The influence of oscillations on global existence for a class of semi-linear wave equations

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u(tt) - a(t)(2) Delta u = u(t)(2) - a(t)(2)vertical bar del u vertical bar(2). In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions. Copyright c 2011 John Wiley & Sons, Ltd.

Loss of Ergodicity in the Transition from Annealed to Quenched Disorder in a Finite Kinetic Ising Model

We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing ""jumpy"" transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e. g. high level of corruption) to a desirable one (low level of corruption).

Gamma-band oscillations in fronto-central areas during performance of a sensorimotor integration task: A qEEG coherence study

This study aimed to elucidate electrophysiological and cortical mechanisms involved in anticipatory actions when 23 healthy right-handed subjects had to catch a free falling object by qEEG gamma-band (30-100 Hz). It is involved in cognitive processes, memory, spatial/temporal and proprioceptive factors. Our hypothesis is that an increase in gamma coherence in frontal areas will be observed during moment preceding ball drop, due to their involvement in attention, planning, selection of movements, preparation and voluntary control of action and in central areas during moment after ball drop, due to their involvement in motor preparation, perception and execution of movement. However, through a paired t-test, we found an increase in gamma coherence for F3-F4 electrode pair during moment preceding ball drop and confirmed our hypothesis for C3-C4 electrode pair. We conclude that gamma plays an important role in reflecting binding of several brain areas in a complex motor task as observed in our results. Moreover, for selection of movements, preparation and voluntary control of action, motor preparation, perception and execution of movement, the integration of somatosensory and visual information is mandatory. (C) 2010 Elsevier Ireland Ltd. All rights reserved.

Gamma band oscillations under influence of bromazepam during a sensorimotor integration task: An EEG coherence study

The goal of the present study was to explore the dynamics of the gamma band using the coherence of the quantitative electroencephalography (qEEG) in a sensorimotor integration task and the influence of the neuromodulator bromazepam on the band behavior. Our hypothesis is that the needs of the typewriting task will demand the coupling of different brain areas, and that the gamma band will promote the binding of information. It is also expected that the neuromodulator will modify this coupling. The sample was composed of 39 healthy subjects. We used a randomized double-blind design and divided subjects into three groups: placebo (n = 13), bromazepam 3 mg (n = 13) and bromazepam 6 mg (n = 13). The two-way ANOVA analysis demonstrated a main effect for the factors condition (i.e., C4-CZ electrode pair) and moment (i.e., C3-CZ, C3-C4 and C4-CZ pairs of electrodes). We propose that the gamma band plays an important role in the binding among several brain areas in complex motor tasks and that each hemisphere is influenced in a different manner by the neuromodulator. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Idiopathic Toe Walking A Kinematic and Kinetic Profile

Purpose: The differential diagnosis in children who walk on their toes includes mild spastic diplegia and idiopathic toe walking (ITW). A diagnosis of ITW is often one of exclusion. To better characterize the diagnosis of ITW, quantitative gait analysis was utilized in a series of patients with an established diagnosis of ITW. Study Design: Patients with an established diagnosis of ITW were analyzed by quantitative gait analysis. Data were recorded as each subject walked in a self-selected toe-walking pattern. The subject was then asked to ambulate making every effort to walk in a normal heel-toe reciprocating fashion. Data were collected to determine if this group of idiopathic toe walkers was able to normalize their gait. Data sets were compared with each other and with historical normal controls. Results: Fifty-one neurologically normal children ( 102 extremities) with ITW were studied in the Motion Analysis Laboratory at a mean age of 9.3 years. In the self-selected trials, significant deviations in both kinematics and kinetics at the level of the ankle were identified. Disruption of all 3 ankle rockers and a plantar flexion bias of the ankle throughout the gait cycle were most commonly seen. When asked to attempt a normal heel-toe gait, 17% of the children were able to normalize both stance and swing variables. In addition, 70% were able to normalize some but not all of the stance and swing variables. Conclusion: Quantitative gait analysis is an effective tool for differentiating mild cerebral palsy from ITW. Kinematic and kinetic distinctions between the diagnoses are evident at the knee and ankle. The ability to normalize on demand at least some of the kinematic and kinetic variables associated with toe walking is seen in most children with ITW.

