Local solvability and loss of smoothness of the Navier–Stokes–Maxwell equations with large initial data

The existence of a local-in-time unique solution and loss of smoothness of a full Magneto-Hydro-Dynamics (MHD) system are considered for periodic initial data. The result is proven using Fujita–Kato’s method in ${?}^1$ based (for the Fourier coefficients) functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to Maxwell’s equations. A loss of smoothness result is shown for the velocity and magnetic field. It comes from the damped-wave operator which does not have any smoothing effect.     

Réactivité de l’acide déhydroacétique hydrogené en c5-c6 : obtention des pyrano-1,5-benzodiazépines différemment substituées et de la structure enaminone

A number of 1,5-benzodiazepines derivatives 4 were obtained via the interaction of dehydroacetic acid hydrogenated at C₅-C₆, orthophenylenediamines and aromatic aldehydes. The interpretation of the results is enriched by a study of the electronic effects of the DHA hydrogenated at C₅-C₆. Accordingly, it leads us to obtain the original structure cynnamoyle 5.     

Cooperating and Non-cooperating Firms in Inventive and Absorptive Research

We consider a duopoly competing in quantity, where firms can invest in both innovative and absorptive research and development to reduce their unit production cost, and where they benefit from free spillovers between them. We analyze the case where firms act non-cooperatively and the case where they cooperate by forming a research joint venture. We show that, in both modes of play, there exists a unique symmetric solution. We find that the level of investment in innovative research and development is always the highest and that the efficiency of investment in absorptive research has almost no impact on the equilibrium solution.     

Targeting the proangiogenic VEGF-VEGFR protein-protein interface with drug-like compounds by in silico and in vitro screening

Protein-protein interactions play a central role in medicine, and their modulation with small organic compounds remains an enormous challenge. Because it has been noted that the macromolecular complexes modulated to date have a relatively pronounced binding cavity at the interface, we decided to perform screening experiments over the vascular endothelial growth factor receptor (VEGFR), a validated target for antiangiogenic treatments with a very flat interface. We focused the study on the VEGFR-1 D2 domain, and 20 active compounds were identified. These small compounds contained a (3-carboxy-2-ureido)thiophen unit and had IC₅₀ values in the low micromolar range. The most potent compound inhibited the VEGF-induced VEGFR-1 transduction pathways. Our findings suggest that our best hit may be a promising scaffold to probe this macromolecular complex and for the development of treatments of VEGFR-1-dependent diseases.     

Chemical composition and biological potential of seed oil and leaf extracts of Henophyton deserti Coss. & Durieu

Henophyton deserti was characterized in respect to its chemical composition, antioxidant potential and antimicrobial activity. Fourteen compounds were identified by LC/MS, GC/MS, and GC in leaf and seed extracts. Total flavonoids ranged between 45.66 and 181.2 mg QE g^?1 and 2.03 and 38.95 mg QE g^?1 dry weight (dw) in leaf and seed polar extracts, respectively. Rutin, Kaempferol 3-rutinoside, Diosmetin 7-O-Glucoside, and Acacetin 7-O-Glucoside flavonoids were tentatively identified in this plant. The profile of seed fatty acids revealed oleic acid (C18:1, 27%), linoleic acid (C18:2, 12%) and linolenic acid (C18:3, 17%). The highest antioxidant activities of 85.2% and 67.5% were obtained with methanol and ethyl acetate leaf extracts. All H. deserti extracts were active against at least one of the tested bacteria, leaf ethyl acetate extract showed the lowest MIC of 0.156 mg ml^?1. Only seed ethyl acetate extract showed antifungal activity with a MIC of 2.5 mg ml^?1.     

Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics

In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and atmospheric dynamics. In this paper we show that for certain class of initial data the corresponding smooth solutions of the inviscid (non-viscous) primitive equations, if they exist, they blow up in finite time. Specifically, we consider the three-dimensional inviscid primitive equations in a three-dimensional infinite horizontal channel, subject to periodic boundary conditions in the horizontal directions, and with no-normal flow boundary conditions on the solid, top and bottom boundaries. For certain class of initial data we reduce this system into the two-dimensional system of primitive equations in an infinite horizontal strip with the same type of boundary conditions; and then we show that for specific sub-class of initial data the corresponding smooth solutions of the reduced inviscid two-dimensional system develop singularities in finite time.     

Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

We prove some optimal logarithmic estimates in the Hardy space H ^∞(G) with Hölder regularity, where G is the open unit disk or an annular domain of ?. These estimates extend the results established by S.Chaabane and I.Feki in the Hardy-Sobolev space H ^k,∞ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem for the Laplace operator and the Robin inverse problem.     

卫星系统中的混沌控制

对于非线性扰动系统对指令信号的跟踪问题,提出解析条件和实现方法.对在反馈中包含线性动力和非线性两部份的非线性扰动设备进行了研究,设备的非线性部份和扰动是未知的但是有界的.提出控制卫星天平动角的算法,用图示对该算法作了说明.     

Synthesis and crystal structure determination of yttrium ultraphosphate YP5O14

The crystal structure of monoclinic YP₅O₁₄ (space group C2/c, a=12.919(2) Å, b=12.796(4) Å, c=12.457(2) Å, β=91.30(1)°, Z=8) has been refined from single-crystal X-ray diffraction data. Full-matrix least-squares refinement on F² using 2249 independent reflections for 183 refinable parameters results in a final R value of 0.027 (ωR=0.069). The structure is isotypic with HoP₅O₁₄. This structure is built up from infinite layers of PO₄ tetrahedra linked through isolated YO₈ polyhedra. The three-dimensional cohesion of the framework results from Y-O-P bridges. This crystal structure refinement leads to the calculated X-ray diffraction powder pattern of this monoclinic polymorph, which has been the starting point of a thorough study of the solid-state synthesis of this ultraphosphate. This investigation further leads to a better outstanding of features observed during the synthesis of powdered samples. The thermal behavior of this ultraphosphate has been studied by DTA and TGA analyses. The infrared and Raman spectroscopic characterizations have been carried out on polycrystalline samples. The luminescence properties of the Eu³⁺ ion incorporated in the monoclinic C2/c polymorph of YP₅O₁₄ as local structural probe show that in YP₅O₁₄: 5% Eu³⁺ sample, the Eu³⁺ ions are distributed over the two Y³⁺ crystallographic sites of C₂ symmetry of this structure.