贝叶斯公式的几个应用

介绍了贝叶斯公式的一些应用实例及分析,以使在教学中能帮助学生更深入地理解该公式.     

Optical multi-image encryption based on frequency shift

We present a novel multi-image encryption and decryption algorithm based on Fourier transform and fractional Fourier transforms. Lower frequency parts of the original images are selected, frequency shifted and encrypted by using double phase encoding in fractional Fourier domains. Multiple images are encrypted together into a single one. A simple optical setup is given to implement the proposed algorithm. This scheme has features of enhancement in decryption accuracy and high optical efficiency. Numerical results have been given to verify the validity and efficiency of the proposed scheme.     

Effects of geometrical symmetry on the vortex in mesoscopic superconductors

We first systematically study the multivortex states in mesoscopic superconductors via self-consistent Bogoliubov-de Gennes equations. Our work focuses on how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors and find that the key parameter determining the entrance of the vortex is the current density at the hot spots on the edge of sample. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconductors with their topological geometries, and they can be easily generalized to the confined superfluids and Bose-Einstein condensates.     

Diffusion interaction and quantitative analysis of zinc dialkyldithiophosphate content in lube base oils in terahertz regime

We investigate the diffusion interaction and quantitative analysis of zinc dialkyldithiophosphate (ZDDP) mixed with lube base oil (LBO) at different concentrations using terahertz time-domain spectroscopy (THzTDS).When the concentration exceeds 6.78%,the characteristic absorption peaks exhibit significantly shift,and the absorption coefficient peak value is nonlinear against concentration.Moreover,the absorption coefficients of mixed samples follow the Beer’s law at a concentration below 6.78%.The quantitative analysis enables a strategy for monitoring the formulation of lubricating oil in real time.     

Spin-glass behavior and magnetocaloric effect in melt-spun TbCuAl alloys

Magnetic properties and magnetocaloric effects of amorphous and crystalline TbCuAl ribbons are investigated by measuring their ac susceptibilities including a nonlinear term and dc magnetizations. The in-phase third harmonic ac susceptibility is found to be negative. It can be well fitted by the expression at high temperatures, indicating a spin-glass behavior in amorphous TbCuAl alloy. ΔT_f(ω)/[T_f(ω)Δlog₁₀ω], a possible distinguishing criterion to judge the presence of a spin-glass behavior is ∼0.011. The frequency-dependent data can be well fitted by the conventional critical slowing down law and the spin-glass transition temperature is obtained to be 20.1 K. The maximum of magnetic entropy change reaches 4.5 J kg⁻¹ K⁻¹ for a field change of 0-50 000 Oe, while the crystalline TbCuAl compound experiences a simple ferromagnetic-to-paramagnetic phase transition. The peak value of magnetic entropy change is obtained at the Curie temperature and reaches 14.4 J kg⁻¹ K⁻¹ for the same field change, which is much larger than that of amorphous TbCuAl alloy.     

Facile synthesis of SERS active Ag nanoparticles in the presence of tri-n-octylphosphine sulfide

A facile and novel way was reported here for the synthesis of hydrophobic Ag nanoparticles (NPs), using AgNO₃, tri-n-octylphosphine (TOP) and sulfur (S) powder in process. TOP was used as solvent, reducing agent and stabilizer. S could chelate with excessive TOP to form trioctylphosphine sulfide (TOPS), which served as second capping agent. The hydrophobic Ag NPs could be transformed into hydrophilic state through ligand exchange. Furthermore, surface-enhanced Raman scattering (SERS) spectra of 4-aminothiophenol (4-ATP) were obtained on the hydrophobic and hydrophilic Ag NPs modified substrates, indicating that the as-synthesized Ag NPs had great potential for high sensitive optical detection applications.     

傅里叶变换中红外光谱法检测脑膜瘤的研究

采用傅里叶变换衰减全反射中红外光谱法检测了24例液氮冻存的脑膜瘤离体样品(其中良性肿瘤12例,有恶性倾向的肿瘤12例),对得到的红外光谱进行整理分析,发现不同类型脑膜瘤组织(如纤维型脑膜瘤和内皮型脑膜瘤)的红外光谱存在着差异,并且同一种类型的脑膜瘤组织,其恶性倾向的程度不同,他们的红外光谱也表现出较为明显的区别,因此,我们可以从各个特征吸收峰的峰位、峰形及峰强等信息的变化来区分脑膜瘤,并可以初步鉴别脑膜瘤的性质;研究结果发现,通过某些特征吸收峰(如1 160cm-1)峰位的变化来鉴别脑膜瘤的性质与病理诊断结果的符合率大于85%,说明傅里叶变换衰减全反射中红外光谱法有可能发展成为一种对样品无损伤、快速的脑肿瘤诊断新方法。     

Long time behavior of the Fokker-Planck-Boltzmann equation

This paper is devoted to the existence and long time behavior of the global classical solution to Fokker-Planck-Boltzmann equation with initial data near the absolute Maxwellian.     

A class of weighted estimators for additive hazards model in case-cohort studies

Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose＇a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.     

Inhomogeneous Quantum Codes （III）： The Asymmetric Case

The stabilizer （additive） method and non-additive method for constructing asymmetric quantum codes have been established. In this paper, these methods are gen- eralized to inhomogeneous quantum codes.