Motivated by a question of Sárközy, we study the gaps in the product sequence B = A · A = {b1 < b2 < · · · } of all products aiaj with 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 r...

There is compelling evidence that genetic factors play an important role in prostate cancer, but no unequivocally disease causing mutations in prostate cancer susceptibility genes have been identified. In 2002, Carpten et al reported that variants in the gene RNASEL were present in some multiple case prostate cancer families. RNASEL maps to the region of chromosome 1q that has been linked to pr...

A+A = {ai + aj : ai, aj ∈ A}, A−A = {ai − aj : ai, aj ∈ A}, A +̂A = {ai + aj : ai, aj ∈ A and ai 6= aj} respectively. Here we refer to sets A with |A+A| > |A−A| as sum-dominant (some authors use the term MSTD, for more sums than differences sets). Though the fact that addition is commutative but subtraction usually is not might naively suggest that sum-dominant sets are rare if they exist at all...

We present a comparison of the gas and dust properties of the dense interstellar matter in six nearby star−forming regions (d <500 pc): ρ Oph, Cha I, R CrA, IC 348, NGC 1333, and Orion. We measure from Chandra and XMM−Newton observations the X-ray absorption toward pre-main sequence stars (PMS) without accretion disks (i.e., Class III sources) to obtain the total hydrogen column density NH,X. F...

Definition 1. Given a vector |v〉 ∈ H, by a Schmidt decomposition across the (i, i + 1) cut we shall mean a decomposition |v〉 = ∑j=1 λj|aj〉|bj〉 with {|aj〉} (respectively {|bj〉} ) a family of orthonormal vectors of H[1,i] (respectively H[i+1,n]) and with λj ≥ λj+1 > 0 for all 1 ≤ j ≤ D. The vectors |aj〉 will be called the left Schmidt vectors across that cut, and the vectors |bj〉 the right Schmid...

Let s,t be two given real numbers, s = t and m ∈ N . We determine the coefficients aj(s,t) in the asymptotic expansion of integral (or differential) mean of polygamma functions ψ (m)(x) : 1 t− s ∫ t s ψ (m)(x+u)du ∼ ψ (m) ( x ∞ ∑ j=0 aj(s,t) x j ) , x → ∞. We derive the recursive relations for polynomials aj(t,s) , and also as polynomials in intrinsic variables α = 2 (s + t − 1) , β = 4 [1− (t ...

Strains of the bacterium, Corynebacterium glutamicum, are widely used for the industrial production of L-glutamic acid and various other substances. C. glutamicum ssp. lactofermentum AJ 1511, formerly classified as Brevibacterium lactofermentum, and the closely related C. glutamicum ATCC 13032 have been used as industrial strains for more than 50 years. We determined the whole genome sequence o...

This paper considers spectrally efficient anti-jamming system design based on message-driven frequency hopping (MDFH). As a highly efficient frequency hopping scheme, MDFH is particularly robust under strong jamming. However, disguised jamming from sources of similar power strength can cause performance losses. To overcome this drawback, in this paper, we first propose an anti-jamming MDFH (AJ-...

k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...