) denote the number of pairs of adjacent edges in a graph
. Ahlswede and Katona considered the problem of maximizing
) over all simple graphs with a given number
of vertices and a given number
of edges. They showed that
) is either maximized by a quasi-complete graph or by a quasi-star. They also studied the range of
) for which the quasi-complete graph is superior to the quasi-star (and vice versa) and formulated two questions on distributions in this context. This paper is devoted to the solution of these problems.
Let be a Schrödinger operator on the Heisenberg group , where is the sublaplacian on and the nonnegative potential V belongs to the reverse Hölder class with . Here is the homogeneous dimension of . Assume that is the heat semigroup generated by. The Lusin area integral and the Littlewood–Paley–Stein function associated with the Schrödinger operator are deﬁned, respectively, by
Where is a parameter. In this article, the author shows that there is a relationship between and the operator and for any , the following inequality holds true:
Based on this inequality and known results for the Lusin area integral , the author establishes the strong-type and weak-type estimates for the Littlewood–Paley–Stein function on . In this article, the author also introduces a class of Morrey spaces associated with the Schrödinger operator on . By using some pointwise estimates of the kernels related to the nonnegative potential V, the author establishes the boundedness properties of the operator acting on the Morrey spaces for an appropriate choice of . It can be shown that the same conclusions hold for the operator on generalized Morrey spaces as well.
Authors:Yating Liu, Yunhai Liu, Xiaohong Cao, Rong Hua, Youqun Wang, Cui Pang, Ming Hua, and Xiaoyan Li
The cross-linked chitosan (CS) gels synthesized by using glutaraldehyde (GLA), epichlorohydrin (EC), and ethylene glycol diglycidyl
ether (EGDE) as cross-linkers respectively were used to investigate the adsorption of U(VI) ions in an aqueous solution. The
pure chitosan (PCS) and the cross-linked chitosan gels were characterized by FTIR and SEM analysis. The kinetic, thermodynamic
adsorption and adsorption isotherms of U(VI) ions onto unmodified and modified cross-linked chitosan were studied in a batch
adsorption experiments. The effect of pH, contact time and temperature on the adsorption capacity were also carried out. At
the optimum pH, the maximum adsorbed amount of PCS, GLACS, ECCS and EGDECS were 483.05, 147.05, 344.83 and 67.56 mg/g, respectively.
The uranium (VI) adsorption process of PCS and ECCS followed better with pseudo-second-order kinetic model, while GLACS and
EGDECS followed pseudo-first-order kinetic model well. The results obtained from the equilibrium isotherms adsorption studied
of U(VI) ions were analyzed in two adsorption models, namely, Langmuir and Freundlich isothms models, the results showed that
the Langmuir isotherm had better conformity to the equilibrium data. The thermodynamic parameters such as enthalpy (ΔHº), entropy (ΔSº), and Gibbs free energy (ΔGº) showed that the adsorption process was both spontaneous and endothermic.
Authors:Lu Songsheng, Xu Hua, Wang Mingming, Song Xiaoping, and Liu Qiong
The bentonite from Gaomiaozi county (Inner Mongolia, China) (denoted as GMZ bentonite) was characterized by X-ray powder diffraction
and Fourier transform infrared spectroscopy. The effect of pH, contact time, ionic strength, humic acid (HA) and Eu(III) concentrations
on Eu(III) sorption to the GMZ bentonite was studied by batch technique under ambient conditions. The sorption of Eu(III)
on GMZ bentonite was strongly dependent on pH and independent of ionic strength. The sorption of Eu(III) on GMZ bentonite
was mainly dominated by surface complexation rather than by ion exchange. The presence of HA enhanced Eu(III) sorption at
low pH values, but decreased Eu(III) sorption at high pH values. The enhanced sorption of Eu(III) on GMZ bentonite at low
pH was attributed to the strong complexation of Eu(III) with surface adsorbed HA on GMZ bentonite and the reduced sorption
of Eu(III) at high pH was attributed to the formation of soluble HA–Eu complexes in aqueous solution. The strong sorption
of Eu(III) on GMZ bentonite suggested that the GMZ bentonite could be used as the backfill material in nuclear waste disposal.
