Averaging for retarded functional differential equations

We consider retarded functional differential equations in the setting of Kurzweil-Henstock integrable functions and we state an averaging result for these equations. Our result generalizes previous ones. (C) 2011 Elsevier Inc. All rights reserved.

Maple tools for the Kurzweil integral

Riemann sums based on delta fine partitions are illustrated with a Maple procedure

Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

Existence de solution antipériodique de l’équation impulsive de Liénard avec une force Henstock-Kurzweil intégrable

Notre travail se consacre à l’étude de l’existence de solution T-anti-périodique de l’équation de Liénard dans le cas impulsif. Dans notre thèse, cette équation sera appliquée à l’équation du pendule simple, de Josephson dans la super-conductivité et enfin à l’équation de Van der Pol pour modéliser un circuit de triode à tube vide. On considérera [florin] et J des actions extérieures sur le système où [florin] est une force Lebesgue intégrable (respectivement Henstock-Kurzweil intégrable au second chapitre) et J (parfois noté I) une stimulation impulsive. En appliquant le théorème du point fixe de Banach, on obtient des théorèmes d’existence de solution au sens de fonctions généralisées soumise à un ensemble de conditions données par les bornes à priori. Ensuite, par le même théorème, la suite d’itérations G[indice supérieur n] ([théta][indice inférieur 0]) converge uniformément vers la solution [théta] à la vitesse de convergence bornée avec la première dérivée […] est de variation totale finie sur [0; 2T] et la dérivée seconde généralisée […] Lebesgue intégrable sur [0; 2T] dans le cas non impulsif. Finalement, sous les mêmes hypothèses avec [florin] Henstock-Kurzweil (HK) intégrable, nous obtiendrons des conditions qui garantissent l’existence d’une solution T-antipériodique [théta] absolument continue sur R de l’équation de Liénard, qui admet à la fois une dérivée première […] de variation bornée et la seconde dérivée généralisée […] qui est HK--intégrable dans le cas non impulsif. Comme au premier chapitre nous considérerons également le cas des instants d’impulsion [gamma][indice inférieur kappa] indépendants d’état avec [florin] HK--intégrable. À chaque fois nous donnons quelques exemples d’illustration pour appuyer nos résultats. [Certains symboles non conformes]

Bit-pattern based integral attack

Integral attacks are well-known to be effective against byte-based block ciphers. In this document, we outline how to launch integral attacks against bit-based block ciphers. This new type of integral attack traces the propagation of the plaintext structure at bit-level by incorporating bit-pattern based notations. The new notation gives the attacker more details about the properties of a structure of cipher blocks. The main difference from ordinary integral attacks is that we look at the pattern the bits in a specific position in the cipher block has through the structure. The bit-pattern based integral attack is applied to Noekeon, Serpent and present reduced up to 5, 6 and 7 rounds, respectively. This includes the first attacks on Noekeon and present using integral cryptanalysis. All attacks manage to recover the full subkey of the final round.

Intuitionistic fuzzy Choquet integral operator-based approach for black-start decision-making

Determining the optimal of black-start strategies is very important for speeding the restoration speed of a power system after a global blackout. Most existing black-start decision-making methods are based on the assumption that all indexes are independent of each other, and little attention has been paid to the group decision-making method which is more reliable. Given this background, the intuitionistic fuzzy set and further intuitionistic fuzzy Choquet integral operator are presented, and a black-start decision-making method based on this integral operator is presented. Compared to existing methods, the proposed algorithm cannot only deal with the relevance among the indexes, but also overcome some shortcomings of the existing methods. Finally, an example is used to demonstrate the proposed method. © 2012 The Institution of Engineering and Technology.

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.