Electrostastic control of spontaneous curvature in catanionic reverse micelles

By means of small-angle neutron scattering and conductivity measurements, we study the microstructure of octylammoniumoctanoate/octane/water catanionic reverse microemulsions with an excess of anionic or cationic surfactant. Increasing the surface charge makes the microemulsion able to incorporate much more water than in the neutral case, up to 10 water molecules per surfactant. Even with charges in the surfactant film, wormlike micelles are present in the microemulsion domain. Along water dilution lines, the classical rod-to-sphere transition due to the minimization of the curvature energy of the rigid surfactant film is observed. When temperature is decreased, a re-entrant phase transition associated with the liquid-gas equilibrium of attractive cylinders is observed. Using the framework of the Tlusty-Safran theory, attraction could originate from junctions between wormlike reverse micelles. In any case, the spontaneous curvature of the catanionic surfactant film depends on both the temperature and the net charge, whatever the sign of the latter.     

Intramolecular cyclization of <Emphasis Type="Italic">N</Emphasis>-propargyl anilines: a new synthetic entry into highly substituted indoles

Indole derivatives are an important class of heterocycle found in a large number of natural products and synthetic pharmaceuticals. Given the low cost and easy availability of N-propargyl anilines, synthesis of indole cores from these versatile structural motifs has attracted a lot of attention in the past decade. In this review, we summarize the most representative and interesting reports on this rapidly advancing area, with special emphasis on mechanistic aspects of the reactions.     

On the transposition anti-involution in real Clifford algebras I: the transposition map

A particular orthogonal map on a finite-dimensional real quadratic vector space (V,?Q) with a non-degenerate quadratic form Q of any signature (p,?q) is considered. It can be viewed as a correlation of the vector space that leads to a dual Clifford algebra C?(V*,?Q) of linear functionals (multiforms) acting on the universal Clifford algebra C?(V,?Q). The map results in a unique involutive automorphism and a unique involutive anti-automorphism of C?(V,?Q). The anti-involution reduces to reversion (resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When applied to a general element of the algebra, it results in transposition of the element matrix in the left regular representation of C?(V,?Q). We also give an example for real spinor spaces. The general setting for spinor representations will be treated in part II of this work [R. Ab?amowicz and B. Fauser, On the transposition anti-involution in real Clifford algebras II: Stabilizer groups of primitive idempotents, Linear Multilinear Algebra, to appear].     

A basic family of iteration functions for polynomial root finding and its characterizations

Let p(x) be a polynomial of degree n?2 with coefficients in a subfield K of the complex numbers. For each natural number m?2, let L_m(x) be the m×m lower triangular matrix whose diagonal entries are p(x) and for each j=1,…,m−1, its jth subdiagonal entries are . For i=1,2, let L_m^i)(x) be the matrix obtained from L_m(x) by deleting its first i rows and its last i columns. L₁⁽¹⁾(x)≡1. Then, the function B_m(x)=x−p(x) defines a fixed-point iteration function having mth order convergence rate for simple roots of p(x). For m=2 and 3, B_m(x) coincides with Newton's and Halley's, respectively. The function B_m(x) is a member of S(m,m+n−2), where for any M?m, S(m,M) is the set of all rational iteration functions g(x) ∈ K(x) such that for all roots θ of p(x), then g(x)=θ+∑_i=m^Mγ_i(x)(θ−x)ⁱ, with γ_i(x) ∈ K(x) and well-defined at any simple root θ. Given g ∈ S(m,M), and a simple root θ of p(x), gⁱ(θ)=0, i=1, …, m−1 and the asymptotic constant of convergence of the corresponding fixed-point iteration is . For B_m(x) we obtain . If all roots of p(x) are simple, B_m(x) is the unique member of S(m,m + n − 2). By making use of the identity , we arrive at two recursive formulas for constructing iteration functions within the S(m,M) family. In particular, the family of B_m(x) can be generated using one of these formulas. Moreover, the other formula gives a simple scheme for constructing a family of iteration functions credited to Euler as well as Schröder, whose mth order member belongs to S(m,mn), m>2. The iteration functions within S(m,M) can be extended to any arbitrary smooth function f, with the uniform replacement of p^(j) with f^(j) in g as well as in γ_m(θ).     

Finite deformation analysis of COD,J-integral and crack tip intense strain region in plane strain large-scale yielding

A finite element analysis was performed to simulate crack tip blunting and the development of the intense strain region in a small compact tension specimen (0.4 T CT) of SA533B-1 under plane strain large-scale yielding, with the condition of large-geometry change around the crack tip taken into consideration. The region where the equivalent plastic strain $\text{}\text{?}$g3_p is greater than 0.15 was defined as the intense strain region, which corresponded to the recrystallized-etched zone delineated experimentally around the blunting crack tip. The development of the intense strain region was discussed as a function of the J-integral and the crack opening displacement. A linear relationship was obtained between the plastic work W_p dissipated within the intense strain region and (J/σ_y)² or b², where b is the crack opening displacement, defined as the separation of the two points at which the boundary of the intense strain region surrounding the crack tip intersects with the free surfaces of the crack.     

Metamaterial absorber based on circular ring structure with and without copper lines

This paper presents the analysis of circular ring metamaterial absorber with the existing of copper lines. The structure is designed using lossy FR4 substrate with thin copper layers. The circular ring shape with copper lines is printed on the top surface of FR4 substrate, while at the bottom surface is printed with full copper ground plane. Parametric study is done to investigate the effect of copper lines on the resonance frequency. From the simulation, the circular ring metamaterial absorber with vertical copper lines can resonates at lower frequency, but this structure is polarized sensitive. This drawback can be improved by adding horizontal copper lines together with the vertical copper lines. The circular ring structure with vertical and horizontal copper lines is not only polarization insensitive, but it can works at wide operating angle of incident waves.     

与星象函数有关的拟共形近于凸调和映射

讨论了一类解析部分为星象函数的拟共形近于凸调和映射的基本性质,得到了此类映射的系数不等式、积分表达式、增长定理、面积定理与部分和的近于凸半径.     

Supported Preyssler Nanoparticles in Synthesis of 1,3‐Diaryl‐5‐Spirohexahydropyrimidines

Silica‐supported Preyssler nanoparticles (H₁₄[NaP₅W₃₀O₁₁₀])/SiO₂ are used as a new and recyclable catalyst for the preparation of 1,3‐diaryl‐5‐spirohexahydropyrimidines via a one‐pot condensation of anilines, formaldehyde, and cyclohexanone.     

On Difference Fields with Quantifier Elimination

This paper proves that a difference field (E, ) admits quantifierelimination if and only if E is an algebraically closed field,and is an integer power of the Frobenius automorphism. 1991Mathematics Subject Classification 03C60, 12H10.