On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Growth Rate Estimation in the presence of Unit Roots

This study addresses the issue of the presence of a unit root on the growth rate estimation by the least-squares approach. We argue that when the log of a variable contains a unit root, i.e., it is not stationary then the growth rate estimate from the log-linear trend model is not a valid representation of the actual growth of the series. In fact, under such a situation, we show that the growth of the series is the cumulative impact of a stochastic process. As such the growth estimate from such a model is just a spurious representation of the actual growth of the series, which we refer to as a “pseudo growth rate”. Hence such an estimate should be interpreted with caution. On the other hand, we highlight that the statistical representation of a series as containing a unit root is not easy to separate from an alternative description which represents the series as fundamentally deterministic (no unit root) but containing a structural break. In search of a way around this, our study presents a survey of both the theoretical and empirical literature on unit root tests that takes into account possible structural breaks. We show that when a series is trendstationary with breaks, it is possible to use the log-linear trend model to obtain well defined estimates of growth rates for sub-periods which are valid representations of the actual growth of the series. Finally, to highlight the above issues, we carry out an empirical application whereby we estimate meaningful growth rates of real wages per worker for 51 industries from the organised manufacturing sector in India for the period 1973-2003, which are not only unbiased but also asymptotically efficient. We use these growth rate estimates to highlight the evolving inter-industry wage structure in India.

Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

Polynomial functors and polynomial monads

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.

An algorithm for semi-infinite polynomial optimization

"Vegeu el resum a l'inici del document del fitxer adjunt."

Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Daisy Roots Garden Project

In the summer of 2009 a local Men’s group that met in St Helena’s thought that it might be a good idea to sow a wild garden on the site.  Then came the raised beds – 2 were placed in the garden area opposite the front door of the house and as it was winter there was not much happening and they were quickly renamed the ‘coffins’.  This was the start of ‘Daisy Roots’. Dublin City Council provided top soil and water butts.  An Taisce funded the start up phase of the project and now continue to provide funds for insurance and some development work.  At the right hand side of St Helena’s there is, what was the old stable yard of the ‘big house’.  This had been used to house a large ‘lock up container and a porta-cabin.  These have been now removed and this is where the main part of the garden is. Following a conference of Business in the Community Ireland, DX Ltd expressed an interest in getting involved in a local project.  Together DX staff and the volunteers reclaimed the old stables and gave them new roofs and new doors.  Paths were put in between the raised vegetable beds and new raised beds were built.  A seating area was developed.  The garden is now wheelchair accessible and there are wheelchair accessible flowerbeds in the garden also.  The newest projects in the garden are a memorial flowerbed and a propagator. Dublin City Council via Cherry Orchard Regeneration Board Initiative Type Community Food Growing Projects Location Dublin 11 Funding Dublin City Council via Cherry Orchard Regeneration Board Partner Agencies An Taisce Dublin City Council HSE Tolka Area Partnership

Fettercairn Growing Community Roots

Fettercairn Growing Community Roots will deliver a range of programmes around exercise and healthy eating to improve, encourage and integrate the target schools into the wider local community through linkages with community based projects e.g. Fettercairn Community Garden. Part of theCFI Programme 2013-2015 Initiative Type Community Food Growing Projects Nutrition Education and Training Programmes Location Dublin 24 Partner Agencies safefood

Use of the pyrophosphatase activity as a reliable tonoplast marker in maize roots.

Membranes of maize (Zea mays L., cv LG 11) roots were fractionated by sucrose (in presence or absence of Mg2+) or dextran density gradient centrifugations and the locations of organelles were determined using marker enzymes. Latent UDPase was used as a Golgi marker, catalase for the peroxysomes, cytochrome c oxidase for the mitochondria, UDP-Gal-galactosyltransferase for the amyloplast membranes and NADH-cytochrome c reductase for the ER. Two markers were selected for the plasmalemma, the vanadate-sensitive ATPase and UDP-Glc-sterolglucosyltransferase. The distributions of the PPase and vacuolar ATPase were found to be similar after density gradient centrifugation. The PPase and vacuolar ATPase activities were clearly separated from almost all the other markers tested, however, a partial association of both activities with the ER cannot be completely ruled out. The PPase of maize roots is more active and easier to measure than the vacuolar ATPase and is therefore an excellent candidate for use as a tonoplast marker.

