Cyclic Maximal Ideals of Rings of Differential Operators over Power Series Rings

In [3], Bratti and Takagi conjectured that a first order differential operator S=11 +...+ nn+ with 1,..., n, {x1,..., xn} does not generate a cyclic maximal left (or right) ideal of the ring of differential operators. This is contrary to the case of the Weyl algebra, i.e., the ring of differential operators over the polynomial ring [x1,..., xn]. In this case, we know that such cyclic maximal ideals do exist. In this article, we prove several special cases of the conjecture of Bratti and Takagi.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

Relationship between training status and maximal fat oxidation rate

This study aimed to compare maximal fat oxidation rate parameters between moderate-and low-performance runners. Eighteen runners performed an incremental treadmill test to estimate individual maximal fat oxidation rate (Fat(max)) based on gases measures and a 10,000-m run on a track. The subjects were then divided into a low and moderate performance group using two different criteria: 10,000-m time and VO(2)max values. When groups were divided using 10,000-m time, there was no significant difference in Fat(max) (0.41 +/- 0.16 and 0.27 +/- 0.12 g.min(-1), p = 0.07) or in the exercise intensity that elicited Fat(max) (59.9 +/- 16.5 and 68.7 +/- 10.3 % (V) over dotO(2max), p = 0.23) between the moderate and low performance groups, respectively (p > 0.05). When groups were divided using VO(2max) values, Fat(max) was significantly lower in the low VO(2max) group than in the high VO(2max) group (0.29 +/- 0.10 and 0.47 +/- 0.17 g.min(-1), respectively, p < 0.05) but the intensity that elicited Fat(max) did not differ between groups (64.4 +/- 14.9 and 61.6 +/- 15.4 % VO(2max)). Fat(max) or % VO(2max) that elicited Fat(max) was not associated with 10,000 m time. The only variable associated with 10,000-m running performance was % VO(2max) used during the run (p < 0.01). In conclusion, the criteria used for the division of groups according to training status might influence the identification of differences in Fat(max) or in the intensity that elicits Fat(max).

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.