Relationship Between MP and DPP for the Stochastic Optimal Control Problem of Jump Diffusions

This paper is concerned with the stochastic optimal control problem of jump diffusions. The relationship between stochastic maximum principle and dynamic programming principle is discussed. Without involving any derivatives of the value function, relations among the adjoint processes, the generalized Hamiltonian and the value function are investigated by employing the notions of semijets evoked in defining the viscosity solutions. Stochastic verification theorem is also given to verify whether a given admissible control is optimal.     

On existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system

By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system. Some well-known results in the literature are generalized and improved. An example is presented to illustrate the application of our main result.     

A characteristic-mixed finite element method for time-dependent convection-diffusion optimal control problem

In this paper, we examine the method of characteristic-mixed finite element for the approximation of convex optimal control problem governed by time-dependent convection-diffusion equations with control constraints. For the discretization of the state equation, the characteristic finite element is used for the approximation of the material derivative term (i.e., the time derivative term plus the convection term), and the lowest-order Raviart-Thomas mixed element is applied for the approximation of the diffusion term. We derive some a priori error estimates for both the state and control approximations.     

近红外光谱快速检测丙氨酸氨基转移酶

在探讨近红外光谱快速检测丙氨酸氨基转移酶的可行性过程中,首先对不同厚度(0.5,1,2和4mm)血液样品的近红外透射光谱进行了分析.发现全血样品0.5 mm厚时的近红外透射光谱更适合于进行光谱分析.进而采集了176个全血样品0.5 mm厚时的近红外光谱.对采集的光谱进行多元散射校正、二阶微分法光谱预处理后,采用逐步多元线性回归和偏最小二乘回归方法建立定量分析模型,预测了全血丙氨酸氨基转移酶的含量.结果表明:利用近红外光谱法测定丙氨酸氨基转移酶时,采用偏最小二乘回归方法建立的定标模型预测效果最好,定标相关系数、定标标准差和预测标准差的值分别为:0.98,2.42和7.22.     

Simultaneous nonvanishing of automorphic L-functions at the central point

Let g be a holomorphic Hecke eigenform and {u _j } an orthonormal basis of even Hecke?CMaass forms for ${\textup{SL}(2,\mathbb{Z})}$ . Denote L(s, g × u _j ) and L(s, u _j ) the corresponding L-functions. In this paper, we give an asymptotic formula for the average of ${L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)}$ , from which we derive that there are infinitely many u _j ??s such that ${L(\frac{1}{2},g\times u_j)L(\frac{1}{2},u_j)\neq0}$ .     

Integral points on quadrics with prime coordinates

Let f (x ₁, . . . , x _s ) be a regular indefinite integral quadratic form, and t an integer. Denote by V the affine quadric {x : f (x) = t}, and by \({V(\mathbb {P})}\) the set of \({{\bf x}\in V}\) whose coordinates are simultaneously prime. It is proved that, under suitable conditions, \({V(\mathbb{P})}\) is Zariski dense in V as long as s ≥ 10.     

D-spaces and thick covers

The following results are obtained.

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An open neighbornet U of X has a closed discrete kernel if X has an almost thick cover by countably U-close sets.

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Every hereditarily thickly covered space is aD and linearly D.

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Every t-metrizable space is a D-space.

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X is a D-space if X has a cover {Xα:α<λ} by D-subspaces such that, for each β<λ, the set ?{Xα:α<β} is closed.

     

Bragg gratings in rectangular microfiber for temperature independent refractive index sensing

We present fiber Bragg grating fabricated in rectangular microfiber for temperature-independent refractive index (RI) measurement. The grating has two Bragg peaks due to the high geometrical birefringence of the rectangular microfiber. The two peaks present different RI responses because the modes along the orthogonal polarizations have different energy fractions in terms of evanescent field outside the silica microfiber and hence the light/liquid interaction strength are different. In contrast, they exhibit identical temperature sensitivities because most mode energy is confined in the microfiber and the thermal-optic effect of silica dominantly determines the temperature response. As a result, temperature-independent RI sensing can be realized by monitoring the wavelength separation between the two peaks.     

Synthesis and characterization of core-shell structured SiO2@YVO4:Yb,Er microspheres

In this paper, the core-shell structured SiO₂@YVO₄:Yb³⁺,Er³⁺ microspheres have been successfully prepared via a facile sol-gel process followed by a heat treatment. X-ray diffraction, field emission scanning electron microscopy, energy disperse X-ray spectroscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, and photoluminescence spectra were used to characterize the samples. The results reveal that the SiO₂ spheres have been successfully coated by YVO₄:Yb³⁺,Er³⁺ phosphors to form core-shell structures and the size of obtained microspheres has a uniform distribution. Additionally, the samples exhibit bright green luminescence under the excitation of a 980 nm laser diode. The photoluminescence intensity increases with the number of coatings. These core-shell structured SiO₂@YVO₄:Yb³⁺,Er³⁺ microspheres may have great potential in the fields of infrared detection and display devices.