Differential equations uniquely determined by algebras of point symmetries

We continue to investigate strongly and weakly Lie remarkable equations, which we defined in a recent paper. We consider some relevant algebras of vector fields on ℝ^k (such as the isometric, affine, projective, or conformal algebras) and characterize strongly Lie remarkable equations admitted by the considered Lie algebras. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 486–494, June, 2007.     

Maximizing the xylitol production from sugar cane bagasse hydrolysate by controlling the aeration rate

Batch fermentations of sugar cane bagasse hemicellulosic hydrolysate treated for removing the inhibitors of the fermentation were performed byCandida guilliermondii FTI20037 for xylitol production. The fermentative parameters agitation and aeration rate were studied aiming the maximization of xylitol production from this agroindustrial residue. The maximal xylitol volumetric productivity (0.87 g/L h) and yield (0.67 g/g) were attained at 400/min and 0.45 v.v.m. (K_La 27/h). According to the results, a suitable control of the oxygen input permitting the xylitol formation from sugar cane bagasse hydrolysate is required for the development of an efficient fermentation process for large-scale applications.     

Lattice Uniformities on Effect Algebras

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations − and + of L are uniquely determined by their system of neighborhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0,+∞]-valued functions on L.     

Fell topology on the hyperspace of a non-Hausdorff space

Fell topology is very widely used today, even in metric spaces; but J. Fell introduced it in a non-Hausdorff context in the connection with the theory of C ^*-algebras. In spite of this, it has been studied only on the hyperspace of a Hausdorff space, except for the first results due to Fell himself. The present paper aims to fill this gap, in particular extending some results of H. Poppe and of G. Beer to the general case. Project 10251002 supported by National Natural Science Foundation of China.     

Null Lagrangians for nematic elastomers

In this paper, we calculate all possible null Lagrangians (null energies) for the mechanics of a distinguished class of continua, the nematic elastomers. The calculation is done in order to help to relate different physically equivalent theories of nematic elastomers. We discuss both local and global (hence topological) aspects of the problem. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.     

Hexokinase production fromS. cerevisiae

Applied Biochemistry and Biotechnology - The effects of pH (4.0, 4.5, or 5.0), temperature (T) (30, 35, or 40°C) and dissolved oxygen (DO) (0.2, 2.0, 4.0, or 6.0 mg O2/L) on hexokinase and...     

Measures and submeasures on $$\hbox {d}_{0}$$-algebras

The structure of \(\hbox {d}_{0}\)-algebra is a generalization of a D-lattice. We extend to this structure the definitions of measure and submeasure, and investigate their properties. We also investigate the relationships between uniformities and measures (or submeasures).     

Gauge invariance,charge conservation,and variational principles

We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations.     

Zymomonas mobilis as catalyst for the biotechnological production of sorbitol and gluconic acid

The conversion of glucose and fructose into gluconic acid (GA) and sorbitol (SOR) was conducted in a batch reactor with free (CTAB-treated or not) or immobilized cells of Zymomonas mobilis. High yields (more than 90%) of gluconic acid and sorbitol were attained at initial substrate concentration of 600 g/L (glucose plus fructose at 1:1 ratio), using cells with glucose-fructose-oxidoreductase activity of 75 U/L. The concentration of the products varied hyperbolically with time according to the equations (GA)=t(GA)(max)/(W(GA) +t), (SOR)=t (SOR)(max)/(W(Sor)+t), v(GA)=[W(GA) (GA)(max)]/(W(GA)+t)(2) and V(SOR)=[W(SOR) (SOR)(max)]/(W(SOR)+t)(2). Taking the test carried out with free CTAB-treated cells as an example, the constant parameters were (GA)(max)= 541 g/L, (SOR)(max)=552 g/L, W(GA)=4.8h, W(SOR)=4.9h, upsilon(GA)=112.7 g/L. and upsilon(SOR)=112.7 g/L.     

Extreme value laws in dynamical systems under physical observables

Extreme value theory for chaotic deterministic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block maximum method is often used in applications for statistical prediction of large value occurrences. In this method, one performs statistical inference for the parameters of the Generalised Extreme Value (GEV) distribution, using maxima over blocks of regularly sampled observable values along an orbit of the system. The observables studied so far in the theory are expressed as functions of the distance with respect to a point, which is assumed to be a density point of the system’s invariant measure. However, at least with respect to the ambient (usually Euclidean) metric, this is not the structure of the observables typically encountered in physical applications, such as windspeed or vorticity in atmospheric models. In this paper we consider extreme value limit laws for observables which are not expressed as functions of the distance (in the ambient metric) from a density point of the dynamical system. In such cases, the limit laws are no longer determined by the functional form of the observable and the dimension of the invariant measure: they also depend on the specific geometry of the underlying attractor and of the observable’s level sets. We present a collection of analytical and numerical results, starting with a toral hyperbolic automorphism as a simple template to illustrate the main ideas. We then formulate our main results for a uniformly hyperbolic system, the solenoid map. We also discuss non-uniformly hyperbolic examples of maps (Hénon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models). Our purpose is to outline the main ideas and to highlight several serious problems found in the numerical estimation of the limit laws.