Generalized super Gabor duals with bounded invertible operators

In this paper, we introduce generalized super Gabor duals with bounded invertible operators by combining ideas concerning super Gabor frames with the idea of g-duals as proposed by Dehgham and Fard in 2013. Given a super Gabor frame and a bounded invertible operator A, we characterize its generalized super Gabor duals with A, and derive a parametric expression of all its generalized super Gabor duals with A. The perturbation of generalized super Gabor duals is considered as well.     

Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach

We consider an estimating equations approach to parameter estimation in adaptive varying-coefficient linear quantile model. We propose estimating equations for the index vector of the model in which the unknown nonparametric functions are estimated by minimizing the check loss function, resulting in a profiled approach. The estimating equations have a bias-corrected form that makes undersmoothing of the nonparametric part unnecessary. The estimating equations approach makes it possible to obtain the estimates using a simple fixed-point algorithm. We establish asymptotic properties of the estimator using empirical process theory, with additional complication due to the nuisance nonparametric part. The finite sample performance of the new model is illustrated using simulation studies and a forest fire dataset.     

Kadison-Singer代数研究综述

回顾了建立KS-代数的研究背景,系统介绍了KS-代数的定义和性质以及超有限KS-代数、非超有限KS-代数、KS-格的构造和强KS-代数的研究结果,同时分析了KS-代数和经典的不变子空间、Kadison可迁代数、von Neumann代数生成元等问题之间的联系;讨论了非自伴代数的运算,给出了两种不同构造非自伴代数的运算法则;在此基础上,提出了未来学科发展有待研究的16个问题.     

Rainbow k-connectivity of Random Bipartite Graphs

Acta Mathematicae Applicatae Sinica, English Series - A path in an edge-colored graph G is called a rainbow path if no two edges of the path are colored the same color. The minimum number of colors...     

Iterative reweighted methods for $$\ell _1-\ell _p$$ minimization

In this paper, we focus on the \(\ell _1-\ell _p\) minimization problem with \(0<p<1\), which is challenging due to the \(\ell _p\) norm being non-Lipschizian. In theory, we derive computable lower bounds for nonzero entries of the generalized first-order stationary points of \(\ell _1-\ell _p\) minimization, and hence of its local minimizers. In algorithms, based on three locally Lipschitz continuous \(\epsilon \)-approximation to \(\ell _p\) norm, we design several iterative reweighted \(\ell _1\) and \(\ell _2\) methods to solve those approximation problems. Furthermore, we show that any accumulation point of the sequence generated by these methods is a generalized first-order stationary point of \(\ell _1-\ell _p\) minimization. This result, in particular, applies to the iterative reweighted \(\ell _1\) methods based on the new Lipschitz continuous \(\epsilon \)-approximation introduced by Lu (Math Program 147(1–2):277–307, 2014), provided that the approximation parameter \(\epsilon \) is below a threshold value. Numerical results are also reported to demonstrate the efficiency of the proposed methods.     

Dynamical behaviors for 1D compressible Navier-Stokes equations with density-dependent viscosity

The dynamical behaviors of vacuum states for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefficient are considered. It is first shown that a unique strong solution to the free boundary value problem exists globally in time, the free boundary expands outwards at an algebraic rate in time, and the density is strictly positive in any finite time but decays pointwise to zero time-asymptotically. Then, it is proved that there exists a unique global weak solution to the initial boundary value problem when the initial data contains discontinuously a piece of continuous vacuum and is regular away from the vacuum. The solution is piecewise regular and contains a piece of continuous vacuum before the time T_∗>0, which is compressed at an algebraic rate and vanishes at the time T_∗, meanwhile the weak solution becomes either a strong solution or a piecewise strong one and tends to the equilibrium state exponentially.     

基于混合物理论的非饱和土的热-水-力耦合分析模型Ⅰ

以混合物理论为基础研究了非饱和土的热-水-力多场耦合问题.将非饱和土视为由土骨架、液态水、水蒸气、干燥气体及溶解气体共5种组分构成的混合物,在组分的质量、动量守恒方程及整体能量守恒方程的基础上,引入了37个补充方程以形成封闭方程组.其中,利用水与水蒸气的化学势改变量相同,推导了在气压力变化条件下水与水蒸气相变平衡所满足的限制方程.最终控制方程以增量形式给出,6个方程求解6个未知量(3个土骨架位移、水压力、气压力及温度),充分反映了热膨胀、热渗流、水的相变、气体溶解及土骨架变形等多种现象的耦合过程.     

