A convergent star product for linear Poisson structures

An explicit star product ⋆ _α ^Γ on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between this star product and the Kontsevich star product in [K₁] is given and diverse properties of the star product ⋆ _α ^Γ are studied. It is also proved that the star product ⋆ _α ^Γ provides a convergent deformation quantization in the sense of Rieffel [R₁].     

Nonlinear ion-acoustic solitary waves in an electron-positron-ion plasma with relativistic positron beam

The propagation characteristics of nonlinear ion–acoustic(IA) solitary waves(SWs) are studied in thermal electron–positron–ion plasma considering the effect of relativistic positron beam. Starting from a set of fluid equations and using the reductive perturbation technique, we derive a Korteweg–de Vries(KdV) equation which governs the evolution of weakly nonlinear IA SWs in relativistic beam driven plasmas. The properties of the IA soliton are studied, and it is shown that the presence of relativistic positron beam significantly modifies the characteristics of IA solitons.     

Optimal design of midsurface of shells: Differentiability proof and sensitivity computation

We suppose that a shell submitted to a given load (self-weight or wind, for instance), has to resist as well as possible towards given criteria. We aim at the following problem: Is it possible to find an optimal design of the midsurface of the shell with respect to this criteria? This problem can be worked using gradient-type algorithms. In this paper we work on the differentiability proof and numerical computation of the gradient. For a given shape of the midsurface, we consider that the shell works in linear elastic conditions. We use the Budiansky-Sanders model for elastic shells, from which we get the displacement field in the shell. The criteria to be minimized are supposed to depend on the shape directly, and also through the displacement field. In this paper, we prove that the displacement field depends on the shape in a Fréchet-differentiable manner (for an appropriate topology on the set of admissible shapes). Then we give a way to compute the gradient of a given criteria from a theoretical point of view and from a numerical point of view. This allows us to use descent-type methods of optimization. They will lead to shapes which react better and better. Notice that we know nothing about convergence of these methods, the existence and unicity of a theoretical optimal solution. But from a practical point of view, it is quite interesting to be able to modify a given shape to obtain a better one.     

Optimizing Markovian modeling of chaotic systems with recurrent neural networks

In this paper, we propose a methodology for optimizing the modeling of an one-dimensional chaotic time series with a Markov Chain. The model is extracted from a recurrent neural network trained for the attractor reconstructed from the data set. Each state of the obtained Markov Chain is a region of the reconstructed state space where the dynamics is approximated by a specific piecewise linear map, obtained from the network. The Markov Chain represents the dynamics of the time series in its statistical essence. An application to a time series resulted from Lorenz system is included.     

The acute toxicity of tri-n-butyltin taurocholate

The acute toxicity for tri-n-butyltin taurocholate (TBT-TA), a newly synthesized organotin steroid, was determined using Long Evans rats. The organotin compound was suspended in corn oil and administered by gavage using standard techniques. The TBT-TA exhibited a taurocholic acid toxicity at 24 h and a tributyltin toxicity at three days. The LD₅₀ values were 611 and 384 mg kg^?1 respectively. The dead rats exhibited distended stomachs, enlarged cecums, and lesions in the gastrointestinal tract. The toxicity is similar to that observed with other trialkyltin compounds.