The Convergence Analysis of the Decomposition Method for the (1+1)-Parabolic Problem in Nonuniform Media

A modified Adomian decomposition method is used to find approximate solutions for the reaction diffusion convection equation in nonuniform medium, i.e., with space-dependent coefficients. In this approach, the solutions are found in the form of a convergent power series with easily computed components. Convergence analysis of modified Adomian series solution for a class of these type of PDEs is discussed.     

Fucoxanthin Holds Potential to Become a Drug Adjuvant in Breast Cancer Treatment: Evidence from 2D and 3D Cell Cultures

Fucoxanthin (Fx) is a carotenoid derived from marine organisms that exhibits anticancer activities. However, its role as a potential drug adjuvant in breast cancer (BC) treatment is still poorly explored. Firstly, this study investigated the cytotoxic effects of Fx alone and combined with doxorubicin (Dox) and cisplatin (Cis) on a panel of 2D-cultured BC cell lines (MCF7, SKBR3 and MDA-MB-231) and one non-tumoral cell line (MCF12A). Fucoxanthin induced cytotoxicity against all the cell lines and potentiated Dox cytotoxic effects towards the SKBR3 and MDA-MB-231 cells. The combination triggering the highest cytotoxicity (Fx 10 µM + Dox 1 µM in MDA-MB-231) additionally showed significant induction of cell death and genotoxic effects, relative to control. In sequence, the same combination was tested on 3D cultures using a multi-endpoint approach involving bioactivity assays and microscopy techniques. Similar to 2D cultures, the combination of Fx and Dox showed higher cytotoxic effects on 3D cultures compared to the isolated compounds. Furthermore, this combination increased the number of apoptotic cells, decreased cell proliferation, and caused structural and ultrastructural damages on the 3D models. Overall, our findings suggest Fx has potential to become an adjuvant for Dox chemotherapy regimens in BC treatment.     

On the general cubic decomposition of polynomial sequences

We present the main results about the general cubic decomposition (CD) of polynomial sequences. We deal particularly with the diagonal CD and the CD of orthogonal sequences. This allows us to generalize a result of Barrucand and Dickinson about the CD of a symmetric orthogonal sequence.     

Selection of intensity modulated radiation therapy treatment beam directions using radial basis functions within a pattern search methods framework

The selection of appropriate radiation incidence directions in radiation therapy treatment planning is important for the quality of the treatment plan, both for appropriate tumor coverage and for better organ sparing. The objective of this paper is to discuss the benefits of using radial basis functions within a pattern search methods framework in the optimization of the highly non-convex beam angle optimization (BAO) problem. Pattern search methods are derivative-free optimization methods that require few function value evaluations to converge and have the ability to avoid local entrapment. These two characteristics gathered together make pattern search methods suited to address the BAO problem. The pattern search methods framework is composed by a search step and a poll step at each iteration. The poll step performs a local search in a mesh neighborhood and assures convergence to a local minimizer or stationary point. The search step provides the flexibility for a global search since it allows searches away from the neighborhood of the current iterate. Radial basis functions are used and tested in this step both to influence the quality of the local minimizer found by the method and to obtain a better coverage of the search space in amplitude. A set of retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra is used to discuss the benefits of using this approach in the optimization of the BAO problem.     

Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces

The purpose here is to investigate, by means of the constructal principle, the influence of the convective heat transfer flux at the cavity surfaces over the optimal geometry of a T-shaped cavity that intrudes into a solid conducting wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The convective heat flux is imposed as a boundary condition of the cavity surfaces and the geometric optimization is achieved for several values of parameter a = (2hA^1/2/k)^1/2. The structure of the T-shaped cavity has four degrees of freedom: L₀/L₁ (ratio between the lengths of the stem and bifurcated branches), H₁/L₁ (ratio between the thickness and length of the bifurcated branches), H₀/L₀ (ratio between the thickness and length of the stem), and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (φ). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for fixed values of H/L = 1.0 and φ = 0.1. Even for the first and second levels of optimization, (L₁/L₀) _○○ and (H₀/L₀)_○, the results revealed that there is no universal shape that optimizes the cavity geometry for every imposed value of a. The T-shaped cavity geometry adapts to the variation of the convective heat flux imposed at the cavity surfaces, i.e., the system flows and morphs with the imposed conditions so that its currents flow more and more easily. The three times optimal shape for lower ratios of a is achieved when the cavity has a higher penetration into the solid domain and for a thinner stem. As the magnitude of a increases, the bifurcated branch displaces toward the center of the solid domain and the number of highest temperature points also increases, i.e., the distribution of temperature field is improved according to the constructal principle of optimal distribution of imperfections.     

