Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

Application of low-pressure gas chromatography-ion-trap mass spectrometry to the analysis of the essential oil of Turnera diffusa (Ward.) Urb.

Turnera diffusa Willd. var. afrodisiaca (Ward) Urb. (syn. T. aphrodisiaca) belongs to the family of Turneraceae and is an aromatic plant growing wild in the subtropical regions of America and Africa. It is widely used in the traditional medicine as e.g. anti-cough, diuretic, and aphrodisiac agent. This work presents a 3 min chromatographic analysis using low-pressure (LP) gas chromatography (GC)-ion-trap (IT) mass spectrometry (MS). The combination of a deactivated 0.6 m x 0.10 mm i.d., restrictor with a wide-bore CP-Wax 52 capillary column (10 m x 0.53 mm i.d., 1 mum) reduces the analysis time by a factor of 3-7 in comparison to the use of a conventional narrow bore column. Chromatographic conditions have been optimized to achieve the fastest separation with the highest signal/noise ratio in MS detection. These results allow fast and reliable quality control of the essential oil to be achieved. (C) 2003 Elsevier B.V. All rights reserved.

Avaliação do óleo de soja submetido ao processo de fritura de alimentos diversos

The main objective of this study was to evaluate the degree of degradation of the soybean oil used in frying processes. The quality of the oil during the frying process was evaluated by means of physical-chemical analyses, such: conjugated dienes (%) and TBA index (mmoles g(-1)), and determination of total polar compounds (%). It was observed that the values of conjugated dienes increasing significantly with time until 1.87% after 15 hours for fry pans I and 1.76% after 22.5 hours for fry pans II. The TBA indexes reached at the end the frying process values of 0.0265 and 0.0210 mmoles g(-1) for fry pans I and II, respectively. The percentages of total polar compounds have shown an increase of six and eight times in relation to the original sample starting from 5.9% and 3.7% and reaching values of 36.8% and 29.2%, for fry pan I and II, after 15 and 22.5 hours of heating, respectively. It has been concluded that the alterations of the soybean oil increased as the time of frying increased, for both fry pans. The oil used in fry pan I showed greater alteration than the that observed in the oil used in fry pan II, in spite of the time of heating being shorter. Taking into consideration that the levels of polar compounds should be less than 25% according to the legislation of several countries, the oils used in both fry pans were already inadequate conditions at the moment of disposal.

Cultivation of Rubrivivax gelatinosus in fish industry effluent for depollution and biomass production

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

Ileal and caecal microbial populations in broilers given specific essential oil blends and probiotics in two consecutive grow-outs

Specific essential oil (EO) blends and probiotics used as feed additives have been shown to promote healthy digestive microbials resulting in improved poultry production. Two consecutive experiments were conducted with broilers fed corn-soybean meal diets to determine comparative effects of feed additives on ileal and caecal microbial populations (MP). Ross 708 broilers were placed in 84 pens with previously used litter and treatments maintained in the same pens for both experiments. Eight treatment groups were fed diets containing: Bacitracin methylene disalicylate (BMD) as positive control (PC); no additives as negative control (NC); three probiotics: BC-30; BioPlus 2B (B2B); and Calsporin; and the essential oil blends Crina Poultry Plus (CPP) at 300 or 150 ppm in the first experiment; and CPP at 300 ppm and Crina Poultry AF at 100 ppm in experiment 2. Starter and grower diets contained the ionophore (Coban). Ileal and caecal samples were collected at 43 days of age from male broilers. The DNA of microbial populations was isolated from digesta samples and analysed by denaturing gradient gel electrophoresis to generate percentage similarity coefficients (%SC) from band pattern dendrograms. Differences were observed in ileal and caecal populations depending on treatment, respectively, and especially between experiments. Broilers fed diets with probiotics had very similar MP. The EO CPP at 300 ppm resulted in ilea! MP similar to those observed in chickens fed probiotics. We concluded that antibiotic treatment affected ileal, but no caecal MP. More pronounced changes in ileal and caecal MP were seen in broilers at 43 days of age following probiotic and essential oil treatments.

Control of lipase production by Rhizopus oligosporus under various growth conditions

Some factors influencing the growth and production of extracellular lipase by Rhizopus oligosporus were studied. Highest yields of enzyme were obtained when Tweens were the carbon source. Soybean meal extract supported good growth and enzyme production. Carbohydrates, vegetable oils, proteins or amino acids did not stimulate lipase production. The fungus grew well with carbohydrate- or protein-supplemented media but not with oils, unless emulsified with a non-metabolizable gum. The production of biomass in static cultures was maximum at 35-40°C after 4 d at pH 5.5. The yield of lipase was maximum at 25°C after 3 d at pH 6.5. Shaking cultures enhanced growth but decreased lipase production.

