Existence results for degenerate <Emphasis Type="Italic">p</Emphasis>(<Emphasis Type="Italic">x</Emphasis>)-Laplace equations with Leray-Lions type operators

We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.     

All harmonic 2-spheres in the unitary group, completely explicitly

We give a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to the unitary group U(n) in any dimension, and so all harmonic maps from the 2-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual ${\bar{\partial}}We give a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to the unitary group U(n) in any dimension, and so all harmonic maps from the 2-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual [`(?)]{\bar{\partial}} -problems or loop group factorizations. We interpret our constructions using Segal’s Grassmannian model, giving an explicit factorization of the algebraic loop group, and showing how to obtain harmonic maps into a Grassmannian.     

A spring-embedding approach for the facility layout problem

The facility layout problem is concerned with finding the most efficient arrangement of a given number of departments with unequal area requirements within a facility. The facility layout problem is a hard problem, and therefore, exact solution methods are only feasible for small or greatly restricted problems. In this paper, we propose a spring-embedding approach that unlike previous approaches results in a model that is convex. Numerical results demonstrating the potential of our model and the efficiency of our solution procedure are presented.     

On the “Hidden” Harmonics Associated to Best Approximants Due to Quasi-periodicity in Splitting Phenomena

The effects of quasi-periodicity on the splitting of invariant manifolds are examined. We have found that some harmonics that could be expected to be dominant in some ranges of the perturbation parameter actually are nondominant. It is proved that, under reasonable conditions, this is due to the arithmetic properties of the frequencies.     

The Assessment of Reservation Prices of an Intermediate R&amp;D Result and Patent Reward Under Oligopolistic Competitive Behaviour

One of the shortcomings of R&D evaluation is a lack of emphasis on analytical assessment of the value of an on-going R&D project. This paper addresses the problem concerning the distributive aspect of access to superior knowledge. Decision tree analysis and probability models appear to be appropriate tools for assessing the values of an intermediate result and patent reward of a firm's R&D decision in an environment of perfect information and oligopolistic competition. The assessed values are used as minimum prices acceptable to the firm when the knowledge is disseminated to the public. This paper will attempt to resolve this problem through the determination of the appropriate values of the reservation price of the first-stage invention in terms of the final reward and of a patent reward for which the inventor is willing to apply.     

Courtship and agonistic sounds by the cichlid fish Pseudotropheus zebra

Courtship and agonistic interactions in an African cichlid species present a richer diversity of acoustic stimuli than previously reported. Male cichlids, including those from the genus Pseudotropheus (P.), produce low frequency short pulsed sounds during courtship. Sounds emitted by P. zebra males in the early stages of courtship (during quiver) were found to be significantly longer and with a higher number of pulses than sounds produced in later stages. During agonistic intrasexual quiver displays, males produced significantly longer sounds with more pulses than females. Also, male sounds had a shorter duration and pulse period in courtship than in male-male interactions. Taken together, these results show that the acoustic repertoire of this species is larger than what was previously known and emphasize the importance of further research exploiting the role of acoustic stimuli in intra- and interspecific communication in African cichlids.     

A novel cacalolide from Psacalium decompositum

A new cacalolide sesquiterpenoid, named as Romo-A, was isolated from the roots of Psacalium decompositum, Asteraceae, a Mexican medicinal shrub with antidiabetic properties. Its structure was elucidated by NMR, MS, IR, UV, and confirmed by X-ray diffraction studies.     

Square-wave voltammetric techniques for determination of psychoactive 1,4-benzodiazepine drugs

Direct square-wave voltammetry (SWV) and square-wave cathodic stripping voltammetry (SWCSV) at hanging mercury drop electrodes have been developed for determination of the psychoactive 1,4-benzodiazepine compounds clonazepam, bromazepam, midazolam, diazepam, medazepam, and flurazepam over a wide range of concentrations. Analysis was performed with better precision, lower detection limits, and much more rapidly than by previously reported voltammetric techniques.The applicability of both procedures is discussed. The methods were applied to the analysis of commercially available tablets with minimum sample manipulation. The accuracy of the results was accessed by comparison with those obtained by use of the methods described in official pharmacopoeias. A critical comparison with those procedures is also presented.