Hyperbolic smoothing and penalty techniques applied to molecular structure determination

This work considers the problem of estimating the relative positions of all atoms of a protein, given a subset of all the pair-wise distances between the atoms. This problem is NP-hard, and the usual formulations are nonsmoothed and nonconvex, having a high number of local minima. Our contribution is an efficient method that combines the hyperbolic smoothing and the penalty techniques that are useful in obtaining differentiability and reducing the number of local minima.     

含距离位势的拟线性椭圆方程解的存在性

变分原理证明了一类含距离位势的拟线性椭圆方程齐次Dirichlet边界条件下第一特征值问题的可解性.进一步,利用临界点理论得到了一类含距离位势的非线性椭圆方程非平凡解的存在性.     

Segregation characteristics of irregular binaries in gas solid fluidized beds—An ANN-approach

Binary mixtures of irregular materials of different particle sizes and/or particle densities are fluidized in a 15-cm diameter column with a perforated plate distributor. An attempt has been made in this work to determine the segregation characteristics of jetsam particles for both the homogeneous and heterogeneous binary mixtures in terms of segregation distance by correlating it to the various system parameters, viz. initial static bed height, height of a layer of particles above the bottom grid, superficial gas velocity and average particle size and/or particle densities of the mixture through the dimensional analysis. Correlation on the basis of Artificial Neural Network approach has also been developed with the above system parameters thereby authenticating the development of correlation by the former approach. The calculated values of the segregation distance obtained for both the homogeneous and heterogeneous binary mixtures from both the types of ftuidized beds （i.e. under the static bed condition and the ftuidized bed condition） have also been compared with each other.     

Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems

We use the homology groups of the path space of an arbitrary Riemannian manifold to define some analogs of the distance function and study their main properties. For the natural systems with gyroscopic forces we prove an existence theorem for solutions to the two-point boundary value problem, which complements the results of [1]. We apply the geodesic modeling method of [1, 2], using the generalized distance functions.     

On the distance function of a connected graph

An axiomatic characterization of the distance function of a connected graph is given in this note. The triangle inequality is not contained in this characterization.     

Radio number for trees

Let G be a connected graph with diameter diam(G). The radio number for G, denoted by rn(G), is the smallest integer k such that there exists a function f:V(G)→{0,1,2,…,k} with the following satisfied for all vertices u and v: |f(u)-f(v)|?diam(G)-d_G(u,v)+1, where d_G(u,v) is the distance between u and v. We prove a lower bound for the radio number of trees, and characterize the trees achieving this bound. Moreover, we prove another lower bound for the radio number of spiders (trees with at most one vertex of degree more than two) and characterize the spiders achieving this bound. Our results generalize the radio number for paths obtained by Liu and Zhu.     

基于数学方法的不完全投影数据估计

主要对不完全投影图像恢复问题中不完全投影数据进行了研究.对于投影数据不完全时,运用线性插值法和样条插值法在角度缺失的地方进行数据估计.最后通过仿真实验,将得到的估计投影图像与原始投影图像进行比较并分析.实验结果表明:在恢复投影图像的过程当中,采用线性插值误差更小,恢复的投影图像的精度更高,并且恢复速度快.     

Detection range modeling of blue whale calls in Southwestern Indian Ocean

In the Southwestern Indian Ocean, one year of continuous acoustic data from calibrated hydrophones maintained by the International Monitoring System provided data on blue whale calls from two subspecies Antarctic and pygmy blue whales. Using an automatic detection method with a fixed threshold, both call types were detected and received levels were measured for each detected call. By using a parabolic equation loss model configured with the precise characteristics of the biological source, hydroacoustic station, and environment in the study area, distances at which calls could be detected were estimated. These methods were used to define the maximum detection range around each array of hydrophones and the influence of the seasonal variation of the ambient noise and sound velocity on the detection ranges. Results showed that detection ranges were critically dependent on the choice of the biological source’s input parameters, including frequency bandwidth and source level. Over the course of the year, detection distances were different for both subspecies; the pygmy blue whale seemed to be consistently closer to the station than the Antarctic blue whale. The distribution of the estimated distances confirmed the presence of both subspecies of blue whales near the Crozet Islands showing the importance of this sub-Antarctic area for these endangered species, especially during the austral summer feeding season.     

Segregation characteristics of irregular binaries in gas solid fluidized beds——An ANN-approach

Binary mixtures of irregular materials of different particle sizes and/or particle densities are fluidized in a 15-cm diameter column with a perforated plate distributor. An attempt has been made in this work to determine the segregation characteristics of jetsam particles for both the homogeneous and heterogeneous binary mixtures in terms of segregation distance by correlating it to the various system parameters, viz. initial static bed height, height of a layer of particles above the bottom grid, superficial gas velocity and average particle size and/or particle densities of the mixture through the dimensional analysis. Correlation on the basis of Artificial Neural Network approach has also been developed with the above system parameters thereby authenticating the development of correlation by the former approach. The calculated values of the segregation distance obtained for both the homogeneous and heterogeneous binary mixtures from both the types of fluidized beds (i. e. under the static bed condition and the fluidized bed condition) have also been compared with each other.     

On the duality between the profit and the indirect distance functions in production theory

Färe and Primont [3] stated, without proofs, duality results between the profit and the indirect distance functions in production theory. The aim of this note is to state these duality results in precise terms and to prove them.