Etude comparative des adjectifs similaire et semblable en français contemporain

This article proposes a comparative study of the French adjectives similaire and semblable which express a relationship of identity between two or more terms. I will show that beyond their partial synonymy, the two adjectives diverge on an essential point, namely on how they construct the relationship of identity. To this end, we will propose a semantic identity for each adjective in terms of Schematic Form (Forme schématique), defined as an operation reconstituting a complex relation between the abstract parameters involved. I will show that this Schematic Form can account for the various constructions and the distributional constraints associated with each unit

Two-Dimensional Quaternionic Windowed Fourier Transform

Signal processing is a fast growing area today and the desired effectiveness in utilization\ud of bandwidth and energy makes the progress even faster. Special signal processors have\ud been developed to make it possible to implement the theoretical knowledge in an efficient\ud way. Signal processors are nowadays frequently used in equipment for radio, transportation,\ud medicine, and production, etc.In this paper, by using the adjoint operator of the (right-sided) QFT, we derive the Plancherel\ud theorem for the QFT. We apply it to prove the orthogonality relation and reconstruction\ud formula of the two-dimensional quaternionic windowed Fourier transform (QWFT). Our\ud results can be considered as an extension and continuation of the previous work of Mawardi\ud et al. (2008).We then present several examples to show the differences between the QWFT and\ud the WFT. Finally, we present a generalization of the QWFT to higher dimensions

Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework

A construction of multiwavelets

AbstractA class of r-regular multiwavelets, depending on the smoothness of the multiwavelet functions, is introduced with the appropriate notation and definitions. Oscillation properties of orthonormal systems are obtained in Lemma 1 and Corollary 1 without assuming any vanishing moments for the scaling functions, and in Theorem 1 the existence of r-regular multiwavelets in L2(Rn) is established. In Theorem 2, a particular r-regular multiresolution analysis for multiwavelets is obtained from an r-regular multiresolution analysis for uniwavelets. In Theorem 3, an r-regular multiresolution analysis of split-type multiwavelets, which are perhaps the simplest multiwavelets, is easily obtained by using an r-regular multiresolution analysis for uniwavelets and a (2n − 1)-fold regular multiresolution analysis for uniwavelets. For some split-type multiwavelets, the support or width of the wavelets is shorter than the support or width of the scaling functions without loss of regularity nor of vanishing moments. Examples of split-type multiwavelets in L2(R) are constructed and illustrated by means of figures. Symmetry and antisymmetry are preserved in the case of infinite support