Bifurcations and distribution of limit cycles which appear from two nests of periodic orbits

In this paper, we study the distribution and simultaneous bifurcation of limit cycles bifurcated from the two periodic annuli of the holomorphic differential equation , after a small polynomial perturbation. We first show that, under small perturbations of the form , where is a polynomial of degree 2m−1 in which the power of z is odd and the power of is even, the only possible distribution of limit cycles is (u,u) for all values of u=0,1,2,…,m−3. Hence, the sharp upper bound for the number of limit cycles bifurcated from each two period annuli of is m−3, for m≥4. Then we consider a perturbation of the form , where is a polynomial of degree m in which the power of z is odd and obtain the upper bound m−5, for m≥6. Moreover, we show that the distribution (u,v) of limit cycles is possible for 0≤u≤m−5, 0≤v≤m−5 with u+v≤m−2 and m≥9.     

Enhancement of Human γ-Interferon Production in Recombinant <Emphasis Type="Italic">E. coli</Emphasis> Using Batch Cultivation

Development of inexpensive and simple culture media and appropriate induction conditions are always favorable for industry. In this research, chemical composition and stoichiometric data for γ-interferon production and recombinant Escherichia coli growth were used in order to achieve a simple medium and favorable induction conditions. To achieve this goal, the effects of medium composition and induction conditions on the production of γ-interferon were investigated in batch culture of E. coli BL21 (DE3) [pET3a-ifnγ]. These conditions were considered as suitable conditions for the production of γ-interferon: 2.5× M9 medium, supplemented with a mixture of amino acids (milligram per liter), including glutamic acid 215, aspartic acid 250, lysine 160, and phenylalanine 90, and induction at late-log phase (OD₆₀₀ = 4.5). Under these conditions, dry cell weight of 6 ± 0.2 g/l and γ-interferon concentration of 2.15 ± 0.1 g/l were obtained. Later, without changing the concentration ratio of amino acids and glucose, the effect of increase in the primary glucose concentration on productivity of γ-interferon was investigated. It was found that 25 g/l glucose will result in maximum attainable biomass and recombinant human γ-interferon. At improved conditions, a dry cell weight of 14 ± 0.2 g/l, concentration and overall productivity of γ-interferon 4.2 ± 0.1 g/l and 420 ± 10 mg/l h, respectively, were obtained.     

Comparative study of reductive amination reaction on 5-(4-formyl-3,5-dimethoxyphenoxy)valeric acid and its monomethoxy analog using the Multipin™ approach

The 5-(4-formyl-3,5-dimethoxyphenoxy)valeric acid (Barany)linker and its monomethoxy analog were applied to theMultipin method of solid phase synthesis. Acomparative assessment of reductive amination and cleavage ofthese linkers under conditions of multiple synthesis indicatedthat both were applicable to a broad range of primary aminesincluding aniline and 4-nitroaniline. Apart from the greaterlability of the dimethoxy version under TFA cleavage, there wasno observable advantage of one linker over the other within thedescribed experiment.     

Study of Phenolic Compounds Removal from Aqueous Solution by Polymeric Sorbent

This study describes preparation of polymeric sorbent and its use in removal of some phenolic compounds from aqueous solution. The polymer [poly(ethylene glycol dimethacrylate ‐ co‐methacrylic acid)] is stable both thermally and chemically. High temperature (200°C) and strong acidic or alkaline solutions (4 M HCl or NaOH) are not effective on the adsorption characteristics of polymer. Removal process of phenols is pH‐dependent and from the obtained results pH = 7.0 was selected as an optimum pH. Different parameters affecting sorption process were tested, and it was found that the kinetic of sorption is fast; therefore, column experiment at higher flow rates or batch experiment can be used. Methanol was selected as a washing solvent in column experiments. Capacity of sorbent for the studied compounds was tested and the following order was obtained: p‐chlorophenol > p‐aminophenol > phenol.     

Modulated Differential Scanning Calorimetry

The reproducibility and reliability of the TA Instruments Modulated Differential Scanning Calorimeter (MDSC) was tested over a range of conditions. The equipment base line was found to be fairly constant with a very small fluctuation (10 W), which means a 0.1 % fluctuation on the scale of a normal polymer MDSC curve. The excellent stability of the base line and the reasonable reproducibility of the curves (5%) suggest that frequent calibration is not required.The heat capacities calculated from the modulated response to the variable temperature depend on the frequency for a given cell constant. The heat capacity cell constant is a unique function of the modulation frequency:k _c =K _c ^o p/(p–6.3) wherep is the time of the periodicity expressed in seconds and K _c ^o is the heat capacity cell constant measured on a standard material and reduced to zero frequency. The cell constants depend on the flow rate of the helium according to:K(He)=K ^o(1.298–0.004424He+1.438·10^–5 He ²) whereHe is the flow rate of helium in ml min^–1 andK ^o represents a constant at 100 cm³ min^–1. There is a strong dependence of cell constant on the flow rate ranges from 10 to 80 cm³ min^–1, while above this rate (up to 135 ml min^–1) the cell constant approaches a plateau.     

