UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR OF ANY ORDER

Let Ω be a connected bounded domain in R^n. Denote by λi the i-th eigenvalue of the Lapla^ian operator with any order p：{u=Эn→^-Эu=…=Эn→p-1^-Эp-1u=0 on ЭΩ （-△）pu=λu in Ω.In this article, we give some expressions for upper bound of the （k ＋ 1）-th eigenvalue ）λk＋l in terms of the first k eigenvalues.

Cyber-Physical Systems as General Distributed Parameter Systems:Three Types of Fractional Order Models and Emerging Research Opportunities

Cyber-physical systems(CPSs) are man-made complex systems coupled with natural processes that, as a whole,should be described by distributed parameter systems(DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.

Multi Object Tracking Using Gradient-Based Learning Model in Video-Surveillance

On accomplishing an efficacious object tracking,the activity of an object concerned becomes notified in a forthright manner.An accurate form of object tracking task necessitates a robust object tracking procedures irrespective of hardware assistance.Such approaches inferred a vast computational complexity to track an object with high accuracy in a stipulated amount of processing time.On the other hand,the tracking gets affected owing to the existence of varied quality diminishing factors such as occlusion,illumination changes,shadows etc.,In order to rectify all these inadequacies in tracking an object,a novel background normalization procedure articulated on the basis of a textural pattern is proposed in this paper.After preprocessing an acquired image,employment of an Environmental Succession Prediction algorithm for discriminating disparate background environment by background clustering approach have been accomplished.Afterward,abstract textural characterizations through utilization of a Probability based Gradient Pattern(PGP)approach for recognizing the similarity between patterns obtained so far.Comparison between standardized frame obtained in prior and those processed patterns detects the motion exposed by an object and the object concerned gets identified within a blob.Hence,the system is resistant towards illumination variations.These illumination variation was interpreted in object tracking residing within a dynamic background.Devised approach certainly outperforms other object tracking methodologies like Group Target Tracking(GTT),Vi PER-GT,grabcut,snakes in terms of accuracy and average time.Proposed PGP-based pattern texture analysis is compared with Gamifying Video Object(GVO)approach and hence,it evidently outperforms in terms of precision,recall and F1 measure.

SEMILINEAR ELLIPTIC EQUATIONS ON FRACTAL SETS

In this article, the authors consider a class of semilinear elliptic equations on fractal sets under some new conditions, which are more weaker than those in usual cases. The authors get the non-trivial and non-negative solution of the zero boundary Dirichlet problem using Mountain Pass Lemma.

Weighted Marginal Fisher Analysis with Spatially Smooth for aircraft recognition

Due to limitations to extract invariant features for recognition when the aircraft presents various poses and lacks enough samples for training, a novel algorithm called Weighted Marginal Fisher Analysis with Spatially Smooth （WMFA-SS） for extracting invariant features in aircraft rec- ognition is proposed. According to the Graph Embedding （GE） framework, Heat Kernel function is firstly introduced to characterize the interclass separability when choosing the weights of penalty graph. Furthermore, Laplacian penalty is applied to constraining the coefficients to be spatially smooth in this algorithm. Laplacian penalty is able to incorporate the prior information that neigh- boring pixels are correlated. Besides, using a Laplacian penalty can also avoid the singularity of Laplacian matrix of intrinsic graph. Once compact representations of the images are obtained, it can be considered as invariant features and then be performed in classification to recognize different patterns of aircraft. Real aircraft recognition experiments show the superiority of our proposed WMFA-SS in comparison to other GE algorithms and the current aircraft recognition algorithm; the accuracy rate of our proposed method is 90.00% for dataset BH-AIR1.0 and 99.25% for dataset BH-AIR2.0.

On Triangular Lattice Boltzmann Schemes for Scalar Problems

We propose to extend the d’Humi`eres version of the lattice Boltzmann scheme to triangular meshes.We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be constant.On such meshes,it is possible to define the lattice Boltzmann scheme as a discrete particle method,without need of finite volume formulation or Delaunay-Voronoi hypothesis for the lattice.We test this idea for the heat equation and perform an asymptotic analysis with the Taylor expansion method for two schemes named D2T4 and D2T7.The results show a convergence up to second order accuracy and set new questions concerning a possible super-convergence.

Fine edge detection in single-pixel imaging

Typical single-pixel imaging techniques for edge detection are mostly based on first-order differential edge detection operators.In this paper,we present a novel edge detection scheme combining Fourier single-pixel imaging with a second-order Laplacian of Gaussian(LoG)operator.This method utilizes the convolution results of an LoG operator and Fourier basis patterns as the modulated patterns to extract the edge detail of an unknown object without imaging it.The simulation and experimental results demonstrate that our scheme can ensure finer edge detail,especially under a noisy environment,and save half the processing time when compared with a traditional first-order Sobel operator.