Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Cassava root peel as a replacement for maize in diets for growing pigs: effects on energy and nutrient digestibility, performance and carcass characteristics

Two experiments were conducted to evaluate cassava root peel (CRP) as diet component for fattening pigs. In the first experiment, ten male pigs were used to investigate the nutrient digestibility and the nutritive value of CRP as replacement for maize in the diet at 0 %, 30 %, 40 %, 50 % and 60 %, while supplementing free amino acids (fAA). During two experimental periods, faeces were quantitatively collected and analysed for chemical composition. In the second experiment, 40 pigs received the same diets as in Experiment 1, and daily feed intake and weekly weight changes were recorded. Four pigs per diet were slaughtered at 70 kg body weight to evaluate carcass traits. Digestibility of dry and organic matter, crude protein, acid detergent fibre and gross energy were depressed (p<0.05) at 60 % CRP; digestible energy content (MJ kg^(−1) DM) was 15.4 at 0 % CRP and 12.7 at 60 % CRP. In the second experiment, CRP inclusion had only a small impact on feed intake, weight gain and feed conversion ratio (p>0.05) as well as on the length of the small intestine and the Longissimus dorsi muscle area. The missing correlation of daily weight gain and feed-to-gain ratio up to a CRP inclusion of 40 % indicates that negative effects of CRP on pig growth can be avoided by respecting upper feeding limits. Hence, a combined use of CRP and fAA can reduce feeding costs for small-scale pig farmers in countries where this crop-by product is available in large amounts.

Effects of phosphorus and water stress on shoot and root growth and on mycorrhization of different pearl millet (Pennisetum glaucum (L.) R. Br.) varieties from West Africa

This research work aimed at investigating the physiological mechanisms of tolerance of pearl millet to low soil Phosphorus availability and drought under the Sahelian conditions.

Pathogens occuring in the winter pea-maize-winter wheat rotation, their host specificity and the potential of compost in suppressing foot and root disease of peas

The overall aim of the work presented was to evaluate soil health management with a specific focus on soil borne diseases of peas. For that purpose field experiments were carried out from 2009 until 2013 to assess crop performance and pathogen occurrence in the rotation winter pea-maize-winter wheat and if the application of composts can improve system performance. The winter peas were left untreated or inoculated with Phoma medicaginis, in the presence or absence of yard waste compost at rate of 5 t dry matter ha-1. A second application of compost was made to the winter wheat. Fusarium ssp. were isolated and identified from the roots of all three crops and the Ascochyta complex pathogens on peas. Bioassays were conducted under controlled conditions to assess susceptibility of two peas to Fusarium avenaceum, F. solani, P. medicaginis and Didymella pinodes and of nine plant species to F. avenaceum. Also, effects of compost applications and temperature on pea diseases were assessed. Application of composts overall stabilized crop performance but it did not lead to significant yield increases nor did it affect pathogen composition and occurrence. Phoma medicaginis was dominating the pathogen complex on peas. F. graminearum, F. culmorum, F. proliferatum, Microdochium nivale, F. crookwellense, F. sambucinum, F. oxysporum, F. avenaceum and F. equiseti were frequently isolated species from maize and winter wheat with no obvious influence of the pre-crop on the Fusarium species composition. The spring pea Santana was considerably more susceptible to the pathogens tested than the winter pea EFB33 in both sterile sand and non-sterilized field soil. F. avenaceum was the most aggressive pathogen, followed by P. medicaginis, D. pinodes, and F. solani. Aggressiveness of all pathogens was greatly reduced in non-sterile field soil. F. avenaceum caused severe symptoms on roots of all nine plant species tested. Especially susceptible were Trifolium repens, T. subterraneum, Brassica juncea and Sinapis alba in addition to peas. Reduction of growing temperatures from 19/16°C day/night to 16/12°C and 13/10°C did not affect the efficacy of compost. It reduced plant growth and slightly increased disease on EFB33 whereas the highest disease severity on Santana was observed at the highest temperature, 19/16°C. Application of 20% v/v of compost reduced disease on peas due to all four pathogens depending on pea variety, pathogen and growing media used. Suppression was also achieved with lower application rate of 3.5% v/v. Tests with γ sterilized compost suggest that the suppression of disease caused by Fusarium spp. is biological in origin, whereas chemical and physical properties of compost are playing an additional role in the suppression of disease caused by D. pinodes and P. medicaginis.

