A variational principle is presented, by means of which the equation of motion of the damped harmonic oscillator is found. Starting from this variational principle a systematic reformulation of the classical mechanics leads us to a Hamilton–Jacobi equation with an additional term, which is proportional to the action. The quantization of this Hamilton–Jacobi equation, following a method originally due to Schrödinger, gives the Langevin–Schrödinger equation.

No abstract

At the foundation of the problem of light propagation through optical turbulence is the classical Obukhov-Kolmogorov theory. It rests in the requirement that the refractive index fluctuations should be homogeneous and isotropic. These, with other necessary assumptions, lead to the very well-known -11/3-power exponent spectrum on the inertial range; although departures have been found, they are usually associated with partially developed turbulence or its intrinsic intermittency. Recently, in optics, the interest in anisotropic fluctuations of the refractive index has gained attention. These studies are mostly theoretical, and reduce anisotropic effects to a dilatation along a coordinate direction in the three-dimensional wavenumber space. Few experimental works exists, but all of them employ simulated turbulence. In this Letter, we describe an experiment to produce anisotropic turbulence under controlled conditions; moreover, we observe anisotropy by studying the spectral power exponent of a temporal series of laser beam wandering.

The effect of yeast strain, the agave age and the cultivation field location of agave were evaluated using kinetic parameters and volatile compound production in the tequila fermentation process. Fermentations were carried out with Agave juice obtained from two cultivation fields (CF1 and CF2), as well as two ages (4 and 8 years) and two Saccharomyces cerevisiae yeast strains (GU3 and AR5) isolated from tequila fermentation must. Sugar consumption and ethanol production varied as a function of cultivation field and agave age. The production of ethyl acetate, 1-propanol, isobutanol and amyl alcohols were influenced in varying degrees by yeast strain, agave age and cultivation field. Methanol production was only affected by the agave age and 2-phenylethanol was influenced only by yeast strain. This work showed that the use of younger Agave tequilana for tequila fermentation resulted in differences in sugar consumption, ethanol and volatile compounds production at the end of fermentation, which could affect the sensory quality of the final product.

whilst the organism was in the stationary phase but exoglucanase activityy decreased sharply at the onset of the stationary phase'. Addition of the protease inhibitor phenylmethylsulphonyl fluoride (PMSF) towards the end of growth produced complete protection toward protease inactivation, exoglucanase being stabilized even in prolonged stationary phase. The stability of exoglucanase in the presence or absence of mycelium, with and without PMSF addition, showed that endogenous cell-free and cell-associated proteases weree responsible for exoglucanase inactivation i n the stationary phase. Inactivation of exoglucanase depended on the physiological stage of the cultures, the enzyme remaining stable as long as the culture was in an active growth phase. R6sum6Production et stabilisation de cellulases de Trichoderma reesei La production d'exoglucanase et d'endoglucanase dans les cultures de T. reesei QM 9414 en milieu non renouvel6 est associ6e ~t la croissance tant du lactose que du jus d'extraction de la pulpe de betterave. L'endo-glucanase reste stable tant que le microorganisme est darts sa phase stationnaire de croissance tandis que l'activit6 exoglucanasique d6croit rapidement d6s le d6but de cette phase stationnaire. L'ajour du fluorure de phenylmethylsulfonate (PMSF), un inhibiteur prot6olytique, vers la fin de la croissance a exerc6 une protection compl6te contre l'inactivation par la prot6ase: l'exoglucanase 6tait prot6g6e dans ces conditions m6me en phase stationnaire prolong6e. La stabilit6 de l'exoglucanase en pr6sence ou en absence de mycelium, avec ou sans ajout de PMSF d6montre la responsabilit6 des exo-prot6ases endog~nes solubles et de prot6ases associ6es aux cellules dans l'inactivation de l'exoglucanase dans la phase stationnaire. L'inactivation de l'exoglucanase d6pend de l'6tat physiologique des cultures. En effet, l'enzyme reste stable aussi longtemps que la culture est en phase active de croissance. Resumen Producci6n y estabilizaci6n de celulasas de Trichoderma reeseiLa producci6n de exoglucanase y endoglucanasa de T. reesei QM 9414 en cultivo pot lotes en medios con tactosa y coseta agotada de remolacha como fuentes de carbono, fue asociada al crecimiento. La endoglucanasa permaneci6 estable en fase estacionaria, pero la actividad de exoglucanase disminuy6 dr~sticamente al entrar el cultivo en dicha fase. La adici6n del inhibidor de proteasas PMSF hacia el final de la fase de crecimiento provoc6 la total inactivaci6n de las proteasas producidas, logrfindose estabilizar la exoglucanasa at~n en prolongada fase estacionaria. Se analiz6 la estabilidad de exoglucanasa en presencia y ausencia de micelio, con y sin adici6n de PMSF; los resultados muestran que proteasas endogenas extracelulares y asociadas a la c61ula son responsables de la inestabilidad de la exoglucanasa en fase estacionaria. La inactivaci6n de la exoglucanasa depende del estado fisiol6gico del cultivo, ya que la enzima permanece estable mientras el cultivo se encuentra en crecimiento.