Abstract Designing perfect anomalous reflectors is crucial for achieving many metasurface-based applications, but available design approaches the cases of extremely large bending angles either require unrealistic gain–loss materials or rely on brute-force optimizations lacking physical guidance. Here, we propose a deterministic approach to passive metasurfaces that can reflect impinging light a...

We study the convergence and asymptotic normality of a generalized form of stochastic approximation algorithm with deterministic perturbation sequences. Both one-simulation and two-simulation methods are considered. Assuming a special structure of deterministic sequence, we establish sufficient condition on the noise sequence for a.s. convergence of the algorithm. Construction of such a special...

In this paper, we show that for any BL-general L-fuzzy automaton (BL-GLFA) there exists a complete deterministic accessible reduced BL-general L-fuzzy automaton that recognizing the behavior of the BL-GLFA. Also, we prove that for any finite realization β, there exists a minimal complete deterministic BL-GLFA recognizing β. We prove any complete deterministic accessible reduced BL-GLFA is a min...

In this paper we present a new family of discrete sequences having “random like” uniformly decaying auto-correlation properties. The new class of infinite length sequences are higher order chirps constructed using irrational numbers. Exploiting results from the theory of continued fractions and diophantine approximations, we show that the class of sequences so formed has the property that the w...

We study the rigidity of body-and-cad frameworks which capture the majority of the geometric constraints used in 3D mechanical engineering CAD software. We present a combinatorial characterization of the generic minimal rigidity of a subset of body-and-cad frameworks in which we treat 20 of the 21 body-and-cad constraints, omitting only point-point coincidences. While the handful of classical c...

Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers....