The paper studies the structure of restricted pre-Lie algebras. More specifically speaking, we first give the definitions of restricted pre-Lie algebras and restrictable pre-Lie algebras. Second, we obtain some properties of p-mappings and restrictable preLie algebras, and research restricted pre-Lie algebras with semisimple elements. Finally, quasi-toral restricted pre-Lie algebras are discussed and the uniqueness of decomposition for restricted pre-Lie algebras is determined.
We are concerned with the following semilinear elliptic equations with Sobolev-Hardy exponent .jpg){kind=small}
-Δu-μ(u)/(|x|2)=λu+(|u|2*(s)-2)/(|x|s)u+f, in Ω,
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u=0, on ∂Ω,
Where 2*(s)=(2(N-S))/(N-2) is the critical Sobolev-Hardy exponent, N≥3, 0≤s<2, 0≤μ<ū=((N-2)2)/(4). We show that for 0≤λ<λ1, where λ1 is the first eigenvalue of the operator -Δ-(μ)/(|x|2) and f∈(H01(Ω)*), the dual space of H01(Ω), with f(x).jpg){kind=small}
0. Under appropriate assumptions on f(x), we show that has at least two solutions. Moreover, if f≥0, the obtained solutions are non-negative.
Let X, Y be complex Banach spaces with dimentions greater than 1. Let A, B be normed closed subalgebras of B(X), B(Y) containing finite rank operators, respectively. For any A, B∈A, we define the quasi-product of A and B as A.jpg){kind=small}
B=A+B-AB. In this paper, A characterization of additive mappings from A onto B which preserve any one of (left, right) quasi-invertibility and (left, right, semi) quasizero divisors in both directions is given.
Let x:Mn→Sn+1 be a hypersurface in the (n+1)-dimensional unit sphere Sn+1 without umbilics. Four basic invariants of x under the Moebius transformation group in Sn+1 are Moebius metric g, Moebius second fundamental form B; Moebius form Φ and Blaschke tensor A. We classify the Moebius isoparametric hypersurfaces in Sn+1 with four distinct principal curvatures which multiplies are 1, 1, 1, m(m≥2).
By using a generalized Grunsky inequality, we obtain some estimates of the essential norm of the Grunsky operator for a univalent function in terms of the boundary distortion of the quasiconformal extension. As a corollary, we deduce the compactness criterion of the Grunsky operator.
According to the denseness and closedness of range of an operator, its point spectrum and residual spectrum are split into 1, 2-point-spectrum and 1, 2-residualspectrum, respectively. For 3×3 upper triangular operator matrices, the possible point spectra and possible residual spectra, ∪D, E, Fσ*, i(MD, E, F)(*=p, r; i=1, 2), are given by means of the analysis method and block operator technique.
The automorphism group of an extraspecial Z-group is determined. Let G be an extraspecial Z-group, where G=.jpg)
|αj∈Z, j=1, 2, ..., 2n+1.jpg){kind=small}
,
let AutcG be the normal subgroup of AutG consisting of all elements of AutG which act trivially on ζG. Then AutG=AutcG.jpg){kind=small}
Z2, and there is an exact sequence 1→.jpg){kind=small}
→AutcG→Sp(2n, Z)→1.
Let W be a self-orthogonal class of left R-modules. This paper concerns the class of n-strongly W-Gorenstein modules, which is a common generalization of strongly W-Gorenstein modules, strongly Gorenstein projective modules and n-strongly Gorenstein projective modules. Special attention is given to n-strongly WP-Gorenstein mod-ules and n-strongly WI-Gorenstein modules. The stability of n-strongly W-Gorenstein category is considered, some concrete characterizations of WP-Gorenstein modules in BC(R) are given and new versions of Foxby equivalence with respect to n-strongly WP-Gorenstein (resp., n-strongly WI-Gorenstein) modules are established. The properties of n-strongly WF-Gorenstein modules are also investigated.
We establish the first and the second-order asymptotics of distributions of normalized maxima of independent and non-identically distributed bivariate Gaussian triangular arrays, where each vector of the n-th row follows from a bivariate Gaussian distribution with correlation coefficient being a monotone continuous positive function of i/n. Furthermore, parametric inference for this unknown function is studied. Some simulation study and real data sets analysis are also presented.
Longitudinal data are usually analyzed using mixed effects models under the assumption of normal distributions. A departure from normality may result in invalid inference. Compared with the traditional mean regression, quantile regression can characterize a complete scan of the conditional distribution of the response variable and provide more robust inferences for nonnormal error distributions. In this paper, we focus on the quantile estimation and variable selection of censored mixed effects models. Firstly, the inverse censoring probability weighted (ICPW) method is utilized to obtain parameters estimation. Furthermore, the LASSO penalties are incorporated into the ICPW method to implement variable selection. Monte Carlo simulations demonstrate that the proposed method performs superior to the "naive" method which ignores censored data. Finally, an AIDS data set is analyzed to illustrate the proposed method.
We studied the derivations and the second cohomology group of the classical N=2 Lie conformal superalgebra. Furthermore, we investigated the universal central extension of this Lie conformal superalgebra by applying the result on the second cohomology group.
The paper is about the asymptotic properties of Degasperis-Procesi equation. That is, using the method of asymptotic density, under the assumption that it is unique, the paper proves that the positive momentum density of the Degasperis-Procesi equation is a combination of Dirac measures supported on the positive axis. This means that as time goes to infinity, the momentum density concentrates in small intervals moving right with different constant speeds.
We study the weighted Poincaré inequality and log-Sobolev inequality for one dimensional Cauchy distribution. We offer the optimal weighted functions, prove the sharpness, and estimate the orders of the constants in the inequalities.
