Abstract:
The use of heterogeneous catalysts in the transesterification reaction of vegetable oils has getting emphasis in recent years, mainly by the alternative of obtaining clean fuel derived from renewable sources. Metal oxide such as MgO or CaO, supported ones like and zeolites are often applied in transesterification process. Among them, hydrotalcite has shown potential as catalysts on this reaction due to their physicochemical properties, such as: thermal stability, porosity, specific surface area, memory effect, basicity, acidity and anion exchange capacity. This work studies the catalytic performance of the calcium and aluminum based hydrotalcite in the transesterification reaction of soybean oil in methanol and ethanol. The hydrotalcite samples treated at 450?C were impregnated with KOH. The efficiency of impregnated and non- impregnated samples was compared and the non-impregnated one showed the best performance. This property was attributed to the higher availability of active sites used in the transesterification process.

Abstract:
the kinetic model for change of phases developed by m. avrami at the end of the thirties has been used to describe the temporal behavior of phase changes. until today this model is studied and adapted to include broader hypotheses. however, the mathematical format presented by m. avrami is difficult to be understood by beginners. the purpose of this work is to clarify the mathematical treatment of avrami's work, going straightforward to the arguments that led to his main results.

Abstract:
The kinetic model for change of phases developed by M. Avrami at the end of the thirties has been used to describe the temporal behavior of phase changes. Until today this model is studied and adapted to include broader hypotheses. However, the mathematical format presented by M. Avrami is difficult to be understood by beginners. The purpose of this work is to clarify the mathematical treatment of Avrami's work, going straightforward to the arguments that led to his main results.

Abstract:
This article considers two weight estimates for the single layer potential --- corresponding to the Laplace operator in $\mathbf{R}^{N+1}$ --- on Lipschitz surfaces with small Lipschitz constant. We present conditions on the weights to obtain solvability and uniqueness results in weighted Lebesgue spaces and weighted homogeneous Sobolev spaces, where the weights are assumed to be radial and doubling. In the case when the weights are additionally assumed to be differentiable almost everywhere, simplified conditions in terms of the logarithmic derivative are presented, and as an application, we prove that the operator corresponding to the single layer potential in question is an isomorphism between certain weighted spaces of the type mentioned above. Furthermore, we consider several explicit weight functions. In particular, we present results for power exponential weights which generalize known results for the case when the single layer potential is reduced to a Riesz potential, which is the case when the Lipschitz surface is given by a hyperplane.

Abstract:
This article investigates how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain in the case when the domains involved are of class $C^1$. We consider the Laplacian and use results developed previously for the corresponding Lipschitz case. In contrast with the Lipschitz case however, in the $C^1$-case we derive an asymptotic formula for the eigenvalues when the domains are of class $C^1$. Moreover, as an application we consider the case of a $C^1$-perturbation when the reference domain is of class $C^{1,\alpha}$.

Abstract:
Cepheids have been observed in NGC 5236 (M 83) using the ANTU (UT1) 8.2 meter telescope of the ESO VLT with FORS1. Observations over 34 epochs in V and I have been made between January 2000 and July 2001. Twelve Cepheid candidates have periods between 12 and 55 days. The true distance modulus is adopted to be (m-M)_0 = 28.25 +/- 0.15, which corresponds to a distance of 4.5 +/- 0.3 Mpc. The distance of NGC 5253 has been rediscussed. The mean distance of (m-M)_0 = 28.01 +/- 0.15 (based on SN 1972E) shows the galaxy to be a close neighbor of M 83 (separation = 0.5 +/- 0.4 Mpc), suggesting that the two galaxies may have interacted in the past and thus possibly explaining the amorphous morphology of NGC 5253. M 83 is the principal member of the nearby M 83 group containing also, besides NGC 5253, several dwarf members, for five of which TRGB distances are available (Karachentsev et al. 2002a, A&A, 385, 21). The adopted group distance of (m-M)_0 = 28.28 +/- 0.10 (4.5 +/- 0.2 Mpc) together with its mean recession velocity of v_LG = 249 +/- 42 km/s shows again the extreme quietness of the local (1 Mpc to 10 Mpc) expansion field. M 83 fits onto the local mean Hubble flow line of the velocity-distance relation (with H_0 ~ 60) with no significant deviation, supporting the earlier conclusion that the local velocity expansion field is remarkably cold on a scale of 10 Mpc, contrary to the predictions of the simplest cold dark matter model for large scale structure. The role of a cosmological constant has been invoked as a possible solution in providing a nearly uniform force field everywhere in the presence of a lumpy galaxy distribution. (abridged)