Authors:Ya-juan Wang, Jun Guo, Hui Chen, and Zhi-hua Shan
The thermal stability of sheepskin collagen cross-linked with chrome sulfate and mimosa (MI)–oxazolidine (OZ), respectively,
had been researched in this experiment. All samples’ shrinkage temperatures (Ts) are determined by a special Ts-testing-apparatus and denaturation temperatures (Td) are determined by the differential scanning calorimetry. The relations between the modified collagens containing moisture
and their hydrothermal stability, Ts or Td, were studied. The results show that the cross linking agents can enhance the thermal stability of modified collagen whose
Ts are 109.8 and 110.6 °C for collagen treated with chrome and MI–OZ, respectively. When the samples contain 25–71.9% moisture
for chrome leather and 20–71.1% for leather treated with MI–OZ, the hydrothermal stability will decrease with the increase
of moisture. It was found that the difference between Ts and Td of collagen modified by chrome is more obvious than that of collagen modified with MI–OZ. And when the moisture of chrome
leather exceeds 55%, Td cannot express thermal stability of modified collagen as a substitute for Ts, and the moisture is 40% for leather tanned with MI–OZ.
Authors:JianHua Zhang, Ling Wang, Xi Zhu, Xue Bai, and Hua Yin
You-Gui-Yin (YGY), a famous traditional Chinese medicine, has been widely used in clinics for the treatment of kidney-yang deficiency, yang deficiency caused by excessive yin, and osteoporosis. A rapid and sensitive ultraperformance liquid chromatography–electrospray ionization–mass spectrometry (UPLC–ESI–MS) method for simultaneous determination of six Aconitum alkaloids including aconitine (AC), hypaconitine (HA), mesaconitine (MA), benzoylaconine (BAC), benzoylhypaconine (BHA), and benzoylmesaconine (BMA) in rat plasma after oral administration of YGY was developed in this study. Chromatographic separation was performed on an ACQUITY UPLC™ BEH C18 column (2.1 × 100 mm, 1.7 μm) using gradient elution with the mobile phase consisting of 2 mmol/L ammonium formate in 0.05% formic acid aqueous solution and 0.05% formic acid methanol solution, at a flow rate of 0.20 mL/min. MS detection was performed in the positive ion mode. The calibration curves were linear in the concentration range of 0.04160–41.60 ng/mL, 0.1070–107.0 ng/mL, 0.07358–73.50 ng/mL, 0.03228–32.28 ng/mL, 0.01809–18.09 ng/mL, and 0.1320–132.0 ng/mL for AC, HA, MA, BAC, BHA, and BMA, respectively. The intra- and inter-day precisions (relative standard deviation [RSD]) were less than 11.6% and 12.6%, respectively. The accuracies Relative Error (RE) ranged from −10.2% to 5.6%, while the recoveries ranged from 70.4% to 99.3%. The method for simultaneous quantitation of Aconitum alkaloids of You-Gui-Yin in rat plasma is accurate and repeatable, and this method was successfully applied to investigate the pharmacokinetics of the six Aconitum alkaloids in rat plasma after oral administration of YGY. For the pharmacokinetic study, the pharmacokinetics of the six Aconitum alkaloids were best described by a two-compartment open model.
Authors:Nan Zhang, Qin Zhang, Ke Wang, Hua Deng, and Qiang Fu
The effects of nucleating duality, imposed by a mixed nucleating agent (NA) system containing multi-walled carbon nanotubes (MWCNTs) and a rare earth (WBG), on the crystallization behaviors of isotactic polypropylene (iPP) including the peak temperature of crystallization (Tcp), polymorphic composition, and crystalline morphology, were probed in detail by calorimetry, X-ray diffraction, and polarized light microscopy. In such mixed nucleating agent system, MWCNTs is active filler to induce α-nucleation for iPP, while WBG serves as β-nucleating agent. When the WBG content was low (0.05%), the crystals of WBG were as a form of individual isotropic dendrite, and the enhancement of Tcp was achieved by the incorporation of MWCNTs. As the WBG content was high as 0.1%, a percolated NA network consisted of needlelike crystals of WBG yielded before nucleating the prevalent crystallization of iPP. In this case, the addition of MWCNTs has no obvious effect on Tcp. However, by varying the mass proportion of MWCNTs/WBG, the polymorphic composition was adjusted significantly, indicating a nucleation competition between MWCNTs and WBG. Although the competitive growth existed between α-crystals nucleated by MWCNTs and β-crystals nucleated by WBG, the formation of primary β-crystallite was always prior to the α-nucleated crystallization, as confirmed by crystalline morphology. These findings are useful for developing a new pathway to prepare iPP-based composite with good mechanical property via the addition of mixed nucleating system containing active inorganic filler and β-nucleating agent.
