A simple observation concerning contraction mappings

In this short note we show that the results obtained by Walter in [4] remain valid if we change the metric by another metric. Furthermore, if we use the norm jjT; given in [3], Theorem B in[4] remains valid.

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Théorèmes de point fixe et principe variationnel d'Ekeland

Le principe de contraction de Banach, qui garantit l'existence d'un point fixe d'une contraction d'un espace métrique complet à valeur dans lui-même, est certainement le plus connu des théorèmes de point fixe. Dans plusieurs situations concrètes, nous sommes cependant amenés à considérer une contraction qui n'est définie que sur un sous-ensemble de cet espace. Afin de garantir l'existence d'un point fixe, nous verrons que d'autres hypothèses sont évidemment nécessaires. Le théorème de Caristi, qui garantit l'existence d'un point fixe d'une fonction d'un espace métrique complet à valeur dans lui-même et respectant une condition particulière sur d(x,f(x)), a plus tard été généralisé aux fonctions multivoques. Nous énoncerons des théorèmes de point fixe pour des fonctions multivoques définies sur un sous-ensemble d'un espace métrique grâce, entre autres, à l'introduction de notions de fonctions entrantes. Cette piste de recherche s'inscrit dans les travaux très récents de mathématiciens français et polonais. Nous avons obtenu des généralisations aux espaces de Fréchet et aux espaces de jauge de quelques théorèmes, dont les théorèmes de Caristi et le principe variationnel d'Ekeland. Nous avons également généralisé des théorèmes de point fixe pour des fonctions qui sont définies sur un sous-ensemble d'un espace de Fréchet ou de jauge. Pour ce faire, nous avons eu recours à de nouveaux types de contractions; les contractions sur les espaces de Fréchet introduites par Cain et Nashed [CaNa] en 1971 et les contractions généralisées sur les espaces de jauge introduites par Frigon [Fr] en 2000.

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

Pharmacological antagonism of Anchietia salutaris extracts on the contraction induced by prostaglandin D2 and U46619 in guinea-pig lung parenchymal strips

Anchietia salutaris tea is traditionally used in Brazil to treat allergies, suggesting it contains compounds with antagonistic activity on the allergic mediators. We have evaluated extracts and semi-purified fractions of Anchietia salutaris as a source of compounds having this type of antagonism on the contraction induced in guinea-pig lung parenchymal strips and on platelet aggregation and shape change. After 10 min pre-incubation dichloromethane extracts containing 30 or 100 μg mL-1 inhibited the contraction induced by prostaglandin D2 (PGD2) in guinea-pig lung parenchymal strips with dose ratios (DR) of 0.76 ± 0.14 and 0.93 ± 0.19, respectively; the amount of inhibition depended both on the concentration and on the time of preincubation (DR after 30 min pre-incubation was 1.21 ± 0.51). The dichloromethane extract and its semi-purified fractions also inhibited the contractions induced by U46619, a more potent, stable, synthetic agonist of thromboxane A2 (TxA2) prostanoid (TP) receptors, the receptors acted upon by PGD2 to produce lung contractions. The dichloromethane extract did not inhibit the lung parenchymal contractions induced by histamine, leukotriene D4 (LTD4) or platelet-activating factor (PAF). Platelet aggregation induced by U46619, adenosine 5'-diphosphate (ADP) or PAF was not inhibited by the dichloromethane extract. Indeed, the extract potentiated platelet aggregation induced by low concentrations of these agonists and also potentiated the shape change induced by U46619. These results imply that the dichloromethane extract of Anchietia salutaris and its semipurified fractions contain an active principle that competitively inhibits TxA2 TP receptors, the stimulation of which causes lung parenchymal contraction. The inhibition seems to be selective for this receptor subtype, because the extract fails to inhibit platelet aggregation or shape change. This provides additional support of earlier reports suggesting the occurrence of TP receptor subtypes.

EMG activity of trunk stabilizer muscles during Centering Principle of Pilates Method

This study aimed to analyze the electromyographic (EMG) activity of iliocostalis lumborum (IL), internal oblique (IO) and multifidus (MU) and the antagonist cocontraction (IO/MU and IO/IL) during the performance of Centering Principle of Pilates Method. Participating in this study were eighteen young and physically fit volunteers, without experience in Pilates Method, divided in two groups: low back pain group (LBPG, n = 8) and control group (CG, n = 10). Two isometric contractions of IO muscles (Centering Principle) were performed in upright sitting posture. EMG signal amplitude was calculated by Root Mean Square (RMS), which was normalized by RMS maximum value. The common area method to calculate the antagonist cocontraction index was used. MU and IO activation and IO/MU cocontraction (. p < 0.05) were higher in CG. The CG therefore showed a higher stabilizer muscles recruitment than LBPG during the performance of Centering Principle of Pilates Method. © 2012 Elsevier Ltd.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

Metal-free synthesis of indanes by iodine(III)-mediated ring contraction of 1, 2-dihydronaphthalenes

A metal-free protocol was developed to synthesize indanes by ring contraction of 1, 2-dihydronaphthalenes promoted by PhI(OH)OTs (HTIB or Koser's reagent). This oxidative rearrangement can be performed in several solvents (MeOH, CH3CN, 2 , 2, 2-trifluoroethanol (TFE), 1 , 1, 1, 3, 3, 3-hexafluoroisopropanol (HFIP), and a 1:4 mixture of TFE:CH2Cl2) under mild conditions. The ring contraction diastereoselectively gives functionalized trans-1, 3-disubstituted indanes, which are difficult to obtain in synthetic organic chemistry

