Sobolev-Morrey Type Inequality for Riesz Potentials, Associated with the Laplace-Bessel Differential Operator

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points

The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to direct sums of regularly solvable operators defined on the separate subintervals, there are other regularly solvable restrications of the maximal operator which involve linking the various intervals together in interface like style.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

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.

Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Variational Principles for Monotone and Maximal Bifunctions

2000 Mathematics Subject Classification: 49J40, 49J35, 58E30, 47H05

Undulatory Physical Resistance Training Program Increases Maximal Strength In Elderly Type 2 Diabetics.

To investigate the effects of a specific protocol of undulatory physical resistance training on maximal strength gains in elderly type 2 diabetics. The study included 48 subjects, aged between 60 and 85 years, of both genders. They were divided into two groups: Untrained Diabetic Elderly (n=19) with those who were not subjected to physical training and Trained Diabetic Elderly (n=29), with those who were subjected to undulatory physical resistance training. The participants were evaluated with several types of resistance training's equipment before and after training protocol, by test of one maximal repetition. The subjects were trained on undulatory resistance three times per week for a period of 16 weeks. The overload used in undulatory resistance training was equivalent to 50% of one maximal repetition and 70% of one maximal repetition, alternating weekly. Statistical analysis revealed significant differences (p<0.05) between pre-test and post-test over a period of 16 weeks. The average gains in strength were 43.20% (knee extension), 65.00% (knee flexion), 27.80% (supine sitting machine), 31.00% (rowing sitting), 43.90% (biceps pulley), and 21.10% (triceps pulley). Undulatory resistance training used with weekly different overloads was effective to provide significant gains in maximum strength in elderly type 2 diabetic individuals.

Relationship Between Aerobic And Anaerobic Parameters From 3-minute All-out Tethered Swimming And 400-m Maximal Front Crawl Effort.

The main aim of this investigation was to verify the relationship of the variables measured during a 3-minute all-out test with aerobic (i.e., peak oxygen uptake [(Equation is included in full-text article.)] and intensity corresponding to the lactate minimum [LMI]) and anaerobic parameters (i.e., anaerobic work) measured during a 400-m maximal performance. To measure force continually and to avoid the possible influences caused by turns, the 3-minute all-out effort was performed in tethered swimming. Thirty swimmers performed the following tests: (a) a 3-minute all-out tethered swimming test to determine the final force (equivalent to critical force: CF3-MIN) and the work performed above CF3-MIN (W'3-MIN), (b) a LMI protocol to determine the LMI during front crawl swimming, and (c) a 400-m maximal test to determine the (Equation is included in full-text article.)and total anaerobic contribution (WANA). Correlations between the variables were tested using the Pearson's correlation test (p ≤ 0.05). CF3-MIN (73.9 ± 13.2 N) presented a high correlation with the LMI (1.33 ± 0.08 m·s; p = 0.01) and (Equation is included in full-text article.)(4.5 ± 1.2 L·min; p = 0.01). However, the W'3-MIN (1,943.2 ± 719.2 N·s) was only moderately correlated with LMI (p = 0.02) and (Equation is included in full-text article.)(p = 0.01). In summary, CF3-MIN determined during the 3-minute all-out effort is associated with oxidative metabolism and can be used to estimate the aerobic capacity of swimmers. In contrast, the anaerobic component of this model (W'3-MIN) is not correlated with WANA.

The Geometric Curvature Of The Spine Of Runners During Maximal Incremental Effort Test.

This study sought to analyse the behaviour of the average spinal posture using a novel investigative procedure in a maximal incremental effort test performed on a treadmill. Spine motion was collected via stereo-photogrammetric analysis in thirteen amateur athletes. At each time percentage of the gait cycle, the reconstructed spine points were projected onto the sagittal and frontal planes of the trunk. On each plane, a polynomial was fitted to the data, and the two-dimensional geometric curvature along the longitudinal axis of the trunk was calculated to quantify the geometric shape of the spine. The average posture presented at the gait cycle defined the spine Neutral Curve. This method enabled the lateral deviations, lordosis, and kyphosis of the spine to be quantified noninvasively and in detail. The similarity between each two volunteers was a maximum of 19% on the sagittal plane and 13% on the frontal (p<0.01). The data collected in this study can be considered preliminary evidence that there are subject-specific characteristics in spinal curvatures during running. Changes induced by increases in speed were not sufficient for the Neutral Curve to lose its individual characteristics, instead behaving like a postural signature. The data showed the descriptive capability of a new method to analyse spinal postures during locomotion; however, additional studies, and with larger sample sizes, are necessary for extracting more general information from this novel methodology.

A influência de palmares e parachute na coordenação dos nados

Universidade Estadual de Campinas . Faculdade de Educação Física

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).

ZETA DETERMINANT AND OPERATOR DETERMINANTS

We apply techniques of zeta functions and regularized products theory to study the zeta determinant of a class of abstract operators with compact resolvent, and in particular the relation with other spectral functions.

Study of the influence of indium segregation on the optical properties of InGaAs/GaAs quantum wells via split-operator method

In the case of quantum wells, the indium segregation leads to complex potential profiles that are hardly considered in the majority of the theoretical models. The authors demonstrated that the split-operator method is useful tool for obtaining the electronic properties in these cases. Particularly, they studied the influence of the indium surface segregation in optical properties of InGaAs/GaAs quantum wells. Photoluminescence measurements were carried out for a set of InGaAs/GaAs quantum wells and compared to the results obtained theoretically via split-operator method, showing a good agreement.