The second order pullback equation Csató, G.; Dacorogna, B.; Kneuss, O.
Calculus of variations and partial differential equations,
2014/1, Letnik:
49, Številka:
1-2
Journal Article
Recenzirano
Odprti dostop
Let
be two closed
-forms over
The pullback equation studies the existence of a diffeomorphism
such that
We prove two types of results. The first one sharpens some of the existing regularity results. ...The second one discusses the possibility of choosing the map
as the gradient of a function
We show that this is a very rare event unless the two forms are constant.
The Pullback Equation for Differential Forms Csató, Gyula; Dacorogna, Bernard; Kneuss, Olivier
Progress in nonlinear differential equations and their applications,
2012., Letnik:
83
eBook
Odprti dostop
An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map - so that it satisfies the ...pullback equation In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge-Morrey decomposition and to give several versions of the Poincaré lemma. The core of the book discusses the case k = n, and then the case 1? k ? n?1 with special attention on the case k = 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Hölder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation. The Pullback Equation for Differential Forms is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.
We consider the problem{divu+〈a;u〉=finΩu=u0on∂Ω. We show that if curla(x0)≠0 for some x0∈Ω, then the problem is solvable without restriction on f. We also discuss the regularity of the solution.
A three‐dimensional quantitative stratigraphic forward model is employed to investigate the controls leading to the Messinian events in the lacustrine Pannonian Basin of Central Paratethys, and the ...link between the Messinian salinity crisis in the Mediterranean and the late Miocene‐Pliocene stratigraphy of the Pannonian Basin. Subsurface geological data show that a prominent unconformity surface formed during Messinian time in the Pannonian Basin associated with a sudden forced regression, abrupt basinward shift of facies and a subsequent, prolonged lowstand normal regression. The lowstand prograding series filled up the shallow basin fast, while, at the same time, the marginal areas of the basin were subject to tectonic inversion. The Dionisos program used in this research is built on a nonlinear water‐driven sediment diffusion process, and it employs multiple sediment classes, basin flexure and compaction. Four different scenarios were built in the experiments to test possible basin histories with different rates and timing of tectonic inversion. Each scenario was modelled in two versions: including and not including a lake‐level fall in the Messinian. The results confirm that the Pannonian Basin in the study area has undergone a tectonic inversion since the Messinian, although the exact rates of uplift at different locations remain uncertain. The unconformity and the observed stratigraphic architecture and facies pattern could be modelled adequately only in the versions that applied a Messinian lake‐level fall. Our research concludes that the Messinian unconformity in the Pannonian Basin was caused by an absolute lake‐level drop, likely linked to the desiccation of the Mediterranean, followed by subsidence and normal regression in the basin centre and concomitant tectonic inversion and uplift along the basin margins.
Aims
Myeloperoxidase (MPO) catalyses the formation of a wide variety of oxidants, including hypochlorous acid (HOCl), and contributes to cardiovascular disease progression. We hypothesized that ...during its action MPO evokes substantial vasomotor responses.
Methods
Following exposure to MPO (1.92 mU mL−1) in the presence of increasing concentrations of hydrogen peroxide (H2O2), changes in arteriolar diameter of isolated gracilis skeletal muscle arterioles (SMAs) and coronary arterioles (CAs) and in the isometric force in basilar arteries (BAs) of the rat were monitored.
Results
Myeloperoxidase increased vascular tone to different degrees in CAs, SMAs and BAs. The mechanism of increased vasoconstriction was studied in detail in SMAs. MPO‐evoked vasoconstrictions were prevented by the MPO inhibitor 4‐aminobenzhydrazide (50 μm), by endothelium removal in the SMAs. Surprisingly, the HOCl scavenger L‐methionine (100 μm), the thromboxane A2 (TXA2) antagonist SQ‐29548 (1 μm) or the non‐specific cyclooxygenase (COX) antagonist indomethacin (1 μm) converted the MPO‐evoked vasoconstrictions to pronounced vasodilations in SMAs, not seen in the presence of H2O2. In contrast to noradrenaline‐induced vasoconstrictions, the MPO‐evoked vasoconstrictions were not accompanied by significant increases in arteriolar Ca2+ levels in SMAs.
Conclusion
These data showed that H2O2‐derived HOCl to be a potent vasoconstrictor upon MPO application. HOCl activated the COX pathway, causing the synthesis and release of a TXA2‐like substance to increase the Ca2+ sensitivity of the contractile apparatus in vascular smooth muscle cells and thereby to augment H2O2‐evoked vasoconstrictions. Nevertheless, inhibition of the HOCl–COX–TXA2 pathway unmasked the effects of additional MPO‐derived radicals with a marked vasodilatory potential in SMAs.
