Inequalities relating to Lp-version of Petty＇s conjectured projection inequality

Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.     

光纤传感器对机敏复合材料结构性能的影响

本文通过实验研究了光纤传感器对埋光纤机敏复合材料机械性能的影响，详细分析了埋光纤机敏复合材料层板在外载作用下的应力分布，针对三种不同铺层方式，研究了六种树脂填充区对机敏复合材料层板应力集中的影响，得出了减小应力集中的有效方案。     

Cyclopalladated Ferrocenylimine Catalyzed Chlorination of 2‐Arylbenzoxazoles

An efficient and facile protocol for palladacycle‐catalyzed chlorination of 2‐arylbenzoxazoles was developed. The results represent the first examples involving the palladacycle as the catalyst for such chlorination. This chlorination was not a ligand‐directed ortho‐C H activation, but an electrophilic substitution process at the para‐position of the nitrogen atom in the benzo ring of benzoxazole moiety, the regiochemistry of which had been confirmed by HMBC spectral analysis. The catalytic system could tolerate various halogen atoms, such as F, Cl and Br, affording the corresponding products in moderate to excellent yields.     

Heterogeneous reaction of suspended phosmet particles with NO3 radicals

As an organophosphorous insecticide, phosmet is widely used for plant protection as well as against the ectoparasites on productive livestock. It emits into the atmosphere in both gas and particulate phases via spray drift from treatments and postapplication emissions, but its degradation in the atmosphere is not well-known up to now. In this study, the heterogeneous reaction of phosmet absorbed on the azelaic acid particles with NO(3) radicals is investigated in real-time using a vacuum ultraviolet photoionization aerosol time-of-flight mass spectrometer (VUV-ATOFMS). Two primary products and their nitro-substituted derivates are observed. The apparent reaction rate of phosmet particles with NO(3) radicals is also obtained by a relative rate method with isoprene and 1,4-cyclohexadiene as the reference compounds. The concentrations of the reference substance and phosmet particles are synchronously detected with an atmospheric gas analysis mass spectrometer and the VUV-ATOFMS. Under the experimental conditions, the average apparent reaction rate obtained is (1.92 ± 0.09) × 10(-12) cm(3) molecule(-1) s(-1), and the corresponding atmospheric lifetime toward NO(3) radicals is roughly estimated to be ~0.3 h.     

Global energy minimization of alanine dipeptide via barrier function methods

This paper presents an interior point method to determine the minimum energy conformation of alanine dipeptide. The CHARMM energy function is minimized over the internal coordinates of the atoms involved. A barrier function algorithm to determine the minimum energy conformation of peptides is proposed. Lennard-Jones 6-12 potential which is used to model the van der Waals interactions in the CHARMM energy equation is used as the barrier function for this algorithm. The results of applying the algorithm for the alanine dipeptide structure as a function of varying number of dihedral angles are reported, and they are compared with that obtained from genetic algorithm approach. In addition, the results for polyalanine structures are also reported.     

The method of upper and lower solutions for diffraction problems of quasilinear elliptic reaction-diffusion systems

The aim of this paper is to show the existence of solutions of the n-dimensional diffraction problem for weakly coupled quasilinear elliptic reaction-diffusion system. The coefficients of the equations under consideration are allowed to be discontinuous. We extend the method of upper and lower solutions for reaction-diffusion equations with continuous coefficients to the elliptic diffraction problem. An application of these results is given to the steady-state problem of Lotka-Volterra cooperation model with two cooperating species.     

A strong law of large numbers on the harmonic <Emphasis Type="Italic">p</Emphasis>-combination

In this paper, we establish a strong law of large numbers for the harmonic p-combinations of random star bodies. Starting from this theorem, we prove a strong law of large numbers in L _p space and provide the probabilistic version of dual Brunn-Minkowski inequality.     

Paley‐Wiener‐Type theorems for the Clifford‐Fourier transform

In the framework of Clifford analysis, we consider the Paley‐Wiener type theorems for a generalized Clifford‐Fourier transform. This Clifford‐Fourier transform is given by a similar operator exponential as the classical Fourier transform but containing generators of Lie superalgebra.     

Quasi Lp-Intersection Bodies

The purpose of this paper is to generalize the notion of intersection bodies to that of quasi Lp-intersection bodies. The Lp-analogs of the Busemann intersection inequality and the Brunn- Minkowski inequality for the quasi Lp-intersection bodies are obtained. The Aleksandrov Fenchel inequality for the mixed quasi Lp-intersection bodies is also established.