On the Product of Integro Differential Equations and Their Solutions in Direct Sum Spaces

In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.

Obstacle avoidance method of three-dimensional obstacle spherical cap

Focusing on obstacle avoidance in three-dimensional space for unmanned aerial vehicle(UAV), the direct obstacle avoidance method in dynamic space based on three-dimensional velocity obstacle spherical cap is proposed, which quantifies the influence of threatening obstacles through velocity obstacle spherical cap parameters. In addition, the obstacle avoidance schemes of any point on the critical curve during the multi-obstacles avoidance are given. Through prediction, the insertion point for the obstacle avoidance can be obtained and the flight path can be replanned. Taking the Pythagorean Hodograph(PH) curve trajectory re-planning as an example, the three-dimensional direct obstacle avoidance method in dynamic space is tested. Simulation results show that the proposed method can realize the online obstacle avoidance trajectory re-planning, which increases the flexibility of obstacle avoidance greatly.

STUDY ON STEADY SURGE PRESSURE FOR YIELD-PSEUDOPLASTIC FLUID IN A CONCENTRIC

Surge pressure caused by pipe moving through the wellbore full of drilling.fluid is the main factor affecting wellbore stability,on which the additional mud density isdesigned.Thus if is desired to predict the surge pressure with high accuracy.While this is closely,related with the selection of mud rheological models.Yield-Pseudoplastic model which has three parameters and is.famous for its higher accuracy has been used to describe the mud rheological properties in recent years.Based on this model the paper presents a new theoretical model for calculating surge pressure caused by mud viscosity during tripping or casing in a concentric annulus of directional wells under steady laminar situation.For convenience,the paper plots the distribution of the coefficients of surge pressure for different conditions.An example is given.These results provide the basis for controlling pressure surges and tripping velocity.

Edge detection based on directional space

A new method for edge detection based on directional space is proposed.The principle is that:firstly,the directional differential space is set up in which the ridge edge pixels and valley edge pixels are abstracted with the help of the method of logical judgments along the direction of differential function,forming a directional roof edge map;secondly,step edge pixels are abstracted between the neighboring directional ridge edge and directional valley edge along the direction of differential function;finally,the ridge edge map,valley edge map and step edge map gained along different directions are combined into corresponding ridge edge map,valley edge map and step edge map.This method is different from classical algorithms in which the gray differential values of the mutual vertical direction are combined into one gradient value.The experiment of edge detection is made for the images of nature scenery,human body and accumulative raw material,whose result is compared with the one of classical algorithms and showing the robustness of the proposed method.

DOA estimation and mutual coupling calibration with the SAGE algorithm

In this paper, a novel algorithm is presented for direction of arrival（DOA） estimation and array self-calibration in the presence of unknown mutual coupling. In order to highlight the relationship between the array output and mutual coupling coefficients, we present a novel model of the array output with the unknown mutual coupling coefficients. Based on this model, we use the space alternating generalized expectation-maximization（SAGE） algorithm to jointly estimate the DOA parameters and the mutual coupling coefficients. Unlike many existing counterparts, our method requires neither calibration sources nor initial calibration information. At the same time,our proposed method inherits the characteristics of good convergence and high estimation precision of the SAGE algorithm. By numerical experiments we demonstrate that our proposed method outperforms the existing method for DOA estimation and mutual coupling calibration.