Operational Solution to the Nonlinear Klein-Gordon Equation

Supported by Grant SEP-CONACYT 220603, the first author was supported by SEP-PRODEP through the project UAM-PTC-630, the third author was supported by Portuguese National Funds through the FCT Foundation for Science and Technology under the project PEst-UID/EEA/00066/2013We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions.authorsversionpublishe

In vitro antimicrobial and antiproliferative activity of amphipterygium adstringens

Amphipterygium adstringens is a plant widely used in Mexican traditional medicine for its known anti-inflammatory and antiulcer properties. In this work, we evaluated the in vitro antimicrobial and antiproliferative activities of the methanolic extract of A. adstringens against oral pathogens such as Streptococcus mutans, Porphyromonas gingivalis, Aggregatibacter actinomycetemcomitans, Candida albicans, and Candida dubliniensis, using microdilution (MIC) and agar diffusion methods (MBC), and the antiproliferative activity evaluating total growth inhibition (TGI) by staining the protein content with sulforhodamine B (SRB), using nine human cancer cell lines. Crude extract (CE) of A. adstringens showed some degree of activity against one or more of the strains with a MIC from 0.125 mg/mL to 63 mg/mL and MBC from 1.6 to 6.3 mg/mL and cytotoxic activity, particularly against NCI-ADR/RES, (a)n ovarian cell line expressing multiple resistance drugs phenotype. The CE is a complex mixture of possible multitarget metabolites that could be responsible for both antimicrobial and antiproliferative activities, and further investigation is required to elucidate the identity of active compounds. Nevertheless the CE itself is useful in the development of new antimicrobial treatment based on natural products to prevent oral diseases and as alternative natural source for cancer treatment and prevention2015PROMEP, Mexic

Discrete Moyal-type representations for a spin

In Moyal’s formulation of quantum mechanics, a quantum spin s is described in terms of continuous symbols, i.e., by smooth functions on a two-dimensional sphere. Such prescriptions to associate operators with Wigner functions, P or Q symbols, are conveniently expressed in terms of operator kernels satisfying the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal formalism is defined on the basis of a modified set of postulates. It is shown that appropriately modified postulates single out a well-defined set of kernels that give rise to discrete symbols. Now operators are represented by functions taking values on (2s+1)2 points of the sphere. The discrete symbols contain no redundant information, contrary to the continuous ones. The properties of the resulting discrete Moyal formalism for a quantum spin are worked out in detail and compared to the continuous formalism

In Vitro

Amphipterygium adstringens is a plant widely used in Mexican traditional medicine for its known anti-inflammatory and antiulcer properties. In this work, we evaluated the in vitro antimicrobial and antiproliferative activities of the methanolic extract of A. adstringens against oral pathogens such as Streptococcus mutans, Porphyromonas gingivalis, Aggregatibacter actinomycetemcomitans, Candida albicans, and Candida dubliniensis, using microdilution (MIC) and agar diffusion methods (MBC), and the antiproliferative activity evaluating total growth inhibition (TGI) by staining the protein content with sulforhodamine B (SRB), using nine human cancer cell lines. Crude extract (CE) of A. adstringens showed some degree of activity against one or more of the strains with a MIC from 0.125 mg/mL to 63 mg/mL and MBC from 1.6 to 6.3 mg/mL and cytotoxic activity, particularly against NCI-ADR/RES, an ovarian cell line expressing multiple resistance drugs phenotype. The CE is a complex mixture of possible multitarget metabolites that could be responsible for both antimicrobial and antiproliferative activities, and further investigation is required to elucidate the identity of active compounds. Nevertheless the CE itself is useful in the development of new antimicrobial treatment based on natural products to prevent oral diseases and as alternative natural source for cancer treatment and prevention