a b s t r a c tIn this paper, a kind of improved univariate multiquadric quasi-interpolation operators is proposed by using Hermite interpolating polynomials. Error analysis shows that the convergence rate of the operators depends heavily on the shape parameter c, which indicates that our operators could provide the desired smoothness and precision by choosing a suitable value of c. Numerical examples show that the operators provide a high degree of accuracy. Moreover, operators are applied to the fitting of discrete solutions of initial value problems.
We present exact solutions of solitonic profile mass Schrödinger equation with a modified Pöschl–Teller potential. We find that the solutions can be expressed analytically in terms of confluent Heun functions. However, the energy levels are not analytically obtainable except via numerical calculations. The properties of the wave functions, which depend on the values of potential parameter [Formula: see text] are illustrated graphically. We find that the potential changes from single well to a double well when parameter [Formula: see text] changes from minus to positive. Initially, the crest of wave function for the ground state diminishes gradually with increasing [Formula: see text] and then becomes negative. We notice that the parities of the wave functions for [Formula: see text] also change.
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is that the size of data is very large, which makes usual gradient-based methods infeasible. Recently, Necoara, Nesterov, and Glineur [8] proposed an efficient randomized coordinate descent method to solve this type of optimization problems and presented an appealing convergence analysis. In this paper, we develop new techniques to analyze the convergence of such algorithms, which are able to greatly improve the results presented in [8]. This refined result is achieved by extending Nesterov's second technique [4] to the general optimization problems with linearly coupled constraints. A novel technique in our analysis is to establish the basis vectors for the subspace of the linearly constraints.
Spin-dependent transport through ferromagnetic/semiconductor/ferromagnetic double quantum rings is studied in this paper. It is found that the average value of the spin-dependent electron transmission coefficient of the double quantum ring is larger than that of the single quantum ring under the condition of zero magnetic flux and antiparallel configration of the ferromagnetic electrodes. When the magnetization directions of the ferromagnetic electrodes are parallel, the average tunneling coefficient of the spin-down electrons in double quantum rings increases distinctly. When the Rashba spin-orbit coupling is considered, the average tunneling coefficient of the spin electrons in double quantum rings is bigger than that in single quantum ring. The applied magnetic field enhences the tunneling coefficient. The δ barrier of the double quantum rings suspresses the tunneling of the electron. The tunneling coefficient decreases monotonically and nonlinearly with the δ barrier strength Z increasing.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.