Hybrid materials covalently incorporated with isophorone-based dyes through sol-gel process for nonlinear optical applications

Two new push-pull type second-order nonlinear optical (NLO) active isophorone-based alkoxysilane dyes with the same acceptor were synthesized and characterized. One silane (ICTES-HEMA) bears a chromophore with a hydroxyethyl methylamino donor and the other silane (ICTES-HMPP) is a bulkier analogue with a hydroxymethyl diphenylamino donor. Transparent, homogeneous films were prepared via the copolymerization of tetraalkoxysilane (TEOS) and different NLO silanes with the ratio of 5:1. The d(33) values obtained for the HEMA and HMPP films are 46.3 and 20.6 pm/V, respectively. Normalized UV-vis spectra reveal that the introduction of a diaryl group would help to prevent unfavorable organization of the chromophores. The reorientation dynamic stabilities of the samples were studied by second-harmonic generation (SHG) measurements, demonstrating that bulkier chromophores incorporated in sol-gel materials would not necessarily lead to higher stabilities over time.     

Observation of two new N* peaks in J/psi-->ppi-n and ppi+n decays

The decay J/psi-->NNpi provides an effective isospin 1/2 filter for the piN system due to isospin conservation. Using 58x10(6) J/psi decays collected with the Beijing Electromagnetic Spectrometer at the Beijing Electron Positron Collider, more than 100 thousand J/psi-->ppi-n+c.c. events are obtained. Besides the two well-known N* peaks at around 1500 MeV/c2 and 1670 MeV/c2, there are two new, clear N* peaks in the ppi invariant mass spectrum around 1360 MeV/c2 and 2030 MeV/c2 with statistical significance of 11sigma and 13sigma, respectively. We identify these as the first direct observation of the N*(1440) peak and a long-sought missing N* peak above 2 GeV/c2 in the piN invariant mass spectrum.     

Small prime solutions of a pair of linear equations in five prime variables

Assume an additional congruent condition on the coefficients. We prove that the pair 5 of linear equations ∑j=1^5 αλjpj = bλ （λ= 1, 2） has solutions in primes pj satisfying pj 〈〈 （｜b1｜＋｜b2｜＋1） maxλ,j ｜αλj｜^2318＋ε. This improves the exponent 79680 without assuming the additional condition of the second author＇s.     

Automorphism group and representation of a twisted multi-loop algebra

Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.     

On invariant sets in Lagrangian graphs

In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.     

拟-Armendariz模

For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.     

Isochronicity Problem of Higher-Order Singular Point for Polynomial Differential Systems

Due to the difficulty, the isochronicity problems with respect to higher-order singular point (or degenerate singular point) of polynomial differential systems are far from being solved. The calculation of period constants is an effective way to find necessary conditions for isochronicity. In this paper, by means of a homeomorphic transformation, higher-order singular point is transferred into the origin. At the same time, a new recursive algorithm to compute period constants at the origin of the transformed system is deduced which is easy to realize with the computer algebraic system such as MATHEMATICA or MAPLE. Finally, to illustrate the effectiveness of our algorithm, the pseudo-isochronous center conditions of higher-order singular point for a class of septic system are investigated. Our work is new in terms of research about the isochronicity problem of higher-order singular point and consists of the existing results related to the origin as a special case when it is an elementary singular point.     

Inverse Coefficient Problems for Elliptic Hemivariational Inequalities

This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.     

Hazard regression with penalized spline: The smoothing parameter choice and asymptotics

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.