2,3-Butanediol from Crude Glycerol Using an Engineered Metabolic Pathway in <Emphasis Type="Italic">Escherichia coli</Emphasis>

meso-2,3-Butanediol (meso-2,3-BDO) is essential for the synthesis of various economically valuable biosynthetic products; however, the production of meso-2,3-BDO from expensive carbon sources is an obstacle for industrial applications. In this study, genes involved in the synthesis of 2,3-BDO in Klebsiella pneumoniae were identified and used to genetically modify Escherichia coli for meso-2,3-BDO production. Two 2,3-BDO biosynthesis genes—budA, encoding acetolactate, and meso-budC, encoding meso-SADH—from K. pneumoniae were cloned into the pUC18 plasmid and introduced into E. coli. In 2 l batch culture, the SGSB03 E. coli strain yielded meso-2,3-BDO at 0.31 g/g_glucose (with a maximum of 15.7 g/l_culture after 48 h) and 0.21 g/g_{crude glycerol} (with a maximum of 6.9 g/l_culture after 48 h). Batch cultures were grown under optimized conditions (aerobic, 6% carbon source, 37 °C, and initial pH 7). To find the optimal culture conditions for meso-2,3-BDO production, we evaluated the enzyme activity of meso-SADH and the whole cell conversion yield (meso-2,3-BDO/acetoin) of the E. coli SGSB02, which contains pSB02. meso-SADH showed high enzyme activity at 30–37 °C and pH 7 (30.5–41.5 U/mg of protein), and the conversion yield of SGSB02 E. coli was highest at 37–42 °C and a pH of 7 (0.25–0.28 g _meso-2,3-BDO/g_acetoin).     

Visible‐Light‐Induced ortho‐Selective Migration on Pyridyl Ring: Trifluoromethylative Pyridylation of Unactivated Alkenes

The photocatalyzed ortho‐selective migration on a pyridyl ring has been achieved for the site‐selective trifluoromethylative pyridylation of unactivated alkenes. The overall process is initiated by the selective addition of a CF₃ radical to the alkene to provide a nucleophilic alkyl radical intermediate, which enables an intramolecular endo addition exclusively to the ortho‐position of the pyridinium salt. Both secondary and tertiary alkyl radicals are well‐suited for addition to the C2‐position of pyridinium salts to ultimately provide synthetically valuable C2‐fluoroalkyl functionalized pyridines. Moreover, the method was successfully applied to the reaction with P‐centered radicals. The utility of this transformation was further demonstrated by the late‐stage functionalization of complex bioactive molecules.