On positive solutions for a nonlinear boundary value problem with impulse

In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.     

Synthesis and polymerization of new di‐octadecyl ester derivatives of α‐hydroxymethyl acrylate: A structure‐property correlation for their copolymers with methyl methacrylate

New ether dimer (ED‐Od) and diester (ODE) derivatives of α‐hydroxymethylacrylate, each having two octadecyl side chains, were synthesized and (co)polymerized to evaluate the effects of differences in the structures of the monomers on final (co)polymer properties, particularly glass transition temperature. The free radical polymerizations of both monomers yielded high‐molecular weight polymers. Cyclopolymer formation of ED‐Od was confirmed by ¹³C NMR analysis and the cyclization efficiency (0.95 or greater) was found to be as high as the cyclization efficiencies of the cyclopolymerizations of ether dimers of various alkyl α‐hydroxymethylacrylates synthesized previously. Copolymers of both ED‐Od and ODE with methyl methacrylate (MMA) showed significant T_g decreases over PMMA due to octadecyl side groups causing “internal” plasticization. Comparison of the T_g's of the copolymers of octadecyl methacrylate, ED‐Od and ODE with MMA revealed that the impacts of these monomers on depression of T_g's are identical. That is, the magnitude of decrease in T_g's was quantitatively related to the number of the octadecyl side groups in the copolymers rather than their placement on the same or randomly incorporated repeat units. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7785–7793, 2008     

范式理论与平均法的等价性分析

分析了范式理论与平均法的等价性。得到的结论是：对含有一对纯虚根的二维非线性系统，使用两种方法得到的结果是等价的，并提供了两个算例来证实其结论的正确性。虽然分析是针对一类二维非线性系统，但其结论同样适合于高维非线性系统。     

Isolation and identification of a new neo-clerodane diterpenoid from Teucrium chamaedrys L.

Teucrium chamaedrys L. is an aromatic and medicinal plant used as traditional medicine. Aerial parts of the plant material were dried and extracted with hexane–dichloromethane (extract 1), ethyl acetate–dichloromethane (extract 2) and methanol–dichloromethane (extract 3) in a ratio of 1:1 at rt successively. The solvents were evaporated to give crude extracts. Extract 1 was suspended in water at 60°C then partitioned successively with hexane and ethyl acetate to give hexane and ethyl acetate portions. After the column chromatography (silica gel) of ethyl acetate extract, one new and four known compounds were isolated. The new compound was named as 1(12S,18R)-15,16-epoxy-2β,6β-dihydroxy-neo-cleroda-13(16),14-dien-20,l2-olide-l8,l9-hemiacetal (teuchamaedryn D) (4). The known compounds were teucrin A (1), dihydroteugin (2), teucroxide (3), syspirensin A (5). The chromatographic methods were also applied for extract 3 to isolate verbascoside (6) and teucrioside (7). The structure of isolated compounds was elucidated by spectroscopic methods including LC-TOF/MS, 1D NMR and 2D NMR.     

Thermodynamic investigations on the component dependences of high-entropy alloys

In the present research, a study on the thermodynamical properties of the quinary Co–Cu–Cr–Fe–Ni high-entropy alloys and ternary Ca–Sb–Yb is carried out by the models Kohler, Chou’s general solution method (GSM) and Muggianu. The dependences of composition variation on thermodynamic properties, such as enthalpy of mixing of Co–Cu–Cr–Fe–Ni alloys in simple FCC phase are investigated at the temperatures 1273, 1373, and 1473 K. Moreover, a comparison between the results of the three models and those of other theoretical models shows good mutual agreement.     

Determination of bismuth and zinc in pharmaceuticals by first derivative UV-Visible spectrophotometry

A first order derivative spectrophotometric method has been developed for the simultaneous determination of bismuth and zinc by dithizone without time-consuming extraction step. The reactions of bismuth and zinc with dithizone in a three component solution prepared in water, acetone and n-propanol mixture have been investigated. These cations react with dithizone in this mixture at pH 5.0, forming coloured complex that is stable for at least 2 h. The linear range in D evaluation was between 3.0 × 10⁻⁶ and 1.8 × 10⁻⁵ mol l⁻¹ for Zn and 2.4 × 10⁻⁶ and 1.2 × 10⁻⁵ mol l⁻¹ for Bi. The limits of detection for the analytical procedure were found 0.05 mg l⁻¹ for both cations. The relative standard deviations for the determination of 0.5 mg l⁻¹ bismuth and 0.5 mg l⁻¹ zinc were 1.2 and 1.1%, respectively, for five determinations. The procedure is simple, rapid and reliable. This method was applied to the determination of bismuth and zinc in the pharmaceutical materials successfully. Good agreement was achieved between the results obtained by the proposed and comparative methods.     

An algorithm for approximating piecewise linear concave functions from sample gradients

An effective algorithm for solving stochastic resource allocation problems is to build piecewise linear, concave approximations of the recourse function based on sample gradient information. Algorithms based on this approach are proving useful in application areas such as the newsvendor problem, physical distribution and fleet management. These algorithms require the adaptive estimation of the approximations of the recourse function that maintain concavity at every iteration. In this paper, we prove convergence for a particular version of an algorithm that produces approximations from stochastic gradient information while maintaining concavity.     

Comparison of flow structures in the downstream region of a cylinder and sphere

An experimental investigation of flow structures downstream of a circular cylinder and sphere immersed in a free-stream flow is performed for Re = 5000 and 10,000 using qualitative and quantitative flow visualization techniques. The obtained results are presented in terms of time-averaged velocity vectors, patterns of streamlines, vorticity, Reynolds stress correlations and turbulent kinetic energy distributions. Flow data reveal that the size of wake flow region, the location of singular and double points, the peak values of turbulence quantities, such as Reynolds stress correlations, vorticity fluctuations and turbulent kinetic energy vary as a function of models’ geometry and Reynolds Numbers. The concentration of small scale vortices is more dominant in the wake of the sphere than that of the cylinder. The maximum value of turbulent kinetic energy (TKE) occurs close to the saddle point for the cylinder case while two maximum values of TKE occur along shear layers for the sphere one because of the 3-D flow behavior.     

Direct generation of 81 nJ pulses and external compression to a subpicosecond regime with a 4.9 MHz chirped-pulse multipass-cavity Cr⁴⁺:forsterite oscillator

We report direct generation of 81 nJ chirped pulses from a room-temperature, Kerr lens mode-locked Cr??:forsterite oscillator operating at 1258 nm. To increase the pulse energy, the pulse repetition rate of the short x-type resonator was lowered from 143 to 4.9 MHz by the addition of a q-preserving multipass cavity, which provided an additional effective optical path length of 59.4 m. The duration of the chirped pulses was around 5.5 ps with a spectral width of 21 nm. The pulses were externally compressed to 607 fs by using a diffraction grating pair. To our knowledge, this is the highest reported pulse energy directly generated from a room-temperature mode-locked Cr??:forsterite laser.     

Indices defect theory of singular Hahn-Sturm-Liouville operators

In this article, we extend the results concerning the deficiency index problem to singular Hahn-Sturm-Liouville difference operators. We establish some criteria under which the singular Hahn-Sturm-Liouville equation is of limit-point case at infinity.