A set A = Ak,n ⇢ [n] [ {0} is said to be an additive k-basis if each element in {0, 1, . . . , kn} can be written as a k-sum of elements of A in at least one way. Seeking multiple representations as k-sums, and given any function (n) ! 1, we say that A is said to be a truncated (n)-representative k-basis for [n] if for each j 2 [↵n, (k ↵)n] the number of ways that j can be represented as a k-su...

BACKGROUND Previous studies suggest that adenylate kinase locus 1 (Ak 1 ) has an important role in the control of blood glucose level and in the glycation of structural and functional proteins in type 2 diabetes and in the balanced development of feto-placental unit in healthy puerperae (HP). In this study, an attempt was made to investigate the relationship of Ak 1 with maternal and neonatal p...

We present a new approach to evaluating combinatorial sums by using finite differences. Let {ak}k=0 and {bk}k=0 be sequences with the property that ∆bk = ak for k ≥ 0. Let gn = ∑n k=0 ( n k ) ak, and let hn = ∑n k=0 ( n k ) bk. We derive expressions for gn in terms of hn and for hn in terms of gn. We then extend our approach to handle binomial sums of the form ∑n k=0 ( n k ) (−1)ak, ∑ k ( n 2k ...

In the field of software architecture, there has been a paradigm shift from describing structural information, such as components and connectors, to documenting Architectural Knowledge (AK), such as design decisions and rationale. To this end, a series of industrial and academic domain models have been proposed for defining the concepts and their relationships in the field of AK. To a large ext...

BACKGROUND/OBJECTIVE Although Angelica keiskei (AK) has widely been utilized for the purpose of general health improvement among Asian, its functionality and mechanism of action. The aim of this study was to determine the protective effect of ethanol extract of AK (AK-Ex) on acute hepatotoxicity induced by acetaminophen (AAP) in HepG2 human hepatocellular liver carcinoma cells and HepaRG human ...

1 Geophysical Institute, University of Alaska, Fairbanks, AK, USA 2 ABR, Inc., Fairbanks, AK, USA 3 Department of Botany, University of Florida, Gainesville, FL, USA 4 Department of Civil and Environmental Engineering, University of Alaska, Fairbanks, AK, USA 5 Institute of Northern Engineering, University of Alaska, Fairbanks, AK, USA 6 Department of Geology, Moscow State University, Moscow, R...

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...

Let Vn(q) denote a vector space of dimension n over the field with q elements. A set P of subspaces of Vn(q) is a partition of Vn(q) if every nonzero vector in Vn(q) is contained in exactly one subspace of P. If there exists a partition of Vn(q) containing ai subspaces of dimension ni for 1 ≤ i ≤ k, then (ak, ak−1, . . . , a1) must satisfy the Diophantine equation ∑k i=1 ai(q ni − 1) = q− 1. In...