Trans ligand influence in cobalt(III) Schiff base complexes: Electronic and steric effects on the kinetics of hydrolysis

Rate constants for the hydrolysis (k_h) of six different amines in trans‐[Co((BA)₂en)(amine)₂]ClO₄ complexes (amine = aniline 1a , para‐toluidine 1b , benzylamine 1c (primary amines), pyrrolidine 2a , piperidine 2b , morpholine 2c (secondary amines), and (BA)₂en = Bisbenzoylacetoneethylenediiminato) in mixed methanol/water (1:1) solvent have been determined between 30 and 55°C. The hydrolysis product of 2c , trans‐[Co((BA)₂en)(morpholine)(H₂O)]ClO₄, has been separately prepared and characterized by UV–vis and ¹H NMR spectroscopy. Depending on the nature of the axial amine ligand the limiting first‐order rate constants for the amine hydrolysis at 40°C range from (3.42 ± 0.10) × 10^?5 to (5.32 ± 0.13) × 10^?5 s^?1. At the first glance, a reasonable trend cannot be established between k_h and the basicity or the inductive trans effect of the amine ligands. However, when the complexes are classified into two groups, based on the type of the amine (primary and secondary), the values of k_h correlate well with the basicity or inductive effect of the amine in each group. The observed trend in k_h values for the complexes with primary amines is 1a (5.32 ± 0.13) × 10^?5 s^?1 > 1b (3.51 ± 0.14) × 10^?5 > 1c (1.72 ± 0.03) × 10^?5 (40°C), which is opposite to the amine basicity strength. In the case of the complexes with secondary amines, the observed trend in k_h values is in accord with amine basicity (or inductive trans effect), i.e. 2a (5.02 ± 0.22) × 10^?5 > 2b (4.18 ± 0.10) × 10^?5 > 2c (3.42 ± 0.10) × 10^?5 s^?1 (40°C). © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 387–393, 2002     

Synthesis of a new hyperbranched,vinyl macromonomer through the use of click chemistry: Synthesis and characterization of copolymer hydrogels with PEG diacrylate

A new biodegradable, water‐soluble macromonomer based on the commercial hyperbranched polyester Boltorn^®H20 has been synthesized through the use of click chemistry. The macromonomer was developed with the aim of being injected with a comacromonomer, poly(ethylene glycol) (PEG) diacrylate, for in situ copolymerization to form biodegradable polymer hydrogels. Copolymer hydrogels were prepared from the macromonomer and PEG diacrylate (FW 700) by free radical copolymerization. A degree of phase separation of the hydrogels was observed during polymerization and with increasing incorporation of the Boltorn macromonomer an increasing tendency for the formation of macropores was observed. The swelling ratios of the gels in water and phosphate buffered saline solution, PBS, all increase with increasing Boltorn macromonomer concentration, as did the penetrant diffusion coefficients and the degradation rate in PBS. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A converse of Baer’s theorem

Schur’s classical theorem states that for a group $G$ , if $G/Z(G)$ is finite, then $G'$ is finite. Baer extended this theorem for the factor group $G/Z_n(G)$ , in which $Z_n(G)$ is the $n$ -th term of the upper central series of $G$ . Hekster proved a converse of Baer’s theorem as follows: If $G$ is a finitely generated group such that $\gamma _{n+1}(G)$ is finite, then $G/Z_n(G)$ is finite where $\gamma _{n+1}(G)$ denotes the $(n+1)$ st term of the lower central series of $G$ . In this paper, we generalize this result by obtaining the same conclusion under the weaker hypothesis that $G/Z_n(G)$ is finitely generated. Furthermore, we show that the index of the subgroup $Z_n(G)$ is bounded by a precisely determined function of the order of $\gamma _{n+1}(G)$ . Moreover, we prove that the mentioned theorem of Hekster is also valid under a weaker condition that $Z_{2n}(G)/Z_{n}(G)$ is finitely generated. Although in this case the bound for the order of $\gamma _{n+1}(G)$ is not achieved.     

掺杂双(N-2-甲基苯基-水杨醛亚胺)合铜(II)配合物的碳糊电极电催化测量过氧化氢(英文)

The electrochemical behavior of a bis (N-2-methylphenyl-salicyldenaminato)copper (II) complex spiked in a carbon paste electrode (BMPSCu-CPE) and its electrocatalytic reduc-tion of H2 O2 were examined using cyclic voltammetry, chronoamperometry, and differen-tial pulse voltammetry. Cyclic voltammetry was used to study the redox properties of BMPSCu-CPE at various potential scan rates. The apparent charge transfer rate constant and the transfer coefficient for the electron transfer between BMPSCu and the carbon paste electrode (CPE) were 1.9 ± 0.1 s–1 and 0.43, respectively. BMPSCu-CPE had excel-lent electrocatalytic activity for H2 O2 reduction in 0.1 mol/L phosphate buffer solution (pH 5.0), and it decreased the overpotential by 300 mV as compared to CPE alone. The diffusion coefficient and kinetic parameters such as the heterogeneous catalytic electron transfer rate constant and electron transfer coefficient for the reduction of H2 O2 at the BMPSCu-CPE surface were also determined using electrochemical methods. Differential pulse voltammetry showed two linear dynamic ranges of 1.0–10.0 and 10.0–300.0 μmol/L and a detection limit of 0.63 μmol/L H2 O2. The BMPSCu-CPE has excellent repro-ducibility and long term stability, and it was successfully applied for the determination of H2 O2 in two pharmaceutical samples: an antiseptic solution and a hair dying cream.