Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

Quick preparative separation of natural naphthopyranones with antioxidant activity by high-speed counter-current chromatography

The natural naphthopyranones paepalantine (1), paepalantine-9O-β-D-glucopyranoside (2) and paepalantine-9-O-β-D-allopyranosyl-(1→6)-O-β-D-glucopyranoside (3) were separated in a preparative scale from the ethanolic extract of the capitula of Paepalanthus bromelioides by high-speed counter-current chromatography (HSCCC). The solvent system used was composed of water-ethanol-ethyl acetate-hexane (10:4:10:4, v/v/v/v). This technique led to the separation of the three different naphthopyranone glycosides in pure form in approximately 7 hours. Paepalantine showed a good antioxidant activity when assayed by the DPPH radical spectrophotometric assay.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

Investigation into the impact of embedded generators on distribution system performance using theorem of superposition

Since the 1980s, huge efforts have been made to utilise renewable energy sources to generate electric power. One of the interesting issues about embedded generators is the question of optimal placement and sizing of the embedded generators. This paper reports an investigation of impact of the integration of embedded generators on the overall performances of the distribution networks in the steady state, using theorem of superposition. Set of distribution system indices is proposed to observe performances of the distribution networks with embedded generators. Results obtained from the case study using IEEE test network are presented and discussed.

Fast preparative separation of flavones from capitula of Eriocaulon ligulatum (Vell.) L.B.Smith (Eriocaulaceae) by High-speed countercurrent chromatography (HSCCC)

High-speed countercurrent chromatography (HSCCC) is a leading method for the fast separation of natural products from plants. It was used for the preparative isolation of two flavone monoglucosides present in the capitula of Eriocaulon ligulatum (Veil.) L.B.Smith (Eriocaulaceae). This species, known locally as botão-dourado, is exported to Europe, Japan and North America as an ornamental species, constituting an important source of income for the local population of Minas Gerais State, Brazil. The solvent system, optimized in tests prior to the HSCCC run, consisted of the two phases of the mixture ethyl acetate: n-propanol: water (140:8:80, v/v/v), which led to the successful separation of 6-methoxyluteolin-7-O-β-D-allopyranoside and 6-methoxyapigenin-7-O-β-D-allopyranoside in only 3 hours. The two flavonoids were identified by NMR (1-D and 2-D) and ESI-MS, comparing their spectra with published data.

Separation of the toxic zierin from Zollernia ilicifolia by high speed countercurrent chromatography

Preliminary pharmacological assays of the 70% methanol extract from the leaves of the Brazilian medicinal plant Zollernia ilicifolia Vog. (Fabaceae) showed analgesic and antiulcerogenic effects. Previous analyses have shown that this extract contains, besides flavonoid glycosides and saponins, a toxic cyanogenic glycoside. Flavonoids and saponins are compounds reported in literature with antiulcerogenic activity. In this work, we developed a methodology to separate the cyanogenic glycoside from these compounds in order to obtain enough amount of material to perform pharmacological assays. The cyanogenic glycoside zierin (2S)-β-D-glucopyranosyloxy-(3-hydroxy-phenyl)- acetonitrile was separated from the other components by high speed countercurrent chromatography (HSCCC). The solvent system used was composed of chloroform-methanol-n-propanol-water (5:6:1:4, v/v/v/v). This technique led to the separation of zierin from the possible active compounds of Zollernia ilicifolia.

Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

Peixoto's Theorem for vector fields on S2 with impasse points

The structural stability of vector fields with impasse regular curves on S2 is studied and a version of Peixoto's Theorem is established. Moreover a global analysis of normal forms of the constrained systems. A(x).ẋ=F(x),x∈R3,A∈M(3),F:R3→R3 in the Poincaré ball (i.e. in the compactification of R3 with the sphere S2 of the infinity) is made. © 2013 Elsevier Masson SAS.

Separation of satured and unsaturated fatty acids from palm fatty acids distillates in continuous multistage countercurrent columns with supercritical carbon dioxide as solvent: a process design methodology

In this work the separation of multicomponent mixtures in counter-current columns with supercritical carbon dioxide has been investigated using a process design methodology. First the separation task must be defined, then phase equilibria experiments are carried out, and the data obtained are correlated with thermodynamic models or empirical functions. Mutual solubilities, Ki-values, and separation factors aij are determined. Based on this data possible operating conditions for further extraction experiments can be determined. Separation analysis using graphical methods are performed to optimize the process parameters. Hydrodynamic experiments are carried out to determine the flow capacity diagram. Extraction experiments in laboratory scale are planned and carried out in order to determine HETP values, to validate the simulation results, and to provide new materials for additional phase equilibria experiments, needed to determine the dependence of separation factors on concetration. Numerical simulation of the separation process and auxiliary systems is carried out to optimize the number of stages, solvent-to-feed ratio, product purity, yield, and energy consumption. Scale-up and cost analysis close the process design. The separation of palmitic acid and (oleic+linoleic) acids from PFAD-Palm Fatty Acids Distillates was used as a case study.

Separation of Scaptotrigona postica Workers into Defined Task Groups by the Chemical Profile on Their Epicuticle Wax Layer

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A trade off between separation, detection and sustainability in liquid chromatographic fingerprinting

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Green chromatographic fingerprinting: An environmentally friendly approach for the development of separation methods for fingerprinting complex matrices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interaction of Maternal Separation on the UCh Rat Cerebellum

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)