A generalized Lefschetz number for local Nielsen fixed point theory

AbstractLet X be a connected, finite dimensional, locally compact polyhedron. Let f:U→X be a compactly fixed map defined on an open, connected subset U of X, and let H be any normal subgroup of π1(X). We seek information about NH(f), the local H-Nielsen number of f. It is a lower bound for min{|Fix g|: g≃f}, where the homotopies must be admissible.Let NH(f; f̃, ĩ) denote the well-known sum Σα∈Wi(NαH[α], where i(NαH) is the local fixed point index of an H-Nielsen class, [α] is the Reidemeister orbit associated with that class and W is a set of representatives of the Reidemeister orbits. Then NH(f) is the number of terms of NH(f;f̃,ĩ) with nonzero coefficient. We call NH(f;f̃,ĩ) a Nielsen-Reidemeister chain, and we prove that for certain subsets of U, N H(f; f̃, ĩ) splits into the sum of the Nielsen-Reidemeister chains for the subsets.We define the local generalized H-Lefschetz number LH(f; f̃, ĩ) in terms of a globally defined trace. We prove that, for X a connected, triangulable n-manifold with n⩾3, LH(f;f̃, ĩ) = NH(f; f̃, ĩ). Thus, LH(f; f̃, ĩ) can provide a means to compute NH(f). Also, for H = 1, a generalization of the converse of the Lefschetz fixed point theorem holds

Numerical Simulation of Fluidic Actuators for Flow Control Applications

Active flow control technology is finding increasing use in aerospace applications to control flow separation and improve aerodynamic performance. In this paper we examine the characteristics of a class of fluidic actuators that are being considered for active flow control applications for a variety of practical problems. Based on recent experimental work, such actuators have been found to be more efficient for controlling flow separation in terms of mass flow requirements compared to constant blowing and suction or even synthetic jet actuators. The fluidic actuators produce spanwise oscillating jets, and therefore are also known as sweeping jets. The frequency and spanwise sweeping extent depend on the geometric parameters and mass flow rate entering the actuators through the inlet section. The flow physics associated with these actuators is quite complex and not fully understood at this time. The unsteady flow generated by such actuators is simulated using the lattice Boltzmann based solver PowerFLOW R . Computed mean and standard deviation of velocity profiles generated by a family of fluidic actuators in quiescent air are compared with experimental data. Simulated results replicate the experimentally observed trends with parametric variation of geometry and inflow conditions

Magnetic field, differential rotation and activity of the hot-Jupiter hosting star HD 179949

HD 179949 is an F8V star, orbited by a giant planet at ~8 R* every 3.092514 days. The system was reported to undergo episodes of stellar activity enhancement modulated by the orbital period, interpreted as caused by Star-Planet Interactions (SPIs). One possible cause of SPIs is the large-scale magnetic field of the host star in which the close-in giant planet orbits. In this paper we present spectropolarimetric observations of HD 179949 during two observing campaigns (2009 September and 2007 June). We detect a weak large-scale magnetic field of a few Gauss at the surface of the star. The field configuration is mainly poloidal at both observing epochs. The star is found to rotate differentially, with a surface rotation shear of dOmega=0.216\pm0.061 rad/d, corresponding to equatorial and polar rotation periods of 7.62\pm0.07 and 10.3\pm0.8 d respectively. The coronal field estimated by extrapolating the surface maps resembles a dipole tilted at ~70 degrees. We also find that the chromospheric activity of HD 179949 is mainly modulated by the rotation of the star, with two clear maxima per rotation period as expected from a highly tilted magnetosphere. In September 2009, we find that the activity of HD 179949 shows hints of low amplitude fluctuations with a period close to the beat period of the system.Comment: Accepted for publication in Monthly Notices of The Royal Astronomical Societ

Relationships between the AE, ap and Dst indices near solar minimum (1974) and at solar maximum (1979)

