A characterization of the periods of periodic points of 1-norm nonexpansive maps

In this paper the set of minimal periods of periodic points of 1-norm nonexpansive maps is studied. This set is denoted by R(n). The main goal is to present a characterization of R(n) by arithmetical and combinatorial constraints. More precisely, it is shown that , where denotes the set of periods of restricted admissible arrays on 2n symbols. The important point of this equality is that is determined by arithmetical and combinatorial constraints only, and that it can be computed in finite time. By using this equality the set R(n) is computed for . Furthermore it is shown that the largest element of R(n) satisfies:      

Neuronal expression of muskelin in the rodent central nervous system

Background  

The kelch repeat protein muskelin mediates cytoskeletal responses to the extracellular matrix protein thrombospondin 1, (TSP1), that is known to promote synaptogenesis in the central nervous system (CNS). Muskelin displays intracellular localization and affects cytoskeletal organization in adherent cells. Muskelin is expressed in adult brain and has been reported to bind the Cdk5 activator p39, which also facilitates the formation of functional synapses. Since little is known about muskelin in neuronal tissues, we here analysed the tissue distribution of muskelin in rodent brain and analysed its subcellular localization using cultured neurons from multiple life stages.     

Identification of complex,naturally occurring flavonoid glycosides in kale (Brassica oleracea var. sabellica) by high‐performance liquid chromatography diode‐array detection/electrospray ionization multi‐stage mass spectrometry

Kale is a member of the Brassicaceae family and has a complex profile of flavonoid glycosides. Therefore, kale is a suitable matrix to discuss in a comprehensive study the different fragmentation patterns of flavonoid glycosides. The wide variety of glycosylation and acylation patterns determines the health‐promoting effects of these glycosides. The aim of this study is to investigate the naturally occurring flavonoids in kale. A total of 71 flavonoid glycosides of quercetin, kaempferol and isorhamnetin were identified using a high‐performance liquid chromatography diode‐array detection/electrospray ionization multi‐stage mass spectrometry (HPLC‐DAD/ESI‐MSⁿ) method. Of these 71 flavonol glycosides, 27 were non‐acylated, 30 were monoacylated and 14 were diacylated. Non‐acylated flavonol glycosides were present as mono‐, di‐, tri‐ and tetraglycosides. This is the first time that the occurrence of four different fragmentation patterns of non‐acylated flavonol triglycosides has been reported in one matrix simultaneously. In addition, 44 flavonol glycosides were acylated with p‐coumaric, caffeic, ferulic, hydroxyferulic or sinapic acid. While monoacylated glycosides existed as di‐, tri‐ and tetraglycosides, diacylated glycosides occurred as tetra‐ and pentaglycosides. To the best of our knowledge, 28 compounds in kale are reported here for the first time. These include three acylated isorhamnetin glycosides (isorhamnetin‐3‐O‐sinapoyl‐sophoroside‐7‐O‐D‐glucoside, isorhamnetin‐3‐O‐feruloyl‐sophoroside‐7‐O‐diglucoside and isorhamnetin‐3‐O‐disinapoyl‐triglucoside‐7‐O‐diglucoside) and seven non‐acylated isorhamnetin glycosides. Copyright © 2010 John Wiley & Sons, Ltd.     

High-sensitivity microchip electrophoresis determination of inorganic anions and oxalate in atmospheric aerosols with adjustable selectivity and conductivity detection

A sensitive and selective separation of common anionic constituents of atmospheric aerosols, sulfate, nitrate, chloride, and oxalate, is presented using microchip electrophoresis. The optimized separation is achieved in under 1 min and at low background electrolyte ionic strength (2.9 mM) by combining a metal-binding electrolyte anion (17 mM picolinic acid), a sulfate-binding electrolyte cation (19 mM HEPBS), a zwitterionic surfactant with affinity towards weakly solvated anions (19 mM N-tetradecyl,N,N-dimethyl-3-ammonio-1-propansulfonate), and operation in counter-electroosmotic flow (EOF) mode. The separation is performed at pH 4.7, permitting pH manipulation of oxalate's mobility. The majority of low-concentration organic acids are not observed at these conditions, allowing for rapid subsequent injections without the presence of interfering peaks. Because the mobilities of sulfate, nitrate, and oxalate are independently controlled, other minor constituents of aerosols can be analyzed, including nitrite, fluoride, and formate if desired using similar separation conditions. Contact conductivity detection is utilized, and the limit of detection for oxalate (S/N = 3) is 180 nM without stacking. Sensitivity can be increased with field-amplified sample stacking by injecting from dilute electrolyte with a detection limit of 19 nM achieved. The high-sensitivity, counter-EOF operation, and short analysis time make this separation well-suited to continuous online monitoring of aerosol composition.