On Osgood theorem in Banach spaces

Let $X$ be a real Banach space, $\omega:[0,+\infty)\to\R$ be an increasing continuous function such that $\omega(0)=0$ and $\omega(t+s)\leq\omega(t)+\omega(s)$ for all $t,s\in[0,+\infty)$. By the Osgood theorem, if $\int_{0}^1\frac{dt}{\omega(t)}=\infty$, then for any $(t_0,x_0)\in R\times X$ and any continuous map $f: R\times X\to X$ and such that $\|f(t,x)-f(t,y)\|\leq\omega(\|x-y\|)$ for all $t\in R$, $x,y\in X$, the Cauchy problem $\dot x(t)=f(t,x(t))$, $(t_0)=x_0$ has a unique solution in a neighborhood of $t_0$ . We prove that if $X$ has a complemented subspace with an unconditional Schauder basis and $\int_{0}^1\frac{dt}{\omega(t)}

Counterexample to Peano's theorem in infinite-dimensional F '-spaces

Let $E$ be a nonnormable Frechet space, and let $E'$ be the space of all continuous linear functionals on $E$ in the strong topology. A continuous mapping $f : E' \to E'$ such that for any $t_0\in R$ and $x_0\in E'$, the Cauchy problem $\dot x= f(x)$, x(t_0) = x_0$ has no solutions is constructed.

Monkey mountain as a megazoo: analysing the naturalistic claims of “wild monkey parks” in Japan

In Japan yaen koen or ‘wild monkey parks’ are popular visitor attractions that show free-ranging monkey troops to the paying public. Unlike zoos, which display animals through confinement, monkey parks control the movements of the monkeys through provisioning. The parks project an image of themselves as ‘natural zoos’, claiming to practice a more authentic form of wild animal display than that practiced by the zoo. This article critically evaluates the monkey park’s claim by examining park management of the monkeys. The monkey park’s claim to display ‘wild monkeys’ is shown to be questionable because of the way that provisioning changes monkey behaviour. Against the background of human encroachment onto the forest habitat of the monkey, the long-term effect of provisioning is to sedentarize what were nomadic monkeys and to turn the ‘wild monkey park’ into a megazoo.

Increased cerebral output of free radicals during hypoxia: implications for acute mountain sickness?

Bailey DM, Taudorf S, Berg RMG, Lundby C, McEneny J, Young IS, Evans KA, James PE, Shore A, Hullin DA, McCord JM, Pedersen BK, Moller K. Increased cerebral output of free radicals during hypoxia: implications for acute mountain sickness? Am J Physiol Regul Integr Comp Physiol 297: R1283-R1292, 2009. First published September 2, 2009; doi: 10.1152/ajpregu.00366.2009.-This study examined whether hypoxia causes free radical-mediated disruption of the blood-brain barrier (BBB) and impaired cerebral oxidative metabolism and whether this has any bearing on neurological symptoms ascribed to acute mountain sickness (AMS). Ten men provided internal jugular vein and radial artery blood samples during normoxia and 9-h passive exposure to hypoxia (12.9% O-2). Cerebral blood flow was determined by the Kety-Schmidt technique with net exchange calculated by the Fick principle. AMS and headache were determined with clinically validated questionnaires. Electron paramagnetic resonance spectroscopy and ozone-based chemiluminescence were employed for direct detection of spin-trapped free radicals and nitric oxide metabolites. Neuron-specific enolase (NSE), S100 beta, and 3-nitrotyrosine (3-NT) were determined by ELISA. Hypoxia increased the arterio-jugular venous concentration difference (a-v(D)) and net cerebral output of lipid-derived alkoxyl-alkyl free radicals and lipid hydroperoxides (P

Antimicrobial peptides from the skin secretion of the Wuyi Mountain torrent frog, Amolops wuyiensis: An inhabitant of a pristine aquatic environment

The antimicrobial peptides of amphibian skin secretions are proposed to aid survival in microbe-rich environments. While many amphibians inhabit such environments, other such as the Wuyi Mountain torrent frog, Amolops wuyiensis, live in pristine waters flowing from underground mountain springs. This species thus represents an interesting model in which to study antimicrobial peptides. “Shotgun” cloning of a skin-derived cDNA library from this species identified transcripts encoding a brevinin-1 and a ranatuerin-2. Peptides with coincident molecular masses to both predicted mature peptides were identified in HPLC fractions of skin secretion. Synthetic replicates of both peptides were generated by solid-phase peptide synthesis and tested for activity using Staphylococcus aureus, Escherichia coli and Candida albicans. The brevinin was found to be broad-spectrum and potent with minimum inhibitory concentrations (MICs) of 24 µM (Sa), 5 µM (Ec) and 20 µM (Ca). In contrast, the ranatuerin was less effective and of narrower spectrum with an MIC > 200 µM for Sa, 40 µM (Ec) and 120 µM (Ca). Thus this species of amphibian that lives in a pristine environment does indeed possess at least one potent and broad-spectrum antimicrobial peptide in its skin secretion arsenal. This phenomenon could be explained in several ways. Firstly, it may represent an ancestral peptide required when the stem species inhabited microbe-rich environments. However, there is mounting evidence for the second reason, that suggests the function of such peptides is not primarily in antimicrobial defence.

From PASS 1 to YES to AND logic: building parallel processing into molecular logic gates by sequential addition of receptors

The synthesis and photophysical characterization of a novel molecular logic gate 4, operating in water, is demonstrated based on the competition between. fluorescence and photoinduced electron transfer (PET). It is constructed according to a 'fluorophore-spacer-receptor(1)-spacer-receptor(2)' format where anthracene is the. fluorophore, receptor(1) is a tertiary amine and receptor(2) is a phenyliminodiacetate ligand. Using only protons and zinc cations as the chemical inputs and. fluorescence as the output, 4 is demonstrated to be both a two-input AND and INH logic gate. When 4 is examined in context to the YES logic gates 1 and 2, and the two-input AND logic gate 3 and three-input AND logic gate 5, each with one or more of the following receptors including a tertiary amine, phenyliminodiacetate or benzo-15-crown-5 ether, logic gate 4 is the missing link in the homologous series. Collectively, the molecular logic gates 1-5 corroborate the PET 'fluorophore-spacer-receptor' model using chemical inputs and a light-signal output and provide insight into controlling the. fluorescence quantum yield of future PET-based molecular logic gates.

Prospective information for pass decisional behaviour in Rugby Union

Decision-making requires the perception of relevant information variables that emerge from the player–environment interaction. The purpose of the present article is to empirically assess whether players’ decisional behavior about which type of pass to make is influenced by the spatio-temporal variable tau. Time series positional data of rugby players were analyzed from video footage taken in real match scenarios. The tau of the distance motion gap between attacker and defender was calculated, along with the duration of the next pass. Results revealed that the initial tau value predicted 64% of the variance found in pass duration. A qualitative distinction of tau dynamics between two periods of the approach between the attacker and the defender was also observed. We argue that the time-to-contact between the attacker and the defender may yield information about future pass possibilities. Additionally, the informational fields constraining attacker–defender interaction may be viewed as a convergent channeling of possibilities towards a single pass solution.