A Depth Formula for Generic Singularities and Their Weak Normality

Let X be a smooth projective variety of dimension r and π:X → ?^m a generic projection with r + 1 ≤ m ≤ 2r. It is shown that, at any point on X′ = π(X) of multiplicity μ, off a closed subset of the triple locus of codimension four, the depth of the local ring is equal to r ? (μ ? 1)(m ? r ? 1). This leads to some improvements on the affirmation of a conjecture of Andreotti–Bombieri–Holm on the weak normality of X′ and a conjecture of Piene on the weak normality of Sing(X′).     

Gröbner basis and free resolution of the ideal of 2-minors of a 2 × n matrix of linear forms *

We give a Gröbner basis for the ideal of 2-minors of a 2 × n utiatrix of linear forms. The minimal free resolution of such an ideal is obtained in [4] when the corresponding Kronecker-Weierstrass normal form has no iiilpotent blocks. For the general case, using this result, the Grobner basis and the Eliahou-Kervaire resolution for stable monomial ideals, we obtain a free resolution with the expected regularity. For a specialization of the defining ideal of ordinary pinch points, as a special case of these ideals, we provide a minimal free resolution explicitly in terms of certain Koszul complex.     

Analysis and design of simple low-loss wide-angle waveguide bends

In this paper a simple low-loss planar waveguide wide-angle bend is proposed and analyzed. The waveguide bend of this work consists of a curved tapered angle such that its tapering can be adjusted for a minimum loss (maximum transmission coefficient) and small dimension of bend. The analysis is done using wide-angle BPM (beam propagation method) type Pade (4,4). The simulated results of different bends show that at the same transmission coefficient the area required for the proposed bends are smaller than those of the abrupt bends.     

Emission and performance analysis of DI diesel engines fueled by biodiesel blends via CFD simulation of spray combustion and different spray breakup models: a numerical study

Journal of Thermal Analysis and Calorimetry - In the current study, computational fluid dynamics code was used to perform 3D simulation of mixture formation and combustion of biodiesel fuel spray...     

Unraveling the role of binder concentration on the electrochemical behavior of mesocarbon microbead anode in lithium–ion batteries: understanding the formation of the solid electrolyte interphase

Journal of Solid State Electrochemistry - Binders play a significant role in the electrochemical performance of anodes in lithium–ion batteries. In this study, mesocarbon microbead (MCMB)...     

Electronic and transport properties of monolayer graphene defected by one and two carbon ad-dimers

Using density functional theory combined with non-equilibrium Green’s function method, we have investigated the electronic and transport properties of graphenes defected by one and two carbon ad-dimers (CADs), placed parallel to the graphene lattice. Addition of these CADs to graphenes creates 3D paired pentagon–heptagon defects (3D-PPHDs). The band structure, density of states (DOS), quantum conductance, projected DOS, as well as the current–voltage characteristic per graphene super-cells containing each type of 3D-PPHD are calculated. The local strain introduced to graphene by 3D-PPHDs forces the C-bonds in the dimers to hybridize in sp ³-like rather than sp ²-like orbitals, creating localized states at the center of the corresponding defect below the Fermi energy. Simulations show that the zero-bias conductances per super-cells containing defects created by one and two CADs exhibit dip about ~0.579 and ~0.253 eV below their corresponding Fermi levels, respectively. These can be attributed to the localized states around the same energy levels. Simulations also show that the enhanced carriers scatterings within the graphenes defected by the 3D-PPHDs have increased their overall resistances, as compared with the pristine graphene. Moreover, the current–voltage characteristic calculated per super-cell for each case shows that the current for those containing one and two CADs, at an applied voltage of 0.5 V, is ~5 and 13 % less than the current calculated for the pristine super-cell of the same size.     

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).     

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.     

Determination of the dihedral angle of the monoanion of succinic acid in aprotic media

A value of 74(+/-4) degrees was determined from NMR-observed dipolar couplings for the rotational dihedral angle of the monosuccinate anion in an aprotic liquid-crystal solution of the gauche conformation of tetraoctylammonium monosuccinate. This value is in reasonable agreement with other, somewhat less definitive, evidence gleaned from isotropic vicinal proton-proton couplings of the essentially completely gauche preference of the monosuccinate anion in tert-butyl alcohol and aprotic solvents, such as DMSO and THF, and quantum computations for the monoanion in THF.     

Thermodynamic properties of surfactant sodium n-heptyl sulfonate in water and in aqueous solutions of poly(ethylene glycol) at different temperatures

The volumetric, compressibility and electrical conductivity properties of sodium n-heptyl sulfonate (C₇SO₃Na) in pure water and in aqueous poly(ethylene glycol) (PEG) solutions were determined at different temperatures below and above the micellar composition range. At each temperature, the infinite dilution apparent molar volumes of the monomer and micellar state of C₇SO₃Na in aqueous PEG solutions respectively are smaller and larger than those in pure water. However, the values of the infinite dilution apparent molar isentropic compressibility of both monomer and micellar states of C₇SO₃Na in aqueous PEG solutions are larger than those in pure water. Thermodynamic parameters of micellization of investigated surfactant in water and in aqueous solutions of PEG at different temperatures were estimated and it was found that the micelle formation process is endothermic and therefore, this process must be driven by entropy increase. The calculated Gibbs free energies of micellization for aqueous PEG solutions are more negative than those for pure water and become more negative by increasing temperature. The variation of the critical micelle concentration (CMC) of C₇SO₃Na in water and in aqueous PEG solutions with temperature was obtained and a comparison between the CMC of C₇SO₃Na obtained from different thermodynamic properties was also made.