Abstract:
The local expansion field is mapped using Cepheids, a complete sample of TF distances, and nearby cluster distances. The large-scale field is mapped using Cepheid-calibrated blue SNeIa. These data give Ho(local)=59.2+/-1.4 [km/s Mpc^-1] and Ho(cosmic)=57.4+/-2.3. The intermediate expansion field (1200 < v < 10000km/s) is less well calibrated but fully consistent with Ho~60. Ho is therefore (nearly) scale-invariant (high-density regions excluded). -- The P-L relation of Cepheids is based on an improved zero point of (m-M)_{LMC}=18.56. The slope of the P-L relation for P>10days, as judged from OGLE data (Udalski et al. 1999) is flatter than anticipated, which tends to increase the above values of Ho by 3.4 units. No significant metallicity effect on the Cepheid distances seems to be indicated. For all practical purposes Ho=60 is recommended with a systematic error of probably less than 10%. -- The corresponding expansion age is T=15.7+/-1.5Gy (with Omega(Matter)=0.3, Omega(Lambda)=0.7), which compares well with the formation time of 15+/-2Gy for the apparently oldest globular cluster M107.

Abstract:
We made an asymmetric phantom and investigated it with two different intravascular ultrasound (IVUS) systems and one optical coherence tomography (OCT) system. The asymmetry of the phantom allowed determination of the spatial orientation of the cross-sectional images. On all tested systems, an observer should imagine herself/himself standing proximal to the cross-section when looking at the intravascular images.The tested intracoronary imaging modalities displayed cross-sectional images with a spatial orientation corresponding to a proximal point of view. Knowledge of the spatial orientation is mandatory when comparing and validating different imaging modalities aimed at plaque characterization.Many intravascular ultrasound (IVUS) and optical coherence tomography (OCT) cross-sectional images of coronary arteries are published in biomedical journals. Sometimes these images are presented together with images from microscopic examination of the same arterial positions illustrating how the imaging modality correctly displays tissue characteristics [1,2].When comparing cross-sectional images obtained with different techniques, such as intravascular imaging and microscopy, efforts must be made to assure that the images are from exactly the same arterial position along the longitudinal axis of the coronary artery, and this is often devoted a lot of attention.Also, when comparing cross-sectional images, rotational adjustment is usually required to obtain correct co-localization of identifiable landmark structures such as sidebranches. Rotation of a cross-sectional image does not change area measurements or intraplaque location of a certain component of interest. Therefore rotation does not affect interpretation.However, in addition to longitudinal position and rotation, cross-sectional images also possess a spatial orientation of the cross-sectional plane. This is only rarely commented on but cannot be taken as lightly as rotation [3,4]. Changing spatial orientation, and th

Abstract:
This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of the proximity quantity described above when this is relatively small. We consider two applications: the Laplacian in both $C^{1,\alpha}$ and Lipschitz domains. For the $C^{1,\alpha}$ case, an asymptotic result for the eigenvalues is given together with estimates for the remainder, and we also provide an example which demonstrates the sharpness of our obtained result. For the Lipschitz case, the proximity of eigenvalues is estimated.

Abstract:
Repeated imaging observations have been made of NGC 4527 with the Hubble Space Telescope between April and June 1999, over an interval of 69 days. Images were obtained on 12 epochs in the F555W band and on five epochs in the F814W band. The galaxy hosted the type Ia supernova SN1991T, which showed relatively unusual behavior by having both an abnormal spectrum near light maximum, and a slower declining light curve than the proto-typical Branch normal SNe Ia. A total of 86 variables that are putative Cepheids have been found, with periods ranging from 7.4 days to over 70 days. From photometry with the DoPHOT program, the de-reddened distance modulus is determined to be (m-M)_0 = 30.67 +/- 0.12 (internal uncertainty) using a subset of the Cepheid data whose reddening and error parameters are secure. A parallel analysis of the Cepheids using photometry with ROMAFOT yields (m -M)_0 =30.82 +/- 0.11. The final adopted modulus is (m -M)_0 =30.74 +/- 0.12 +/- 0.12 (d=14.1 +/- 0.8 +/- 0.8 Mpc). The photometric data for SN1991T are used in combination with the Cepheid distance to NGC 4527 to obtain the absolute magnitude for this supernova of M_V^0(max) = -19.85 +/- 0.29. The relatively large uncertainty is a result of the range in estimates of the reddening to the supernova. Thus SN1991T is seen to be only moderately brighter (by ~ 0.3 mag) than the mean for spectroscopically normal supernovae, although magnitude differences of up to 0.6 mag cannot be ruled out.