On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy

We give a simple algebraic proof that the two different Lax pairs for the Kac-van Moerbeke hierarchy, constructed from Jacobi respectively super-symmetric Dirac-type difference operators, give rise to the same hierarchy of evolution equations. As a byproduct we obtain some new recursions for computing these equations.Comment: 8 page

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur

Quasi-Solitons in Dissipative Systems and Exactly Solvable Lattice Models

A system of first-order differential-difference equations with time lag describes the formation of density waves, called as quasi-solitons for dissipative systems in this paper. For co-moving density waves, the system reduces to some exactly solvable lattice models. We construct a shock-wave solution as well as one-quasi-soliton solution, and argue that there are pseudo-conserved quantities which characterize the formation of the co-moving waves. The simplest non-trivial one is given to discuss the presence of a cascade phenomena in relaxation process toward the pattern formation.Comment: REVTeX, 4 pages, 1 figur

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione

Delaying berry ripening through manipulating leaf area to fruit ratio

The viticulture practices have always been focused on the production of grapes with higher sugar level, and this tendency has been pronounced by the climate change. The objective consists on delaying berry ripeness by decreasing the ratio between the leaf area and yield, performing intense trimming treatments after berry set and establishing the consequences on grapevine productivity in the following years. Severe shoot trimming with two different intensity treatments were done during a 3-year period (2010-2012). Phenological, vegetative and productive parameters were examined. Veraison date was delayed around twenty days. Regarding the same harvesting date, the trim treatments had lower soluble solids level (15 % reduction), lower pH (0.1-0.3) and less total anthocyanin content (10-27 % reduction). The trim effect was also reflected in berry weight; as a consequence of that, bunch size and yield were also reduced by around 9 and 15 %. Overall, single trim treatment was superior to double trim treatment because it can achieve the same results in delayed ripening, reduced °Brix, pH and production but with a smaller reduction in anthocyanin content and without having any negative impact on following years.Peer Reviewe

Quantifying the effect of temperature on decoupling anthocyanins and sugars of the grape (Vitis vinifera L. 'Maturana Tinta de Navarrete')

The objective of this work consists of the quantification of decoupling anthocyanin: sugar ratio produced by higher temperature on Vitis vinifera L. 'Maturana Tinta de Navarrete'. Two vineyards were studied in two different climatic areas during a 3-year period (2010-2012). The average Winkler index during the three years in the two studied areas was 1364°C and 1619°C, respectively. This implies a difference of 1.3°C for the mean temperature between both areas from April to October. Both total anthocyanins and the anthocyanins: sugars ratio decreased, significantly, in the warmer area during the three years. The highest anthocyanin sugars decoupling occurred in the warmest year (2012) and the lowest in the coolest year (2010). Given that the grape ripening begins in August, it could be concluded that the above decoupling is higher as higher is the temperature in August. For further research, it would be very interesting to study the anthocyanins: sugar ratio at different times from veraison onwards.Peer Reviewe

Delaying berry ripening through manipulating leaf area to fruit ratio

The viticulture practices have always been focused on the production of grapes with higher sugar level, and this tendency has been pronounced by the climate change. The objective consists on delaying berry ripeness by decreasing the ratio between the leaf area and yield, performing intense trimming treatments after berry set and establishing the consequences on grapevine productivity in the following years. Severe shoot trimming with two different intensity treatments were done during a 3-year period (2010-2012). Phenological, vegetative and productive parameters were examined. Veraison date was delayed around twenty days. Regarding the same harvesting date, the trim treatments had lower soluble solids level (15 % reduction), lower pH (0.1-0.3) and less total anthocyanin content (10-27 % reduction). The trim effect was also reflected in berry weight; as a consequence of that, bunch size and yield were also reduced by around 9 and 15 %. Overall, single trim treatment was superior to double trim treatment because it can achieve the same results in delayed ripening, reduced °Brix, pH and production but with a smaller reduction in anthocyanin content and without having any negative impact on following years.

Quantifying the effect of temperature on decoupling anthocyanins and sugars of the grape (Vitis vinifera L. 'Maturana Tinta de Navarrete')

The objective of this work consists of the quantification of decoupling anthocyanin:sugar ratio produced by higher temperature on Vitis vinifera L. 'Maturana Tinta de Navarrete'. Two vineyards were studied in two different climatic areas during a 3-year period (2010-2012). The average Winkler index during the three years in the two studied areas was 1364 °C and 1619 °C, respectively. This implies a difference of 1.3 °C for the mean temperature between both areas from April to October. Both total anthocyanins and the anthocyanins:sugars ratio decreased, significantly, in the warmer area during the three years. The highest anthocyanin sugars decoupling occurred in the warmest year (2012) and the lowest in the coolest year (2010). Given that the grape ripening begins in August, it could be concluded that the above decoupling is higher as higher is the temperature in August. For further research, it would be very interesting to study the anthocyanins : sugar ratio at different times from veraison onwards

Reducing the pH of wine by increasing grape sunlight exposure: a method to mitigate the effects of climate warming

The objective of this work was reducing the pH of wine through manipulating grape exposure. Two different training systems (VSP = vertical shoot positioning and free cordon) combined with leaf thinning treatments were performed within a commercial vineyard in order to modify bunch exposition levels to the sunlight radiation during 2010 and 2011 years. Leaf thinning and trellis systems involved significant differences in the pH of wine during the two years: the pH of wine decreased when the bunch exposure was increased in the vineyard. Manipulating grape exposure is a valuable tool in order to modify the pH of wine

Dynamics of broken symmetry nodal and anti-nodal excitations in Bi_{2} Sr_{2} CaCu_{2} O_{8+\delta} probed by polarized femtosecond spectroscopy

The dynamics of excitations with different symmetry is investigated in the superconducting (SC) and normal state of the high-temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) using optical pump-probe (Pp) experiments with different light polarizations at different doping levels. The observation of distinct selection rules for SC excitations, present in A$_{{\rm 1g}}$ and B$_{{\rm 1g}}$ symmetries, and for the PG excitations, present in A$_{{\rm 1g}}$ and B$_{{\rm 2g}}$ symmetries, by the probe and absence of any dependence on the pump beam polarization leads to the unequivocal conclusion of the existence of a spontaneous spatial symmetry breaking in the pseudogap (PG) state