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K E V I N M . S I R K , † N A V I D B . S A L E H , ‡ T A N A P O N P H E N R A T , ‡ H Y E J I N K I M , ‡ B R U N O D U F O U R , § J E O N G B I N O K , § P A T R I C I A L . G O L A S , § K R Z Y S Z T O F M A T Y J A S Z E W S K I , § G R E G O R Y V . L O W R Y , ‡ A N D R O B E R T D . T I L T O N * , † , | Center for Environmental Implications of Nanotechnology and Departments of Chemic...

ion : règle (comb-K). M est de la forme fun z → C où C est soit une variable différente de z, soit un opérateur, soit un setm, soit un getm. Dans ce cas, [M ] vaut K C. On cherche à montrer que fun z → C ≃ (fun x → fun y → x)C. Or on a : (fun x → fun y → x)C / s → fun y → C / s (on suppose ici que C n’est pas la variable y pour éviter les considérations sur l’alpha-conversion lors de l’applicat...

In [1, 4], Fulton defines the notion of the Segre class s(X, Y) ∈ A∗X of a closed embedding of schemes X→ Y over a field k. As in Fulton, all of our schemes are finite type over a ground field k which may be of arbitrary characteristic unless stated otherwise. The Segre class allows us to measure the way in which X sits inside Y, and is functorial for sufficiently nice maps ([1, 4.2]). One impo...

Let B be the closed unit ball in R and S its boundary. We define a family of pseudo metrics on B. As an application, we prove that for any countable-to-one function f : S → [0, a], the set NMnf = {x ∈ S 2 | there exists y ∈ S2 such that f(x)−f(y) > ndE(x, y)} is uncountable for all n ∈ N, where dE is the Euclidean metric on R . 2000 Mathematics Subject Classification ; 57N05, 57M40 1 The family...

Models of spatially homogeneous walks in the quarter plane Z2+ with steps taken from a subset S of the set of jumps to the eight nearest neighbors are considered. The generating function (x, y, z) 7→ Q(x, y; z) of the numbers q(i, j;n) of such walks starting at the origin and ending at (i, j) ∈ Z2+ after n steps is studied. For all nonsingular models of walks, the functions x 7→ Q(x, 0; z) and ...

Proof of Lemma 1: This retailer would see (y/L) of the total demand, hence the cumulative distribution function of its demand is H(s) = F(sL/y) where F() gives the cumulative distribution function for total market demand, x. Differentiating H(s) gives the required result. () parts) by on (integrati) () () () () () () () () () () () 0 , max(0 0 0 0 0 0 ds s F L y ds s f s y Lq L y ds s f s y Lq ...

A special case, called the divergence-free case, of the Jacobian Conjecture in dimension two is proved. This note outlines an argument for a special case of the Jacobian conjecture in dimension two: Suppose F : C → C is a polynomial so that F (0) = 0, F ′(0) = I, det(F ′(z)) = 1, z ∈ C. (1) where I is the identity transformation on C. Write F (x, y) = ( r(x, y) + x s(x, y) + y ) , (x, y) ∈ C wh...

Let S be a jinite subset of a lattice and let us(L), the number of points of S IL for each line L, denote the discrete Radon transform of S. The problem is to reconstruct S from a knowledge (possibly noisy) of the restriction of US to a subset Y of the set of all lines in any of a few given directions through the lattice. Reconstructing a density from its line integrals is a well-understood pro...