Absorption/Scattering of Scalar Waves by Dilatonic Black Hole

We investigate the scattering and absorption cross sections of scalar waves by Garfinkle-Horowitz-Strominger (GHS) black hole spacetime with partial wave method. We find that the total absorption cross section oscillates around the geometric optical value, and the scattering angle width becomes narrower and the damping oscillation pattern becomes more complex as l increases. With fixed frequency ω, the main glory peak value becomes higher and the glory width becomes wider as the magnetic parameter a increases.     

On the fast Khintchine spectrum in continued fractions

For $x\in [0,1)$ x ∈ [ 0 , 1 ) , let $x=[a_1(x), a_2(x),\ldots ]$ x = [ a 1 ( x ) , a 2 ( x ) , ... ] be its continued fraction expansion with partial quotients $\{a_n(x), n\ge 1\}$ { a n ( x ) , n ≥ 1 } . Let $\psi : \mathbb{N } \rightarrow \mathbb{N }$ ψ : N → N be a function with $\psi (n)/n\rightarrow \infty $ ψ ( n ) / n → ∞ as $n\rightarrow \infty $ n → ∞ . In this note, the fast Khintchine spectrum, i.e., the Hausdorff dimension of the set $$\begin{aligned} E(\psi ):=\left\{ x\in [0,1): \lim _{n\rightarrow \infty }\frac{1}{\psi (n)}\sum _{j=1}^n\log a_j(x)=1\right\} \end{aligned}$$ E ( ψ ) : = x ∈ [ 0 , 1 ) : lim n → ∞ 1 ψ ( n ) ∑ j = 1 n log a j ( x ) = 1 is completely determined without any extra condition on $\psi $ ψ . This fills a gap of the former work in Fan et al. (Ergod Theor Dyn Syst 29:73–109, 2009).     

On a certain type of nonlinear differential equations admitting transcendental meromorphic solutions

We study the differential equations w ²+R(z)(w ^(k))² = Q(z), where R(z),Q(z) are nonzero rational functions. We prove

1. if the differential equation w ²+R(z)(w′)² = Q(z), where R(z), Q(z) are nonzero rational functions, admits a transcendental meromorphic solution f, then Q ≡ C (constant), the multiplicities of the zeros of R(z) are no greater than 2 and f(z) = √C cos α(z), where α(z) is a primitive of $\tfrac{1} {{\sqrt {R(z)} }}$ such that √C cos α(z) is a transcendental meromorphic function.
2. if the differential equation w ² + R(z)(w ^(k))² = Q(z), where k ? 2 is an integer and R,Q are nonzero rational functions, admits a transcendental meromorphic solution f, then k is an odd integer, Q ≡ C (constant), R(z) ≡ A (constant) and f(z) = √C cos (az + b), where $a^{2k} = \tfrac{1} {A}$ .

     

Fast and Accurate Computation of the Exact Confidence Limits for the Common Odds Ratio in Several 2 × 2 Tables

Abstract

Mehta, Patel, and Gray proposed a network algorithm for the exact confidence limits of the common odds ratio in several 2 × 2 tables. Their algorithm was implemented in the StatXact and Egret statistical packages and further discussed by Vollset, Hirji, and Elashoff. The need to evaluate polynomials of potentially very high degrees, however, poses some numerical difficulties. This article presents a method that cuts the degree of polynomials by at least one half. Two other modifications to further stabilize and speed the computation are also proposed.     

