Soft Consistency Reconstruction: A Robust 1-bit Compressive Sensing Algorithm

A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics of the objective function under noisy environments. With a family of re-designed consistency criteria, SCRs achieve remarkable counter-noise performance gain over the existing counterparts, thus acquiring the desired robustness in many real-world applications. The benefits of soft decisions are exemplified through structural analysis of the objective function, with intuition described for better understanding. As expected, through comparisons with existing methods in simulations, SCRs demonstrate preferable robustness against noise in low signal-to-noise ratio (SNR) regime, while maintaining comparable performance in high SNR regime

Constructivist learning method of ordinary differential equations in college mathematics teaching

The article uses ordinary differential to solve inhomogeneous equations by the constructivist learning concept. We use the equivalent equations to study the n-Th order non-homogeneous linear ordinary differential equations with constant coefficients and get the method of solving this equation. Then we use the Filippov transformation and comparison theorem to prove the boundedness of all system trajectories. Numerical results show that the calculation formula is effective for solving stiff ordinary differential equations

Modelling of sediment transport and bed deformation in rivers with continuous bends

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Passivity and Passification of Fuzzy Systems with Time Delays

AbstractTakagi-Sugeno (T-S) fuzzy model provides an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output submodels. Recently, a number of authors studied the T-S fuzzy systems with time delays. In this paper, the passivity and feedback passification of T-S fuzzy systems with time delays are considered. Both delay-independent and delay-dependent results are presented, and the theoretical results are given in terms of linear matrix inequalities (LMIs). Numerical examples are given which illustrate the effectiveness of the theoretical results

Characteristics of transient pressure performance of horizontal wells in fractured-vuggy tight fractal reservoirs considering nonlinear seepage

International audienceSince the classical seepage theory has limitations in characterizing the heterogeneity of fractured-vuggy tight reservoirs, well test interpretation results are not consistent with actual production by far. Based on the nonlinear percolation theory, a new nonlinear seepage equation considering the boundary layer and yield stress was derived to describe the seepage characteristics of dense matrix blocks and the stress sensitivity and fractal features of fracture systems were characterized by applying the fractal theory. Thus, the nonlinear model of a horizontal well in a fractured-vuggy tight fractal reservoir was established naturally. Then the finite element method was applied to solve the bottom hole pressure based on the processing of internal boundary conditions. After solving the model, the seepage characteristics of different models were summarized by analyzing the bottom hole pressure dynamic curves and the sensitivity analysis of multiple parameters such the nonlinear parameter and fractal index were conducted. Finally, the practicality of the model was proved through a field application. The results show that the pressure dynamic curves can be divided into nine flow stages and the increase of the nonlinear parameter will cause the intensity of the cross flow from matrix blocks to the fracture system to decrease. The fractal index is irrelevant to the intensity of the cross flow while it decides the upwarping degree of the curve at the middle and late flow stages. On the basis of the results of the field application, it can be concluded that the model fits well with actual production and the application of this model can improve the accuracy of well test interpretation