Unfolding physics from the algebraic classification of spinor fields

After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under such classification. In particular, we pithily focus on the new aspects — as well as current concrete possibilities. They mainly arise when we deal with some non-standard spinor fields concerning, in particular, their applications in physics.     

Quadruplex CARS micro‐spectroscopy

We demonstrate a technique for simultaneous detection of coherent anti‐Stokes Raman scattering (CARS) at four vibrational frequencies, using simple passive optical elements and without spectrally resolved detection. The technique is based on pump and Stokes femtosecond pulses selectively exciting vibrational resonances through spectral focusing. By replicating the pump and Stokes pair into four pairs, each traveling through appropriate glass elements, we simultaneously excite four different vibrational frequencies. The resulting CARS is a periodic train of intensities detected by a single photomultiplier and frequency analyzed to retrieve its Fourier coefficients. We demonstrate detection of methanol and ethanol mixtures in water and quantitative determination of their concentration owing to the improved chemical selectivity of this quadruplex CARS scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Kinetic studies on the influence of temperature and growth rate history on crystal growth

Crystallization experiments of sucrose were performed in a batch crystallizer to study the effect of temperature and growth rate history on the crystal growth kinetics. In one of the growth methods adopted, the isothermal volumetric growth rate (R_V) is determined as a function of supersaturation (S) at 35, 40 and 45 ºC. In the other, crystals are allowed to grow at constant supersaturation by automatically controlling the solution temperature as the solute concentration decreased. Using the latter method R_V is calculated as the solution is cooled. The obtained results are interpreted using empirical, engineering and fundamental perspectives of crystal growth. Firstly, the overall activation energy (E_A) is determined from the empirical growth constants obtained in the isothermal method. The concept of falsified kinetics, widely used in chemical reaction engineering, is then extended to the crystal growth of sucrose in order to estimate the true activation energy (E_T) from the diffusion‐affected constant, E_A. The differences found in the isothermal and constant supersaturation methods are explained from the viewpoint of the spiral nucleation mechanism, taking into account different crystal surface properties caused by the growth rate history in each method. Finally, the crystal growth curve obtained in the batch crystallizer at 40 ºC is compared with the one obtained in a fluidized bed crystallizer at the same temperature. Apparently divergent results are explained by the effects of crystal size, hydrodynamic conditions and growth rate history on the crystallization kinetics of sucrose. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anti-Leishmania and cytotoxic activities of perillaldehyde epoxide synthetic positional isomers

Leishmaniasis belongs to a complex of zoonotic disease caused by protozoa of the genus Leishmania and is considered a major public health problem. Several essential oil chemical components have inhibitory effect against protozoa, including Leishmania donovani. Thus, the aim of this study was to evaluate for the first time the anti-Leishmania activity of two p-menthane monoterpene isomers (EPER-1: perillaldehyde 1,2-epoxide and EPER-2: perillaldehyde 8,9-epoxide) against L. donovani promastigotes as well as evaluating cytotoxic effect on mononuclear peripheral blood cells. Results of anti-Leishmania assay revealed that EPER-2 (IC₅₀ = 3.8 μg.mL^?1) was 16-fold more potent than its isomer EPER-1 (IC₅₀ = 64.6 μg.mL^?1). In contrast to PBMC cells, EPER-2 was not cytotoxic (IC₅₀ > 400 μg.mL^?1) when compared to positive control. These data suggest that the disposition of epoxide group into the p-menthane skeleton affects the anti-Leishmania activity, being that the presence of the exocyclic epoxide group considerably increased potency. Thus, it was possible to observe that the location of the epoxide group into the p-menthane skeleton resulted in different potencies.