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...

A3 Start with a finite sequence a1, a2, . . . , an of positive integers. If possible, choose two indices j < k such that aj does not divide ak, and replace aj and ak by gcd(aj , ak) and lcm(aj , ak), respectively. Prove that if this process is repeated, it must eventually stop and the final sequence does not depend on the choices made. (Note: gcd means greatest common divisor and lcm means leas...

AIM Impact of gender on aminoglycoside induced nephrotoxicity is still controversial and inconclusive. The objective of this study was to investigate the nephrotoxic potential of amikacin (AK) and gentamicin (GM) in male and female hospitalized patients. METHODOLOGY A one-year, non-interventional prospective study of patients administered either GM or AK. The study was carried out at the inte...

der anwesenden AK-Mitglieder mit derzeitigen Arbeitsschwerpunkten. 3. Einigung mit Gerd Frackenpohl. 2. Situation im AK Die Teilnehmer Ulrich Heid, Universität Stuttgart, und Andrea Beurer, Universität Trier, erklärten sich bereit, den Sprecher des AK beratend und gegebenalls organisatorisch zu unterstützen. Eine Sitzung des AK hat seit der letzten Jahrestagung in Gießen nicht mehr stattgefunde...

In addition to their role in antigen presentation, major histocompatibility complex (MHC) class II molecules have been widely described as signaling proteins in diverse antigen-presenting cells (APCs) including B cells and dendritic cells. By contrast, little is known of the signaling function of MHC class II molecules expressed in solid tumors. We describe the functional organization and signa...

The mitochondrion of sea urchin sperm is located at the base of the sperm head, and the flagellum extends from the mitochondrion for approximately 40 microM. These sperm have two known flagellar, non-mitochondrial, enzymatic systems to rephosphorylate ADP. The first involves the phosphocreatine shuttle, where flagellar creatine kinase (Sp-CK) uses phosphocreatine to rephosphorylate ADP. The sec...

and Applied Analysis 3 Generalized derivations first appeared in the context of operator algebras 7 . Later, these were introduced in the framework of pure algebra 8, 9 . Definition 1.1. LetA be an algebra and let X be anA-bimodule. A linear mapping d : A → X is called i derivation if d ab d a b ad b , for all a, b ∈ A; ii generalized derivation if there exists a derivation in the usual sense δ...

Example 3. For k′/k a finite separable extension and H any linear algebraic k-group, we have H ↪−→ Rk′/k(Hk′) =: H ′, where Rk′/k(Hk′) is the Weil restriction functor (which is representable by a linear algebraic k-group). This functor is defined by Rk′/k(Hk′)(A) = Hk′(A⊗k k′), so the injection H ↪−→ Rk′/k(Hk′) is given by sending a k-morphism SpecA→ H to its base change by k′. Then we have [H ...