The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and th...

In view of the good properties of nonstationary wavelet frames and the better flexibility of wavelets in Sobolev spaces, the nonstationary dual wavelet frames in a pair of dual Sobolev spaces are studied in this paper. We mainly give the oblique extension principle and the mixed extension principle for nonstationary dual wavelet frames in a pair of dual Sobolev spaces H(R) and H−s(Rd). Keywords...

Motivic measure on the space of functions was introduced by Campillo, Delgado and Gusein-Zade as an analog of the motivic measure on the space of arcs . In this paper we prove that the measure on the space of functions can be related to the motivic measure on the space of arcs by a factor, which can be defined explicitly in geometric terms. This provides a possibility to rewrite motivic integra...

In this paper we prove that any degree d deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again. This is a generalization of Ilyashenko’s result on Hamiltonian differential equations. The main tools are PicardLefschetz theory of a polynomial with complex coefficients in two variables, specially the Gusein-Zade/A’Campo’s theorem o...

Boolean Function and Block Cipher A Note on Semi-bent and Hyper-bent Boolean Functions . . . . . . . . . . . . . . . 3 Chunming Tang, Yu Lou, Yanfeng Qi, Maozhi Xu, and Baoan Guo New Construction of Differentially 4-Uniform Bijections . . . . . . . . . . . . . . . 22 Claude Carlet, Deng Tang, Xiaohu Tang, and Qunying Liao Automatic Security Evaluation of Block Ciphers with S-bP Structures Again...

The Necessary Maximality Principle for c.c.c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. The Necessary Maximality Principle for c.c.c. forcing, denoted 2mpccc(R), asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already tr...

The Necessary Maximality Principle for c.c.c. forcing with real parameters is equiconsistent with the existence of a weakly compact cardinal. The Necessary Maximality Principle for c.c.c. forcing, denoted 2mpccc(R), asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already tr...