International audienceThree-hourly average values of the Dst, AE and ap geomagnetic activity indices have been studied for 1 year's duration near the solar minimum (1974) and also at the solar maximum (1979). In 1979 seven intense geomagnetic storms (Dst <?100 nT) occurred, whereas in 1974 only three were reported. This study reveals: (1) the yearly average of AE is greater in 1974 than in 1979, whereas the inverse seems to be true for the yearly average of Dst, when a higher number of intense storms is present. These averages indicate the kind of activity occurring on the sun as shown in earlier work. (2) The seasonal variation of Dst is higher than that of ap and is almost negligible in AE. (3) The correlation coefficient of ap × AE is in general the highest, as the magnetometers that monitor both indices are close, and is surpassed only by the ap × Dst correlation during geomagnetic storms, when the influence of the ring current is dominant. The correlation of ap × Dst also shows a seasonal variability. (4) For the first time a study of correlation between ap and a linear combination of AE and Dst has also been made. We found higher correlation coefficients in this case as compared to those between ap × Dst and ap × AE

Burden of Neurological Disorders Across the US From 1990-2017

IMPORTANCE Accurate and up-to-date estimates on incidence, prevalence, mortality, and disability-adjusted life-years (burden) of neurological disorders are the backbone of evidence-based health care planning and resource allocation for these disorders. It appears that no such estimates have been reported at the state level for the US. OBJECTIVE To present burden estimates of major neurological disorders in the US states by age and sex from 1990 to 2017. DESIGN, SETTING, AND PARTICIPANTS This is a systematic analysis of the Global Burden of Disease (GBD) 2017 study. Data on incidence, prevalence, mortality, and disability-adjusted life-years (DALYs) of major neurological disorders were derived from the GBD 2017 study of the 48 contiguous US states, Alaska, and Hawaii. Fourteen major neurological disorders were analyzed: stroke, Alzheimer disease and other dementias, Parkinson disease, epilepsy, multiple sclerosis, motor neuron disease, migraine, tension-type headache, traumatic brain injury, spinal cord injuries, brain and other nervous system cancers, meningitis, encephalitis, and tetanus. EXPOSURES Any of the 14 listed neurological diseases. MAIN OUTCOME AND MEASURE Absolute numbers in detail by age and sex and age-standardized rates (with 95% uncertainty intervals) were calculated. RESULTS The 3 most burdensome neurological disorders in the US in terms of absolute number of DALYs were stroke (3.58 [95% uncertainty interval [UI], 3.25-3.92] million DALYs), Alzheimer disease and other dementias (2.55 [95% UI, 2.43-2.68] million DALYs), and migraine (2.40 [95% UI, 1.53-3.44] million DALYs). The burden of almost all neurological disorders (in terms of absolute number of incident, prevalent, and fatal cases, as well as DALYs) increased from 1990 to 2017, largely because of the aging of the population. Exceptions for this trend included traumatic brain injury incidence (−29.1% [95% UI, −32.4% to −25.8%]); spinal cord injury prevalence (−38.5% [95% UI, −43.1% to −34.0%]); meningitis prevalence (−44.8% [95% UI, −47.3% to −42.3%]), deaths (−64.4% [95% UI, −67.7% to −50.3%]), and DALYs (−66.9% [95% UI, −70.1% to −55.9%]); and encephalitis DALYs (−25.8% [95% UI, −30.7% to −5.8%]). The different metrics of age-standardized rates varied between the US states from a 1.2-fold difference for tension-type headache to 7.5-fold for tetanus; southeastern states and Arkansas had a relatively higher burden for stroke, while northern states had a relatively higher burden of multiple sclerosis and eastern states had higher rates of Parkinson disease, idiopathic epilepsy, migraine and tension-type headache, and meningitis, encephalitis, and tetanus. CONCLUSIONS AND RELEVANCE There is a large and increasing burden of noncommunicable neurological disorders in the US, with up to a 5-fold variation in the burden of and trends in particular neurological disorders across the US states. The information reported in this article can be used by health care professionals and policy makers at the national and state levels to advance their health care planning and resource allocation to prevent and reduce the burden of neurological disorders

