MULTIPLE BOUNDARY LAYER PHENOMENA OF THE SOLUTION OF NONLINEAR HIGHER ORDER ELLIPTIC EQUATIONS WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.

COMPUTER COMPUTATION OF THE METHOD OF MULTIPLE SCALES-DIRICHLET PROBLEM FOR A CLASS OF SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations . The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales .

Detection performance and inversion processing of logging-while-drilling extra-deep azimuthal resistivity measurements

We present systematic investigations on the physics,detection performance and inversion of logging-while-drilling extradeep azimuthal resistivity measurements(EDARM).First,the definitions of EDRAM measurements are discussed,followed by the derivation of the attenuation and phase-shift geometrical factors to illustrate the relative contributions of formation units to the observed signals.Then,a new definition of detection depth,which considers the uncertainty of inversion results caused by the data noise,is proposed to quantify the detection capability of ED ARM.Finally,the B ayesian theory associated with Markov chain Monte Carlo sampling is introduced for fast processing of EDARM data.Numerical results show that ED ARM is capable of detecting the azimuth and distance of remote bed boundaries,and the detection capability increases with increasing spacing and resistivity contrast.The EDARM tool can accommodate a large range of formation resistivity and is able to provide the resistivity anisotropy at arbitrary relative dipping angles.In addition,multiple bed boundaries and reservoir images near the borehole are readily obtained by using the Bayesian inversion.

Fast Multi-Pattern Matching Algorithm on Compressed Network Traffic

Pattern matching is a fundamental approach to detect malicious behaviors and information over Internet, which has been gradually used in high-speed network traffic analysis. However, there is a performance bottleneck for multi-pattern matching on online compressed network traffic(CNT), this is because malicious and intrusion codes are often embedded into compressed network traffic. In this paper, we propose an online fast and multi-pattern matching algorithm on compressed network traffic(FMMCN). FMMCN employs two types of jumping, i.e. jumping during sliding window and a string jump scanning strategy to skip unnecessary compressed bytes. Moreover, FMMCN has the ability to efficiently process multiple large volume of networks such as HTTP traffic, vehicles traffic, and other Internet-based services. The experimental results show that FMMCN can ignore more than 89.5% of bytes, and its maximum speed reaches 176.470MB/s in a midrange switches device, which is faster than the current fastest algorithm ACCH by almost 73.15 MB/s.

MULTIPLE BOUNDARY LAYER PHENOMENAOF SOLUTION OF BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper, we study the multiple boundary layer phenomena of solution ofboundary value problem for third order semilinear ordinary differential equationwith two small parameters. Under suitable conditions, using the method of differential inequalities, we prove the existence of solution and give its estimation of remmainder term.

MULTIPLE LAYER BEHAVIOR OF BOUNDARY VALUE PROBLEM FOR SINGULARLY PERTURBED n-TH ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper, we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation, the solution is shown to exhibit multiple layer behavior. According to different layers and by introducing extended variable, we obtain the uniformly effective asymptotic expansion with different boundary layer correction term.