Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water

Summary The thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability bility constant K_o which can be derived from solubility data. At 25°C, this constant amounts to 80 cm³/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.     

Efficient synthesis of magnetic nanoparticle-Musa acuminata peel composite for the adsorption of anionic dye

The impregnation of magnetite (Mt) nanoparticle (NPs) onto Musa acuminata peel (MApe), to form a novel magnetic combo (MApe-Mt) for the adsorption of anionic bromophenol blue (BPB) was studied. The SEM, EDX, BET, XRD, FTIR and TGA were used to characterize the adsorbents. The FTIR showed that the OH and CO groups were the major sites for BPB uptake onto the adsorbent materials. The average Mt crystalline size on MApe-Mt was 21.13 nm. SEM analysis revealed that Mt NPs were agglomerated on the surface of the MApe biosorbent, with an average Mt diameter of 25.97 nm. After Mt impregnation, a decrease in BET surface area (14.89 to 3.80 m²/g) and an increase in pore diameter (2.25–3.11 nm), pore volume (0.0052–0.01418 cm³/g) and pH point of zero charge (6.4–7.2) was obtained. The presence of Pb(II) ions in solution significantly decreased the uptake of BPB onto both MApe (66.1–43.8%) and MApe-Mt (80.3–59.1%), compared to other competing ions (Zn(II), Cd(II), Ni(II)) in the solution. Isotherm modeling showed that the Freundlich model best fitted the adsorption data (R² > 0.994 and SSE < 0.0013). In addition, maximum monolayer uptake was enhanced from 6.04 to 8.12 mg/g after Mt impregnation. Kinetics were well described by the pseudo-first order and liquid film diffusion models. Thermodynamics revealed a physical, endothermic adsorption of BPB onto the adsorbents, with ΔH^o values of 15.87–16.49 kJ/mol, corroborated by high desorption (over 90%) of BPB from the loaded materials. The viability of the prepared adsorbents was also revealed in its reusability for BPB uptake.     

One-dimensional model with rotational and liquid-crystalline phase transitions

A one-dimensional system of hard-rod particles with rotational-like internal degrees of freedom is considered. Particles interact with each other through the infinite-range, infinitely weak attractive Kac potential, and through a nearest-neighbor short-range potential. The latter depends also on the internal states of the interacting particles. Exact results for thermodynamic properties and for some correlation functions are obtained. It is found that the considered system exhibits several first-order transitions between phases with different rotational structure, i.e., with different ordering with respect to the internal degrees of freedom. The calculated equation of state seems to suggest that in the solutions of liquid-crystalline substances in neutral solvents there may exist regions in which the coefficient of thermal expansion is negative—an effect similar to that well known in liquid water.     

Root determination by use of Padé approximants

In this paper we describe a new technique for generating iteration formulas — of arbitrary order — for determining a zero (assumed simple) of a functionf, assumed analytic in a region containing the zero. The 1/p Padé Approximant (p0) to the functiong(t)f(z) is formed wherez=w+t, using the Taylor series forf at the pointw, an approxination to the zero off. The value oft for which the 1/p Padé Approximant vanishes provides the basis of iteration formulas of orderp+2.Some known iteration formulas, e.g., Newton-Raphson's, Halley's and Kiss's of order of convergence two, three and four, are directly obtained by settingp=0,1 and 2, respectively.     

二阶三点数值微分公式的外推算法

利用Taylor公式，给出了二阶三点数值微分公式在各点的截断误差的渐近展开式，并利用Richardson外推算法，提高二阶三点数值微分公式的收敛阶数，得到高精度的二阶数值微分公式．     

高阶Euler多项式和高阶Bernoulli多项式的计算公式

利用Stirling数给出高阶Euler多项式和高阶Bernoulli多项式的一类新的计算公式,这些公式结构精美,便于应用.     

二阶抛物问题的扩展混合元方法

对二阶抛物问题提出了一种新的混合元方法一扩展混合元方法．该方法能同时逼近未知函数、未知函数的梯度和流体的流量，较好地模拟了带有混合型边界条件的二阶抛物问题．通过数值分析进一步证明了未知函数、未知函数的梯度和流体的流量的最优L^2-误差估计。     

一类n阶差分方程特征值问题的正解

利用锥上的不动点定理对一类n阶差分方程的特征值问题进行了讨论，得到了存在一个及两个正解的特征值的范围。     

k阶伴随矩阵C*k(AB)的性质

对于给定的数域F上的n阶矩阵A,给出并证明了k阶子式阵Ck(AB)的伴随矩阵C*k(AB)的一个性质:C*k(AB)=C*k(B)C*k(A),从而使一般意义下的伴随矩阵的性质(AB)*=(B)*(A)*得到推广.     

一阶拟线性椭圆型复方程的广义DC型边值问题

研究了一般的一阶拟线性椭圆型复方程的边界条件中含有斜微商的广义Carleman型边值问题。采用直接将广义DC型问题化为奇异积分方程的方法析出特征部分，然后通过对特征方程的研究得到了广义DC问题的可解条件和计算指标。