Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

The prediction of coal properties using compressed infrared data from osculating polynomials

Reduction of the representation of infrared spectra from coal samples by osculating polynomials of degree nine is discussed. The reduced representation contains polynomial coefficients of order zero to four. Mathematical models of the original spectra are obtained by linear combination of the coefficients. These compressed models are statistically correlated to coal properties, namely, volatile matter, fixed carbon, ash content, heating value, hydrogen, carbon, sulphur, nitrogen, and maximum vitrinite reflectance, and the results are compared with those previously obtained from second derivatives of the same spectra. The use of compressed data, while giving slightly better correlations for some of the properties, has the advantage of requiring less computational time.     

An improved process of separation of R- and S-timolol

Diastereomeric timolol tartrates 4 are obtained in a one-pot synthesis from the racemic base 2 and optically active O,O-diacetyl- or O,O-dibenzoyltartaric anhydrides 3 , as only one of the diastereomers precipitates from acetone solution. Acidic hydrolysis as the corresponding 4 leads to timolol in high yield and optical purity.     

Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.     

New fir laser lines and frequency measurements from optically pumped13CD3OH3

We report the discovery of 57 new fir laser lines from¹³CD₃OH molecule optically pumped by a waveguide CO₂ laser of 300 MHz tunability. For all lines, precise frequency offset measurements between the CO₂ line center and the center of the absorbing¹³CD₃OH line were performed using the transferred Lamb-Dip technique. We have also measured directly the frequency of seven FIR laser lines by heterodyning with already known laser lines. We present a complete list of all known laser lines (134) and frequency measurements (24) for this molecule.Work supported by CNPq, FAPESP, FAEP-Brasil, and CNR-Italia     

An Approach to Fuzzy Noncooperative Nash Games

Systems that involve more than one decision maker are often optimized using the theory of games. In the traditional game theory, it is assumed that each player has a well-defined quantitative utility function over a set of the player decision space. Each player attempts to maximize/minimize his/her own expected utility and each is assumed to know the extensive game in full. At present, it cannot be claimed that the first assumption has been shown to be true in a wide variety of situations involving complex problems in economics, engineering, social and political sciences due to the difficulty inherent in defining an adequate utility function for each player in these types of problems. On the other hand, in many of such complex problems, each player has a heuristic knowledge of the desires of the other players and a heuristic knowledge of the control choices that they will make in order to meet their ends.In this paper, we utilize fuzzy set theory in order to incorporate the players' heuristic knowledge of decision making into the framework of conventional game theory or ordinal game theory. We define a new approach to N-person static fuzzy noncooperative games and develop a solution concept such as Nash for these types of games. We show that this general formulation of fuzzy noncooperative games can be applied to solve multidecision-making problems where no objective function is specified. The computational procedure is illustrated via application to a multiagent optimization problem dealing with the design and operation of future military operations.     

Limit Regimes of Braking of Disc-Type Composite Flywheels Made by Filament Winding

A set of invariants describing the limit regimes of braking disk-type wound composite flywheels is suggested. The limit regime is determined by using a linear failure criterion. It is shown that, for generating short-time impulses of very high power, a set of small identical flywheels is more effective than one large flywheel with an equivalent mass. Particular examples illustrating the theory considered are discussed.     

Phenomenological and neural-network modeling of cephalosporin C production bioprocess

Cephalosporin C production process withCephalosporium acremonium ATCC 48272 in synthetic medium was investigated and the experimental results allowed the development of a mathematical model describing the process behavior. The model was able to explain fairly well the diauxic phenomenon, higher growth rate during the glucose-consumption phase, and the production occurring only in the sucrose-consumption phase. Moreover, the process was simulated utilizing the neural-networks technique. Two feed-forward neural-networks with one hidden layer were employed. Both models, phenomenological and neural-networks based, satisfactorily describe the bioprocess. The difficulties in determining kinetic parameters are avoided when neural networks are utilized.     

Characterization and complementation of a Pichia stipitis mutant unable to grow on d-xylose or l-arabinose

Pichia stipitis CBS 6054 will grow on d-xylose, d-arabinose, and l-arabinose. d-Xylose and l-arabinose are abundant in seed hulls of maize, and their utilization is important in processing grain residues. To elucidate the degradation pathway for l-arabinose, we obtained a mutant, FPL-MY30, that was unable to grow on d-xylose and l-arabinose but that could grow on d-arabinitol. Activity assays of oxidoreductase and pentulokinase enzymes involved in d-xylose, d-arabinose, and l-arabinose pathways indicated that FPL-MY30 is deficient in d-xylitol dehydrogenase (D-XDH), d- and l-arabinitol dehydrogenases, and d-ribitol dehydrogenase. Transforming FPL-MY30 with a gene for xylitol dehydrogenase (PsXYL2), which was cloned from CBS 6054 (Gen Bank AF127801), restored the D-XDH activity and the capacity for FPL-MY30 to grow on l-arabinose. This suggested that FPL-MY30 is critically deficient in XYL2 and that the d-xylose and l-arabinose metabolic pathways have xylitolas a common intermediate. The capacity for FPL-MY30 to grow on d-arabinitol could proceed through d-ribulose.     

Measurement of acid-catalyzed isomerization of unsaturated aldehyde-2,4-dinitrophenylhydrazone derivatives by high-performance liquid chromatography analysis

Aldehyde-2,4-dinitrophenylhydrazones exist as (E)- and (Z)-geometrical isomers, and adventitious isomerization during sample preparation can cause analytical errors. Purified alkenal-2,4-dinitrophenylhydrazone derivatives comprise only the (E)-isomer. However, partial isomerization to the (Z)-isomer occurs upon addition of acid to attain an equilibrium isomer ratio. The UV-visible spectral properties of the isomers differ; the (Z)-isomer exhibiting a 6-10 nm lower absorption maximum compared to the (E)-isomer. Alkenal-2,4-dinitrophenylhydrazones having a CC double bond at the 2- or 3-position of the alkenal exhibited similar absorption maxima with an equilibrium isomer ratio (0.035) that was much lower than those of other alkenals. The CC double bond at the 3-position migrates to a position of conjugation with the CN double bond during hydrazone synthesis to form a stabilized molecular structure. Alkenal-2,4-dinitrophenylhydrazones having a double bond at the 4-position or greater exhibited a similar absorption maxima equilibrium isomer ratio (0.14) to alkanal-2,4-dinitrophenylhydrazones. The quantitative analysis of carbonyl compounds in air or water using DNPH is usually conducted in the presence of an acid catalyst. Consequently, the solution of the direct extract prepared for HPLC or GC analysis contains both (E)- and (Z)-isomers.