Consistency restrictions on maximal electric-field strength in quantum field theory

Quantum field theory with an external background can be considered as a consistent model only if backreaction is relatively small with respect to the background. To find the corresponding consistency restrictions on an external electric field and its duration in QED and QCD, we analyze the mean-energy density of quantized fields for an arbitrary constant electric field E, acting during a large but finite time T. Using the corresponding asymptotics with respect to the dimensionless parameter eET(2), one can see that the leading contributions to the energy are due to the creation of particles by the electric field. Assuming that these contributions are small in comparison with the energy density of the electric background, we establish the above-mentioned restrictions, which determine, in fact, the time scales from above of depletion of an electric field due to the backreaction.

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

ACUTE EFFECT OF A BALLISTIC AND A STATIC STRETCHING EXERCISE BOUT ON FLEXIBILITY AND MAXIMAL STRENGTH

Bacurau, RFP, Monteiro, GA, Ugrinowitsch C, Tricoli, V, Cabral, LF, Aoki, MS. Acute effect of a ballistic and a static stretching exercise bout on flexibility and maximal strength. J Strength Cond Res 23(1): 304-308, 2009-Different stretching techniques have been used during warm-up routines. However, these routines may decrease force production. The purpose of this study was to compare the acute effect of a ballistic and a static stretching protocol on lower-limb maximal strength. Fourteen physically active women (169.3 +/- 8.2 cm; 64.9 +/- 5.9 kg; 23.1 +/- 3.6 years) performed three experimental sessions: a control session (estimation of 45 degrees leg press one-repetition maximum [1RM]), a ballistic session (20 minutes of ballistic stretch and 45 degrees leg press 1RM), and a static session (20 minutes of static stretch and 45 degrees leg press 1RM). Maximal strength decreased after static stretching (213.2 +/- 36.1 to 184.6 +/- 28.9 kg), but it was unaffected by ballistic stretching (208.4 +/- 34.8 kg). In addition, static stretching exercises produce a greater acute improvement in flexibility compared with ballistic stretching exercises. Consequently, static stretching may not be recommended before athletic events or physical activities that require high levels of force. On the other hand, ballistic stretching could be more appropriate because it seems less likely to decrease maximal strength.

Comparison between constant and decreasing rest intervals: influence on maximal strength and hypertrophy

de Souza Jr, TP, Fleck, SJ, Simao, R, Dubas, JP, Pereira, B, de Brito Pacheco, EM, da Silva, AC, and de Oliveira, PR. Comparison between constant and decreasing rest intervals: influence on maximal strength and hypertrophy. J Strength Cond Res 24(7): 1843-1850, 2010-Most resistance training programs use constant rest period lengths between sets and exercises, but some programs use decreasing rest period lengths as training progresses. The aim of this study was to compare the effect on strength and hypertrophy of 8 weeks of resistance training using constant rest intervals (CIs) and decreasing rest intervals (DIs) between sets and exercises. Twenty young men recreationally trained in strength training were randomly assigned to either a CI or DI training group. During the first 2 weeks of training, 3 sets of 10-12 repetition maximum (RM) with 2-minute rest intervals between sets and exercises were performed by both groups. During the next 6 weeks of training, the CI group trained using 2 minutes between sets and exercises (4 sets of 8-10RM), and the DI group trained with DIs (2 minutes decreasing to 30 seconds) as the 6 weeks of training progressed (4 sets of 8-10RM). Total training volume of the bench press and squat were significantly lower for the DI compared to the CI group (bench press 9.4%, squat 13.9%) and weekly training volume of these same exercises was lower in the DI group from weeks 6 to 8 of training. Strength (1RM) in the bench press and squat, knee extensor and flexor isokinetic measures of peak torque, and muscle cross-sectional area (CSA) using magnetic resonance imaging were assessed pretraining and posttraining. No significant differences (p <= 0.05) were shown between the CI and DI training protocols for CSA (arm 13.8 vs. 14.5%, thigh 16.6 vs. 16.3%), 1RM (bench press 28 vs. 37%, squat 34 vs. 34%), and isokinetic peak torque. In conclusion, the results indicate that a training protocol with DI is just as effective as a CI protocol over short training periods (6 weeks) for increasing maximal strength and muscle CSA; thus, either type of program can be used over a short training period to cause strength and hypertrophy.

Is acute static stretching able to reduce the time to exhaustion at power output corresponding to maximal oxygen uptake?