A Ca2+/H+ antiport system driven by the tonoplast pyrophosphate-dependent proton pump from maize roots.

Calcium uptake by tonoplast enriched membrane vesicles from maize (Zea mays L. cv. LG 11) primary roots was studied. A pH gradient, measured by the fluorescence quenching of quinacrine, was generated across sealed vesicles driven by the pyrophosphate-dependent proton pump. The fluorescence quenching was strongly inhibited by Ca2+; moreover, when increasing Ca2+ concentrations were added to vesicles at steady-state, a concomitant decrease in the proton gradient was observed. Ca2+ uptake using Ca-45(2+) was linear from 10 min when oxalate (10 mM) was present, while Ca2+ uptake was completely inhibited with proton ionophores (FCCP and monensin), indicating a Ca2+/H+ antiport. Membranes were further fractionated using a linear sucrose density gradient (10-45%) and were identified with marker enzymes. Ca2+ uptake co-migrated with the tonoplast pyrophosphate-dependent proton pumping, pyrophosphatase and ATPase activities: the Ca2+/H+ antiport is consequently located at the tonoplast.

Tonoplast localization of a calmodulin-stimulated Ca2+-pump from maize roots.

The subcellular localization of a calmodulin-stimulated calcium (Ca2+)-ATPase activity from maize roots (Zea mays L., cv LG 11) was studied. For this purpose, an efficient procedure was developed to prepare sealed plasma membrane vesicles allowing the measurement of proton and Ca2+ transport activities. Two-day-old root membranes were fractionated by sucrose and dextran density gradient centrifugation. Marker enzymes were used to study the distribution of the different membranes in the gradients and a filtration technique was developed to measure Ca-45(2+) transport in sealed vesicles. Most of the ATP-dependent Ca2+ transport activity was associated with the ER. However, a small part of this activity was associated with the tonoplast (corresponding to the activity of the H+/Ca2+ antiport) and the plasma membrane. When the Ca2+ transport was measured in the presence of exogenous calmodulin (1 muM), a 3-5-fold increase of uptake was measured. The calmodulin-stimulated activity was associated with the tonoplast vesicles only. This activity was insensitive to monensin, a proton ionophore, ruling out a direct effect of calmodulin on the H+/Ca2+ antiport. In conclusion, four different Ca2+ transporters are present in young maize root cells. A Ca2+/H+ antiport system is present on the tonoplast, whereas, the plasma membrane and the ER possess each a calmodulinin-sensitive Ca2+-ATPase. Finally, a calmodulin-stimulated Ca2+-ATPase is associated with the tonoplast.

Characterization of the tonoplast Ca2+/H+ antiport system from maize roots.

The tonoplast calcium Ca2+/H+ antiport system of maize (Zea mays L. cv LG 11) roots was characterized using the ''pH jump'' technique in order to avoid interference from the tonoplast proton and Ca2+ pumps. Ca2+ uptake was recorded in the presence of different inhibitors and divalent ions. Chemical modification of amino acid residues of the antiport was used to elucidate the amino acid residues participating in the Ca2+ transport activity. The Ca2+/H+ antiport activity was found to be strongly inhibited by ruthenium red and verapamil, whereas diethylstilbestrol was less effective. Vanadate, erythrosin B, cyclopiazonic acid, bafilomycin, thapsigargin, N,N'-dicyclohexylcarbodiimide (DCCD) and 4,4'-diisothiocyanatostilbene-2,2'-disulfonate (DIDS) were without effect. Lanthanum and divalent ions were strongly inhibitory (Cd2+ > Mn2+ > Sr2+ > Ba2+). While reagents modifying sulfhydryl groups (N-ethylmaleimide and 5,5'-dithio-bis(2-nitrobenzoate)) did not affect the antiport activity, modification of trytophan residues (N-bromosuccinimide) was strongly inhibitory. We conclude that ruthenium red, verapamil, lanthanum and divalent cations directly inhibit Ca2+ uptake independent of the function of the proton and Ca2+ pumps. Moreover, the results of chemically modified amino acid residues suggest that sulfhydryl groups are not involved in Ca2+ transport, while tryptophan residues seem important for this translocation.