We give a very simple proof of the caracterization of Lipschitz regularity of a function by the size of its Haar coefficients. It is well known that given a real function I periodic with period 27r satisfying a Lipschitz 0: condition for 0 < 0: ::::; 1, its kth Fourier coefficient is bounded by Ikl-a . More precisely, the following result holds (see for example Chapter 12 of [9]). (A) Let I be ...

Yves Francois Meyer was born July 19th, 1939 in Paris, but he grew up in Tunisia. After his studies at the École Normale Supérieure he was a teacher for three years at the school Prytanée Militaire in La Flèche (Loire Valley) and obtained a position in Strasbourg afterwards. During this period he prepared his PhD which he presented in 1966. Formally Jean-Pierre Kahane was his advisor, but he co...

Since the introduction of the behavioral approach to systems theory by Willems [13, 14, 15, 16, 17] the main emphasis has been on discrete time systems. Papers dealing with continuous time systems generally have assumed from the start that a set of differential equations was given. In his thesis Soethoudt has given necessary and sufficient conditions on the behavior of a continuous time system ...

Does God exist? This is a question that philosophers have sought to answer for centuries. But consider the following: What value impact of God's existence? Would existence be good or bad? Should we want These are questions only very recently garnered attention from philosophers. To date, they mostly been tackled by comparing world where exists another as similar it possible but doesn't exist. T...

We heartily agree with the target article and focus on how positive sociocultural change can be accelerated through the systematic use of scenario planning –what we call sociotecture. Scenario planning is a design process for the creation and selection of symbotypes that make a positive difference. It cuts through complexity by integrating cognitive and affective processes across multiple scale...

The federal Supplemental Security Income (SSI) program has become a primary source of cash assistance for low-income families with children in the United States, with 1.04 million children currently receiving SSI benefits and 6 percent of children in a household with some SSI income. In this paper we use data from the Survey of Income and Program Participation (SIPP) to investigate the impact t...

The subject of this paper is the calculation of the chromatic polynomials of families of graphs that have cyclic symmetry. Generally speaking, there are no elegant methods in this eld. The standard method of deletion-and-contraction is both ineecient and inelegant: it requires exponentially many steps, and any symmetry that the graph possesses is destroyed at the very rst step. In this paper we...

We are interested in the following problem: to describe the closed translation-invariant subspaces of lp(Z). For l2 there is a complete solution due to Wiener, in terms of zeros of Fourier transform. However, the situation when p 6= 2 is much harder. In this talk we will present a proof of Malliavin’s theorem which shows the difficulty of characterizing all invariant subspaces of l1. We will us...

We have shown that a subset of early postmitotic progenitors that originates along the medial part of the epithelial somite gives rise to the primary myotome (Kahane, N., Cinnamon, Y. and Kalcheim, C. (1998). Mech. Dev. 74, 59-73). Because of its postmitotic nature, further myotome expansion must be achieved by cell addition from extrinsic sources. Here we investigate the mechanism whereby the ...