Searching for Star-Planet interactions within the magnetosphere of HD 189733

HD 189733 is a K2 dwarf, orbited by a giant planet at 8.8 stellar radii. In order to study magnetospheric interactions between the star and the planet, we explore the large-scale magnetic field and activity of the host star. We collected spectra using the ESPaDOnS and the NARVAL spectropolarimeters, installed at the 3.6-m Canada-France-Hawaii telescope and the 2-m Telescope Bernard Lyot at Pic du Midi, during two monitoring campaigns (June 2007 and July 2008). HD 189733 has a mainly toroidal surface magnetic field, having a strength that reaches up to 40 G. The star is differentially rotating, with latitudinal angular velocity shear of domega = 0.146 +- 0.049 rad/d, corresponding to equatorial and polar periods of 11.94 +- 0.16 d and 16.53 +- 2.43 d respectively. The study of the stellar activity shows that it is modulated mainly by the stellar rotation (rather than by the orbital period or the beat period between the stellar rotation and the orbital periods). We report no clear evidence of magnetospheric interactions between the star and the planet. We also extrapolated the field in the stellar corona and calculated the planetary radio emission expected for HD 189733b given the reconstructed field topology. The radio flux we predict in the framework of this model is time variable and potentially detectable with LOFAR

On the chromospheric activity of stars with planets

Context. Signatures of chromospheric activity enhancement have been found for a dozen stars, pointing to a possible star-planet interaction. Nevertheless in the coronal activity regime, there is no conclusive observational evidence for such an interaction. Does star-planet interaction manifest itself only for a few particular cases, without having a major effect on stars with planets in general? Aims. We aim to add additional observational constraints to support or reject the major effects of star-planet interactions in stellar activity, based on CaII chromospheric emission flux. Methods. We performed a statistical analysis of CaII emission flux of stars with planets, as well as a comparison between CaII and X-ray emission fluxes, searching for dependencies on planetary parameters. Results. In the present sample of stars with planets, there are no significant correlations between chromospheric activity indicator log(R'HK) and planetary parameters. Further, the distribution of the chromospheric activity indicator for stars without planets is not distinguishable from the one with planets.Comment: 6 pages, 5 figures, submitted to A&

Signatures of Star-planet interactions

Planets interact with their host stars through gravity, radiation and magnetic fields, and for those giant planets that orbit their stars within $\sim$10 stellar radii ($\sim$0.1 AU for a sun-like star), star-planet interactions (SPI) are observable with a wide variety of photometric, spectroscopic and spectropolarimetric studies. At such close distances, the planet orbits within the sub-alfv\'enic radius of the star in which the transfer of energy and angular momentum between the two bodies is particularly efficient. The magnetic interactions appear as enhanced stellar activity modulated by the planet as it orbits the star rather than only by stellar rotation. These SPI effects are informative for the study of the internal dynamics and atmospheric evolution of exoplanets. The nature of magnetic SPI is modeled to be strongly affected by both the stellar and planetary magnetic fields, possibly influencing the magnetic activity of both, as well as affecting the irradiation and even the migration of the planet and rotational evolution of the star. As phase-resolved observational techniques are applied to a large statistical sample of hot Jupiter systems, extensions to other tightly orbiting stellar systems, such as smaller planets close to M dwarfs become possible. In these systems, star-planet separations of tens of stellar radii begin to coincide with the radiative habitable zone where planetary magnetic fields are likely a necessary condition for surface habitability.Comment: Accepted for publication in the handbook of exoplanet

Exploring nonlinear intra-annual growth dynamics in Fagus sylvatica L. trees at the Italian ICP-forests level II network

The European beech (Fagus sylvatica L.) is a widely distributed tree species across Europe, highly sensitive to climate change and global warming. This study illustrates results of a 5-year monitoring time period from eight sites of the ICP-Forests Level II (intensive monitoring network) along the Italian latitudinal gradient. The tree-level relationship between tree growth dynamics and environmental factors, including seasonal climate fluctuations were investigated by means of tree-level Generalized Additive Mixed Models (GAMMs). Model results revealed that climate was responsible for just a portion of the variability in beech growth dynamics. Even if climatic predictors were highly significant in almost all sites, the model explained nearly 30% of the total variance (with just a maximum value of 71.6%), leaving the remaining variance unexplained and likely connected with forest management trajectories applied to each site (e.g., aged coppice and fully grown high forest). Climate change scenarios were then applied to predict site-specific future responses. By applying climate change scenarios, it was predicted that central and northern Italy would face similar climatic conditions to those currently detected at southern latitudes. A special case study was represented by VEN1 plot (Veneto, Northern Italy) whose current and future climate regimes were grouped in a unique and separated cluster