Extreme compression behaviour of equations of state

The extreme compression (P→∞) behaviour of various equations of state with K′_∞>0 yields (P/K)_∞=1/K′_∞, an algebraic identity found by Stacey. Here P is the pressure, K the bulk modulus, K^′=dK/dP, and K′_∞, the value of K^′ at P→∞. We use this result to demonstrate further that there exists an algebraic identity also between the higher pressure derivatives of bulk modulus which is satisfied at extreme compression by different types of equations of state such as the Birch–Murnaghan equation, Poirier–Tarantola logarithmic equation, generalized Rydberg equation, Keane's equation and the Stacey reciprocal K-primed equation. The identity has been used to find a relationship between λ_∞, the third-order Grüneisen parameter at P→∞, and pressure derivatives of bulk modulus with the help of the free-volume formulation without assuming any specific form of equation of state.     

Fourier Analysis of Semistable Distributions

We consider the generalized convolution powers G _α ^*u (x) of an arbitrary semistable distribution function G _α (x) of exponent α∈(0,2), and prove that for all j, k∈{0,1,2,…} and u>0 the derivatives G _α ^(k,j)(x;u)=∂ ^k+j G _α ^*u (x)/∂ x ^k ∂ u ^j , x∈ℝ, are of bounded variation on the whole real line ℝ. The proof, along with an integral recursion in j, is new even in the special case of stable laws, and the result provides a framework for possible asymptotic expansions in merge theorems from the domain of geometric partial attraction of semistable laws. An erratum to this article can be found at     

Divergent reaction pathways for one-pot,three-component synthesis of novel 4H-pyrano[3,2-h]quinolines under ultrasound irradiation

The present paper deal with the multi-component condensation of 8-hydroxy quinoline, aromatic aldehydes, and sulfone derivatives catalyzed by p-toluenesulfonic acid for the synthesis of a series of 4H-pyrano[3,2-h]quinoline derivatives in ethanol under ultrasonic irradiations. We provide a series of quinoline derivatives containing sulfone moiety interesting for biological screening tests. The reactions were carried out under both conventional and ultrasonic irradiation conditions. In general, improvement in rates and yields were observed when reactions were carried out under sonication compared with classical silent conditions. Also, also, sonochemical reaction give different reaction pathway other than silent reaction. These remarkable effects appeared in sonicated reactions can be reasonably interpreted in terms of acoustic cavitation phenomenon. Structures of the products were established on analytical and spectral data.     

On the zeros ofζ (1)(s) — a (on the zeros of a class of a generalized Dirichlet series — XVII)

Some very precise results (see Theorems 4 and 5) are proved about thea-values of thelth derivative of a class of generalized Dirichlet series, forl≥l _o =l _o(a) (l _o being a large constant). In particular for the precise results on the zeros ofζ ⁽¹⁾ (s) —a (a any complex constant andl≥l _o) see Theorems 1 and 2 of the introduction.     

吐昔烯衍生物分子的电荷传输性质

根据爱因斯坦方程和Marcus电荷传输模型, 使用密度泛函理论B3lyp/6-31g^**理论水平计算6 个吐昔烯衍生物分子的结构和电荷传输性质. 结果显示: 6个吐昔烯的衍生物分子的空穴迁移速率为0.018–0.062 cm²·V^-1·s^-1, 电子迁移率为0.055–0.070 cm²·V^-1·s^-1, 其中3, 8, 13-辛烷氧基吐昔烯衍生物分子适合作为双极性传输材料. 三条烷氧基链的吐昔烯衍生物分子上引入三个甲氧基或羟基, 均使空穴和电子传输率降低. 引入给电子基团或共轭性基团可减小吐昔烯衍生物分子的能隙, 达到有机半导体的能隙要求. 关键词： 吐昔烯衍生物 空穴传输 电子传输 有机半导体     

Spectral meshless radial point interpolation (SMRPI) method to two‐dimensional fractional telegraph equation

