A Turán type inequality for rational functions with prescribed poles

Summary By employing a novel idea and simple techniques, we substantially generalize the Turán type inequality for rational functions with real zeros and prescribed poles established by Min [5] to include L^pspaces for 1≤p≤∞<span style='font-size:10.0pt'>while loosing the restriction ρ > 2 at the same time.     

Synthesis of some chiral liquid crystals and study of the effect of intramolecular hydrogen bonding on the phase behaviour

The synthesis of three new series of chiral Schiff's bases containing benzilideneaniline and 2-hydroxybenzilideneaniline moieties as mesogenic cores is presented. Differential scanning calorimetry, optical polarizing microscopy and X-ray diffraction measurements were used to study the phase transition temperatures and behaviour. The results reveal that most of these materials show chiral smectic mesomorphism.     

Miniature InGaAsP/InP phase modulator for integrated opto-electronics

Miniature, etching ridge InGaAsP/InP Phase Modulator with highly efficient phase shifting efficiency of 60°/V.mm and 43°/V.mm for TE and TM modes, respectively, and 3 dB bandwidth of 650 MHz at 1.52 μm are reported. It is well suited for integrated opto-electronics. Some functions depending on bandwidth of the devices are discussed.     

Ditzian—Totik型的Besov空间和Bernstein—Durrmeyer算子

对任一函数f∈L_p[0,1],n阶Bernstein—Durrnieyer算子为     

红外折/衍混合离轴望远系统设计

本文针对空间光学系统轻型特点,设计了一个二元光学折/衍混合红外反射式望远系统。采用了离轴式格里高利(Gregorian)结构形式,消除了望远系统中的中心遮拦问题。用衍射光学元件校正系统象差,使反射面为球面,二元光学表面尺寸比施密特(Schmidt)校正板(位于入瞳处)缩小于3～4倍,光学设计运用OSLO软件,光学系统的通光孔径φ=120mm,焦距f=-1000mm,波长λ=4.3μm,视场2ω=2°×6°(子午×弧矢),分辨率Res=0.05mm,MTF≥0.4(空间频率fre≤10cl/mm).     

First observation of yrast band in odd-odd162Lu

High spin states of the odd-odd¹⁶²Lu nucleus have been studied via¹⁴⁷Sm(¹⁹F,4nγ)¹⁶²Lu reaction at 95 MeV beam energy. Level scheme for yrast band based onπ[h_11/2 v[i_13/2] quasiparticle configuration was established up to I ^π = (23^?) for the first time. This band shows the signature inversion in energy before backbending generally appeared in this mass region. It is stressed that the signature splitting in¹⁶²Lu is larger than that in the¹⁶⁰Tm nucleus.     

Modifications of the Wolfe Line Search Rules to Satisfy Second-Order Optimally Conditions in Unconstrained Optimization

The line search method incorporating the Wolfe conditions is modified to ensure that a descent algorithm terminates in a finite number of steps at an approximate stationary point where the second-order conditions of optimality are satisfied. A simple procedure based on conjugate directions is proposed to determine directions of negative curvature.     

Pullback attractors for a non-autonomous incompressible non-Newtonian fluid

This paper studies the pullback asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid in two-dimensional (2D) bounded domains. We first prove the existence of pullback attractors AV in space V (has H²-regularity, see notation in Section 2) and AH in space H (has L²-regularity) for the cocycle corresponding to the solutions of the fluid. Then we verify the regularity of the pullback attractors by showing AV=AH, which implies the pullback asymptotic smoothing effect of the fluid in the sense that the solutions become eventually more regular than the initial data.