Oscillatory integrals on unit square along surfaces

Let Q ² = [0, 1]² be the unit square in two-dimensional Euclidean space ℝ². We study the L ^p boundedness of the oscillatory integral operator T _α,β defined on the set ℒ(ℝ²⁺ⁿ ) of Schwartz test functions by

Study of near-infrared nonvolatile two-center holographic recording in LiNbO3:Fe:Rh crystal

The near-infrared nonvolatile holographic recording has been realized in a doubly doped LiNbO₃:Fe:Rh crystal by the traditional two-center holographic recording scheme, for the first time. The recording performance of this crystal has been investigated by recording with 633 nm red light, 752 nm red light and 799 nm near-infrared light and sensitizing with 405 nm purple light. The experimental results show that, co-doped with Fe and Rh, the near-infrared absorption and the photovoltaic coefficient of shallow trap Fe are enhanced in this LiNbO₃:Fe:Rh crystal, compared with other doubly doped LiNbO₃ crystals such as LiNbO₃:Fe:Mn. It is also found that the sensitizing light intensity affects the near-infrared recording sensitivity in a different way than two-center holographic recording with shorter wavelength, and the origin of experimental results is analyzed.     

Sharpness of Complex Interpolation on $$\alpha $$-Modulation Spaces

In this paper, we solve a long standing problem on the modulation spaces, \(\alpha \)-modulation spaces and Besov spaces. We establish sharp conditions for the complex interpolation between these function spaces. We show that no \(\alpha \)-modulation space \(M_{p,q}^{s,\alpha }\) can be regarded as the interpolation space between \(M_{p_1,q_1}^{s_1,\alpha _1}\) and \(M_{p_2,q_2}^{s_2,\alpha _2}\), unless \(\alpha _1\) is equal to \(\alpha _2\), essentially. Especially, our results show that the \(\alpha \)-modulation spaces can not be obtained by complex interpolation between modulation spaces and Besov spaces.     

L~p ESTIMATES FOR BI-INVARIANT OPERATORS ON CLASSICAL GROUPS

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One-dimensional average on spheres and approximation

In this paper, we consider the approximation of the degeneration of classic average on sphere on Hardy-Sobolev spaces I_λ(H^p) . We prove that the degenerate expression of average on sphere of an L^p function is convergent almost everywhere, and the speed of the approximation depends on λ. And when λ ≥ 2, the approximation of the average operator will be saturated. On the other hand, we also study the generalization of the average on the product of Hardy-Sobolev spaces.     

Derivative estimates of averaging opera tors and extension

We study the derivative operator of the generalized spherical mean S^γt. By considering a more general multiplier m^Ωγ,b=Vn-2/2+γ(|ξ|)|ξ|^bΩ(ξ') and finding the smallest γ such that m^Ωγ,b is an Hp multiplier, we obtain the optimal range of exponents (γ,β,p)to ensure the H^p(R^n) boundedness of a^βS^γ1f(x). As an application, we obtain the derivative estimates for the solution for the Cauchy problem of the wave equation on H^p(R^n) spaces.     

Herz-type Hardy spaces on Vilenkin groups and their applications

Let 1＜q＜∞, 1-1/q≤α＜∞, 0＜p＜∞ and G be a locally compact Vilenkin group.The authors first introduce the general Herz-type Hardy spaces HKα,pq(G) and hKα,pq(G), then present the central atom or the central block and atom decompositions of these spaces. Using this characterization, they discuss some properties of these spaces and investigate the boundedness on the spaces HKα,pq(G) of the fractional integral operators and the boundedness on the spaces hKα,pq(G) of the pseudo-differential operators of order zero.     

（Ce，Cu）：LiNbO3晶体非挥发全息记录理论研究与优化

根据双中心带输运模型，对（Ce，Cu）：LiNbO3晶体双中心非挥发全息记录进行了理论研究与优化。推导了（Ce，Cu）：LiNbO3晶体的微观参量，采用数值方法通过严格求解模拟双中心带输运方程来模拟全息记录过程。分析了记录过程中，记录与敏化光强、Ce和Cu掺杂浓度以及晶体微观参量对（Ce，Cu）：LiNbO3晶体双中心全息记录的影响。发现（Ce，Cu）：LiNbO3晶体非挥发全息记录中实现高衍射效率与固定效率的主导因素是深中心Cu，在记录过程中，深中心Cu建立起了很强的空间电荷场。数值模拟的结果经过实验验证，最高饱和与固定衍射效率别为60．5％和53．8％。     

金属凝固过程界面换热系数的Tikhonov正则化辨识

金属凝固过程中,铸件与铸型间的界面换热系数是数值模拟所必需的边界条件之一.充分考虑非线性瞬态热传导过程测温数据的误差特点,根据Tikhonov正则化理论,构造合适的正则化泛函,利用Arcangeli准则和Morozov偏差原理确定正则参数,采用灵敏度系数和Newton-Raphson迭代法求解该泛函.具体的案例分析表明,该方法克服了热传导反问题的不适定性,能够保证辨识结果的稳定性和精度.与其他方法相比,随着测温误差的增大,该方法具有较高的辨识精度.