Influence of pre-plant densities of Meloidogyne incognita on growth and root infestation of spinach (Spinacia oleracea L.) (Amaranthaceae) – an important dimension towards enhancing crop production

Vegetables represent a main source of micro-nutrients which can improve the health status of malnourished poor in the world. Spinach (Spinacia oleracea L.) is a popular leafy vegetable in many countries which is rich with several important micro-nutrients. Thus, consuming Spinach helps to overcome micro-nutrient deficiencies. Pests and pathogens act as major yield constraints in food production. Root-knot nematodes, Meloidogyne species, constitute a large group of highly destructive plant pests. Spinach is found to be highly susceptible for these nematode attacks. Though agricultural production has largely benefited from modern technologies and innovations, some important dimensions which can minimize the yield losses have been neglected by most of the growers. Pre-plant or initial nematode density in soil is a crucial biotic factor which is directly responsible for crop losses. Hence, information on preplant nematode densities and the corresponding damage is of vital importance to develop successful control procedures to enhance crop production. In the present study, effect of seven initial densities of M. incognita, i.e., 156, 312, 625, 1250, 2,500, 5,000 and 10,000 infective juveniles (IJs)/plant (equivalent to 1000cm3 soil) on the growth and root infestation on potted spinach plants was determined in a screen house. In order to ensure a high accuracy, root infestation was ascertained by the number of galls formed, the percentage galled-length of feeder roots and galled-feeder roots, and egg production, per plant. Fifty days post-inoculation, shoot length and weight, and root length were suppressed at the lowest IJs density. However, the pathogenic effect was pronounced at the highest density at which 43%, 46% and 45% reduction in shoot length and weight, and root length, respectively, was recorded. The highest reduction in root weight (26%) was detected at the second highest density. The Number of galls and percentage galled-length of feeder roots/per plant showed significant progressive increase across the increasing IJs density with the highest mean value of 432.3 and 54%, respectively. The two shoot growth parameters and root length showed significant inverse relationship with the increasing gall formation. Moreover, the shoot and root length were shown to be mutually dependent on each other. Suppression of shoot growth of spinach greatly affects the grower’s economy. Hence, control measures are essentially needed to ensure a better production of spinach via reducing the pre-plant density below the level of 0.156 IJs/cm3.

Suppression of root-knot nematode through innovative mustard biofumigation

The nematicidal activity of mustard plant against hatching, migration and mortality of the root-knot nematode Meloidogyne javanica was investigated. In vitro test confirmed that mixing the sandy clay soil mixture with mustard as 4% as a biofumigant significantly reduce the percentage of egg hatching at all different incubation periods 24, 48, 72, 96 and 168 h, compared to control treatment (un-amended mixture soil and eggs in free water). Results indicate that the percentage of egg hatching reduction was 88.5, 90, 81.4, 74 and 69.4%, respectively. Mustard mixed with soil as a biofumigant led to high percentage of larval mortality at the different intervals periods in vitro. The percentage of larval mortality was 94, 100, 90.5, 90.5, and 79.4%, respectively compared to control. Laboratory results confirmed that the highest reduction in egg hatching and larval mortality was obtained after incubation period for 48 h. In vivo experiment reveals that the incorporation of the soil pots with mustard at all different doses used 3, 5% (48 h before nematode inoculation, or soil infestation with nematode), and 5% (one week before nematode inoculation or 7% of soil weight) significantly reduces all the nematode parameters compared to plant treated nematode alone. All nematode parameters i.e. the number of galls per root system, gall index, number of egg masses per root system, as well as number of juveniles per 250g soil showed high reduction with mixing the soil pots with mustard at 5% (one week before nematode inoculation), followed by the same treatment for 48h before nematode inoculation. Mustard application, one week before nematode inoculation, reduced the nematode parameters by 97, 64, 97, and 93%, respectively, compared to control. The percent of chemical components i.e. total sugars, total amino acids and total phenols were markedly enhanced compared to positive and negative control. The highest percentage was obtained with mustard at 5% one week before nematode inoculation by 68.7, 57.3 and 45%, respectively. Finally, we have to conclude that this modified technology is an innovative and can be used efficiently to control Root-knot nematode under organic agriculture and Global GAP agricultural systems instead of these carcinogenic nematicides.

