Dynamic behaviour modelling of a flexible gear system by the elastic foundation theory in presence of defects

In this paper a novel approach for modelling a spur gear system using finite element method combined with elastic foundation theory is developed. The pinion is modelled by shaft finite element and the wheel by a three-dimensional finite element. Elastic foundation is utilized to model the gearmesh. The modal analysis showed the presence of lower natural frequency for thin rimmed gear cases susceptible to be excited by the operating running condition. The transmission error is affected by the wheel shape and by the presence of lower natural frequencies. Eccentricity error and tooth crack are also modelled to observe their influence on the dynamics behaviour of the system. It was found that they are responsible of the apparition of an amplitude modulation.     

On the stability of the Kalman–Bucy filter with stationary time varying parameters

Linear filtering systems with stationary parameters are considered in continuous time. We generalize the conditionally Gaussian result of Lipster – Shiryaev and Haussmann – Pardoux. Moreover, we show that the Kalman – Bucy filter is exponentially stable under weak conditions of stabile ability and detect ability. This filter will have a well defined asymptotic behaviour     

A characterization of complex lattice homomorphisms

In this paper we discuss the problem of how to recognize a complex lattice homomorphism on the complexification of a real vector lattice L from its behavior on a small subset of .      

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.     

On the buckling of elastic plates

The Föppl-von Kármán equations are used toexplore the onset of linear instability and the subsequent nonlineardevelopment of buckling patterns in a flat elastic plate dueto an imposed shear or body force such as gravity. Experimentalresults are also presented for a clamped and sheared sheet ofNeoprene rubber and these compare favourably with theory.     

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.     

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.     

New fluoride glasses based on 4f and 5f elements

New fluoride glasses have been isolated in the ternary systems ThF₄-LnF₃-BaF₂ with Ln = the lanthanides Yb, Y, Tm. The melt must be quenched to reduce crystallization. They are simply prepared from oxides by an appropriate NH₄F, HF treatment. The IR transmission is remarkable, the optical window lying in the 0.25-10 μm region.