OLEO ESSENCIAL EM ALGUMAS ESPECIES DE EUCALYPTUS

In this work we used leaves of four species of Eucalyptus - E. bicostata Maiden, E. deanei Maiden, E. dunnii Maiden and E. viminalis Labill, grown in Colombo, Parana State, Brazil. Preliminary studies were done, in the following sequence: botanic identification, olfactory research, extraction and purification of the essential oil of each species. The physical and chemical tests done were the following: relative density, refractive index, optical rotation, solubility, coagulation point and cineol percentage. The essential oils analysed through gaseous chromatography, presented the following cineol percentage: E. bicostata Maiden - 26.92%, E. deanei Maiden - 70.21%, E. dunnii Maiden - 53.16% and E. viminalis Labill - 23.05%.

Sensitivity of mycobacteria to different species of eucalyptus l'herit

Sensitivity profile of 10 mycobacteria of clinical interest to eight different species of Eucalyptus L'Herit was studied. A Proportion Method Indirect Test was performed to detect resistant bacilli utilizing 5 and 10 mg/ml of essential oils incorporated to Lowestein-Jensen medium. Mycobaterium tuberculosis and other slow growing mycobacteria were more sensitive to essential oils than faster growing ones. The most effective essential oils, in decreasing order, were Eucalyptus citriodora, Eucalyptus maculata and Eucalyptus tereticornis.

Transient flow of the oil-refrigerant mixture through the radial clearance in rolling piston compressors

Unsteady flow of oil and refrigerant gas through radial clearance in rolling piston compressors has been modeled as a heterogeneous mixture, where the properties are determined from the species conservation transport equation coupled with momentum and energy equations. Time variations of pressure, tangential velocity of the rolling piston and radial clearance due to pump setting have been included in the mixture flow model. Those variables have been obtained by modeling the compression process, rolling piston dynamics and by using geometric characteristics of the pump, respectively. An important conclusion concerning this work is the large variation of refrigerant concentration in the oil-filled radial clearance during the compression cycle. That is particularly true for large values of mass flow rates, and for those cases the flow mixture cannot be considered as having uniform concentration. In presence of low mass flow rates homogeneous flow prevail and the mixture tend to have a uniform concentration. In general, it was observed that for calculating the refrigerant mass flow rate using the difference in refrigerant concentration between compression and suction chambers, a time average value for the gas concentration should be used at the clearance inlet.

The improvement in grinding of inlet engine valves by the adoption of the most effective cuting fluid type

In this paper is presented an experimental research in which the grinding of seating surfaces of inlet engine valves was improved by the adoption of the most effective cutting fluid type, matching the new requirements of cutting fluid application. Four different types of cutting fluids (straight oil and three different types of soluble oils) were analyzed. As qualitative and quantitative evaluation parameters of the performance of the cutting fluids, the roughness, the grinding wheel wear, the cutting force and the workpiece residual stress were determined. As a conclusion, the straight oil was the cutting fluid that presented the best results in all of the parameters analyzed. Copyright © 2000 Society of Automotive Engineers, Inc.

Characterization of lubricating oil using ultrasound

This paper presents an ultrasonic method to measure small concentrations of water in lubricating oil. It uses an ultrasonic measurement cell composed by a piezoceramic emitter (5 and 10 MHz), and a large aperture PVDF receiver that eliminates diffraction effects. The propagation velocity, attenuation coefficient and density of several samples of water-in-oil emulsion were measured. The concentrations of water of the samples were in the range of 0 to 5% in volume, and the results showed that these low concentrations can be discriminated within a resolution of 0.2% in the studied range, using the measurement of the propagation velocity.

Composição fitoquímica dos óleos essenciais de folhas de Lippia alba (Mill.)N.E.Br. em diferentes épocas de colheita e partes do ramo

This work aimed to determine the best harvest time for biomass production, yield and essential oil composition considering the seasonal variation (spring, summer, autumn and winter) on different plant parts (apical, medial and basal). Essential oils were extracted by hydro-distillation with a Clevenger apparatus for both fresh and dry mass obtained in field and lab conditions respectively. The extracted essential oils were analyzed by GS/MS (Shimadzu, QP-5000). The chemical components were identified by comparing their mass spectrum to the patterns filed in the MS computer memory (Wiley,139,Lib.), to the literature references, and by co-injection with authentic standards. Applying phyto-chemical tests on fresh and dry mass, the chemical component percentages of essential oils were calculated and identified as follows: citral (neral and geranial), myrcene, caryophylene and elemene.