3/a) On peut éliminer le cas où bn est nul à partir d’un certain rang (ceci ne peut se produire que si tous le an sont nuls) ; dans ce cas il suffit de prendre un = 1/n. Posons vn = supp≥n bp et un = √ vn. La suite (vn) est une suite décroissante de réels strictement positifs, tend vers 0 car bn → 0, et bn ≤ vn pour tout n ∈ N∗. La suite (un) tend donc vers 0 en décroissant, et puisque bn/un ≤ ...

The construction of a Bayesian Network (BN) model entails two major tasks: realization of the model structure, and the calibration (parameterization) of the model. BN model constructors, ab initio, relied only on domain experts to define both the structure and parameters of a model. Currently, algorithms exist to construct BN models from data. Consequently, there are three BN model construction...

The reaction of N,N'-dibenzyl-2-amino-4-imino-pent-2-ene, nacnac(Bn)H, with 1 or 2 equiv. of MgnBu₂ afforded the homoleptic complex nacnac(Bn)₂Mg. The reaction of nacnac(Bn)H with Mg(N(SiMe₃)₂)₂ yielded nacnac(Bn)MgN(SiMe₃)₂, which reacted with tert-butanol to form nacnac(Bn)MgOtBu. The latter complex crystallizes as an alkoxide bridge dimer and is active in the ring-opening polymerisation of r...

Motivated by a question of Sárközy, we study the gaps in the product sequence B = A · A = {bn = aiaj , ai, aj ∈ A} when A has upper Banach density α > 0. We prove that there are infinitely many gaps bn+1 − bn ¿ α−3 and that for t ≥ 2 there are infinitely many t-gaps bn+t − bn ¿ t2α−4. Furthermore we prove that these estimates are best possible. We also discuss a related question about the cardi...

Most of the current state-of-the-art speech recognition systems are based on HMMs which usually use mixture of Gaussian functions as state probability distribution model. It is a common practice to use EM algorithm for Gaussian mixture parameter learning. In this case, the learning is done in a ”blind”, data-driven way without taking into account how the speech signal has been produced and whic...

Bombesin (BN) and its mammalian counterpart, gastrin-releasing peptide (GRP), are hormonally active peptides which appear to function as autocrine or paracrine growth factors in a variety of cells. As part of a long-term investigation of the relationship of peptide and steroid hormone receptors to breast cancer progression and treatment, we examined the binding of [125I-Tyr4]BN to membranes iso...

Combinatorial Bn-analogues of Schubert polynomials and corresponding symmetric functions are constructed from an exponential solution of the Bn-Yang-Baxter equation that involves the nilCoxeter algebra of the hyperoctahedral group.

There are well-known monomorphisms between the Artin groups of finite type An, Bn = Cn and affine type Ãn−1, C̃n−1. The Artin group A(An) is isomorphic to the (n + 1)strand braid group Bn+1, and the other three Artin groups are isomorphic to some subgroups of Bn+1. The inclusions between these subgroups yield monomorphisms A(Bn) → A(An), A(Ãn−1) → A(Bn) and A(C̃n−1) → A(Bn). There are another typ...