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The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F(u1,…,um) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂i∂jF for all i≠j. This paper concerns the regularity assumptions on F and the equality cases. It is shown here that extended Hardy-Littlewood and Riesz inequalities are valid for supermodular integrands that are just Borel measurable. Under some nondegeneracy conditions, all equality cases are equivalent to radially decreasing functions under transformations that leave the functionals invariant (i.e., measure-preserving maps for the Hardy-Littlewood inequality, translations for the Riesz inequality). The proofs rely on monotone changes of variables in the spirit of Sklar's theorem. 相似文献
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Hichem Mokni 《Positivity》2007,11(3):417-432
The aim of this work is to study norm preserving extensions of positive functionals on some spaces of fractions. The main
result is stated in the case of unitary complex Banach algebras with involution. Moreover, we deal with C*-algebras and the
commutative case as well. An application is also given. 相似文献
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Afifa Hafidh Fathi Touati Faouzi Hosni Ahmed Hichem Hamzaoui Sayda Somrani 《Phosphorus, sulfur, and silicon and the related elements》2018,193(3):155-163
New hybrid materials were synthesized from an inorganic precursor, (tetraethoxysilane: TEOS) and bifunctional organic precursors through the sol-gel process. Indeed, monolithic and transparent hybrid gels were obtained by the reaction of tetraethoxysilicate (TEOS) with 1,2,4-thiadiazole-3,5-diamine (1), 5-amino-1,3,4-thiadiazole-2-thiol (2), and 1H-1,2,4-triazole-3-thiol (3) in ethanol as solvent, using chloric acid (HCl 10?1M) as catalyst. It is shown that TEOS has been cross-linked with bi-functional heterocyclic compounds: (1), (2) and (3) leading to the formation of transparent and colorous gels. The characterization was realized by infrared, 29Si and 13C CP MAS NMR. The xerogels morphology and texture were studied by scanning electron microscopy (SEM) and Brunauer – Emmet – Teller method (BET). The obtained results show that organic adducts (1), (2) and (3) react with TEOS leading to gels in which Si–N and Si–S bridges were formed. According to N2-physisorption results, xerogels are mesoporous with specific surface area varied from 105 to 312 m2g?1 and their isotherms are classified as type IV. The optic and magnetic properties of hybrids were studied respectively by UV-Vis spectroscopy and RPE. This study showed that all materials are paramagnetic semiconductors. 相似文献
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Mael Guennou Hichem Dammak Philippe Djémia Philippe Moch Pham-Thi Mai 《Solid State Sciences》2010,12(3):298-301
In this paper, we compare the electromechanical properties of tetragonal single domain PZN–12%PT single crystals obtained by different methods: resonance–antiresonance method, Brillouin scattering, and resonant ultrasound spectroscopy. The agreement between the different measurements is found satisfactory for many elastic constants within experimental uncertainties. Differences are notable for the elastic constants associated to the propagation of shear waves (c66E and c44E). This can be accounted for by imperfections of the sample in acoustic spectroscopy and specific difficulties of shear resonators used for the resonance method. Strong discrepancies are noted for the hardened elastic constant c33D associated to longitudinal waves propagating along the polarization direction; we suggest this can arise from a frequency dependence of the dielectric constant. 相似文献
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A. BAKLOUTI J. LUDWIG L. SCUTO K. SMAOUI 《数学学报(英文版)》2007,23(7):1173-1188
We study the L^p-Fourier transform for a special class of exponential Lie groups, the strong *-regular exponential Lie groups. Moreover, we provide an estimate of its norm using the orbit method. 相似文献
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Hichem Dammak 《Journal of Physics and Chemistry of Solids》2005,66(10):1838-1843
The charge-balanced random-layer model for ordered lead-based perovskites was investigated by using the standard Metropolis Monte Carlo method on a rigid lattice with simple ionic model. Our results show that in the structure formula Pb[B′]1/2[B″]1/2O3, where all B″-sites are occupied by BV cations, chemical order of BII and BV cations does exist in B′-sites and the ordered structure has an hexagonal symmetry. An order-disorder transition as a function of temperature is evidenced by an abrupt variation of both the heat capacity and a long-range order parameter. Finally, the evolution of the short-range order parameter versus temperature shows that a local order remains in B′-sites contrary to the charge-balanced random-layer model that suggests that B′-sites are randomly occupied. This local order could be helpful to clarify some experimental results. 相似文献
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Aymen Bensouf Hichem Chtioui 《Calculus of Variations and Partial Differential Equations》2011,41(3-4):455-481
In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with n????5, and study the related fourth order elliptic equation. We prove new existence results based on a new type of Euler?CHopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal metrics having the same Q-curvature. 相似文献
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Sayed Abdel-Khalek Kamal Berrada Eied M. Khalil Abdel-Shafy F. Obada Esraa Reda Hichem Eleuch 《Entropy (Basel, Switzerland)》2021,23(5)
In this work, we introduce the standard Tavis-Cummings model to describe two-qubit system interacting with a single-mode field associated to power-law (PL) potentials. We explore the effect of the time-dependent interaction and the Kerr-like medium. We solve the Schrödinger equation to obtain the density operator that allows us to investigate the dynamical behaviour of some quantumness measures, such as von Neumann entropy, negativity and Mandel’s parameter. We provide how these entanglement measures depend on the system parameters, which paves the way towards better control of entanglement generation in two-qubit systems. We find that the enhancement and preservation of the atoms-field entanglement and atom-atom entanglement can be achieved by a proper choice of the initial parameters of the field in the absence and presence of the time-dependent interaction and Kerr medium. We examine the photons distribution of the field and determine the situations for which the field exhibits super-poissonian, poissonian or sub-poissonian distribution. 相似文献