Reliability of electromyographic amplitude values of the upper limb muscles during closed kinetic chain exercises with stable and unstable surfaces

The purpose of the present study was to evaluate the intra and interday reliability of surface electromyographic amplitude values of the scapular girdle muscles and upper limbs during 3 isometric closed kinetic chain exercises, involving upper limbs with the fixed distal segment extremity on stable base of support and on a Swiss ball (relatively unstable). Twenty healthy adults performed the exercises push-up, bench-press and wall-press with different effort levels (80% and 100% maximal load). Subjects performed three maximal voluntary contractions (MVC) in muscular testing position of each muscle to obtain a reference value for root mean square (RMS) normalization. Individuals were instructed to randomly perform three isometric contraction series, in which each exercise lasted 6 s with a 2-min resting-period between series and exercises. Intra and interday reliabilities were calculated through the intraclass correlation coefficient (ICC 2.1), standard error of the measurement (SEM). Results indicated an excellent intraday reliability of electromyographic amplitude values (ICC >= 0.75). The interday reliability of normalized RMS values ranged between good and excellent (ICC 0.52-0.98). Finally, it is suggested that the reliability of normalized electromyographic amplitude values of the analyzed muscles present better values during exercises on a stable surface. However, load levels used during the exercises do not seem to have any influence on variability levels, possibly because the loads were quite similar. (C) 2007 Elsevier Ltd. All rights reserved.

Albendazole-praziquantel interaction in healthy volunteers: kinetic disposition, metabolism and enantioselectivity

center dot Pharmacokinetic interactions between albendazole and praziquantel are based on plasma concentrations of the enantiomeric mixture of both drugs with contradictory data, although the antiparasitic activity arises from (-)-(R)-praziquantel and (+)-albendazole sulfoxide. WHAT THIS STUDY ADDS center dot The pharmacokinetic interaction between albendazole and praziquantel is enantioselective. Praziquantel increased the plasma concentrations of (+)-albendazole sulfoxide more than those of (-)-albendazole sulfoxide and the administration of albendazole did not change the kinetic disposition of (+)-(S)-praziquantel, but increased the plasma concentration of (-)-(R)-praziquantel. AIM This study investigated the kinetic disposition, metabolism and enantioselectivity of albendazole (ABZ) and praziquantel (PZQ) administered alone and in combination to healthy volunteers. METHODS A randomized crossover study was carried out in three phases (n = 9), in which some volunteers started in phase 1 (400 mg ABZ), others in phase 2 (1500 mg PZQ), and the remaining volunteers in phase 3 (400 mg ABZ + 1500 mg PZQ). Serial blood samples were collected from 0-48 h after drug administration. Pharmacokinetic parameters were calculated using a monocompartmental model with lag time and were analyzed using the Wilcoxon test; P < 0.05. RESULTS The administration of PZQ increased the plasma concentrations of (+)-ASOX (albendazole sulphoxide) by 264% (AUC 0.99 vs. 2.59 mu g ml-1 h), (-)-ASOX by 358% (0.14 vs. 0.50 mu g ml-1 h) and albendazole sulfone (ASON) by 187% (0.17 vs. 0.32 mu g ml-1 h). The administration of ABZ did not change the kinetic disposition of (+)-(S)-PZQ (-)-(R)-4-OHPZQ or (+)-(S)-4-OHPZQ, but increased the plasma concentration of (-)-(R)-PZQ by 64.77% (AUC 0.52 vs. 0.86 mu g ml-1 h). CONCLUSIONS The pharmacokinetic interaction between ABZ and PZQ in healthy volunteers was demonstrated by the observation of increased plasma concentrations of ASON, both ASOX enantiomers and (-)-(R)-PZQ. Clinically, the combination of ABZ and PZQ may improve the therapeutic efficacy as a consequence of higher concentration of both active drugs. On the other hand, the magnitude of this elevation may represent an increased risk of side effects, requiring, certainly, reduction of the dosage. However, further studies are necessary to evaluate the efficacy and safety of this combination.

Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

Orbitally induced oscillations in the East Antarctic ice sheet at the Oligocene/Miocene boundary

Between 34 and 15 million years (Myr) ago, when planetary temperatures were 3-4 degreesC warmer than at present and atmospheric CO2 concentrations were twice as high as today(1), the Antarctic ice sheets may have been unstable(2-7). Oxygen isotope records from deep-sea sediment cores suggest that during this time fluctuations in global temperatures and high-latitude continental ice volumes were influenced by orbital cycles(8-10). But it has hitherto not been possible to calibrate the inferred changes in ice volume with direct evidence for oscillations of the Antarctic ice sheets(11). Here we present sediment data from shallow marine cores in the western Ross Sea that exhibit well dated cyclic variations, and which link the extent of the East Antarctic ice sheet directly to orbital cycles during the Oligocene/Miocene transition (24.1-23.7 Myr ago). Three rapidly deposited glaci-marine sequences are constrained to a period of less than 450 kyr by our age model, suggesting that orbital influences at the frequencies of obliquity (40 kyr) and eccentricity (125 kyr) controlled the oscillations of the ice margin at that time. An erosional hiatus covering 250 kyr provides direct evidence for a major episode of global cooling and ice-sheet expansion about 23.7 Myr ago, which had previously been inferred from oxygen isotope data (Mil event(5)).

