We consider a class of second order elliptic operators on a d-dimensional cube Sd . We prove that if the coefficients are of class Ck+δ(Sd ), with k = 0,1 and δ ∈ (0,1), then the corresponding elliptic problem admits a unique solution u belonging to Ck+2+δ(Sd) and satisfying non-standard boundary conditions involving only second order derivatives.  2003 Éditions scientifiques et médicales Else...

A (γ, δ)-elastic channel is a binary symmetric channel between a sender and a receiver where the error rate of an honest receiver is δ while the error rate of a dishonest receiver lies within the interval [γ, δ]. In this paper, we show that from any non-trivial elastic channel (i.e., 0 < γ < δ < 1 2 ) we can implement oblivious transfer with informationtheoretic security. This was previously (K...

For graphs G and H, an H-coloring of G is a map from the vertices of G to the vertices of H that preserves edge adjacency. We consider the following extremal enumerative question: for a given H, which connected n-vertex graph with minimum degree δ maximizes the number of H-colorings? We show that for non-regular H and sufficiently large n, the complete bipartite graph Kδ,n−δ is the unique maxim...

Research in recent years on peroxisome proliferator-activated receptor (PPAR)β/δ indicates that it plays a key role in the maintenance of energy homeostasis, both at the cellular level and within the organism as a whole. PPARβ/δ activation might help prevent the development of metabolic disorders, including obesity, dyslipidaemia, type 2 diabetes mellitus and non-alcoholic fatty liver disease. ...

An oblivious subspace embedding (OSE) for some ε, δ ∈ (0, 1/3) and d ≤ m ≤ n is a distribution D over Rm×n such that for any linear subspace W ⊂ Rn of dimension d, P Π∼D (∀x ∈W, (1− ε)‖x‖2 ≤ ‖Πx‖2 ≤ (1 + ε)‖x‖2) ≥ 1− δ. We prove that any OSE with δ < 1/3 must have m = Ω((d + log(1/δ))/ε2), which is optimal. Furthermore, if every Π in the support of D is sparse, having at most s non-zero entries...

A fast multilevel algorithm (MuST) for evaluating an n-sample sinc interpolant at mn points is presented. For uniform grids, its complexity is 25mn log(1/δ) flops for the sinc kernel and 75mn log(1/δ) for the sincd kernel, where δ is the target evaluation accuracy. MuST is faster than FFTand FMM-based evaluations for large n and/or for large δ. It is also applicable to non-uniform grids and to ...

1 Concentration Inequalities Lemma 1 (Markov’s inequality). Let X be a non-negative random variable. For all λ > 0, Pr[X > λ] ≤ E[X] λ Lemma 2 (Chebyshev Inequality). For all λ > 0, Pr[|X −E[X]| > λ] ≤ var[X] λ2 Lemma 3 (The Chernoff Bound: Upper bound). Let X1, X2, ..., Xn be independent random variables taking values in {0, 1} with E[Xi] = pi. Let X = ∑n i=1Xi, and μ = E[X]. Then the followin...

Green and Marcos [3] call a graded k-algebra δ-Koszul if the corresponding Yoneda algebra Ext(k, k) is finitely generated and Ext(k, k) is zero unless j = δ(i) for some function δ : N→ N. For any integer m ≥ 3 we exhibit a non-commutative quadratic δ-Koszul algebra for which the Yoneda algebra is generated in degrees (1, 1) and (m,m+ 1). These examples answer a question of Green and Marcos. The...

In this paper we shall present discrete Kolmogorov type inequalities for multiply monotone sequences defined on non-positive integers. Moreover, we will provide a more delicate information by obtaining the description of the following modulus of continuity ω j,r p,q (δ ,ε) = sup{‖Δx‖q : x,Δx, . . . ,Δ j x 0, ‖x‖p = δ , ‖Δx‖∞ = ε} for δ ε > 0 and values of j = r−2 or j = r−1 depending on values ...

As part of a structural investigation of strontium tellurate(IV) (STO), SrTeO(3), with particular emphasis on the crystal chemistry and phase transitions, the structure of the δ-phase has been determined at 780 K using a single-crystal analysis. Both structural and non-linear optical measurements indicate that STO undergoes a γ→δ second-order ferroelectric phase transition at 633 K from the C2 ...