ASYMPTOTIC FORMULAE FOR BIVARIATE MELLIN CONVOLUTION OPERATORS

In this paper some Voronovskaya approximation formulae for a class of Mellin convolution operators of the type （Twf）（x,y）=∫R^2＋Kw（tx^-1,vy^-1）f（t,v）dtdv/tv are given. Moreover, various examples are discussed.

Hybrid Efficient Convolution Operators for Visual Tracking

Visual tracking is a classical computer vision problem with many applications.Efficient convolution operators(ECO)is one of the most outstanding visual tracking algorithms in recent years,it has shown great performance using discriminative correlation filter(DCF)together with HOG,color maps and VGGNet features.Inspired by new deep learning models,this paper propose a hybrid efficient convolution operators integrating fully convolution network(FCN)and residual network(ResNet)for visual tracking,where FCN and ResNet are introduced in our proposed method to segment the objects from backgrounds and extract hierarchical feature maps of objects,respectively.Compared with the traditional VGGNet,our approach has higher accuracy for dealing with the issues of segmentation and image size.The experiments show that our approach would obtain better performance than ECO in terms of precision plot and success rate plot on OTB-2013 and UAV123 datasets.

On Fatou Type Convergence of Convolution Type Double Singular Integral Operators

In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].

Application of deep learning technique to the sea surface height prediction in the South China Sea

A deep-learning-based method,called ConvLSTMP3,is developed to predict the sea surface heights(SSHs).ConvLSTMP3 is data-driven by treating the SSH prediction problem as the one of extracting the spatial-temporal features of SSHs,in which the spatial features are“learned”by convolutional operations while the temporal features are tracked by long short term memory(LSTM).Trained by a reanalysis dataset of the South China Sea(SCS),ConvLSTMP3 is applied to the SSH prediction in a region of the SCS east off Vietnam coast featured with eddied and offshore currents in summer.Experimental results show that ConvLSTMP3 achieves a good prediction skill with a mean RMSE of 0.057 m and accuracy of 93.4%averaged over a 15-d prediction period.In particular,ConvLSTMP3 shows a better performance in predicting the temporal evolution of mesoscale eddies in the region than a full-dynamics ocean model.Given the much less computation in the prediction required by ConvLSTMP3,our study suggests that the deep learning technique is very useful and effective in the SSH prediction,and could be an alternative way in the operational prediction for ocean environments in the future.

Multi-function terahertz wave manipulation utilizing Fourier convolution operation metasurface

We propose a novel metasurface based on a combined pattern of outer C-shaped ring and inner rectangular ring.By Fourier convolution operation to generating different predesigned sequences of metasurfaces,we realize various functionalities to flexible manipulate terahertz waves including vortex terahertz beam splitting,anomalous vortex terahertz wave deflection,vortex terahertz wave splitting and deflection simultaneously.The incident terahertz wave can be flexibly controlled in a single metasurface.The designed metasurface has an extensive application prospect in the field of future terahertz communication and sensing.

The Cauchy Problem for a Class of Intergrodifferential Equations

The existence, uniqueness of bounded and continuous solutions of a class of integrodifferential equations and some estimates of solutions are established. Applying these results to integrodifferential systems with a small parameter ε>0 , we obtain, in particular, some estimates of solutions uniform in ε.

Perturbation Analysis for Stability of Convolution Dominated Infinite Matrices

Stability of infinite matrices has important applications to spline approximation, wavelets, Gabor time-frequency analysis, etc. In this paper, perturbation analysis for convolution dominated infinite matrices was studied by introducing an idea of lp-stability at infinity. For infinite matrices in the Gohberg-Baskakov-Sjostrand class, a practical criterion for the lp-stability at infinity of convolution dominated infinite matrices on Zd under perturbation of compact operators was given.

Strongly Singular Convo1ution Operators on the Weighted Herz-Type Hardy Spaces

Let 0【p≤1q【0, and w1, w2 ∈A1 （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqα,p（w1; w2） to the homogeneous weighted Herz spaces Kqα,p（w1;w2）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqα,p（w1, w2） is also investigated.

Convolution Operators on H^p(H_k^n)

Let G=Hkn be the（2n+1）-dimensional Heisenberg group over local field K.In this paper we prove some theorems about convolution operators on HP（G）and vector-valued Hardy spaces.As an example,the distribution ∫k*dt/|t| for some ∈S（G）,/∫=0 is a ramified 0-type kernel.These results can be applied to characterize HP（G）spaces by square functions.

The Approximation Theorem of Convolution Operator in △~p Set-valued Function Space

The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space.

A new remaining useful life estimation method for equipment subjected to intervention of imperfect maintenance activities

As the key part of Prognostics and Health Management（PHM）, Remaining Useful Life（RUL） estimation has been extensively investigated in recent years. Current RUL estimation studies considering the intervention of imperfect maintenance activities usually assumed that maintenance activities have a single influence on the degradation level or degradation rate, but not on both.Aimed at this problem, this paper proposes a new degradation modeling and RUL estimation method taking the influence of imperfect maintenance activities on both the degradation level and the degradation rate into account. Toward this end, a stochastic degradation model considering imperfect maintenance activities is firstly constructed based on the diffusion process. Then, the Probability Density Function（PDF） of the RUL is derived by the convolution operator under the concept of First Hitting Time（FHT）. To implement the proposed RUL estimation method,the Maximum Likelihood Estimation（MLE） is utilized to estimate the degradation related parameters based on the Condition Monitoring（CM） data, while the Bayesian method is utilized to estimate the maintenance related parameters based on the maintenance data. Finally, a numerical example and a practical case study are provided to demonstrate the superiority of the proposed method. The experimental results show that the proposed method could greatly improve the RUL estimation accuracy for the degrading equipment subjected to imperfect maintenance activities.

Local Discontinuous-Galerkin Schemes for Model Problems in Phase Transition Theory

Local Discontinuous Galerkin(LDG)schemes in the sense of[5]are a flexible numerical tool to approximate solutions of nonlinear convection problems with complicated dissipative terms.Such terms frequently appear in evolution equations which describe the dynamics of phase changes in e.g.liquid-vapour mixtures or in elastic solids.We report on results for one-dimensional model problems with dissipative terms including third-order and convolution operators.Cell entropy inequalities and L2-stability results are proved for those model problems.As is common in phase transition theory the solution structure sensitively depends on the coupling parameter between viscosity and capillarity.To avoid spurious solutions due to the counteracting effect of artificial dissipation by the numerical flux and the actual dissipation terms we introduce Tadmors’entropy conservative fluxes.Various numerical experiments underline the reliability of our approach and also illustrate interesting and(partly)new phase transition phenomena.