A high-performance liquid chromatography—diode-array detection method was developed and validated to determine simultaneously eleven major alkaloids in Corydalis decumbens (Thunb.) Pers. The alkaloids detected were corlumidine, protopine, coptisine, tetrahydrojatrorrhizine, palmatine, berberine, sanguinarine, papaverine hydrochloride, tetrahydropalmatine, bicuculline, and corydaline. Chromatographic separation was achieved using a C-18 column with a mobile phase composed of A (0.2% acetic acid solution, adjusted with triethylamine to pH 5.0) and B (acetonitrile), with stepwise gradient elution. Ultraviolet diode-array detection was used; chromatograms were examined at the wavelength of 280 nm. The regression equations showed a good linear relationship between the peak area of each marker and concentration (r = 0.9994–0.9999). The recovery values ranged between 93.66% and 100.54%. The method was fully validated with respect to detection and quantification limits, precision, reproducibility, and accuracy. The described high-performance liquid chromatography (HPLC) method was successfully used for the differentiation and quantification of the eleven major alkaloids in C. decumbens (Thunb.) Pers. and can be considered an effective procedure for the analyses of this important class of natural compounds.
The stability of β-cyclodextrin-cinnamyl alcohol inclusion complex (β-CD·C9H10·8H2O) was investigated using TG and DSC. The mass loss took place in three stages: the dehydration occurred between 50–120°C; the dissociation of β-CD·C9H10O occurred in the range of 210–260°C; and the decomposition of β-CD began at 280°C. The dissociation of β-CD·C9H10O was studied by means of thermogravimetry, and the results showed: the dissociation of β-CD·C9H10O was dominated by a two-dimensional diffusion process (D2). The activation energyE was 161.2 kJ mol−1, the pre-exponential factorA was 4.5×1013 min−1.
Cyclodextrin is able to form inclusion complexes with a great variety of guest molecules, and the interesting of studies focussed on the energy binding cyclodextrin and the guest molecule.
In this paper, β-cyclodextrin-cinnamyl alcohol inclusion complex was studied by fluorescence spectrophotometry and infrared absorption spectroscopy, and the results show: the stable energy of inclusion complexes of β-CD with weakly polar guest molecules consists mainly of Van der Waals interaction.
Authors:Qin Li, Yunhai Liu, Xiaohong Cao, Cui Pang, Youqun Wang, Zhibin Zhang, Yating Liu, and Ming Hua
The biomass pummelo peel was chosen as a biosorbent for removal of uranium(VI) from aqueous solution. The feasibility of adsorption
of U(VI) by Pummelo peel was studied with batch adsorption experiments. The effects of contact time, biosorbent dosage and
pH on adsorption capacity were investigated in detail. The pummelo peel exhibited the highest U(VI) sorption capacity 270.71 mg/g
at an initial pH of 5.5, concentration of 50 μg/mL, temperature 303 K and contacting time 7 h. The adsorption process of U(VI)
was found to follow the pseudo-second-order kinetic equation. The adsorption isotherm study indicated that it followed both
the Langmuir adsorption isotherm and the Freundlich adsorption isotherm. The thermodynamic parameters values calculated clearly
indicated that the adsorption process was feasible, spontaneous and endothermic in nature. These properties show that the
pummelo peel has potential application in the removal of the uranium(VI) from the radioactive waste water.