To date, no standardized international guideline for the testing of chemicals for phototoxic potential has been accepted for regulatory purposes. In 1991, the European Commission (EC), represented ...initially by the Directorate General XI and later by ECVAM (the European Centre for the Validation of Alternative Methods) and COLIPA (the European Cosmetic, Toiletry and Perfumery Association), agreed to establish a joint EU/COLIPA programme on the development and validation of
in vitro phototoxicity tests. The first phase (phase I, 1992–93) was designed as a prevalidation study, to identify
in vitro test procedures and test protocols for a formal validation trial under blind conditions. In the second phase (phase II, 1994–95), the formal validation study, the most promising
in vitro phototoxicity tests were validated with 30 carefully selected test chemicals in 11 laboratories in a blind trial. The 3T3 mouse fibroblast neutral red uptake phototoxicity test (3T3 NRU PT) was performed as a core test in nine laboratories, since it provided the best results in phase I of the study. The purpose of phase II was to confirm the reliability and relevance of the
in vitro tests for predicting phototoxic effects and for identifying phototoxic chemicals. In phase II the phototoxic potential of test chemicals in the 3T3 NRU PT test was either assessed by determining the phototoxicity factor (PIF) by using a cut-off value of 5 as in phase I of the study, or by determining the mean photo effect (MPE) by using a cut-off value of 0.1, as recently proposed by
Holzhütter (1997). Results obtained with both approaches in the 3T3 NRU PT test in phase II were reproducible in the nine laboratories, and the correlation between
in vitro and
in vivo data was very high. Therefore, ECVAM and COLIPA conclude from this formal validation trial under blind conditions that the 3T3 NRU PT test is a scientifically validated
in vitro test which is ready to be considered for regulatory purposes for assessing the phototoxic potential of chemicals. A draft OECD Guideline for
“In Vitro Phototoxicity Testing”, incorporating the standard protocol of the 3T3 NRU PT test, will be submitted to the OECD test guidelines programme in due course.
Earlier studies revealed a prominent unconformity in the Messinian stratigraphic record of the lacustrine Pannonian Basin, but it was unclear what factors were responsible for the formation of this ...unconformity, and thus its origin remained controversial. The problem was further complicated by the fact that stratal patterns in the Messinian varied significantly along the paleo-margins of the lake. Our study introduces quantitative stratigraphic simulations to analyze the role of subsidence, sediment supply, and lake-level changes in the formation of the unconformity and the various architectural patterns that evolved in response to the Messinian events. The results suggest that a relative lake-level fall occurred in the Messinian, accompanied and followed by tectonic inversion in several parts of the basin. Since the rate of tectonic subsidence and/or uplift varied in space and time, the size of the relative lake-level fall varied significantly across the basin, while various stratal architectural patterns formed in the same time interval. The age of the unconformity was estimated, based on seismic correlations with paleomagnetic chronozones, to be between 5–6 Ma, which was refined by stratigraphic simulations.
Galeacysta etrusca cysts were found in the unconformity, which confirmed its late Messinian age. The surface is called the Intra-Messinian Unconformity (IMU) in this paper. Seismic interpretations and simulations of stratal architecture led to the formulation of a basin fill model and identification of four stratigraphic architectural patterns related to Messinian events including a major lake-level fall and coeval and subsequent uplift events in certain parts of the basin.
Results of resonance searches in the Xi(-)pi(-), Xi(-)pi(+), Xi;(+)pi(-), and Xi;(+)pi(+) invariant mass spectra in proton-proton collisions at sqrts=17.2 GeV are presented. Evidence is shown for the ...existence of a narrow Xi(-)pi(-) baryon resonance with mass of 1.862+/-0.002 GeV/c(2) and width below the detector resolution of about 0.018 GeV/c(2). The significance is estimated to be above 4.2sigma. This state is a candidate for the hypothetical exotic Xi(--)(3/2) baryon with S=-2, I=3 / 2, and a quark content of (dsdsū). At the same mass, a peak is observed in the Xi(-)pi(+) spectrum which is a candidate for the Xi(0)(3/2) member of this isospin quartet with a quark content of (dsus-d). The corresponding antibaryon spectra also show enhancements at the same invariant mass.
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► The CCVD method is very efficient in obtaining helical carbon nanotubes. ► Due to their special configuration helical carbon nanotubes have great potential for being used in ...composite materials. ► In addition to nanocomposite reinforcement, the helical CNTs may also be used as mechanical or as electrical sensors.
Recent results from our group and from literature data are summarized. Emphasis is put on the various supported catalysts that can lead to the formation of helical (or coiled) carbon nanotubes. Detailed analysis of transmission electron microscopy images reveals that not all types of nanotubes – having any type of coil pitch and coil diameter – are equally probable: stability islands can be found in the 3D representation of the number of nanotubes as a function of both coil pitch and coil diameter. In most of the cases the coils are formed by introducing pairs of five-membered and seven-membered rings into the nanotubes containing the basic six-membered rings. Possible applications of the helical carbon nanotubes are discussed.
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