H. Ammari In this article, an innovative technique so‐called spectral meshless radial point interpolation (SMRPI) method is proposed and, as a test problem, is applied to a classical type of two‐dimensional time‐fractional telegraph equation defined by Caputo sense for (1 < α≤2). This new methods is based on meshless methods and benefits from spectral collocation ideas, but it does not belong to traditional meshless collocation methods. The point interpolation method with the help of radial basis functions is used to construct shape functions, which play as basis functions in the frame of SMRPI method. These basis functions have Kronecker delta function property. Evaluation of high‐order derivatives is not difficult by constructing operational matrices. In SMRPI method, it does not require any kind of integration locally or globally over small quadrature domains, which is essential of the finite element method (FEM) and those meshless methods based on Galerkin weak form. Also, it is not needed to determine strict value for the shape parameter, which plays an important role in collocation method based on the radial basis functions (Kansa's method). Therefore, computational costs of SMRPI method are less expensive. Two numerical examples are presented to show that SMRPI method has reliable rates of convergence. Copyright © 2015 John Wiley & Sons, Ltd.     

Multimode ultrasonic extraction of polysaccharides from maca (Lepidium meyenii): Optimization,purification, and in vitro immunoregulatory activity

This study evaluates the effect of multimodal ultrasound on the extraction efficiency and immunoregulatory activity of polysaccharides from Lepidium meyenii Walp. (LMP). The separation and purification of maca polysaccharides were investigated by the DEAE-52 cellulose column, and the monosaccharide compositions were identified by HPGPC. Their immune activity was analyzed by the secretion of cytokines (TNF-α and IL-6) from RAW 264.7 macrophage. The results showed that the optimal extraction conditions were energy aggregation alternation dual-frequency ultrasound (EADU) with frequency combinations of 20/35, extraction time of 15 min, material/water ratio of 1:10 g/mL, ultrasonic power intensity of 150 W/L, intermittent time ratio of 4 s/3 s, and extraction temperature of 50 ℃. The extraction rates of purified polysaccharides (US3) increased by 44.90%. The LMP extracted by EADU contained arabinose, galactose, and glucose in the molar ratios of 2.9:2.72:5.05. In addition, US3 promoted the release of TNF-α and IL-6 from RAW 264.7 better than RS3 (purified polysaccharides extracted by hot water), which indicated that US3 exerted remarkable immune activity. It could be an excellent functional additive in food or medicine.     

Neutron scattering from PEEK

An alkali‐soluble polysaccharide, GM5‐1, from the mycelium of Ganoderma tsugae, was fractionated by the nonsolvent addition method. The weight‐average molecular mass (M _w) and intrinsic viscosity ([η]) of fractions were studied by laser light scattering and viscometry with dimethylsulfoxide (DMSO) containing 0.25M LiCl (0.25M LiCl/DMSO) as the solvent at 30°C. The dependences of [η] and the radius of gyration (?S ²?_z ^1/2) on M _w were found to be [η]=9.8×10^?2 M _w ^0.57 (cm³g^?1) and ?S ²?_z ^1/2=1.65×10^?2 M _w ^0.58 (nm) in the M _w range from 8.6×10⁵ to 2.6×10⁶. The analysis based on current theories for a wormlike chain showed that the chain conformational parameters of GM5‐1 were 4.2 nm for persistence length (q) and 833 nm^?1 for linear mass density (M_L) with an obvious excluded volume effect. The results suggested the alkali‐soluble polysaccharide behaves like a semiflexible chain in 0.25M LiCl/DMSO at 30°C.     

Smoothing Properties and Approximation of Time Derivatives for Parabolic Equations: Variable Time Steps

We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational approximations to the exponential function which are A()-stable for suitable (0,/2] with unit bounded maximum norm. First- and second-order approximations of time derivatives based on using difference quotients are considered. Smoothing properties are derived and error estimates are established under the so-called increasing quasi-quasiuniform assumption on the time steps.     

Covariant Hyperelliptic Functions of Genus Two

We report results of investigations concerning the role of representations of in the theory of genus-two hyperelliptic functions. We discuss the role of these representations in the classical theory as well as introduce a family of new, naturally covariant functions.