Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

Let {(ξni, ηni), 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as(S_1, ρ_n S_1 +(1-ρ_n~2S_2)~(1/2)), ρn∈(0, 1), where(S1, S2) is a bivariate spherical random vector. For the distribution function of radius (S_1~2+ S_2~2)~(1/2) belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of ρn to 1 is given. In this paper,under the refinement of the rate of convergence of ρn to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.     

Graphs in which some and every maximum matching is uniquely restricted

A matching M in a graph G is uniquely restricted if there is no matching in G that is distinct from M but covers the same vertices as M. Solving a problem posed by Golumbic, Hirst, and Lewenstein, we characterize the graphs in which some maximum matching is uniquely restricted. Solving a problem posed by Levit and Mandrescu, we characterize the graphs in which every maximum matching is uniquely restricted. Both our characterizations lead to efficient recognition algorithms for the corresponding graphs.     

Anisotropy Effects and Observational Data on the Constraints of Evolution Dark Energy Models

We investigate cosmological dark energy models where the accelerated expansion of the universe is driven by a field with an anisotropic universe. The constraints on the parameters are obtained by maximum likelihood analysis using observational of 194 Type Ia supernovae(SNIa) and the most recent joint light-curve analysis(JLA) sample. In particular we reconstruct the dark energy equation of state parameter w(z) and the deceleration parameter q(z). We find that the best fit dynamical w(z) obtained from the 194 SNIa dataset does not cross the phantom divide line w(z) =-1 and remains above and close to w(z)≈-0.92 line for the whole redshift range 0 ≤ z ≤ 1.75 showing no evidence for phantom behavior. By applying the anisotropy effect on the ΛCDM model, the joint analysis indicates that ?_(σ0)= 0.0163 ± 0.03,with 194 SNIa, ?_(σ0)=-0.0032 ± 0.032 with 238 the SiFTO sample of JLA and ?_(σ0)= 0.011 ± 0.0117 with 1048 the SALT2 sample of Pantheon at 1σ′confidence interval. The analysis shows that by considering the anisotropy, it leads to more best fit parameters in all models with JLA SNe datasets. Furthermore, we use two statistical tests such as the usual χ_(min)~2/dof and p-test to compare two dark energy models with ΛCDM model. Finally we show that the presence of anisotropy is confirmed in mentioned models via SNIa dataset.     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

云层背景目标识别的匹配滤波器设计

提出一种利用最大平均相关高度(MACH)算法识别复杂云层背景目标的改进滤波器设计方法。在MACH滤波器设计中,通过对云层背景功率谱的统计特性分析,数据拟合得到云层背景功率谱的分布函数,用以代替传统的白噪声模型;提取飞行目标的姿态变化图像,并作阈值化处理,得到训练样本。对不同云层背景和姿态变化目标的相关识别结果表明:改进滤波器的平均峰值相关能量比为0.71%,峰值鉴别率为0.92,可以有效抑制云层背景的干扰,对姿态变化目标识别的鲁棒性较好。     

The maximum principle for the Bergman space and the Möbius pseudodistance for the annulus

It is shown that the formula for the Möbius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle.

     

On the elliptic equation on complete Riemannian manifolds and their geometric applications

We study the elliptic equation on complete noncompact Riemannian manifolds with nonnegative. Three fundamental theorems for this equation are proved in this paper. Complete analyses of this equation on the Euclidean space and the hyperbolic space are carried out when is a constant. Its application to the problem of conformal deformation of nonpositive scalar curvature will be done in the second part of this paper.

     

Distribution of the maxima of random Takagi functions

This paper concerns the maximum value and the set of maximum points of a random version of Takagi’s continuous, nowhere differentiable function. Let F(x):=∑ _n=1^∞ ε _n ϕ(2 ⁿ⁻¹ x), x ∈ R, where ɛ ₁, ɛ ₂, ... are independent, identically distributed random variables taking values in {−1, 1}, and ϕ is the “tent map” defined by ϕ(x) = 2 dist (x, Z). Let p:= P (ɛ ₁ = 1), M:= max {F(x): x ∈ R}, and := {x ∈ [0, 1): F(x) = M}. An explicit expression for M is given in terms of the sequence {ɛ _n }, and it is shown that the probability distribution μ of M is purely atomic if p < , and is singular continuous if p ≧ . In the latter case, the Hausdorff dimension and the multifractal spectrum of μ are determined. It is shown further that the set is finite almost surely if p < , and is topologically equivalent to a Cantor set almost surely if p ≧ . The distribution of the cardinality of is determined in the first case, and the almost-sure Hausdorff dimension of is shown to be (2p − 1)/2p in the second case. The distribution of the leftmost point of is also given. Finally, some of the results are extended to the more general functions Σa ^{n − 1} ɛ _n ϕ(2 ^{n − 1} x), where 0 < a < 1.      

Device research on GaAs-based InAlAs/InGaAs metamorphic high electron mobility transistors grown by metal organic chemical vapour deposition

This paper applies a novel quad-layer resist and e-beam lithography technique to fabricate a GaAs-based InAlAs/InGaAs metamorphic high electron mobility transistor (HEMT) grown by metal organic chemical vapour deposition (MOCVD). The gate length of the metamorphic HEMT was 150~nm, the maximum current density was 330~mA/mm, the maximum transconductance was 470~mS/mm, the threshold voltage was -0.6~V, and the maximum current gain cut-off frequency and maximum oscillation frequency were 102~GHz and 450~GHz, respectively. This is the first report on tri-termination devices whose frequency value is above 400~GHz in China. The excellent frequency performances promise the possibility of metamorphic HEMTs grown by MOCVD for millimetre-wave applications, and more outstanding device performances would be obtained after optimizing the material structure, the elaborate T-gate and other device processes further.     

Maximum principles for a class of nonlinear second order elliptic differential equations

In this paper we investigate maximum principles for functionals defined on solutions to special partial diff'erential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one overdetermined problem.