where are closed differential forms and 2kn. Our main results (the case k=n having been handled by Moser [J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286–294] and Dacorogna and Moser [B. Dacorogna, J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 1–26]) are that
– when n is even and k=2, under some natural non-degeneracy condition, we can prove the existence of such diffeomorphism satisfying Dirichlet data on the boundary of a bounded open set and the natural Hölder regularity; at the same time we get Darboux theorem with optimal regularity;
– we are also able to handle the degenerate cases when k=2 (in particular when n is odd), k=n−1 and some cases where 3kn−2.

Résumé

Nous montrons l'existence d'un difféomorphisme satisfaisant
φ*(g)=f
sont des formes différentielles fermées et 2kn. Nos résultats principaux (le cas k=n a été discuté notamment dans Moser [J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286–294] et Dacorogna et Moser [B. Dacorogna, J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 1–26]) sont les suivants.
– Si n est pair, k=2 et sous des conditions naturelles de non dégénérescence, nous montrons l'existence et la régularité dans les espaces de Hölder d'un tel difféomorphisme satisfaisant de plus une condition de Dirichlet. On obtient aussi le théorème de Darboux avec la régularité optimale.
– Par ailleurs quand k=2 et n est impair ou k=n−1, ainsi que quelques cas particuliers où 3kn−2, nous montrons l'existence locale d'un tel difféomorphisme satisfaisant, en outre, des conditions de Cauchy.
Keywords: Darboux theorem; Symplectic forms; Pullback; Hölder regularity  相似文献   
129.
Study of high-temperature ageing and creep on bainitic 5Cr-0.5Mo steel by magnetic NDE techniques     
J.N. Mohapatra  N.R. Bandyopadhyay  A. Mitra 《Journal of magnetism and magnetic materials》2010,322(6):589-595
5Cr-0.5Mo steel having initial bainitic microstructure has been aged at 600 °C for 5000 h and subjected to creep at 600 °C/60 MPa. At different lengths of time the tests were interrupted for magnetic measurement using magnetic Barkhausen emissions (MBE) and magnetic hysteresis loop (MHL) techniques. Composition, morphology and distribution of carbides were studied using scanning electron microscopy (SEM). Magnetic softness was observed in the material up to 1600 h of ageing due to the decrease in pinning density for the coarsening of carbides by accumulation of large number of finer carbides. At higher ageing periods the demagnetizing field offered by the large massive carbides causes magnetic hardening. During creep test since the material has been normalized at 50 h of creep test also the structural change in creep test is accelerated, the magnetic softening for the interstitial carbon migration to the grain boundary and stress relaxation has removed in such early periods of ageing. When the carbides started coarsening the number density of the carbides decreased and inter-carbide distance increased which enhances the magnetic softening in the material in the secondary stage of creep. Formation of massive carbides and micro voids at the late tertiary stage of creep offers demagnetizing field causes magnetic hardening before failure of the material.  相似文献   
130.
Solitons and critical breakup fields in lithium niobate type uniaxial ferroelectrics     
A. K. Bandyopadhyay  P. C. Ray  V. Gopalan 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,65(4):525-531
Ferroelectric materials, such as lithium niobate, show interesting non-linear hysteresis behavior that can be explained by a dynamical system analysis. By using variational principle, a non-linear Klein-Gordon (K-G) equation is derived for lithium niobate type of uniaxial ferroelectrics involving various types of energy, which was not considered previously to construct the Hamiltonian. This leads to soliton solutions under different conditions of soliton velocity. The critical value of the (dimensional) effective electric field has been estimated to be 54–58 kV/cm for lithium niobate depending on the impurity content in these type inhomogeneous ferroelectrics. Beyond this critical field, there is no existence of solitons. This critical field is related to a break-up mechanism of Landau-Ginzburg two-well potential to a single well, as the driving force is increased.  相似文献   
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121.
Level fluctuations in a quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate the level fluctuations to the classical dynamics in the regular and chaotic limit. In this, we show that the spectrum of the system undergoing order to chaos transition displays a characteristic f(-gamma) noise and gamma is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles, respectively, of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.  相似文献   
122.
In this work, we discuss the evolution of modified Holographic Dark Energy (HDE) derived from the UV/IR cutoff in the Randall-Sundrum II (RS-II) braneworld scenario. Choosing future event horizon as the IR cutoff, it is seen that the equation of state parameter for the modified HDE can cross the phantom crossing line ω=−1.  相似文献   
123.
The object of the present paper is to study the semi-decomposibility of a weakly symmetric space introduced by Tamássy and Binh [1]. Also a weakly symmetric space admitting a concurrent or a recurrent vector field has been studied.  相似文献   
124.
The concept of the time-independent correlators for the even- and odd-frequency pairing states that can be defined for both bosonic and fermionic quasiparticles is proposed. These correlators explicitly capture the existence of two distinct classes of pairing states and provide a direct probe of the hidden Berezinskii order. This concept is illustrated in the cases of pairings for Majorana fermions and quasiparticles in Dirac semimetals. It is shown that the time-independent correlator is able to effectively capture the energy scale relevant for pairing.  相似文献   
125.
126.
We discuss β-equilibrated and charge neutral matter involving hyperons and {ie817-1} condensates within relativistic models. It is observed that populations of baryons are strongly affected by the presence of antikaon condensates. Also, the equation of state including {ie817-2} condensates becomes softer resulting in a smaller maximum mass neutron star  相似文献   
127.
128.
We discuss the existence of a diffeomorphism such that
φ*(g)=f
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