RADIATIVE AND NON-RADIATIVE LOSSES IN THE RETINOL POLYENES

Abstract— The radiative fluorescence lifetimes of the all-trans, 9 cis and 13 cis retinol, have been measured at various temperatures, and in various solvents. The comparison of these results and of the data calculated from the absorption spectra using the Strickler and Berg equation shows that the transition probabilities are at least one hundred times lower for the radiative emission than for the absorption. Such a discrepancy, which is a general property of the polyenic structure, is closely related to the magnitude of the shift between absorption and fluorescence spectra. We interpret the observed elongation of the radiative fluorescence lifetimes and the temperature dependence of the radiative transitions in the case of all trans retinol as being due to the fact that only the lowest vibrorotational sublevels of ¹S₁, have a reasonable radiative transition probability: the temperature dependence of the radiationless transitions is considered to be due to the existence of a non radiative decay pathway at 550cal/mole above the '0' level.     

Algebraic Manipulation of Polynomial Matrices: A Survey

A concise review is given of some recent methods for performingalgebraic operations on polynominal matrices. The problems addressedare division, inversion, and extraction of greatest common divisorof a pair of matrices. Based on a presentation at the International Symposium on theMathematical theory of Networks and Systems, Amsterdam, June1989.     

Inversion of Toeplitz Matrices which are not Strongly Non-singular

A type of patterned matrix called r-Toeplitz is introduced.This is more general than a block Toeplitz matrix, which resultswhen the order n of the matrix is a multiple of r.A well-knownalgorithm for inverting Toeplitz matrices is extended to dealwith r-Toeplitz matrices, involving O(rn²) operations.This enablesan algorithm to be produced for inverting Toeplitz matriceswhich are not strongly non-singular, when the standard techniquesbreak down.     

PHOTOELECTRIC EFFECTS IN A BIMOLECULAR LIPID MEMBRANE IN THE PRESENCE OF LIGHT SENSITIVE INORGANIC IONS

Abstract— A new membrane photoeffect of high quantum efficiency is reported. The presence of a number of inorganic ions in the bathing solution of a bimolecular lipid film of oxidized cholesterol causes a change in the measured e.m.f. from -100 to -40 mV (photo e.m.f. effect) and increase in the conductivity by a factor of 100–200 (photoconductive effect) when the ions are excited by light. A model system, based upon the classical Becquerel Effect phenomenon of electronic charge injection into the membrane from electronically excited ions, is suggested and experiments verifying this model are reported. An extension of this model is used to suggest a new mechanism of the visual receptor process in biological photoreceptor structures.     

State-Space Minimal Realizations and Latent Structures of Column-Reduced and Nonsingular Polynomial Matrices

The concept of a column-reduced polynomial matrix is an importantone in the theory of linear systems. The theory of Jordan chainsand minimal realizations is developed for such matrices. Also,the relationships between generalized latent vectors of thenonsingular polynomial matrix and their associated generalizedeigenvectors of the system map are explored in this paper. Thispermits the spectral analysis of an arbitrary nonsingular polynomialmatrix, extending previous work for the monic case.     

Some Applications of the Lyapunov Matrix Equation

The matrix equation A'P+PA = –Q originates in the stabilityanalysis of the system of linear differential equations x =Ax by Lyapunov's direct method. Many other aspects of the stabilityof such systems and of related problems in matrix theory canalso be examined by this matrix equation. Some of these arediscussed in this paper and new applications to the stabilityof second order damped dynamic systems and to stable quasi-Jacobimatrices are given.     

The Cayley-Hamilton Theorem in Two-and N-Dimensional Systems

A rigorous proof of the N-dimensional Cayley-Hamilton theoremis given, together with a slightly shortened proof of the two-dimensionaltheorem.     

Further Results on the Qualitative Theory of Generalized Polynomials

This paper continues on from work presented in a previous one,concerning polynomials expressed in terms of an orthogonal polynomialbasis. Firstly, a Routh-type tabular array for determining thegreatest common divisor of two polynomials is expressed in analternative form which does not involve divisions. A positivityproperty of the elements is then shown to extend to the generalizedcase, and the relationship between the standard and generalizedarrays is given. This is followed by an expression for the generalizedHurwitz determinants introduced in the previous paper in termsof the generalized array. Finally, a different type of tabulararray for determining-the g.c.d. is described.