STRUCTURE OF COMPUTATIVE TREE FOR COMPUTABLE FUNCTION

In this paper, we study the computative structure of computable function - a structure of computative tree, and, by analysis on it, got the most general algorithm and model for computation on computable functions.

Excitation of Elastic Wave of an Arbitrary Plane Source on Surface of a Multilayered Medium

We investigate the elastic waves excited by an arbitrary plane piezoelectric source on the surface of a multilayered medium. Based on the previous studies, the 2D elastic wavefield in the multilayered medium is extended to 3D space. The propagator matrix for the 3D wavefield is investigated and the displacement-stress response for the boundary conditions is obtained. The excitation and propagation of the Rayleigh and Love waves are analysed further. It is found that the propagation velocity of the Rayleigh and Love waves does not depend on the propagation azimuth θ in the plane parallel to the free surface of the multilayered medium while the displacement is strongly dependent on the azimuth θ.

NEW PERIODIC SOLUTIONS OF ITO'S 5th-ORDER mKdV EQUATION AND ITO'S 7th-ORDER mKdV EQUATION

Based on the modified Jocobi elliptic function expansion method and the modified extended tanh function method,a new algebraic method is presented to obtain mu ltiple travelling wave solutions for nonlinear wave equations.By using the metho d,Ito's 5th order and 7th order mKdV equations are studied in detail and more new exact Jocobi elliptic function periodic solutions are found.With modulus m→1 or m→0,these solutions degenerate into corresponding solitary wave s olutions,shock wave solutions and trigonometric function solutions.

随机变量的共轭梯度方法

We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.

Single-atom rhodium anchored on S-doped black phosphorene as a promising bifunctional electrocatalyst for overall water splitting

Superior bifunctional electrocatalysts with ultra-high stability and excellent efficiency are crucial to boost the oxygen evolution reaction(OER) and the hydrogen evolution reduction(HER) in the overall water splitting(OWS) for the sustainable production of clean fuels. Herein, comprehensive density functional theory(DFT) computations were performed to explore the potential of several single transition metal(TM) atoms anchored on various S-doped black phosphorenes(TM/Snx-BP) for bifunctional OWS electrocatalysis. The results revealed that these candidates display good stability, excellent electrical conductivity, and diverse spin moments. Furthermore, the Rh/S12-BP catalyst was identified as an eligible bifunctional catalyst for OWS process due to the low overpotentials for OER(0.43 V) and HER(0.02 V), in which Rh and its adjacent P atoms were identified as the active sites. Based on the computed Gibbs free energies of OH~*, O~*, OOH~* and H~*, the corresponding volcano plots for OER and HER were established.Interestingly, the spin moments and the charge distribution of the active sites determine the catalytic trends of OER and HER. Our findings not only propose a promising bifunctional catalyst for OWS, but also widen the potential application of BP in electrocatalysis.

3D image reconstruction with controllable spatial filtering based on correlation of multiple periodic functions in computational integral imaging

We propose a novel method of slice image reconstruction with controllable spatial filtering by using the correlation of periodic delta-function arrays （PDFAs） with elemental images in computational integral imaging. The multiple PDFAs, whose spatial periods correspond to object＇s depths with the elemental image array （EIA）, can generate a set of spatially filtered EIAs for multiple object depths compared with the conventional method for the depth of a single object. We analyze a controllable spatial filtering effect by the proposed method. To show the feasibility of the proposed method, we carry out preliminary experiments for multiple objects and present the results.

THE COMPUTATION OF PARTIAL COHERENCE FUNCTION APPLIED FOR SOUND SOURCE IDENTIFICATION

In this paper, a new method is applied to get the computation formula of partial coherence function. The main attention is paid to the computation formula of the partial coherence function with three and four signals. The advantages of the method discussed in the paper are clear in physical meaning and easy to compute at the end of the paper,the application of the method to the identification of an air compressor noise source is presented and the results are satisfactory.

The M-computations induced by accessibility relations in nonstandard models M of Hoare logic

Hoare logic is a logic used as a way of specifying semantics of programming languages, which has been extended to be a separation logic to reason about mutable heap structure. In a model M of Hoare logic, each program α induces an M-computable function fα M on the universe of M; and the M-recursive functions are defined on M. It will be proved that the class of all the M-computable functions fα M induced by programs is equal to the class of all the M- recursive functions. Moreover, each M-recursive function is ∑ 1 NM -definable in M, where the universal quantifier is a num- ber quantifier ranging over the standard part of a nonstandard model M.