Synthesis and stereochemistry of some bicyclic gamma-lactones from parasitic wasps (Hymenoptera : Braconidae). Utility of hydrolytic kinetic resolution of epoxides and palladium(II)-catalyzed hydroxycyclization-carbonylation-lactonization of ene-diols

A palladium(II)-catalyzed hydroxycyclization-carbonylation-lactonization sequence with appropriate pent-4-ene-1,3-diols provides efficient access to the bicyclic gamma -lactones, 5-n-butyl- and 5-n-hexyltetrahydrofuro-[3,2-b]furan-2(3H)-ones (3) and (4), respectively, in both racemic and enantiomeric forms. Some of the substrate pent-4-ene-1,3-diols of high enantiomeric excess (ee) have been derived from racemic terminal epoxides by hydrolytic kinetic resolution (HKR) using cobalt (III)-salen complexes. (9Z,12R)-(+)-Ricinoleic acid also serves as a chiral pool source of other pent-4-ene-1,3-diols. These syntheses and enantioselective gas chromatography confirm the structures and absolute stereochemistry of the lactones in some species of parasitic wasps (Hymenoptera: Braconidae). The highly abundant 5-n-hexyltetrahydrofuro-[3,2-b]furan-2(3H)-one (4) in Diachasmimorpha kraussii and D. longicaudata is of high ee (> 99%) with (3aR,5R,6aR) stereochemistry.

Transforming chaos to periodic oscillations

We demonstrate that the dynamics of an autonomous chaotic class C laser can be controlled to a periodic state via external modulation of the pump. In the absence of modulation, above the chaos threshold, the laser exhibits Lorenz-like chaotic pulsations. The average amplitude and frequency of these pulsations depend on the pump power. We find that there exist parameter windows where modulation of the pump power extinguishes the chaos in favor of simpler periodic behavior. Moreover we find a number of locking ratios between the pump and laser output follow the Farey sequence.

Discrimination of adsorption kinetic models for the description of hydrocarbon adsorption in activated carbon

Five kinetic models for adsorption of hydrocarbons on activated carbon are compared and investigated in this study. These models assume different mass transfer mechanisms within the porous carbon particle. They are: (a) dual pore and surface diffusion (MSD), (b) macropore, surface, and micropore diffusion (MSMD), (c) macropore, surface and finite mass exchange (FK), (d) finite mass exchange (LK), and (e) macropore, micropore diffusion (BM) models. These models are discriminated using the single component kinetic data of ethane and propane as well as the multicomponent kinetics data of their binary mixtures measured on two commercial activated carbon samples (Ajax and Norit) under various conditions. The adsorption energetic heterogeneity is considered for all models to account for the system. It is found that, in general, the models assuming diffusion flux of adsorbed phase along the particle scale give better description of the kinetic data.

Hydrolytic kinetic resolution of terminal mono- and bis-epoxides in the synthesis of insect pheromones: routes to (-)-(R)- and (+)-(S)-10-methyldodecyl acetate, (-)-(R)-10-methyl-2-tridecanone, (-)-(R)-(Z)-undec-6-en-2-ol (Nostrenol), (-)-(1R,7R)-1,7-dime

Hydrolytic kinetic resolution (HKR) of functionalised epoxides using (salen)Co(OAc) complexes provides enantiomerically enriched epoxides and diols, which have been transformed into important insect sex pheromones. In this general approach, (-)-(R)- and (+)-(S)-10-methyldodecyl acetates from the smaller tea tortrix moth were obtained, as was (-)-(R)-10-methyltridecan-2-one from the southern corn rootworm. The (S)-epoxide obtained from undec-1-en-6-yne was transformed to (-)-(R)-(Z)-undec-6-en-2-ol (Nostrenol) from ant-lions. HKR of appropriate bisepoxides was also investigated, and transformations of the resulting bisepoxides and epoxydiols provided (-)-(1R,7R)-1,7-dimethylnonylpropanoate from corn rootworms, (-)-(6R,12R)-6,12-dimethylpentadecan-2-one from the female banded cucumber beetle, and (-)-(2S,11S)-2,11-diacetoxytridecane and (+)-(2S,12S)-2,12-diacetoxytridecane from female pea-midges. (C) 2002 Elsevier Science Ltd. All rights reserved.