Samogin Lopes, FA, Menegon, EM, Franchini, E, Tricoli, V, and de M. Bertuzzi, RC. Is acute static stretching able to reduce the time to exhaustion at power output corresponding to maximal oxygen uptake? J Strength Cond Res 24(6): 1650-1656, 2010-This study analyzed the effect of an acute static stretching bout on the time to exhaustion (T(lim)) at power output corresponding to (V) over dotO(2)max. Eleven physically active male subjects (age 22.3 +/- 2.8 years, (V) over dotO(2)max 2.7 +/- 0.5 L . min(-1)) completed an incremental cycle ergometer test, 2 muscle strength tests, and 2 maximal tests to exhaustion at power output corresponding to (V) over dotO(2)max with and without a previous static stretching bout. The T(lim) was not significantly affected by the static stretching (164 +/- 28 vs. 150 +/- 26 seconds with and without stretching, respectively, p = 0.09), but the time to reach (V) over dotO(2)max (118 +/- 22 vs. 102 +/- 25 seconds), blood-lactate accumulation immediately after exercise (10.7 +/- 2.9 vs. 8.0 +/- 1.7 mmol . L(-1)), and oxygen deficit (2.4 +/- 0.9 vs. 2.1 +/- 0.7 L) were significantly reduced (p <= 0.02). Thus, an acute static stretching bout did not reduce T(lim) at power output corresponding to (V) over dotO(2)max possibly by accelerating aerobic metabolism activation at the beginning of exercise. These results suggest that coaches and practitioners involved with aerobic dependent activities may use static stretching as part of their warm-up routines without fear of diminishing high-intensity aerobic exercise performance.

Methods of quantification of training load in exercise performed at maximal lactate steady state

The aim of the present study was to compare and correlate training impulse (TRIMP) estimates proposed by Banister (TRIMP(Banister)), Stagno (TRIMP(Stagno)) and Manzi (TRIMP(Manzi)). The subjects were submitted to an incremental test on cycle ergometer with heart rate and blood lactate concentration measurements. In the second occasion, they performed 30 min. of exercise at the intensity corresponding to maximal lactate steady state, and TRIMP(Banister), TRIMP(Stagno) and TRIMP(Manzi) were calculated. The mean values of TRIMP(Banister) (56.5 +/- 8.2 u.a.) and TRIMP(Stagno) (51.2 +/- 12.4 u.a.) were not different (P > 0.05) and were highly correlated (r = 0.90). Besides this, they presented a good agreement level, which means low bias and relatively narrow limits of agreement. On the other hand, despite highly correlated (r = 0.93), TRIMP(Stagno) and TRIMP(Manzi) (73.4 +/- 17.6 u.a.) were different (P < 0.05), with low agreement level. The TRIMP(Banister) e TRIMP(Manzi) estimates were not different (P = 0.06) and were highly correlated (r = 0.82), but showed low agreement level. Thus, we concluded that the investigated TRIMP methods are not equivalent. In practical terms, it seems prudent monitor the training process assuming only one of the estimates.

Aerobic profile of climbers during maximal arm test

This study compared measurements of upper body aerobic fitness in elite (EC; n = 7) and intermediate rock climbers (IC; n = 7), and a control group (C; n = 7). Subjects underwent an upper limb incremental test on hand cycle ergometer, with increments of 23 W.min(-1), until exhaustion. Ventilation (VE) data were smoothed to 10 s averages and plotted against time for the visual determination of the first (VT1) and second (VT2) ventilatory thresholds. Peak power output was not different among groups [EC = 130.9 (+/- 11.8) W; IC = 122.1 (+/- 28.4) W; C = 115.4 (+/- 15.1) W], but time to exhaustion was significantly higher in EC than IC and C. VO(2PEAK) was significantly higher in EC [36.8 (+/- 5.7) mL.kg(-1).min(-1)] and IC [35.5 (+/- 5.2) mL.kg(-1).min(-1)] than C [28.8 (+/- 5.0) mL.kg(-1).min(-1)], but there was no difference between EC and IC. VT1 was significantly higher in EC than C [EC = 69.0 (+/- 9.4) W; IC = 62.4 (+/- 13.0) W; C = 52.1 (+/- 11.8) W], but no significant difference was observed in VT2 [EC = 103.5 (+/- 18.8) W; IC = 92.0 (+/- 22.0) W; C = 85.6 (+/- 19.7) W]. These results show that elite indoor rock climbers elicit higher aerobic fitness profile than control subjects when measured with an upper body test.

The effect of carbohydrate mouth rinse on maximal strength and strength endurance

It has been previously reported that carbohydrate (CHO) mouth rinse can improve exercise performance. The proposed mechanism involves increased activation of brain regions believed to be responsible for reward/motivation and motor control. Since strength-related performance is affected by central drive to the muscles, it seems reasonable to hypothesize that the positive CNS response to oral CHO sensing may counteract the inhibitory input from the muscle afferent pathways minimizing the drop in the central drive. The purpose of the current study was to test if CHO mouth rinse affects maximum strength and strength endurance performance. Twelve recreationally strength-trained healthy males (age 24.08 +/- 2.99 years; height 178.09 +/- 6.70 cm; weight 78.67 +/- 8.17 kg) took part in the study. All of the tests were performed in the morning, after an 8 h overnight fasting. Subjects were submitted to a maximum strength test (1-RM) and a strength endurance test (six sets until failure at 70% of 1-RM), in separate days under three different experimental conditions (CHO mouth rinse, placebo-PLA mouth rinse and control-CON) in a randomized crossover design. The CHO mouth rinse (25 ml) occurred before every attempt in the 1-RM test, and before every set in the endurance strength test. Blood glucose and lactate were measured immediately before and 5 min post-tests. There were no significant differences in 1-RM between experimental conditions (CHO 101 +/- 7.2 kg; PLA 101 +/- 7.4 kg; CON 101 +/- 7.2 kg; p = 0.98). Furthermore, there were no significance between trial differences in the number of repetitions performed in each set (p = 0.99) or the total exercise volume (number of repetitions x load lifted [kg]) (p = 0.98). A main effect for time (p < 0.0001) in blood lactate concentration was observed in both tests (1-RM and strength endurance). Blood glucose concentration did not differ between conditions. In conclusion, CHO mouth rinse does not affect maximum strength or strength endurance performance.