A numerical study of reignition induced by a diffusion flame

We present a numerical study of the reignition of a cold reactant mixture by the interaction with a nearby diffusion flame. This reignition mechanism may be an important process in turbulent non-premixed flames at high rates of strain where quenched sections of the stoichiometric surface are folded by the turbulent flow and come in close proximity with other burning flame sections. We consider an idealized one-dimensional setup containing the fundamental ingredients that are expected to contribute to this reignition mode. One- and two-step irreversible chemical mechanisms with heat release levels typical of practical hydrocarbon fuels are considered. It is observed that a slow moving reignition kernel originates on the high-temperature region of the burning flame in the one-step chemistry case owing to small leakage of oxidizer from the cold-mixture side. This kernel gradually moves, increasing the local temperature above that provided by diffusion and eventually leads to thermal runaway with the formation of a deflagration wave. The reignition time depends on the chemistry details, the Damköhler number, but in any case it cannot exceed the mixing time. This implies that the flame-induced reignition time is essentially bounded from above by mixing. Unless one of the free streams is hotter, in which case auto-ignition (as opposed to reignition) may proceed first, the reignition time is chemistry dependent. In the case of two-step chemistry, the reignition pathway is different initially owing to leakage of the radical species, but it approaches that of the one-step chemistry case shortly thereafter. It is observed that the only difference between the two cases is in the initial phase of the evolution of the reignition kernel. This phase appears to be very sensitive to the chemistry details, a general aspect of ignition. A parametric study is carried out to elucidate the effect of each non-dimensional quantity on the reignition time for the one-step chemistry case.     

Synthesis,Isolation and X-ray Crystal Structure Characterization of <Emphasis Type="Italic">Trans</Emphasis>-γ-{(C-<Emphasis Type="Italic">meso</Emphasis>-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane)(diisothiocyanato)} Nickel(II) Complex

Abstract  A new isomer of [Ni(tet-a)]²⁺ (assigned as γ-isomer) (tet-a = C-meso-5,5,7,12,12,14−hexamethyl-1,4,8,11-tetraazacyclotetradecane), which is found in the complex of trans-γ-[Ni(tet-a)(NCS)₂], has been isolated from the reaction of β-[Ni(tet-a)](ClO₄)₂ with NaSCN in a mixture of MeOH–H₂O (1:1, v/v) solution and characterized by X-ray crystallography. The complex crystallizes in orthorhombic Pca2(1) space group with the crystal cell parameters of a = 12.5787(10) ?, b = 11.6834(10) ?, c = 15.4019(12) ?, V = 2263.5(3) ?³, and Z = 4. The crystal structure shows that the complex is noncentrosymmetric. The conformations of the six-asymmetric centers are assigned as 1R,4R,8S,11S,7R,14S or 1S,4S,8R,11R,7S,14R (Trans-III). The coordination polyhedron around the nickel atom is axially elongated octahedron with an N₆ chromophore. The association of the complex units through N(3)–H···S(1) (2.665 ?) hydrogen bonding interactions leads one-dimensional hydrogen bonded network along c-axis. Index Abstract  A new isomer of Ni(tet-a)²⁺, which is assigned as γ-isomer, in the complex of trans-γ-[Ni(tet-a)(NCS)₂] has been synthesized, isolated and characterized by X-ray crystallography. The complex units form a one-dimensional self-assembly hydrogen bonded network.      

A Dual‐Surface Amidoximated Halloysite Nanotube for High‐Efficiency Economical Uranium Extraction from Seawater

By chemical cross‐linking the amidoxime group onto dual‐surfaces of natural ore materials, namely halloysite nanotubes (HNTs), an efficient adsorbent, AO‐HNTs, is developed. AO‐HNTs show high uranium adsorption capacity of 456.24 mg g^?1 in 32 ppm uranium‐spiked simulated seawater. In natural seawater, AO‐HNTs reach the high uranium extraction capacity of 9.01 mg g^?1 after 30 days’ field test. The dual‐surface amidoximated hollow nanotubular AO‐HNTs exhibit more coordination active sites for uranium adsorption, which is attributed to the high and fast uranium adsorption capacity. Because of the stable natural ore structure, AO‐HNTs also show long service life. Benefiting from the low cost of HNTs, the cost for uranium extraction from seawater is close to the uranium price in the spot uranium market, suggesting that AO‐HNTs could be used for economical extraction of uranium from the oceans.