Second-Order optical non-linearities of {4-(dimethylamino) stilben z & e 4'-yl} dimesityl borane

Samples of {4-(dimethylamino) stilben Z & E 4'-yl} dimesityl borane (BNS) were synthesised and investigated for their non-linear optical properties. The results show that the quadratic hyperpolarisability of the Z-isomer is smaller than that of the E-isomer, the beta value found for the latter being as high as 60 × 10^?30 esu.     

Asymptotic behaviour of the solution of the projection Riccatidifferential equation

The solution of the Riccati differential equation (RDE) is shown to be asymptotically close to the solution of the projection Riccati differential equation (PRDE). The asymptotic behaviour of the latter is analyzed in an explicit formula. The almost-periodic asymptote of the solution of the PRDE is computed by an algorithm based upon the concepts of an aperiodic/almost-periodic generator (APG) decomposition of a linear map and unit row-staircase form of a polynomial matrix. The analysis ultimately provides a convergence criterion. In particular, it is shown that the solution of the PRDE always converges in the aperiodic case     

Physiological exploration of the eustachian tube using labeled compounds. Applications in the control of treatment (author's transl)]

Sequential scintigraphy enables the qualitative and quantitative study of the drainage function of the Eustachian tube. Use is made of serum albumin labeled with technetium 99 m. After reviewing the various methods employed in an exploration of the functions of the Eustachian tube, and in particular the drainage function, the writers explain the method in detail (indicator, detection system, examination procedure, normal scintigraphic aspects) while stressing the control factors (onset of passage, speed and intensity of passage, length of time for the appearance of a trace on the pharynx, eventual aspects of blocking) and giving the basic characteristics; persistant spotting of the drum, transient image of the tube, partial stoppage at the ostium, and traces along the pharynx. The role of swallowing and the position of the head appear to be essential. Results obtained in various disorders of the middle ear, accessory cavities, the tube and the cavum are given in the form of tables. The writers then indicate the principal merits of the method: demonstration of the pathological role of the Eustachian tube in a work-up of transmission deafness, with its impact on treatment, the role of a deficient drainage function in surgical failures, and control of the efficacy of treatment, in particular crenotherapy. A study of the drainage function of the Eustachian tube, as a complement to the function of equalizing pressure, in an essential factor in formulating indications and in establishing the prognosis for tympanoplasties.     

Open-loop unstable convolution feedback systems with dynamical feedbacks

This paper considers distributed multivariable convolution feedback systems characterized byy₁ = G₁ * e₁,y₂ = G₂ * e₂,e₁ = u₁ ? y₂ ande₂ = u₂ + y₁ where the subsystem transfer functionsG?₁ andG?₂ both admit a pseudo-coprime factorization in the subalgebra of absolutely summable distributions of order zero. The most general result, Theorem 1, gives necessary and sufficient conditions for stability of the system. This condition is specialized to the lumped case in Theorem 1L. Finally for distributed systems which have a finite number of open-loop unstable poles Theorem 1D gives an algorithmic test for stability. The graphical interpretation of both Theorem 1 and 1D is given in detail, and illustrated by examples. The transfer functions considered here are used in modeling transportation lags and communication lags, as well as in distributed systems such as steam in long pipe.     

Admissible controls and attainable states for a class of nonlinear systems with general constraints

We consider nonlinear control systems where the control and the state variables are submitted to explicit constraints. This paper has two objectives. First, for a class of nonlinear systems with constraints, an existence result of nontrivial admissible controls and some of their interesting properties are proved. Then, we investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory. An iterative procedure is also given, which allows one to compute the steering admissible control function. This procedure is illustrated with a classical example.     

Robustness of stability conditions for linear time-invariant feedback systems

The robustness of stability conditions for linear time-invariant feedback systems is examined, assuming three different types of representations: state space representation, coprime matrix fraction representation, and transfer function representation. We stress the importance of certain details of the representation used and, even more, the importance of making sure that the allowed perturbations be relevant to the physical situation under study.     

On polynomial matrix spectral factorization by symmetric extraction

We revise the 1963 Davis algorithm [2] for the spectral factorization of a para-Hermitian nonnegative polynomial matrixPhi, by symmetric factor extraction: this algorithm is careless about zeros at infinity. By introducing the notion of diagonal reducedness ofPhi, we obtain an easy sufficient test for the absence of zeros at infinity. We show then how to getPhi, diagonally reduced by diagonal excess reduction steps (similar to the Oono and Yasuura steps), removing all zeros at infinity, and then how to remove synunetrically finite zeros while keeping el, diagonally reduced (hence, free of zeros at infinity). This results in a revised symmetric extraction spectral factorization algorithm with monotone degree control. An example shows the didactical conceptual simplicity of the method. Appropriate symmetric extraction is discovered by revising and discovering important particular one-sided factor extraction properties of polynomial matrices.