Maria Antònia Canals. El GAMAR, l'experiència de tocar les matemàtiques

El reglets de Maria Antònia Canals són unes caixes plenes de peces de fusta. N'hi ha de diferent mida i color. La combinació de les peces proporciona la possibilitat de resoldre problemes matemàtics sense escriure cap número: l'experiència de tocar la matemàtica. La professora Canals els té a disposició dels mestres al seu despatx del Gabinet de Materials i de Recerca per a la Matemàtica a l'Escola (GAMAR)

Is maternal deprivation the root of all evil?

In this paper we seriously entertain the question, “Is maternal deprivation the root of all evil?” Our consideration of this question is broken down into three parts. In the fi rst part, we discuss the nature of evil, focusing in particular on the legal concept of depravity. In the second part, we discuss the nurture of evil, focusing in particular on the common developmental trajectory seen in those who are depraved. In the third part, we discuss the roots of evil, focusing in particular on the animal and human research regarding maternal deprivation. Our conclusion is that maternal deprivation may actually be the root of all evil, but only because depraved individuals have been deprived of normative maternal care, which is the cradle of our humanity.

Carme Isalt Canals : enseñar a vivir.

Se presenta el perfil personal y profesional de Carme Isalt Canals. La primera vez que pisó un aula, se dio cuenta de que lo importante no era enseñar a leer y escribir sino a vivir. Su periodo en las Escuelas Leber, donde convivían niños sin dificultades con otros que necesitaban ayuda, le enseño que su profesión estaba implicada directamente con la vida de sus alumnos, donde lo importante era despertar el deseo de aprender. Para Carme, una de las maneras de enseñar lo que para ella es importante, es a través de proyectos, trabajar a partir de la propia experiencia, sin una realidad construida a priori como la de los libros de texto, los programas y los controles.

Conversaciones matemáticas con Maria Antònia Canals : o cómo hacer de las matemáticas un aprendizaje apasionante.

Contiene varios anexos con textos informativos sobre la docencia de la asignatura, así como uno último donde se recogen una serie de recursos, la mayoría en internet, sobre la asignatura de matemáticas

Documentos de trabajo Maria Antónia Canals.

Selección de textos de la profesora de matemáticas Maria Antònia Canals de revistas, actas de Congresos, jornadas y sin publicar que reflejan los aspectos fundamentales de su pensamiento. El objetivo es ser un conjunto de materiales de trabajo para enseñar matemáticas en la escuela infantil y primaria.

Proyecto Canals : recursos interactivos de Matemáticas : Infantil y Primaria.

Resumen basado en el de la publicación

Nous llenguatges per a nous canals de comunicaci??

Resumen basado en el de la publicaci??n

Amb M. Antònia Canals al Nepal de Viki Sherpa

Relació del viatge fet per la Maria Antònia Canals a Nepal amb motiu de l’acte de celebració de la signatura del conveni de col·laboració entre la Universitat de Tribhuvan a Katmandu i la Universitat de Vic per crear el centre de formació del professorat d’infantil i de primària M. Antònia Canals