On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira

The classical theorems of Taylor, Lagrange, Laurent and Teixeira, are extended from the representation of a complex function F(z), to its derivative F(ν)(z) of complex order ν, understood as either a Liouville (1832) or a Rieman (1847) differintegration (Campos 1984, 1985); these results are distinct from, and alternative to, other extensions of Taylor's series using differintegrations (Osler 1972, Lavoie & Osler & Tremblay 1976). We consider a complex function F(z), which is analytic (has an isolated singularity) at ζ, and expand its derivative of complex order F(ν)(z), in an ascending (ascending-descending) series of powers of an auxiliary function f(z), yielding the generalized Teixeira (Lagrange) series, which includes, for f(z)=z−ζ, the generalized Taylor (Laurent) series. The generalized series involve non-integral powers and/or coefficients evaluated by fractional derivatives or integrals, except in the case ν=0, when the classical theorems of Taylor (1715), Lagrange (1770), Laurent (1843) and Teixeira (1900) are regained. As an application, these generalized series can be used to generate special functions with complex parameters (Campos 1986), e.g., the Hermite and Bessel types

Somatic embryogenesis in coffee: the evolution of biotechnology and the integration of omics technologies offer great opportunities

One of the most important crops cultivated around the world is coffee. There are two main cultivated species, Coffea arabica and C. canephora. Both species are difficult to improve through conventional breeding, taking at least 20 years to produce a new cultivar. Biotechnological tools such as genetic transformation, micropropagation and somatic embryogenesis (SE) have been extensively studied in order to provide practical results for coffee improvement. While genetic transformation got many attention in the past and is booming with the CRISPR technology, micropropagation and SE are still the major bottle neck and urgently need more attention. The methodologies to induce SE and the further development of the embryos are genotype-dependent, what leads to an almost empirical development of specific protocols for each cultivar or clone. This is a serious limitation and excludes a general comprehensive understanding of the process as a whole. The aim of this review is to provide an overview of which achievements and molecular insights have been gained in (coffee) somatic embryogenesis and encourage researchers to invest further in the in vitro technology and combine it with the latest omics techniques (genomics, transcriptomics, proteomics, metabolomics, and phenomics). We conclude that the evolution of biotechnology and the integration of omics technologies offer great opportunities to (i) optimize the production process of SE and the subsequent conversion into rooted plantlets and (ii) to screen for possible somaclonal variation. However, currently the usage of the latest biotechnology did not pass the stage beyond proof of potential and needs to further improve

Estimación de la capacidad productiva de la estación en bosques secundarios costarricences

Site quality was assessed in four secondary forests dominated by the commercially important tree species Vochysia ferruginea in Northern Costa Rica. A variation of the site quality concept known as site form (i.e. the expected mean height at 25 cm dbh) was used. Twenty-nine sample plots (20 × 20 m) were installed covering soil and topographic variation within and between sites. Site form was estimated for each plot using a linear model. The site form estimations show a high variation between plots (from 16.2 m to 32.2 m), which could indicate large variation in site productivity. Site form of V. ferruginea was significantly correlated with total stand basal area of all species, which supports the potential value of site form as an indicator of site productivity. Twenty-six physical and chemical soil variables showed significant correlation with site form. Adjusted multiple regression models of site form on soil variables were fitted by stepwise regression analysis (forward selection method). The best fit was obtained using only the percentage of sand at 12-30 cm as the independent variable (r2 = 59.3%, s.e.= 3.0 m). The results of this study suggest that site form appears to be a potentially useful indicator of site quality in broadleaved neotropical secondary rainforests when age is unknown.En el presente artículo se presentan los resultados de la evaluación de la calidad de la estación en cuatro bosques secundarios dominados por Vochysia ferruginea en Costa Rica. Como índice de la capacidad productiva de la estación se utilizó el índice de forma (i.e. la altura media esperada a un diámetro a la altura del pecho de 25 cm). Con tal fin se instalaron en campo 29 parcelas (20 × 20 m) de forma tal que cubrieran el rango de variabilidad edáfica y topográfica presente en el área de estudio. El índice de forma presentó una alta variabilidad entre parcelas (entre 16,2 m y 32,2 m), lo cual indica una importante variación en términos de productividad de la estación. El índice de forma de V. ferruginea resultó correlacionado significativamente con el área basimétrica de todas las especies, así como con 26 variables del suelo, quedando entonces respaldado el valor del índice de forma como indicador del rodal de la productividad. Se han ajustado modelos de regresión múltiple entre el índice de forma y las variables edáficas, utilizado el método de inclusión de variable paso a paso. El mejor ajuste se obtuvo al incluir únicamente como variable explicativa el porcentaje de arena en el suelo a una profundidad entre 12-30 cm (r2 = 59,3%, e.e. = 3,0 m). Los resultados del trabajo muestran la potencialidad del índice de forma como indicador de la calidad de estación en los bosques secundarios húmedos neotropicales cuando la edad no es conocida

Enraizamento de estacas de mirtilo provenientes de ramos lenhosos.

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Identification and characterization of a novel cassava (Manihot esculenta Crantz) clone with high free sugar content and novel starch.

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