Influence of angiotensinogen and angiotensin-converting enzyme polymorphisms on cardiac hypertrophy and improvement on maximal aerobic capacity caused by exercise training

Background The allele threonine (T) of the angiotensinogen has been associated with ventricular hypertrophy in hypertensive patients and soccer players. However, the long-term effect of physical exercise in healthy athletes carrying the T allele remains unknown. We investigated the influence of methionine M or T allele of the angiotensinogen and D or I allele of the angiotensin-converting enzyme on left-ventricular mass index (LVMI) and maximal aerobic capacity in young healthy individuals after long-term physical exercise training. Design Prospective clinical trial. Methods Eighty-three policemen aged between 20 and 35 years (mean +/- SD 26 +/- 4.5 years) were genotyped for the M235T gene angiotensinogen polymorphism (TT, n=25; MM/MT, n=58) and angiotensin-converting enzyme gene insertion/deletion (I/D) polymorphism (11, n=18; DD/DI, n=65). Left-ventricular morphology was evaluated by echocardiography and maximal aerobic capacity (VO(2peak)) by cardiopulmonary exercise test before and after 17 weeks of exercise training (50-80% VO(2peak)). Results Baseline VO(2peak) and LVMI were similar between TT and MM/MT groups, and II and DD/DI groups. Exercise training increased significantly and similarly VO(2peak) in homozygous TT and MM/MT individuals, and homozygous II and DD/DI individuals. In addition, exercise training increased significantly LVMI in TT and MM/MT individuals (76.5 +/- 3 vs. 86.7 +/- 4, P=0.00001 and 76.2 +/- 2 vs. 81.4 +/- 2, P=0.00001, respectively), and II and DD/DI individuals (777 +/- 4 vs. 81.5 +/- 4, P=0.0001 and 76 +/- 2 vs. 83.5 +/- 2, P=0.0001, respectively). However, LVMI I in TT individuals was significantly greater than in MM/MT individuals (P=0.04). LVMI was not different between 11 and DD/DI individuals. Conclusion Left-ventricular hypertrophy caused by exercise training is exacerbated in homozygous TT individuals with angiotensinogen polymorphism. Eur J Cardiovasc Prev Rehabil 16:487-492 (C) 2009 The European Society of Cardiology

Physiological and perceived exertion responses at intermittent critical power and intermittent maximal lactate steady state

Okuno, NM, Perandini, LAB, Bishop, D, Simoes, HG, Pereira, G, Berthoin, S, Kokubun, E, and Nakamura, FY. Physiological and perceived exertion responses at intermittent critical power and intermittent maximal lactate steady state. J Strength Cond Res 25(7): 2053-2058, 2011-The aim of this study was to compare the power outputs of the intermittent critical power (CPi) with the intermittent maximal lactate steady state (MLSSi) and to compare the physiological and perceptual responses exercising at CPi and MLSSi. Ten subjects performed intermittent trials on a cycle ergometer to determine CPi and MLSSi using 30: 30 seconds of effort and pause. The oxygen uptake ((V) over dotO(2)), heart rate (HR), blood lactate concentration ([Lac]), and rating of perceived exertion (RPE) responses were compared during 30-minute cycling at CPi and MLSSi. The CPi (267 6 45 W) was similar to MLSSi (254 6 39 W), and they were correlated (r = 0.88; p<0.05). The (V) over dotO(2) and HR responses stabilized throughout exercising at CPi (2.52 +/- 0.52 L.min(-1); 156 +/- 8 b.min(-1)) and MLSSi (2.41 +/- 0.32 L.min(-1); 152 +/- 10 b.min(-1)). These physiological variables were similar between conditions. However, the [Lac] and RPE were higher from the middle to the end of exercise duration at CPi ([Lac] = 6.9 +/- 2.6 mM; RPE = 17.1 +/- 2.1 a.u.) compared to MLSSi ([Lac] = 5.1 +/- 0.9 mM; RPE = 15.7 +/- 1.8 a.u.). Therefore, CPi intensity determined from 30: 30 seconds of effort and rest periods on a cycle ergometer is equivalent to the MLSSi, and there is a physiological steady state throughout both exercise intensities, although the [Lac] and RPE responses at CPi are higher than at MLSSi. Thus, the CPi and MLSSi may be used as tools for intermittent training evaluation and prescription.

Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature. (C) 2011 Elsevier Ltd. All rights reserved.