EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS

This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments, from which we find that the above asymptotics are different from the local asymptotics for the supremum of the random walk. To do this, the article first extends and improves some existing results about the solutions of renewal equations.

4-component 2-D CFDFD method in analysis of lossy circular waveguide with fractal rough surface

In this paper, equivalent surface impedance boundary condition （ESIBC）, which takes fractal parameters （D, G） into SIBC, is implemented in the 4-component 2-D compact finite difference frequency domain （2-D CFDFD） method to an- alyze the propagation characteristics of lossy circular waveguide with fractal rough surface based on Weierstrass-Mandelbrot （W-M） function. Fractal parameters’ effects on attenuation constant are presented in the 3 mm lossy circular waveguide, and the attenuation constants of the first three modes vary monotonically with scaling constant （G） and decrease as the fractal dimension （D） increasing.

ADRC in output and error form:connection,equivalence,performance

In this work,we investigate two specific linear ADRC structures,namely output-and error-based.The former is considered a“standard”version of ADRC,a title obtained primarily thanks to its simplicity and effectiveness,which have spurred its adoption across multiple industries.The latter is found to be especially appealing to practitioners as its feedback error-driven structure bares similarities to conventional control solutions,like PI and PID.In this paper,we describe newly found connections between the two considered ADRC structures,which allowed us to formally establish conditions for their equivalence.Furthermore,the conducted comprehensive performance comparison between output-and error-based ADRCs has facilitated the identification of specific modules within them,which can now be conveniently used as building blocks,thus aiding the control designers in customizing ADRC-based solutions and making them most suitable for their applications.

EQUIVALENCE BETWEEN NONNEGATIVE SOLUTIONS TO PARTIAL SPARSE AND WEIGHTED l_1-NORM MINIMIZATIONS

Based on the range space property （RSP）, the equivalent conditions between nonnegative solutions to the partial sparse and the corresponding weighted l1-norm minimization problem are studied in this paper. Different from other conditions based on the spark property, the mutual coherence, the null space property （NSP） and the restricted isometry property （RIP）, the RSP- based conditions are easier to be verified. Moreover, the proposed conditions guarantee not only the strong equivalence, but also the equivalence between the two problems. First, according to the foundation of the strict complemenrarity theorem of linear programming, a sufficient and necessary condition, satisfying the RSP of the sensing matrix and the full column rank property of the corresponding sub-matrix, is presented for the unique nonnegative solution to the weighted l1-norm minimization problem. Then, based on this condition, the equivalence conditions between the two problems are proposed. Finally, this paper shows that the matrix with the RSP of order k can guarantee the strong equivalence of the two problems.