一类SEI传染病扩散模型及其移动边沿

该文研究一类SEI传染病模型,其中病毒在潜伏期和感染期具有感染性.首先研究固定区域上SEI偏微分方程组,考虑平衡解的局部稳定性和全局稳定性.然后重点研究相应的自由边界问题,其中自由边界表示病毒的移动边沿。给出了该问题解的全局存在性、唯一性,讨论了自由边界的性质,证明了病毒要么蔓延,要么消退.还给出了蔓延和消退的充分条件,结果表明:当有效接触率很小或平均潜伏期较短,且初始染病区域小时,疾病消退;而当有效接触率大或平均潜伏期较长,且初始染病区域大时,疾病蔓延.     

Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.     

Synthesis and Application of N-Tosyl Piperidinyl-Containing α-Aminophosphonates

Abstract

A series of novel (4′-tosyl) piperidin-4-yl containing α-aminophosphonates were synthesized by a one-pot reaction, efficiently catalyzed by magnesium perchlorate, under solvent-free conditions from 1-tosylpiperidin-4-one, substituted aromatic amines, and diethyl phosphite (DEP). The synthesized compounds were characterized by IR, ¹H NMR, ¹³C NMR, ³¹P NMR, and HRMS spectroscopy. A single-crystal X-ray structure of diethyl 4-(2-chlorophenyl) amino-1-(4’-methylbezenesulfonyl) piperidin-4-yl-phosphonate (2a) was obtained, and some of the title compounds displayed insecticidal activities against Plutella xylostella.

Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfer, and Silicon and the Related Elements for the following free supplemental files: Additional figures and tables.     

Recognition of α-Amino Acid from β- and γ-Amino Acid by N -Phosphorylation

The reactivity of N -phosphoryl f -alanine differs from N -phosphoryl g -alanine and N -phosphoryl n -amino butyric acid enormously. N -phospho- f -alanine could self-activate to yield N -phosphopeptides either in aqueous or nonaqueous media, but not g - or n -amino acid analogues. The mechanism of the reaction is discussed.     

A Novel Synthesis of 2-Alkylthiobenzothiazoles and 2-Alkylthiobenzoxazoles

Abstract

3H-Benzothiazole-2-thione and 3H-benzoxazole-2-thione were selectively S-alkylated by use of O-alkylisoureas as the alkylating reagents. The reactions could be performed under mild reaction conditions in short reaction times, and high yields were obtained using O-primary-alkylisoureas, whereas low yields were obtained with sec- and tert-alkylisoureas.     

Effect of Mineral Salts on Steady Rheological Properties of Nonionic Hydrophobically Modified Polyacrylamide and Its Stress-Relaxation Behavior

A micelle-forming polymerizable surfactant monomer, octylphenol polyoxyethylene acrylate (OP-10-AC), was synthesized, and then OP-10-AC was copolymerized with acrylamide (AM) to form nonionic hydrophobically modified polyacrylamide P(AM/OP-10-AC) through micellar copolymerization. In the absence of surfactants, it was investigated in detail that the effect of mineral salts and temperature on steady rheological properties of P(AM/OP-10-AC) solutions and the effect of concentrations on reduced viscosity of P(AM/OP-10-AC) in a dilute solution. The results indicate that concentrations of the copolymer, mineral salts and temperature had a strong influence on shear viscosity of P(AM/OP-10-AC) solutions, and the trend of reduced viscosity of P(AM/OP-10-AC) solutions was distinctly different from polyacrylamide with increasing concentrations of testing solutions. In addition, it was also investigated that stress-relaxation behavior of an aqueous solution of P(AM/OP-10-AC)/KCl. As a result, a stress-relaxation model of the copolymer solutions was proposed, which can further verify the correctness of the conclusion on stress-relaxation behavior of hydrophobic association hydrogels in the paper reported previously.     

pH-Responsive Nanocomposites From Methylcellulose and Attapulgite Nanorods: Synthesis,Swelling and Absorption Performance on Heavy Metal Ions

A pH-responsive methylcellulose-g-poly(sodium acrylate)/attapulgite (MC-g-PNaA/APT) nanocomposite superabsorbent was prepared by the free-radical solution polymerization of methylcellulose (MC), sodium acrylate (NaA) and nanoscale attapulgite (APT) in the presence of the crosslinker N,N′-methylene-bis-acrylamide (MBA). The structure and morphology of the nanocomposite were characterized by FTIR, FESEM, TEM, XRD and EDS techniques, and the effects of the amount of MBA, MC and APT nanorods on swelling behaviors were also evaluated. Results indicate that NaA has been grafted onto MC macromolecular chains and APT nanorods participated in polymerization by its active silanol groups, and APT led to a better dispersion in the MC-g-PNaA matrix. The incorporation of APT clearly enhanced the swelling capacity and rate of the superabsorbent. In addition, the nanocomposite exhibited excellent absorption capacity on heavy metal ions, and its absorption amounts on Ni²⁺, Cu²⁺ and Zn²⁺ ions reached 9.86, 7.66 and 21.86 times greater than active carbon (AC). The biopolymer-based nanocomposite superabsorbents can be used as a potential water-saving material and candidate of AC for heavy metal ion absorption.     

Preparation of Epoxy-Functionalized Magnetic Polymer Nanospheres for Magnetically Targeted Radiotherapy

Magnetic poly(styrene?methyl methacrylate-glycidyl methacrylate)/Fe₃O₄ nanospheres with epoxy groups were prepared by modified one-step mini-emulsion polymerization in the presence of Fe₃O₄ ferrofluids. The products were characterized by fourier-transform infrared spectrum, transmission electron microscopy, thermogravimetric analysis and vibrating sample magnetometer. After surface modification with diaminopropane, histidine was covalently linked to the amine group of magentic nanospheres using glutaraldehyde as crosslinker. Finally, the preliminary labeling study based on non-radioactive rhenium was carried out and the labeling efficiency reached 80.4%. Such magnetic nanospheres had promising potential in magnetically targeted radiotherapy of cancer.