Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation

Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Fixed points on torus fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S-1 for spaces which axe fibrations over S-1 and the fiber is the torus T. For the case where the fiber is a surface with nonpositive Euler characteristic, we establish general algebraic conditions, in terms of the fundamental group and the induced homomorphism, for the existence of a deformation of a map over S-1 to a fixed point, free map. For the case where the fiber is a torus, we classify all maps over S-1 which can be deformed fiberwise to a fixed point free map.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Fixed points and vacuum energy of dynamically broken gauge theories

We show that if a gauge theory with dynamical symmetry breaking has nontrivial fixed points, they will correspond to extrema of the vacuum energy. This relationship provides a different method to determine fixed points.

Statistical mechanical theory of an oscillating isolated system: The relaxation to equilibrium

In this Contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion, in general, and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n ? N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime, we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function.

Myofascial pain associated to trigger points: A literature review. Part 2: Differential diagnosis and treatment

During the last decades the advance in knowledge of myofascial pain has been constant in the medical and dental community. However, although several aspects have been clarified in relation to its epidemiology, clinical characteristics and etiopathogenesis, many uncertainties remain. Many clinical conditions are included in the differential diagnosis of myofascial pain associated to trigger points. A good anamnesis and clinical exploration is thus required in order to ensure correct diagnosis and treatment. Among the numerous treatments used in application to trigger points, the spray-and-stretch technique and direct injection targeted to such trigger points have been found to be the most effective options. In chronic cases, psychosocial intervention is required, due to the high incidence of mood disorders and/or anxiety observed in these patients, who in turn present a poorer prognosis. This underscores the importance of early diagnosis and treatment.

The determination of the helium discharge detector response to fixed gases

The Beckman Helium Discharge Detector has been found to be sensitive to the fixed gases oxygen, nitrogen, and hydrogen at detection levels 10-100 times more sensitive than possible with a Bow-Mac Thermal Conductivity Detector. Detection levels o~ approximately 1.9 E-4 ~ v/v oxygen, 3.1 E-4 ~ v/v nitrogen, and 3.0 E-3 ~ v/v hydrogen are estimated. Response of the Helium Discharge Detector was not linear, but is useable for quantitation over limited ranges of concentration using suitably prepared working standards. Cleanliness of the detector discharge electrodes and purity of the helium carrier and discharge gas were found to be critical to the operation of the detector. Higher sensitivities of the Helium Discharge Detector may be possible by the design and installation of a sensitive, solid-state electrometer.

Pen and sunlight sketches of scenery reached by the Grand Trunk Railway system and connections with summer routes and fares to principal points : including Niagara Falls, Thousand Islands, Rapids of the St. Lawrence, Montreal, Quebec, Parry Sound, Georgian Bay, Muskoka Lakes, Adirondacks, Lake St. John, Mackinac Island, Midland District Lakes, the White Mountains, the Suquenay River, Rangeley Lakes and the sea-shore.--

At head of title: "Great tourist route of America".

Strategies to improve fertility in Bos indicus postpubertal heifers and nonlactating cows submitted to fixed-time artificial insemination

