In [10], Littlewood conjectured that there are positive absolute constants Ax and A2 such that, for arbitrarily large n, one can find anfne^n or a gn€%, such that A.Vin+l) < \fM\ < A2V("+V (1-1) or ^ V ( « + l ) < \gn(0)\<A2V(n+\) (1.2) for all 6. The weaker conjecture (1.2) has been solved by Korner [9] (using a construction of Byrnes [6]) in the affirmative. Soon after this breakthrough, Kaha...

we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

We use the recently-developed multiparameter theory of additive Lévy processes to establish novel connections between an arbitrary Lévy process X in R, and a new class of energy forms and their corresponding capacities. We then apply these connections to solve two long-standing problems in the folklore of the theory of Lévy processes. First, we compute the Hausdorff dimension of the image X(G) ...

The National Highway Traffic Safety Administration (NHTSA) recently updated its 2003 and 2010 logistic regression analyses of the effect of a reduction in light-duty vehicle mass on US societal fatality risk per vehicle mile traveled (VMT; Kahane, 2012). Societal fatality risk includes the risk to both the occupants of the case vehicle as well as any crash partner or pedestrians. The current an...

A preimplantation genetic test to discriminate between severe and mild autism spectrum disorder might be developed in the foreseeable future. Recently, the philosophers Julian Savulescu and Guy Kahane claimed that there are strong reasons for prospective parents to make use of such a test to prevent the birth of children who are disposed to autism or Asperger's disorder. In this paper we will c...

Let Pn(z) = ∑n k=0 ak,nz k ∈ C [z] be a sequence of unimodular polynomials (|ak,n| = 1 for all k, n) which is ultraflat in the sense of Kahane, i.e., lim n→∞ max |z|=1 ∣∣∣(n + 1)−1/2|Pn(z)| − 1∣∣∣ = 0 . We prove the following conjecture of Saffari (1991): ∑n k=0 ak,nan−k,n = o(n) as n → ∞, that is, the polynomial Pn(z) and its “conjugate reciprocal” P ∗ n(z) = ∑n k=0 an−k,nz k become “nearly or...

We have previously found that the myotome is formed by a first wave of pioneer cells generated along the medial epithelial somite and a second wave emanating from the dorsomedial lip (DML), rostral and caudal edges of the dermomyotome (Kahane, N., Cinnamon, Y. and Kalcheim, C. (1998a) Mech. Dev. 74, 59-73; Kahane, N., Cinnamon, Y. and Kalcheim, C. (1998b) Development 125, 4259-4271). In this st...