The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

A brief survey on numerical methods for solving singularly perturbed problems

Automated dynamic malware analysis is a common approach for detecting malicious software. However, many malware samples identify the presence of the analysis environment and evade detection by not performing any malicious activity. Recently, an approach to the automated detection of such evasive malware was proposed. In this approach, a malware sample is analyzed in multiple analysis environments, including a bare-metal environment, and its various behaviors are compared. Malware whose behavior deviates substantially is identified as evasive malware. However, a malware analyst still needs to re-analyze the identified evasive sample to understand the technique used for evasion. Different tools are available to help malware analysts in this process. However, these tools in practice require considerable manual input along with auxiliary information. This manual process is resource-intensive and not scalable. In this paper, we present MalGene, an automated technique for extracting analysis evasion signatures. MalGene leverages algorithms borrowed from bioinformatics to automatically locate evasive behavior in system call sequences. Data flow analysis and data mining techniques are used to identify call events and data comparison events used to perform the evasion. These events are used to construct a succinct evasion signature, which can be used by an analyst to quickly understand evasions. Finally, evasive malware samples are clustered based on their underlying evasive techniques. We evaluated our techniques on 2810 evasive samples. We were able to automatically extract their analysis evasion signatures and group them into 78 similar evasion techniques.

https://dl.acm.org/doi/pdf/10.1145/2810103.2813642

MalGene: Automatic Extraction of Malware Analysis Evasion Signature

Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

In this paper, we review many recent developments and further applications of nonstandard finite difference (NSFD) methods encountered in the past decade. In particular, it is a follow up article of the one published in 2005 [K.C. Patidar, On the use of non-standard finite difference methods, J. Differ. Equ. Appl. 11 (2005), pp. 735–758]. It also includes those research contributions in this field that are very significant and published prior to the above article but were not included in the above paper simply because we did not have access to them when we wrote the above article. We also give a detailed account on various definitions/notions of NSFD methods appeared in the literature in past two decades. All contributions are listed chronologically except that in some instances we have grouped certain works to show connectivity in those fields. While categorizing these research contributions, we considered a number of different application areas. Moreover, due to space limitations, firstly, we have not i...

Nonstandard finite difference methods: recent trends and further developments

B-spline method for a class of singular two-point boundary value problems using optimal grid

Stability analysis of predator–prey system with migrating prey and disease infection in both species

Analytical and numerical treatment of Jungck-type iterative schemes

An adaptive mesh strategy for singularly perturbed convection diffusion problems

In this paper, the collocation method proposed by Cai and Wang1 has been reviewed in detail to solve singularly perturbed reaction diffusion equation of elliptic and parabolic types. The method is based on an interpolating wavelet transform using cubic spline on dyadic points. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples are presented for elliptic and parabolic problems. The purposed method comes up as a powerful tool for studying singular perturbation problems in term of effective grid generation and CPU time.

https://web.iitd.ac.in/~mmehra/publication/IJWMIP071.pdf

Vivek Kumar

Papers

B-spline method for a class of singular two-point boundary value problems using optimal grid

Stability analysis of predator–prey system with migrating prey and disease infection in both species

Analytical and numerical treatment of Jungck-type iterative schemes

An adaptive mesh strategy for singularly perturbed convection diffusion problems

Cubic spline adaptive wavelet scheme to solve singularly perturbed reaction diffusion problems