Mass shifting roles of negative kernel mass in density estimation

f(x) is a univariate density in C ⁴ with bounded support. For any n and sufficiently small kernel bandwidths, the symmetric appendage of any negative mass, –U, to any smooth unimodal symmetric kernel of order p=2 shifts expected estimator mass from regions where f(x)>0 to regions where f(x)<0. For large n, the mean automatic kernel adaptation induced by –U is analyzed in the simplest MISE reduction scenario: The symmetric appendage of –U to the uniform kernel K(x, X) over MISE-optimal bandwidths reduces MISE by shifting K(x, X) mass asymmetrically across the observation X in the direction of decreasing |f(x)|.     

Selective synthesis of isobutanol by means of the Guerbet reaction: Part 2. Reaction of methanol/ethanol and methanol/ethanol/n-propanol mixtures over copper based/MeONa catalytic systems

The synthesis of isobutanol via the Guerbet condensation between methanol and ethanol was studied by using sodium methoxide (MeONa) as soluble basic component and copper-based catalysts as heterogeneous dehydrogenating/hydrogenating metal species. The effect of the nature of the catalyst and the relative amount of its individual components with respect to the reacting alcohols as well as of temperature on productivity and selectivity of the process was investigated. The collected data indicated that the copper chromite/MeONa was more active than Cu-Raney/MeONa system. The reaction was shown to proceed with the formation only of n-propanol and isobutanol. Ethanol conversion up to 61% with selectivity to isobutanol up to 98.4% was obtained. The same catalytic systems were also employed in the reaction of the methanol/ethanol/n-propanol ternary mixture. Again copper chromite/MeONa resulted more active than the Cu-Raney/MeONa system. Finally, experiments were carried out on methanol/n-propanol mixtures in the presence of the copper chromite/MeONa catalytic system by recycling both the recovered solid copper component and the liquid reaction mixture for evidencing eventual copper leaching by MeONa. On the basis of the obtained results it was concluded that in the Guerbet reaction copper chromite works as heterogeneous catalyst.     

基于聚类分析的初三化学学业质量发展研究

以2013-2016年广州市各区（县级市）中考化学成绩的4种数据为指标，运用聚类分析研究广州市区域初三化学学业质量的发展状况。研究发现各区（县级市）主要分为3大类，部分区在不同年份的类别中移动，倾向于建立一个包括越来越多区域的第1大类。广州市区域初三化学学业质量逐步向优质均衡发展。系统的中学生化学探究活动和化学教师研训活动是实现这一发展的重要原因。     

EFFECTS OF COUPLING AGENTS ON THE CRYSTALLIZATION BEHAVIOR OF PP/T-ZnOw COMPOSITES

The objectives of this paper are to understand the crystallization behavior of polypropylene(PP)composites with surface modified tetra-needle-shaped zinc oxide whisker(T-ZnOw).T-ZnOw was surface modified with different coupling agents,such as silane coupling agents(KH-550,KH-560)and titanate coupling agent(NDZ-105),in order to improve the compatibility between PP and T-ZnOw.DSC and POM were used to characterize the melt and crystallization behavior and the crystalline structures of the composites,respectively.The results show that the surface modified T-ZnOw acts as a nucleating agent of PP crystallization,depending on the coupling agent used for modification.KH-550 and KH-560 have more apparent role in improving the interfacial interaction than NDZ-105 and induce PP crystallization at higher temperature and with smaller spherulites size.The results also suggest that the crystallization behavior depends on not only the content of coupling agent,but also the content of the surface modified T-ZnOw used in the composites.     

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.     

‘New mathematics’ and teaching

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

In the truly creative mathematical mind two opposite tendencies coexist: the logical and the imaginative. Apparently it seems that new mathematics can be reduced to a purely logical machinery. In fact it contains as much imaginative contributions as classical mathematics. But it is difficult to show simultaneously the logical sequence of propositions and the clumsy progression of research itself. Mathematical exposition does not always follow the ‘ most natural slopes’ of the mind. Unfamiliar presentations often give an impression of ‘ abstraction ‘, more familiar ones an impression of concreteness ‘.

So it appears that difficulties with new mathematics are mostly of psychological origin. Misuses of it can easily raise up intolerance reactions and emotional blocks. Perhaps insisting upon the fact that, here as elsewhere, it is important to be able to guess, to realize that intuition and imagination are essential, could help to make new mathematics better understood, more useful and more able to be considered as a unifing element among sciences.     

An anti‐diffusive volume of fluid method for interfacial fluid flows

A volume of fluid (VOF) method is developed combining a first‐order limited downwind scheme with higher order accurate schemes. The method is characterized by retaining a sharp fluid interface and a reduction in numerical diffusion near the interface, but avoids complicated geometrical reconstruction as occurs in most volume tracing algorithms. To demonstrate the accuracy and robustness of the method, a selection of numerical experiments are presented involving a pure advection problem, a water wave impact caused by a dam breaking and liquid sloshing in a partially filled tank. Copyright © 2011 John Wiley & Sons, Ltd.     

Dahlberg's theorem in higher co-dimension

In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension $n?1$ in ${\mathbb{R}}^n$, and later this result has been extended to more general non-tangentially accessible domains and beyond.In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph Γ of dimension d in ${\mathbb{R}}^n$, $d<n?1$, with a small Lipschitz constant. We construct a linear degenerate elliptic operator L such that the corresponding harmonic measure ${\omega }_L$ is absolutely continuous with respect to the Hausdorff measure on Γ. More generally, we provide sufficient conditions on the matrix of coefficients of L which guarantee the mutual absolute continuity of ${\omega }_L$ and the Hausdorff measure.     

Ultraviolet Photoelectron Spectra of Potassium Dosed Higher Fullerenes

Abstract

Ultraviolet photoelectron spectra of potassium dosed higher fullerenes are measured with a synchrotron radiation light source. Potassium dosing to higher fullerenes brings a new structure between the spectral onset of pristine fullerenes and the Fermi level. As the spectral edge of the new structure does not cross the Fermi level, potassium dosed higher fullerenes are not metallic but semiconductive. When the potassium is excessively dosed to the fullerenes, the lower binding energy structures above 5 eV become faint. In contrast to this phenomenon, four distinct structures appear between 5 and 14 eV.