The aim of this paper is a) if Σak2 < ∞ then Σak rk(x) is in BMO that{rk(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k nk < 2k+1that f!n(x)g is Walsh system. c) If jakj < 1k then P1k=1 ak!k(x) 2 BMO.

Let θ(a1, a2, · · · , ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, · · · , ak respectively. Assume that 2 ≤ a1 ≤ a2 ≤ · · · ≤ ak. We prove that the graph θ(a1, a2, · · · , ak) is chromatically unique if ak < a1 + a2, and find examples showing that θ(a1, a2, · · · , ak) may not be chromatically unique if ak = a1 + a2.

Three lipase-producing thermophilic bacteria (AK-P1, AK-P2, and AK-P3) were isolated from the Taptapani hot water spring in Orissa, India. The crude extra cellular lipases from cell-free culture supernatant were reacted in an olive oil mixture, and their lipolytic activities were compared. Identification of the bacteria was carried out using biochemical tests, 16SrRNA sequencing and sequences s...

Biosynthesis of aspartate (Asp)-derived amino acids lysine (Lys), methionine (Met), threonine (Thr), and isoleucine involves monofunctional Asp kinases (AKs) and dual-functional Asp kinase-homoserine dehydrogenases (AK-HSDHs). Four-week-old loss-of-function Arabidopsis (Arabidopsis thaliana) mutants in the AK-HSDH2 gene had increased amounts of Asp and Asp-derived amino acids, especially Thr, i...

The Newton-Lagrange interpolation is a well-known problem in elementary calculus. Recall basic facts concerning this problem [6], [2]. Let Ak, k = 0, 1, 2, . . . and ak, k = 0, 1, 2, . . . be two arbitrary sequences of complex numbers (we assume that all ak are distinct ak 6= aj if k 6= j. By interpolation polynomial we mean a n-degree polynomial Pn(z) whose values at points a0, a1, . . . , an ...

Serum adenylate kinase (AK) activity was measured in cerebral vascular diseases and the AK isoenzyme pattern was studied in the patients suffering from cerebral infarction, cerebral hemorrhage, myocardial infarction, and polymyositis. There was a significant difference in AK activity between the control subjects and patients with acute cerebral infarction. Serum AK activity showed a peak on the...

BACKGROUND Actinic keratoses (AK) represent cutaneous carcinoma in situ and have previously been evaluated by reflectance confocal microscopy (RCM). Treatment of AK with imiquimod (IMIQ) 5% cream has been shown to 'highlight' subclinical lesions. OBJECTIVE The aim of this study was to test the applicability of RCM for noninvasive monitoring of actinic field cancerization and detection of subc...