Recursive computational formulas of the least squares criterion functions for scalar system identification

The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (RLS) algorithm, the weighted RLS algorithm, the forgetting factor RLS algorithm and the finite-data-window RLS algorithm without or with a forgetting factor. The recursive computation formulas of the criterion functions are derived by using the recursive parameter estimation equations. The proposed recursive computation formulas can be extended to the estimation algorithms of the pseudo-linear regression models for equation error systems and output error systems. Finally, the simulation example is provided.     

关于整函数超级的进一步结果

运用正规族理论研究了整函数与其高阶导数分担无穷级函数增长级与超级的相关结果.从亚纯函数超级大于零而使球面导数无界的角度出发,然后综合运用Pang-Zaclman引理,数学归纳法和Nevanlinna理论等方法证明了该结果,推广和改进了已有的结果.     

The Boundedness of Composition Operators on Triebel–Lizorkin and Besov Spaces with Different Homogeneities

In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.     

On semi-classical limits of ground states of a nonlinear Maxwell–Dirac system

We study the semi-classical ground states of the nonlinear Maxwell–Dirac system: $$\begin{aligned} \left\{ \begin{array}{l} \alpha \cdot \left( i\hbar \nabla + q(x)\mathbf{A }(x)\right) w-a\beta w -\omega w - q(x)\phi (x) w = P(x)g(\left| w\right| ) w\\ -\Delta \phi =q(x)\left| w\right| ^2\\ -\Delta {A_k}=q(x)(\alpha _k w)\cdot \bar{w}\ \ \ \ k=1,2,3 \end{array} \right. \end{aligned}$$ for \(x\in \mathbb{R }^3\) , where \(\mathbf{A }\) is the magnetic field, \(\phi \) is the electron field and \(q\) describes the changing pointwise charge distribution. We develop a variational method to establish the existence of least energy solutions for \(\hbar \) small. We also describe the concentration behavior of the solutions as \(\hbar \rightarrow 0\) .     

Bernstein Polynomial Estimation in the Partially Linear Model under Monotonicity Constraints

In this paper, a Bernstein-polynomial-based likelihood method is proposed for the partially linear model under monotonicity constraints. Monotone Bernstein polynomials are employed to approximate the monotone nonparametric function in the model. The estimator of the regression parameter is shown to be asymptotically normal and efficient, and the rate of convergence of the estimator of the nonparametric component is established, which could be the optimal under the smooth assumptions. A simulation study and a real data analysis are conducted to evaluate the finite sample performance of the proposed method.     

浙江杜鹃花属植物的研究

本文报道了浙江产杜鹃花属植物16 种及 1 变型其中白花满山红为新变型,丁香杜 鹃和江西杜码为浙江分布新记录.根据最新分类系统,本属分为 5 个亚属,在浙江都有 它们的代表,说明浙江的杜鹃花属植物在该属系统研究中的地位,此外,文中还附有分种 检 索表和种类列举 ( 分布、用途 )     

ON THE BOUNDEDNESS OF SPHERES IN F-SPACES

In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the F*-space are presented. Moreover, some results about the compactness are also given.     

Crystal growth and spectroscopic properties of erbium doped Lu2SiO5

A high optical quality erbium doped Lu₂SiO₅ single crystal has been grown by the Czochralski method. The distribution coefficient of Er³⁺ was measured to be ∼0.926. The absorption and emission spectra as well as the fluorescence decay curve of the excited state ⁴I_13/2 were measured at room temperature. The spectroscopic parameters were calculated using the Judd–Ofelt theory, and the J–O parameters Ω₂, Ω₄ and Ω₆ were found to be 4.451×10^-20, 1.614×10^-20 and 1.158×10^-20 cm², respectively. The room-temperature fluorescence lifetime of the Er³⁺⁴I_13/2→⁴I_15/2 transition was measured to be 7.74 ms. The absorption and emission cross-section as well as the gain cross-section in the eye-safe regime of 1400–1700 nm were also determined and discussed.     

Organocatalyzed synthesis of 2-amino-8-oxo-5,6,7,8-tetrahydro-4H-chromene-3-carbonitriles

2-Amino-8-oxo-tetrahydro-4H-chromene-3-carbonitriles were synthesized for the first time from a tandem Michael addition-cyclization reaction between cyclohexane-1,2-dione and benzylidenemalononitriles. An enantioselective synthesis of these compounds was achieved in moderate ee values (up to 63% ee) by using a cinchona alkaloid-derived thiourea catalyst.