Let un sup(ak )∞ k n and vn sup(bk ) ∞ k n be suprema. Then the following obvious relation ak ≤ un and bk ≤ vn , ∀k ≥ n ⇒ ak + bk ≤ un + vn , ∀k ≥ n shows that, upon taking the supremum over all k with k ≥ n, we get sup(ak + bk )∞ k n ≤ un + vn . This shows that for any n ≥ m, we get lim sup k→∞ (ak + bk ) inf j: j≥m sup(ak + bk )∞ k j ≤ sup(ak + bk ) ∞ k n ≤ un + vn Since we know that (un )∞ n...

Given a sequence (ak) = a0, a1, a2, . . . of real numbers, define a new sequence L(ak) = (bk) where bk = ak − ak−1ak+1. So (ak) is log-concave if and only if (bk) is a nonnegative sequence. Call (ak) infinitely log-concave if L(ak) is nonnegative for all i ≥ 1. Boros and Moll [3] conjectured that the rows of Pascal’s triangle are infinitely log-concave. Using a computer and a stronger version o...

Memory impairment is the most common symptom in patients with Alzheimer's disease (AD). Angelica keiskei (AK) has traditionally been used as a diuretic, laxative, analeptic and galactagogue. However, the anti-amnesic effects of AK and its molecular mechanisms have yet to be clearly elucidated. The aim of the present study is to evaluate the effects of AK on scopolamine-induced memory impairment...

In this report we describe cloning and expression of rat adenosine kinase (AK) in Esccherichaia coli cells as a fusion protein with 6xHis. The recombinant protein was purified and polyclonal antibodies to AK were generated in rabbits. Immunoblot analysis of extracts obtained from various rat tissues revealed two protein bands reactive with anti-AK IgG. The apparent molecular mass of these bands...

Cytokine-secreting, major histocompatibility complex-unrestricted activated killer (AK) cells are toxic to a wide range of virus-infected or malignant target cells and may be generated endogenously, eg, after bone marrow transplantation, or by infusion of cytokines such as recombinant interleukin-2 (rIL-2). Although AK cells secrete cytokines such as gamma-interferon and tumor necrosis factor, ...

We systematically investigate the formation and stability of snowballs formed by femtosecond photoionization of small alkali clusters bound to helium nanodroplets. For all studied alkali species Ak = (Na,K,Rb,Cs) we observe the formation of snowballs Ak(+)He(N) when multiply doping the droplets. Fragmentation of clusters Ak(N) upon ionization appears to enhance snowball formation. In the case o...