非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法,推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式·研究表明,当w0/λ→0时,远场发散角趋于渐近值θmax=63.435°,与阶数无关·使用非傍轴高斯光束代替傍轴高斯光束作为理想光束,研究了非傍轴FG光束的M2因子,并与传统定义的M2因子作了比较·在非傍轴范畴,非傍轴FG光束的M2因子不仅与阶数N有关,而且与w0/λ有关·按照定义,当w0/λ→0时,非傍轴FG光束的M2因子不等于0,对阶数N=1,2,3时,M2因子分别趋于0.913,0.882和0.886·当N→∞时,M2因子取最小值M2min=0.816·     

非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法，推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式.研究表明，当w0/λ→0时，远场发散角趋于渐近值θmax=63.435°，与阶数无关.使用非傍轴高斯光束代替傍轴高斯光束作为理想光束，研究了非傍轴FG光束的M2因子，并与传统定义的M2因子作了比较.在非傍轴范畴，非傍轴FG光束的M2因子不仅与阶数N有关，而且与w0/λ有关.按照定义，当w0/λ→0时，非傍轴FG光束的M2因子不等于0，对阶数N=1, 2, 3时，M2因子分别趋于0.913,0.882和0.886.当N→∞时，M2因子取最小值M2min=0.816.     

Hydrothermal synthesis,thermal decomposition and optical properties of Fe2F5(H2O)(Htaz)(taz)(Hdma)

Crystal structure of Fe₂F₅(H₂O)(Htaz)(taz)(Hdma) which crystallizes in the triclinic system space group $\text{P}\overline{1}$ with unit cell parameters a = 8.8392(5) Å, b = 9.1948(5) Å, c = 9.5877(5) Å, α = 82.070(3)°, β = 63.699(3)°, γ = 89.202(3)°, Z = 2, and V = 690.91(7) ų, was synthesized under hydrothermal conditions at 393 K for 72 h, by a mixture of FeF₂/FeF₃, 1,2,4-triazole molecule (Htaz), and hydrofluoric acid solution (HF 4%) in dimethylformamide solvent (DMF). The main feature of this material is the coexistence of two oxidation states for iron atoms (Fe²⁺, Fe³⁺) in the unit cell, which associate by opposite fluorine corners of FeF₅N and FeF₂N₄ octahedra, and/or triazole molecule which originates the 2D produces material. The structure determination, performed from single crystal X-ray diffraction data, lead to the R₁/_WR₂ reliability factors 0.031/0.087. Thermal stability studies (TG/DTG/DTA) show that the decomposition provides in the temperature range 473–773 K and no mass loss was detected before 473 K. Mass spectrometry (MS) has been used. The optical absorption of the solid was measured at the corresponding λ_max using UV–vis diffuse-reflectance spectrum.     

Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations

In the present work, a three-dimensional (3D) elastic plate model capturing the small scale effects is developed for the free vibration of functionally graded (FG) nanoplates resting on elastic foundations. The theoretical model is formulated employing the nonlocal differential constitutive relations of Eringen in conjunction with the 3D equations of motion of elasticity.The material properties are assumed to vary continuously along the thickness of the nanoplate in accordance with the power law formulation. Through extending the generalized differential quadrature (GDQ) method to the three-dimensional case, the governing equations are simultaneously discretized in every three coordinate directions and are then recast to the standard form of an eigen value problem. Solving the acquired problem, the natural frequencies of the nanoplates with different boundary conditions are calculated. The convergence behavior of the numerical results is checked out and comparison studies are conducted to make sure of the accuracy and reliability of the present model. Finally, the dependence of the vibration behavior of the nanoplate on edge conditions, elastic coefficients of the foundation, scale coefficient, mode number, material and geometric parameters are discussed.     

Mapping Multivalency and Differential Affinities within Large Intrinsically Disordered Protein Complexes with Segmental Motion Analysis

Intrinsically disordered proteins (IDPs) can bind to multiple interaction partners. Numerous binding regions in the IDP that act in concert through complex cooperative effects facilitate such interactions, but complicate studying IDP complexes. To address this challenge we developed a combined fluorescence correlation and time‐resolved polarization spectroscopy approach to study the binding properties of the IDP nucleoporin153 (Nup153) to nuclear transport receptors (NTRs). The detection of segmental backbone mobility of Nup153 within the unperturbed complex provided a readout of local, region‐specific binding properties that are usually masked in measurements of the whole IDP. The binding affinities of functionally and structurally diverse NTRs to distinct regions of Nup153 can differ by orders of magnitudes—a result with implications for the diversity of transport routes in nucleocytoplasmic transport.     

Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity

In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler–Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between FG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FG nanobeam thickness. The nonlinear governing equation includes the von Kármán geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of FG nanobeams is investigated.     

A novel phenylspirodrimane dimer from cultures of the fungus Stachybotrys chartarum

Stachartone A (1), a novel phenylspirodrimane dimer, was isolated from cultures of the tin mine tailings-associated fungus Stachybotrys chartarum. Its structure was elucidated by means of spectroscopic methods. At the same time, compound (1) was tested for its cytotoxicity against five human cancer cell lines.     

Maximal ergodic theorems for some group actions

We prove maximal ergodic inequalities for a sequence of operators and for their averages in the noncommutative Lp-space. We also obtain the corresponding individual ergodic theorems. Applying these results to actions of a free group on a von Neumann algebra, we get noncommutative analogues of maximal ergodic inequalities and pointwise ergodic theorems of Nevo-Stein.     

Duality and interpolation of anisotropic Triebel–Lizorkin spaces

We study properties of anisotropic Triebel–Lizorkin spaces associated with general expansive dilations and doubling measures on using wavelet transforms. This paper is a continuation of (Bownik in J Geom Anal 2007, to appear, Trans Am Math Soc 358:1469–1510, 2006), where we generalized the isotropic methods of dyadic -transforms of Frazier and Jawerth (J Funct Anal 93:34–170, 1990) to non-isotropic settings. By working at the level of sequence spaces, we identify the duals of anisotropic Triebel–Lizorkin spaces. We also obtain several real and complex interpolation results for these spaces. The author was partially supported by the NSF grants DMS-0441817 and DMS-0653881. The author wishes to thank Michael Frazier and Dachun Yang for valuable comments and discussions on this work.