Analysis on intersections between fractures by parallel computation

The discrete fracture network model is a powerful tool for fractured rock mass fluid flow simulations and supports safety assessments of coal mine hazards such as water inrush.Intersection analysis,which identifies all pairs of intersected fractures(the basic components composing the connectivity of a network),is one of its crucial procedures.This paper attempts to improve intersection analysis through parallel computing.Considering a seamless interfacing with other procedures in modeling,two algorithms are designed and presented,of which one is a completely independent parallel procedure with some redundant computations and the other is an optimized version with reduced redundancy.A numerical study indicates that both of the algorithms are practical and can significantly improve the computational performance of intersection analysis for large-scale simulations.Moreover,the preferred application conditions for the two algorithms are also discussed.

Short-duration transient visual evoked potentials and color reflectivity discretization analysis in glaucoma patients and suspects

AIM： To evaluate the use of short-duration transient visual evoked potentials（VEP） and color reflectivity discretization analysis（CORDA） in glaucomatous eyes,eyes suspected of having glaucoma,and healthy eyes.METHODS： The study included 136 eyes from 136 subjects： 49 eyes with glaucoma,45 glaucoma suspect eyes,and 42 healthy eyes.Subjects underwent Humphrey visual field（VF） testing,VEP testing,as well as peripapillary retinal nerve fiber layer optical coherence tomography imaging studies with post-acquisition CORDA applied.Statistical analysis was performed using means and ranges,ANOVA,post-hoc comparisons using Turkey＇s adjustment,Fisher＇s Exact test,area under the curve,and Spearman correlation coefficients.RESULTS： Parameters from VEP and CORDA correlated significantly with VF mean deviation（MD）（P〈0.05）.In distinguishing glaucomatous eyes from controls,VEP demonstrated area under the curve（AUC） values of 0.64-0.75 for amplitude and 0.67-0.81 for latency.The CORDA HR1 parameter was highly discriminative for glaucomatous eyes vs controls（AUC=0.94）.CONCLUSION： Significant correlations are found between MD and parameters of short-duration transient VEP and CORDA,diagnostic modalities which warrant further consideration in identifying glaucoma characteristics.

MULTI-PARAMETER HARDY SPACES VIA DISCRETE LITTLEWOOD-PALEY THEORY

In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces HP（Rn1× … ×Rnk） of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive the boundedness of singular integral operators onHP（Rn1× … ×Rnk） and fromHP（Rn1× … ×Rnk）toLP（Rn1× … ×Rnk）.

Noise reduction in LOS wind velocity of Doppler lidar using discrete wavelet analysis

The line of sight (LOS) wind velocity can be determined from the incoherent Doppler lidar backscattering signals. Noise and interference in the measurement greatly degrade the inversion accuracy. In this paper, we apply the discrete wavelet denoising method by using biorthogonal wavelets and adopt a distance-dependent thresholds algorithm to improve the accuracy of wind velocity measurement by incoherent Doppler lidar. The noisy simulation data are processed and compared with the true LOS wind velocity. The results are compared by the evaluation of both the standard deviation and correlation coefficient. The results suggest that wavelet denoising with distance-dependent thresholds can considerably reduce the noise and interfering turbulence for wind lidar measurement.

Convex Analysis and Duality over Discrete Domains

The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.

Singular Integrals and Weighted Triebel-Lizorkin and Besov Spaces of Arbitrary Number of Parameters

Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon＇s identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe＇s covering lemma in multiparameter setting.

Multi-parameter Triebel-Lizorkin and Besov Spaces Associated with Flag Singular Integrals

Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.

Influence of Features of Interphase Boundaries on Mechanical Properties and Fracture Pattern in Metal-Ceramic Composites

The results of a theoretical study on the influence of strength of interphase boundaries in metal-ceramic composite on macroscopical characteristics of composite response such as strength, deformation capacity, fracture energy and fracture pattern are presented. The study was conducted by means of computer-aided simulation by means of movable cellular automaton method taking account of a developed ＂mesoscopical＂ structural model of particle-reinforced composite. The strength of interphase boundaries is found to be a key structural factor determining not only the strength properties of metal-ceramic composite, but also the pattern and rate of fracture. The principles for achievement of the high-strength values of particle/binder interfaces in the metal-ceramic composition due to the formation of the wide transition zones （areas of variable chemical composition） at the interphase boundaries are discussed. Simulation results confirm that such transition zones provide a change in fracture mechanism and make the achievement of a high-strength and a high deformation capacity of metal-ceramic composite possible.

The CalderSn-Zygmund Decomposition and Interpolation on Weighted Hardy Spaces

We apply discrete Littlewood Paley Stein theory, developed by Han and Lu, to establish Calderon Zygmund decompositions and interpolation theorems on weighted Hardy spaces Hp for w C A∞ in both the one-parameter and two-parameter cases.