5,922 research outputs found
Boundedness of Pseudodifferential Operators on Banach Function Spaces
We show that if the Hardy-Littlewood maximal operator is bounded on a
separable Banach function space and on its associate space
, then a pseudodifferential operator
is bounded on whenever the symbol belongs to the
H\"ormander class with ,
or to the the Miyachi class
with ,
. This result is applied to the case of
variable Lebesgue spaces .Comment: To appear in a special volume of Operator Theory: Advances and
Applications dedicated to Ant\'onio Ferreira dos Santo
Norm inequalities for the minimal and maximal operator, and differentiation of the integral
We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1)
Norm inequalities for the minimal and maximal operator, and differentiation of the integral
We study the weighted norm inequalities for the minimal operator, a new operator analogous to the Hardy-Littlewood maximal operator which arose in the study of reverse Hölder inequalities. We characterize the classes of weights which govern the strong and weak-type norm inequalities for the minimal operator in the two weight case, and show that these classes are the same. We also show that a generalization of the minimal operator can be used to obtain information about the differentiability of the integral in cases when the associated maximal operator is large, and we give a new condition for this maximal operator to be weak (1,1)
Correction of Errors During The Manufacture by Computer Numerical Control (CNC) of Blades for an Axial Hydrokinetic Turbine
The design and manufacture of new systems for providing electric power to non-interconnected areas is one of the challenges for engineering. There are several alternatives, including water or wind-power generation systems, where hydrokinetic turbines are highlighted. This work establishes the methodology, identification and correction of errors generated during the manufacture by machining, using CAD/CAPP/CAM techniques, for an axial hydrokinetic turbine. During the manufacturing process, the generation of an error on the edges of the blades was identified, which was attributed to problems in the design of the model since the degrees of freedom of the manufacturing system used were not considered. For the manufacture of complex surfaces in the design of models, the most extreme points of the surfaces in contact must match the tangent edges to ensure that the tools of machining can reach them with the trajectories generated from the CAM
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
Depth profile of the ferromagnetic order in a YBaCuO / LaCaMnO superlattice on a LSAT substrate: a polarized neutron reflectometry study
Using polarized neutron reflectometry (PNR) we have investigated a
YBa2Cu3O7(10nm)/La2/3Ca1/3MnO3(9nm)]10 (YBCO/LCMO) superlattice grown by pulsed
laser deposition on a La0.3Sr0.7Al0.65Ta0.35O3 (LSAT) substrate. Due to the
high structural quality of the superlattice and the substrate, the specular
reflectivity signal extends with a high signal-to-background ratio beyond the
fourth order superlattice Bragg peak. This allows us to obtain more detailed
and reliable information about the magnetic depth profile than in previous PNR
studies on similar superlattices that were partially impeded by problems
related to the low temperature structural transitions of the SrTiO3 substrates.
In agreement with the previous reports, our PNR data reveal a strong magnetic
proximity effect showing that the depth profile of the magnetic potential
differs significantly from the one of the nuclear potential that is given by
the YBCO and LCMO layer thickness. We present fits of the PNR data using
different simple block-like models for which either a ferromagnetic moment is
induced on the YBCO side of the interfaces or the ferromagnetic order is
suppressed on the LCMO side. We show that a good agreement with the PNR data
and with the average magnetization as obtained from dc magnetization data can
only be obtained with the latter model where a so-called depleted layer with a
strongly suppressed ferromagnetic moment develops on the LCMO side of the
interfaces. The models with an induced ferromagnetic moment on the YBCO side
fail to reproduce the details of the higher order superlattice Bragg peaks and
yield a wrong magnitude of the average magnetization. We also show that the PNR
data are still consistent with the small, ferromagnetic Cu moment of 0.25muB
that was previously identified with x-ray magnetic circular dichroism and x-ray
resonant magnetic reflectometry measurements on the same superlattice.Comment: 11 pages, 7 figure
Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms
Given any smooth toric surface S, we prove a SYM-HILB correspondence which
relates the 3-point, degree zero, extended Gromov-Witten invariants of the
n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal
Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As
we do not specialize the values of the quantum parameters involved, this result
proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture
for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of
reconstructing the cup product for Hilb^n(S) from the orbifold invariants of
[Sym^n(S)].Comment: Revised versio
Clinical and genetic risk factors for acute incident venous Thromboembolism in ambulatory patients with COVID-19.
Importance: The risk of venous thromboembolism (VTE) in ambulatory COVID-19 is controversial. In addition, the association of vaccination with COVID-19-related VTE and relevant clinical and genetic risk factors remain to be elucidated. Objective: To quantify the association between ambulatory COVID-19 and short-term risk of VTE, study the potential protective role of vaccination, and investigate clinical and genetic risk factors for post-COVID-19 VTE. Design, Setting, and Participants: This population-based cohort study of patients with COVID-19 from UK Biobank included participants with SARS-CoV-2 infection that was confirmed by a positive polymerase chain test reaction result between March 1, 2020, and September 3, 2021, who were then propensity score matched to COVID-19-naive people during the same period. Participants with a history of VTE who used antithrombotic drugs (1 year before index dates) or tested positive in hospital were excluded. Exposures: First infection with SARS-CoV-2, age, sex, ethnicity, socioeconomic status, obesity, vaccination status, and inherited thrombophilia. Main Outcomes and Measures: The primary outcome was a composite VTE, including deep vein thrombosis or pulmonary embolism, which occurred 30 days after the infection. Hazard ratios (HRs) with 95% CIs were calculated using cause-specific Cox models. Results: In 18 818 outpatients with COVID-19 (10 580 women [56.2%]; mean [SD] age, 64.3 [8.0] years) and 93 179 matched uninfected participants (52 177 women [56.0%]; mean [SD] age, 64.3 [7.9] years), the infection was associated with an increased risk of VTE in 30 days (incidence rate of 50.99 and 2.37 per 1000 person-years for infected and uninfected people, respectively; HR, 21.42; 95% CI, 12.63-36.31). However, risk was substantially attenuated among the fully vaccinated (HR, 5.95; 95% CI, 1.82-19.5; interaction P = .02). In patients with COVID-19, older age, male sex, and obesity were independently associated with higher risk, with adjusted HRs of 1.87 (95% CI, 1.50-2.33) per 10 years, 1.69 (95% CI, 1.30-2.19), and 1.83 (95% CI, 1.28-2.61), respectively. Further, inherited thrombophilia was associated with an HR of 2.05 (95% CI, 1.15-3.66) for post-COVID-19 VTE. Conclusions and Relevance: In this population-based cohort study of patients with COVID-19, ambulatory COVID-19 was associated with a substantially increased risk of incident VTE, but this risk was greatly reduced in fully vaccinated people with breakthrough infection. Older age, male sex, and obesity were clinical risk factors for post-COVID-19 VTE; factor V Leiden thrombophilia was additionally associated with double the risk, comparable with the risk of 10-year aging. These findings may reinforce the need for vaccination, inform VTE risk stratification, and call for targeted VTE prophylaxis strategies for unvaccinated outpatients with COVID-19
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