n元等比级数

定义了n元等比数列、n元等比级数,给出了它们的通项公式及前n项和.并解决了多元等比级数的敛散性问题,求出了多元等比级数的和.指出了多元等比数列及多元等比级数在特殊情况下与一元等比数列及一元等比级数的一致性.     

Smaller Output Beam Divergence in the Slowly Opened Q-Switch Operation

The mechanism of the slowly opened Q-switch operation was investigated thoroughly. Maximum energy extraction from the resonator could be optimized, and the smallest output beam divergence could be achieved. In this article, we present a detailed analysis that has numerically verified the mode-selection mechanism in the slowly opened Q-switch operation, and the degree of the smaller output laser beam divergence that has been achieved. The mechanism of the slowly opened Q-switch operation is the inherent advantage of the passive saturable absorber in this operation. We can use the maximum energy extraction and the smallest output beam divergence results of the slowly opened Q-switch operation to design and optimize various passive saturable absorbers: plastic dye sheets, LiF:F₂⁻ color center crystals, Cr4⁺: YAG crystals, RG1000 color glass filters, and the single crystal semiconductor saturable absorber wafers that are in developed in our microchip laser systems.     

Ising-like field theory

A field theory model onR ² in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in of the ground state energy, as 0, without using the cluster expansion.Supported in part by Consiglio Nazionale delle Ricerche.     

Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

A combined approach of Kullback–Leibler divergence and background subtraction for moving object detection in thermal video

In this work, a robust method for moving object detection in thermal video frames has been proposed by including Kullback–Leibler divergence (KLD) based threshold and background subtraction (BGS) technique. A trimmed-mean based background model has been developed that is capable enough to reduce noise or dynamic component of the background. This work assumed that each pixel has normally distributed. The KLD has computed between background pixel and a current pixel with the help of Gaussian mixture model. The proposed threshold is useful enough to classify the state of each pixel. The post-processing step uses morphological tool for edge linking, and then the flood-fill algorithm has applied for hole-filling, and finally the silhouette of targeted object has generated. The proposed methods run faster and have validated over various real-time based problematic thermal video sequences. In the experimental results, the average value of F₁-score, area under the curve, the percentage of correct classification, Matthew’s correlation coefficient show higher values whereas total error and percentage of the wrong classification show minimum values. Moreover, the proposed-1 method achieved higher accuracy and execution speed with minimum false alarm rate that has been compared with proposed-2 as well as considered peer methods in the real-time thermal video.     

固体介质间隔层激光标准具性能的影响因素研究

针对固体介质间隔层的镀膜标准具, 以1 064 nm激光镀膜标准具为例, 首先研究了反射膜堆数对反射带宽、基底厚度以及对自由光谱区的影响:标准具的带宽随着膜层堆数增加而减小, 自由光谱区随着基板厚度的增加而减小;其次研究了基底误差对标准具中心波长定位和透过率的影响, 通过定量数值计算证明了基底误差可通过标准具的使用角度补偿;针对典型的H(LH)^m/Substrate/(HL)^mH和L(LH)^m/Substrate/(HL)^mL两个膜系结构, 研究了入射激光发散角对标准具中心波长偏移、通带半宽度、中心波长透过率和最大透过率的影响。随着激光发散角的增加, 中心波长向短波方向移动, 通带半宽度、中心波长透过率和最大透过率呈现下降的趋势, 并且第二个膜系结构的标准具性能优于第一个膜系结构的标准具。     

Analyzing complex networks evolution through Information Theory quantifiers

A methodology to analyze dynamical changes in complex networks based on Information Theory quantifiers is proposed. The square root of the Jensen-Shannon divergence, a measure of dissimilarity between two probability distributions, and the MPR Statistical Complexity are used to quantify states in the network evolution process. Three cases are analyzed, the Watts-Strogatz model, a gene network during the progression of Alzheimer's disease and a climate network for the Tropical Pacific region to study the El Niño/Southern Oscillation (ENSO) dynamic. We find that the proposed quantifiers are able not only to capture changes in the dynamics of the processes but also to quantify and compare states in their evolution.     

On the development of a triple‐preserving Maxwell's equations solver in non‐staggered grids

We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

On the loss of information due to fuzziness in experimental observations

The absence of exactness in the observation of the outcomes of a random experiment always entails a loss of information about the experimental distribution. This intuitive assertion will be formally proved in this paper by using a mathematical model involving the notions of fuzzy information and fuzzy information system (as intended by Tanaka, Okuda and Asai) and Zadeh's probabilistic definition. On the basis of this model we are first going to consider a family of measures of information enclosing some well-known measures, such as those defined by Kagan, Kullback-Leibler and Matusita, and then to establish methods for removing the loss of information due to fuzziness by increasing suitably the number of experimental observations.