Two experiments were designed to evaluate strategies to increase fertility of Bos indicus postpubertal heifers and nonlactating cows submitted to a fixed-time artificial insemination (TAI) protocol consisting of an intravaginal device containing 1.9 g of progesterone (CIDR) insertion + estradiol benzoate on Day 0, CIDR withdrawal + estradiol cypionate on Day 9, and TAI on Day 11. In Experiment 1, heifers (n = 1153) received a new or an 18-d previously used CIDR and, on Day 9, prostaglandin F(2 alpha) (PGF(2 alpha)) + 0, 200, or 300 IU equine chorionic gonadotropin (eCG). Heifers treated with a new CIDR had greater (least squares means +/- SEM) serum concentration of progesterone on Day 9 (3.06 +/- 0.09 ng/mL vs. 2.53 +/- 0.09 ng/mL; P < 0.05) and a smaller follicle at TAI (11.61 +/- 0.11 nim vs. 12.05 +/- 0.12 mm; P < 0.05). Heifers with smaller follicles at TAI had lesser serum progesterone, concentrations on Day 18 and reduced rates of ovulation, conception, and pregnancy (P < 0.05). Treatment with eCG improved (P < 0.05) follicle diameter at TAI (11.50 +/- 0.10 mm, 11.90 +/- 0.11 mm, and 12.00 +/- 0.10 mm, for 0, 100, and 200 IU, respectively), serum progesterone concentration on Day 18 (2.77 +/- 0.11 ng/mL, 3.81 +/- 0.11 ng/mL, and 4.87 +/- 0.11 ng/mL), and rates of ovulation (83.8%, 88.5%, and 94.3%) and pregnancy (41.3%, 47.0%, and 46.7%). In Experiment 2, nonlactating Nelore cows (n = 702) received PGF(2 alpha) treatment on Days 7 or 9 and, on Day 9, 0 or 300 IU cCG. Cows receiving PGF(2 alpha) on Day 7 had lesser serum progesterone concentrations on Day 9 (3.05 +/- 0.21 ng/mL vs. 4.58 +/- 0.21 ng/mL; P < 0.05), a larger follicle at TAI (11.54 +/- 0.21 mm vs. 10.84 +/- 0.21 mm; P < 0.05), and improved (P < 0.05) rates of ovulation (85.4% vs. 77.0%), conception (60.9% vs. 47.2%), and pregnancy (52.0% vs. 36.4%). Treatment with eCG improved (P < 0.05) serum progesterone concentration on Day 18 (3.24 +/- 0.14 ng/mL vs. 4.55 +/- 0.14 ng/mL) and the rates of ovulation (72.4% vs. 90.0%) and pregnancy (37.5% vs. 50.8%). In conclusion, giving PGF(2 alpha) earlier in the protocol in nonlactating cows and eCG treatment in postpubertal heifers and nonlactating cows improved fertility in response to a TAI (progesterone + estradiol) protocol. (C) 2009 Elsevier B.V. All rights reserved.

Effects of temperament on pregnancy rates to fixed-timed AI in Bos indicus beef cows

The objective of the present experiment was to assess the effects of temperament on pregnancy rates to fixed-time AI (FTAI) in Bos indicus beef cows. A total of 761 multiparous lactating Nelore cows, originated from 4 different commercial cow-calf ranches, were evaluated for BCS and temperament at the time of FTAI (day 0). Temperament was assessed by chute score and exit velocity. Further, individual exit score was calculated by dividing exit velocity results into quintiles and assigning cows with a score from 1 to 5 (exit score: 1 = slowest cows; 5 = fastest cow). Temperament scores were calculated by averaging cow chute score and exit score. Cows were also classified for temperament type according to temperament score (<= 3 = adequate temperament, >3 = excitable temperament). Pregnancy status was verified by detecting a viable conceptus with rectal ultrasonography approximately 40 days after FTAI. Chute score, exit velocity, and temperament score were not correlated to BCS (P>0.31). Hence, BCS did not differ (P=0.30) according to temperament type (4.13 vs. 4.09 for cows with excitable and adequate temperament, respectively; SEM = 0.070). Pregnancy rates to FTAI tended to be negatively affected by temperament score (P=0.08), whereas the probability of cows becoming pregnant to FTAI was negatively associated with temperament score (linear effect, P<0.01). Accordingly, pregnancy rates were reduced (P=0.05) in cows with excitable temperament compared to cows with adequate temperament (35.3 vs. 42.8% of pregnant cows/total cows, respectively; SEM = 2.85). Pregnancy rates to FTAI were not affected by chute score (P=0.25), although the probability of cows becoming pregnant to FTAI tended to be negatively associated with chute score (linear effect, P=0.07). Pregnancy rates to FTAI were negatively affected by exit score (P=0.05), and the probability of cows becoming pregnant to FTAI was negatively associated with exit score and with actual exit velocity (linear effects, P<0.01). Results from this experiment indicate that excitable temperament is detrimental to pregnancy rates of B. indicus cows assigned to an estrus synchronization + FTAI protocol. Published by Elsevier B.V.

Characterization of ceramic powders used in the inCeram systems to fixed dental Prosthesis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)