A q-di erence analog of the sixth Painlev e equation is presented. It arises as the condition for preserving the connection matrix of linear q-di erence equations, in close analogy with the monodromy preserving deformation of linear di erential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed. Mathematical Subject Classi cations (19...

We make a detailed study of particular third order linear ordinary di erential equations with a large parameter of Laplace type through integral representations of their solutions, hoping that it will give us a better understanding of the redundant new turning points. In the particular examples we discuss, the redundancy is tied up with a simple function-theoretic property of a real one-dimensi...

In this paper we present some results about analytic machines regarding the power of computations over Q or R solutions of di erential equations and the stability problem of dynamical systems We rst explain the machine model which is a kind of Blum Shub Smale machine enhanced by in nite convergent computations Next we com pare the computational power of such machines over the elds Q and R showi...

The optimization of processes is an omnipresent task in industry and science. In many cases those processes are characterized by partial di erential equations (PDEs), which describe how the state of a considered system can be regulated by a control. The aim is to nd a control which induces a desired state or a close approximation of it. A task of this type is called an optimal control problem. ...

We investigate the derivation and the mathematical properties of a Saint-Venant model with an energy equation and with temperature-dependent transport coe±cients. These equations model shallow water °ows as well as thin viscous sheets over °uid substrates like oil slicks, atlantic waters in the Strait of Gilbraltar or °oat glasses. We exhibit an entropy function for the system of partial di®ere...

Three schemes for linearizing the transconductance of the basic di erential pair in subthreshold CMOS are examined: 1) multiple asymmetric di erential pairs, 2) source degeneration via symmetric di usors, and 3) source degeneration via a single di usor. Using a maximally at optimizing criterion, the linear range of the basic di erential pair can be increased by four-to-eight times.

We study a Hamilton± Jacobi partial di€ erential equation, arising in an optimal control problem for an a ne non-linear singularly perturbed system. This equation is solvable i€ there exists a special invariant manifold of the corresponding Hamiltonian system. We obtain exact slow± fast decomposition of the Hamiltonian system and of the special invariant manifold into slow and fast components....

From a theoretical viewpoint, the vocal folds vibration affects the vocal tract transfer characteristics through nonlinear time-varying interaction between the glottis and vocal tract. Therefore, it is crucial to investigate and model such e ects in order to improve voice quality in parametric rule-based speech synthesis systems. In this paper, we rst conducted analytic experiments on the vocal...

We introduce and study the Koszul complex for a Hecke R-matrix. Its cohomologies, called the Berezinian, are used to de ne quantum superdeterminant for a Hecke R-matrix. Their behaviour with respect to Hecke sum of R-matrices is studied. Given a Hecke R-matrix in n-dimensional vector space, we construct a Hecke R-matrix in 2n-dimensional vector space commuting with a di erential. The notion of ...