Abstract

We investigate the efficiency of orthogonal super greedy algorithm (OSGA) for sparse recovery and approximation under the restricted isometry property (RIP). We first show that under the RIP conditions of the measurement matrix Φ and the minimum magnitude of the nonzero coordinates of the signal, for l 2 bounded or l ∞ bounded noise vector e, with explicit stopping rules, OSGA can recover the support of an arbitrary K-sparse signal x from y = Φx + e in at most K steps. Then, we investigate the error performance of OSGA in m term approximation with regards to dictionaries satisfying the RIP in a separable Hilbert space. We establish a Lebesgue-type inequality for OSGA. Based on this inequality, we obtain the optimal rate of convergence for the sparse class induced by such dictionaries.

Mastering the creep deformation characteristics of rock under different temperature conditions is of great significance for studying the long-term stability and deformation mechanism of geotechnical engineering. Based on the classical Burgers model, the creep model under different temperature conditions is established by introducing a nonlinear Newton body. The parameters of the creep model are identified and the influence law of different parameters on rock creep deformation is analyzed. The relationship between model parameters and temperature is quantitatively expressed. The results show that the newly established model can describe the characteristics of the rock in the decay creep stage and the constant creep stage, especially can quantitatively characterize the relationship between the strain and the time of the rock in the tertiary creep under different temperatures conditions. The model fitting curve is highly consistent with the test data, and the correlation coefficient R2 is above 0.98, which thoroughly verifies the accuracy and rationality of the model. It is found that when the temperature is constant, the creep increases with the increase of the shear modulus of the elastomer G1, the shear modulus of the viscoelastic body G2, and the viscosity coefficient of the viscous body η1 in the constant creep stage. The decay creep property of rock is more obvious with the increase of the viscosity coefficient η2, and the axial strain tends to a constant value. The achievement can be used to predict the deformation trend of geotechnical engineering with time under different temperature conditions and provide the theoretical basis for long-term stability analysis.

In view of the contradiction between dense parking demand and limited parking resources, according to the time-varying characteristics of parking demand of different building types in the city, a dual objective parking allocation model with the highest equilibrium degree of shared parking utilization and the minimum walking distance was established. The model defines the boundary constraints of the walking distance and the equilibrium utilization, weights the multi-objective function, and then uses the genetic algorithm tool to solve it. Taking Tangshan Second Hospital and its surrounding areas as an example, the basic data such as the total number of parking Spaces, parking demand and walking distance after parking in each parking lot were obtained. The simulation output of parking space utilization and parking allocation in the area was carried out by the simulation algorithm, and the feasibility of the model was verified. The results show that the model can be used to allocate shared parking Spaces in urban areas, which can effectively balance the utilization rate of parking lots in the region and alleviate the problem of uneven and inadequate parking resources utilization in the region.

In this paper, we study the efficiency of compressed sensing by using Orthogonal Matching Pursuit (OMP). We show that if a Matrix Φ has coherence less than 1 20K 0.8 and satisfies the Restricted Isometry Property (RIP) of order [CK 1.2 ] with constant δ = cK −0.2 , then a K-sparse signal x can be recovered from y = Φx via Orthogonal Matching Pursuit in at most optimal approximation on the first [CK 1.2 ] iterations.