The squared correlation coefficient r2 (sometimes denoted ∆2) is a measure of linkage disequilibrium that is widely used, but computing its expectation E[r2] in the population has remained an intriguing open problem. The expectation E[r2] is often approximated by the standard linkage deviation σ2 d, which is a ratio of two expectations amenable to analytic computation. In this paper, a method o...

The paper studies the counting function R2(n, k) = ∑ a1+a2+···+ak=n (ai,aj)=1 i 6=j 1, ai ≥ 1, k ≥ 2 with ai, n and k positive integers and establishes a relationship between R2(n, k) and P2(n, k) where P2(n, k) = ∑ a1+a2+···+ak=n 1≤a1≤a2≤···≤ak≤n (ai,aj)=1 i 6=j 1, ai ≥ 1, k ≥ 2 with ai, n, k positive integers. 1. PRELIMINARIES Gould [4], studied the number-theoretic function R(n, k) = ∑ a1+a2...

R2 non-long terminal repeat retrotransposable elements insert specifically into the 28S rRNA genes of a wide range of animals. These elements maintain long-term stable relationships with the host genome. By scoring the variation present at the 5' ends of individual R2 copies, lines of Drosophila simulans have been identified with high rates of R2 retrotransposition. Comparing the R2 elements pr...

AIMS This paper attempts to investigate the role of cellular polysaccharides in the formation and stability of aerobic granules. METHODS AND RESULTS Three column sequential aerobic sludge blanket reactors (R1, R2 and R3) were operated at a superficial air upflow velocity of 0.3 cm s(-1), 1.2 cm s(-1) and 2.4 cm s(-1), respectively. Aerobic granules appeared at cycle 42 in R2 and R3 with a mea...

AIM The study assessed mRNA expression of podocyte-associated molecules in urinary sediments of patients with type 2 diabetes mellitus (DM) in relation to urinary podocytes, biomarkers of podocyte injury and of proximal tubule (PT) dysfunction. METHODS A total of 76 patients with type 2 DM and 20 healthy subjects were enrolled in a cross-sectional study, and assessed concerning urinary podocy...

Ribonucleotide reductase consists of two nonidentical proteins, R1 and R2, and catalyzes the rate-limiting step in DNA precursor synthesis: the reduction of ribonucleotides to deoxyribonucleotides. A strictly balanced supply of deoxyribonucleotides is essential for both accurate DNA replication and repair. Therefore, ribonucleotide reductase activity is under exquisite control both transcriptio...

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that the direct sum of two term rewriting systems is not terminating, even if these systems are both terminating. Keyword: Term rewriting system, termination Introduction A term rewriting system R is a set of rewriting rules M → N , where M and N are terms [1, 3, 5]. The di...

background: in this study the basic radiation properties of n-isopropylacrylamaide polymer gel dosimeter were determined together with verification of its soft tissue equivalency. materials and methods: the nipam gel was prepared and irradiated approximately 2 h after manufacturing. the magnetic resonance (mr) images were made 24 h after irradiation. the nuclear magnetic resonance (nmr) respons...

and Applied Analysis 3 −λ (0, 0, rp) = − N 󵄨󵄨󵄨󵄨󵄨1 + r2 p󵄨󵄨󵄨󵄨󵄨3/2 (0, 0, rp) − (0, 0, 1 r2 p)M0 − ∑ 1≤i<p ( 1 󵄨󵄨󵄨󵄨󵄨ri − rp󵄨󵄨󵄨󵄨󵄨2 + 1 󵄨󵄨󵄨󵄨󵄨ri + rp󵄨󵄨󵄨󵄨󵄨2)Mi (0, 0, 1) − 1 󵄨󵄨󵄨󵄨󵄨2rp󵄨󵄨󵄨󵄨󵄨2Mp (0, 0, 1) . (11) In order to simplify the equations, we defined a0,j = −2/|1+r2 j |3/2, aj,j = −1/4r3 j , where j = 1, . . . , p; ai,j = (1/|ri − rj|2ri − 1/|ri + rj|2ri), when i < j; ai,j = −(1/|ri − rj|2ri + 1/...