Permanence and Global Attractivity of a Discrete Semi-Ratio-Dependent Predator-Prey System with Holling Ⅳ Type Functional Response

In this paper,we investigate a discrete semi-ratio dependent predator-prey system with Holling IV type functional response.For general nonautonomous case,sufficient conditions which ensure the permanence and the global stability of the system are obtained.Meanwhile,we discuss the existence of the positive periodic solution and global stability of the system.     

Effect of structure and thermodynamic stability on the response of lanthanide stannate pyrochlores to ion beam irradiation

The lanthanide stannates, Ln2Sn2O7, Ln=La-Lu and Y, have the isometric pyrochlore structure, A2B2O7, and their structural properties have been refined by Rietveld analysis of powder neutron and synchrotron X-ray diffraction data. In this study, the enthalpies of formation of selected stannate pyrochlores, Ln=La, Nd, Sm, Eu, Dy, and Yb, were measured by high-temperature oxide melt solution calorimetry. Their radiation response was determined by 1 MeV Kr2+ ion irradiation combined with in situ TEM observation over the temperature range of 25 to 1000 K. The enthalpy of formation from binary oxides of stannate pyrochlores became more endothermic (from -145 to -40 kJ/mol) as the size of the lanthanide in the A-site decreases. A more exothermic trend of the enthalpy of formation was observed in stannate pyrochlores with larger lanthanide ions, particularly La, possibly as a result of increased covalency in the Sn-O bond. In contrast to lanthanide titanate pyrochlores, Ln2Ti2O7, that are generally susceptible to radiation-induced amorphization and zirconate pyrochlores, Ln2Zr2O7, that are generally resistant to radiation-induced amorphization, the lanthanide stannate pyrochlores show a much greater variation in their response to ion irradiation. La, Nd, and Gd stannates experience the radiation-induced transformation to the aperiodic state, and the critical amorphization temperatures are approximately 960, 700, and 350 K, respectively. Y and Er stannate pyrochlores cannot be amorphized by ion beam irradiation, even at 25 K, and instead disorder to a defect fluorite structure. Comparison of the calorimetric and ion irradiation data for titanate, zirconate, and stannate pyrochlores reveals a strong correlation among subtle changes in crystal structure with changing composition, the energetics of the disordering process, and the temperature above which the material can no longer be amorphized. In summary, as the structure approaches the ideal, ordered pyrochlore structure, radiation-induced amorphization is more easily attained. This is consistent with an increasingly exothermic trend in the enthalpies of formation of pyrochlores from the oxides, that is, the greater the thermochemical stability of the pyrochlore structure, the more likely it will be amorphized upon radiation damage rather than recover to a disordered fluorite structure.     

Separation of heart rate variability components of the autonomic nervous system by utilizing principal dynamic modes

This work introduces a modified Principal Dynamic Modes (PDM) methodology using eigenvalue/eigenvector analysis to separate individual components of the sympathetic and parasympathetic nervous contributions to heart rate variability. We have modified the PDM technique to be used with even a single output signal of heart rate variability data, whereas the original PDMs required both input and output data. This method specifically accounts for the inherent nonlinear dynamics of heart rate control, which the current method of power spectrum density (PSD) is unable to do. Propranolol and atropine were administered to normal human volunteers intravenously to inhibit the sympathetic and parasympathetic activities, respectively. With separate applications of the respective drugs, we found a significant decrease in the amplitude of the waveforms that correspond to each nervous activity. Furthermore, we observed near complete elimination of these dynamics when both drugs were given to the subjects. Comparison of our method to the conventional low/high frequency ratio of PSD shows that PDM methodology provides much more accurate assessment of the autonomic nervous balance by separation of individual components of the autonomic nervous activities. The PDM methodology is expected to have an added benefit that diagnosis and prognostication of a patient's health can be determined simply via a non-invasive electrocardiogram.