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Effect of eccentric contraction velocity on muscle damage in repeated bouts of elbow flexor exercise

Eccentric exercise induces muscle damage, but controversy exists concerning the effect of contraction velocity on the magnitude of muscle damage, and little is known about the effect of contraction velocity on the repeated-bout effect. This study examined slow (60 degrees.s(-1)) and fast (180 degrees.s(-1)) velocity eccentric exercises for changes in indirect markers of muscle damage following 3 exercise bouts that were performed every 2 weeks. Fifteen young men were divided into 2 groups based on the velocity of eccentric exercise: 7 in the Ecc60 (60 degrees.s(-1)) group, and 8 in the Ecc180 (180 degrees.s(-1)) group. The exercise consisted of 30 maximal eccentric contractions of the elbow flexors at each velocity, in which the elbow joint was forcibly extended from 60 degrees to 180 degrees (full extension) on an isokinetic dynamometer. Changes in maximal voluntary isometric contraction strength, range of motion, muscle soreness, and plasma creatine kinase activity before and for 4 days after the exercise were compared in the 2 groups using a mixed-model analysis (group x bout x time). No significant differences between groups were evident for changes in any variables following exercise bouts; however, the changes were significantly smaller (p < 0.05) after the second and third bouts than after the first bout. These results indicate that the contraction velocity does not influence muscle damage or the repeated-bout effect.

Multicriteria analysis in decision making under information uncertainty

This paper presents results of research related to multicriteria decision making under information uncertainty. The Bell-man-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing multicriteria optimization models (< X, M > models) under deterministic information. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. This circumstance permits one to generalize the classic approach to considering the uncertainty of quantitative information (based on constructing and analyzing payoff matrices reflecting effects which can be obtained for different combinations of solution alternatives and the so-called states of nature) in monocriteria decision making to multicriteria problems. Considering that the uncertainty of information can produce considerable decision uncertainty regions, the resolving capacity of this generalization does not always permit one to obtain unique solutions. Taking this into account, a proposed general scheme of multicriteria decision making under information uncertainty also includes the construction and analysis of the so-called < X, R > models (which contain fuzzy preference relations as criteria of optimality) as a means for the subsequent contraction of the decision uncertainty regions. The paper results are of a universal character and are illustrated by a simple example. (c) 2007 Elsevier Inc. All rights reserved.

On Seliger and Whitham`s variational principle for hydrodynamic systems from the point of view of `fictitious particles`

FAPESP, the Sao Paulo State Research Foundation[04/04611-5]

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

Pimaradienoic acid inhibits vascular contraction and induces hypotension in normotensive rats

The present investigation was designed to investigate the effect of the diterpene ent-pimara-8(14),15-dien-19-oic acid (pimaradienoic acid, PA) on smooth muscle extracellular Ca2+ influx. To this end, the effect of PA on phenylephrine- and KCI-induced increases in cytosolic calcium concentration ([Ca2+](c)) measured by the variation in the ratio of fluorescence intensities (R340/ 380 nm) of Fura-2, was analysed. Whether bolus injection of PA could induce hypotensive responses in conscious normotensive rats was also evaluated. PA inhibited the contraction induced by phenylephrine (0.03 or 10 mu mol L-1) and KCI (30 or 90 mmol L-1) in endothelium-denuded rat aortic rings in a concentration dependent manner. Pre-treatment with PA (110, 100, 200 mu mol L-) attenuated the contraction induced by CaCl2 (0.5 nmol L(-)1 or 2.5 mmol L-1) in denuded rat aorta exposed to Ca2+- free medium containing phenylephrine (0.1 mu mol L-1) or KCI (30 mmol L-1). Interestingly, the inhibitory effect displayed by PA on CaCl2-induced contraction was more pronounced when KCI was used as the stimulant. Phenylephrine- and KCI-induced increases in (Ca2+,](c) were inhibited by PA. Similarly, verapamil, a Ca2+-channel blocker, also inhibited the increase in [Ca2+](c) induced by either phenylephrine or KCI. Finally, bolus injection of PA (1-15 mg kg(-1)) produced a dose-dependent decrease in mean arterial pressure in conscious normotensive rats. The results provide the first direct evidence that PA reduces vascular contractility by reducing extracellular Ca2+ influx through smooth muscle cellular membrane, a mechanism that could mediate the hypotensive response induced by this diterpene in normotensive rats.

Evaluation of the Contraction of Cutaneous Wounds in Wistar Rats Treated with Brazilian Green Propolis Gel

In this work the effects of topic use of Brazilian green propolis gel in the contraction of wounds performed in rat`s skin was evaluated. In ten female Wistar rats were done four wounds in dorsal region. Two wounds in each rat were treated daily with Brazilian green propolis gel during 10 days. The wounds were photographed daily, and the images were analyzed with ImageJ software, in order to measure wound areas and evaluate wound contraction. In the graphic analysis, treated group and control group had similar behavior, and both evolved for complete closure in 10th experimentation day. The wound clots fell down before in treated wounds. Green propolis in the gel formulation at 5% in topical use had not effect in the process of wound contraction. The macroscopic visualization of the contraction of wounds, by itself, does not seem to be a good indicator of the process of tissue repair.