In this paper certain classes of meromorphic functions in punctured unit disk are defined. Some properties including coefficient inequalities, convolution and other results are investigated.

This paper considers approximately sparse signal and low-rank matrix’s recovery via
truncated norm minimization min_x ∥xT ∥q and min_X ∥XT ∥Sq from noisy measurements. We first
introduce truncated sparse approximation property, a more general robust null space property,
and establish the stable recovery of signals and matrices under the truncated sparse approximation
property. We also explore the relationship between the restricted isometry property
and truncated sparse approximation property. And we also prove that if a measurement matrix
A or linear map A satisfies truncated sparse approximation property of order k, then the first
inequality in restricted isometry property of order k and of order 2k can hold for certain different
constants δk and δ2k, respectively. Last, we show that if δ_{s(k+jTcj)} <\sqrt{(s - 1)/s} for some
s ≥ 4/3, then measurement matrix A and linear map A satisfy truncated sparse approximation
property of order k. It should be pointed out that when T^c =\Phi, our conclusion implies that
sparse approximation property of order k is weaker than restricted isometry property of order sk.

In this paper, we consider a Cauchy problem of the time fractional diffusion equation
(TFDE) in x ∈ [0,L]. This problem is ubiquitous in science and engineering applications. The illposedness
of the Cauchy problem is explained by its solution in frequency domain. Furthermore,
the problem is formulated into a minimization problem with a modified Tikhonov regularization
method. The gradient of the regularization functional based on an adjoint problem is deduced
and the standard conjugate gradient method is presented for solving the minimization problem.
The error estimates for the regularized solutions are obtained under Hp norm priori bound
assumptions. Finally, numerical examples illustrate the effectiveness of the proposed method.

In this paper, combining the threshold technique, we reconstruct Nadaraya-Watson estimation using Gamma asymmetric kernels for the unknown jump intensity function of a diffusion process with finite activity jumps. Under mild conditions, we obtain the asymptotic normality for the proposed estimator. Moreover, we have verified the better finite-sampling properties such as bias correction and efficiency gains of the underlying estimator compared with other nonparametric estimators through a Monte Carlo experiment.

Shape correspondence between semantically similar organic shapes with large shape variations is a difficult problem in shape analysis. Since part geometries are no longer similar, we claim that the challenge is to extract and compare prominent shape substructures, which are recurring part arrangements among semantically related shapes. Our main premise is that the challenge can be solved more efficiently on curve skeleton graphs of shapes, which provide a concise abstraction of shape geometry and structure. Instead of directly searching exponentially many skeleton subgraphs, our method extracts the intrinsic reflectional symmetry axis of the skeleton to guide the generation of subgraphs as part arrangements. For any two subgraphs from two skeletons, their orientations are aligned and their pose variations are normalized for matching. Finally, the matchings of all subgraph pairs are evaluated and accumulated to the skeletal feature node correspondences. The comparison results with the state-of-the-art work show that our method significantly improves the efficiency and accuracy of the semantic correspondence between a variety of shapes.

In isogeometric analysis, it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches, such as trimmed surfaces. In this paper, we develop a Gregory solid based method to parameterize those models. First, we extend the Gregory patch representation to the trivariate Gregory solid representation. Second, the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model, thus generating the polyhedral volume parametrization. To improve the regularity of the polyhedral volume parametrization, we formulate the construction of the trivariate Gregory solid as a sparse optimization problem, where the optimization objective function is a linear combination of some terms, including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid. Then, the alternating direction method of multipliers (ADMM) is used to solve the sparse optimization problem. Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.

The online customer reviews provide important information for product improvement and redesign. However, many reviews are redundant with only several short sentences, which may even conflict with each other on the same aspect of a product. Thus it is usually a very challenging task to extract useful design information from the reviews and provide a clear description on the product’s various aspects amongst its competitors. In order to resolve this issue, we propose an approach to build hierarchical product profiles to describe a product’s kernel design aspects quantitatively. It is achieved via three main strategies: a double propagation strategy to achieve the associated features and customers’ descriptions; a deep text processing network to build the aspect hierarchy; an aspect ranking approach to quantify each kernel design aspect. Experimental results validate the effectiveness of the proposed approach on online reviews.