A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Moduli stacks of polarized K3 surfaces in mixed characteristic

2000 Mathematics Subject Classification: 14J28, 14D22.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

PoS-tagging the Web in Portuguese. National varieties, text typologies and spelling systems

The great amount of text produced every day in the Web turned it as one of the main sources for obtaining linguistic corpora, that are further analyzed with Natural Language Processing techniques. On a global scale, languages such as Portuguese - official in 9 countries - appear on the Web in several varieties, with lexical, morphological and syntactic (among others) differences. Besides, a unified spelling system for Portuguese has been recently approved, and its implementation process has already started in some countries. However, it will last several years, so different varieties and spelling systems coexist. Since PoS-taggers for Portuguese are specifically built for a particular variety, this work analyzes different training corpora and lexica combinations aimed at building a model with high-precision annotation in several varieties and spelling systems of this language. Moreover, this paper presents different dictionaries of the new orthography (Spelling Agreement) as well as a new freely available testing corpus, containing different varieties and textual typologies.

Varieties of algebras arising from K-perfect m-cycle systems

A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from {1}-perfect m-cycle systems form a variety for m is an element of {3, 5} only, and that the algebras arising from {1, 2}-perfect m-cycle systems form a variety for m is an element of {3, 5, 7} only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety. (c) 2006 Elsevier B.V. All rights reserved.

The D(D-3)-anyon chain: integrable boundary conditions and excitation spectra

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D-3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z(4) parafermion or a M-(5,M-6) minimal model.

Managing the risk of glyphosate resistance in Australian glyphosate-resistant cotton production systems

BACKGROUND: Glyphosate-resistant cotton varieties are an important tool for weed control in Australian cotton production systems. To increase the sustainability of this technology and to minimise the likelihood of resistance evolving through its use, weed scientists, together with herbicide regulators, industry representatives and the technology owners, have developed a framework that guides the use of the technology. Central to this framework is a crop management plan (CMP) and grower accreditation course. A simulation model that takes into account the characteristics of the weed species, initial gene frequencies and any associated fitness penalties was developed to ensure that the CMP was sufficiently robust to minimise resistance risks. RESULTS: The simulations showed that, when a combination of weed control options was employed in addition to glyphosate, resistance did not evolve over the 30 year period of the simulation. CONCLUSION: These simulations underline the importance of maintaining an integrated system for weed management to prevent the evolution of glyphosate resistance, prolonging the use of glyphosate-resistant cotton.

Integrated Cotton Farming Systems for Central Queensland

This project has delivered outcomes that address major agronomic and crop protection issues closely linked to the profitability and sustainability of cotton production enterprises in CQ. From an agronomic perspective, the CQ environment was always though to support economically viable cotton production in a wide sowing window from the middle of September to early January prior to this research. The ideal positioning of Bollgard II varieties in the CQ planting window was, therefore, critical to the future of the local cotton industry because growers needed baseline information to determine how best to take advantage of the higher yield potential offered by the Bt cotton technology, optimise irrigation water use and fibre characteristics. The project’s outputs include a number of key agronomic findings. Over three growing seasons, Bollgard II crop planted in the traditional sowing window from the middle of September to the end of October consistently produced the highest yields. The project delivers a clear and quantitative assessment of the impacts of planting outside the traditional cropping window - a yield penalty of between 1-4 bales/ha for November and December planted cotton. Whilst yield penalties associated with December-planted crops are clearly linked to declining heat units in the second half of the crop and a cool finish, those associated with November-planted cotton are not consistent with the theoretical yield potential for this sowing date. Further research to understand and minimize the physiological constraints on November-planted cotton would give CQ cotton growers far greater flexibility to develop mixed/double/rotation cropping farming systems that are relevant to the rapidly evolving nature of Agricultural production in Australia. The equivalence of cultivar types with clearly distinguishable, genetically based growth habits, demonstrated in this project, gives growers important information for making varietal choices. The entomological outcomes of this project represent strategic and tactical tools that are highly relevant to the viability and profitability of the cotton industry in Australia. The future of the cotton industry is inextricably linked to the survival and efficacy of GM cotton. Research done in the Callide irrigation area demonstrates the unquestionable potential for development of alternative and highly effective resistance management strategies for Bollgard II using novel technologies and strategies based on products such as Magnet®. Magnet® and similar technologies will be increasingly important in strategies to preserve the shelf life and efficacy of current and future generations of GM technology. However, more research will be required to address logistical and operational issues related to these new technologies before they can be fully exploited in commercial production systems. From an economic perspective, SLW is the sleeping giant in terms of insect nemeses of cotton, particularly from the standpoint of climate change and an increasingly warmer production environment. An effective sampling and management strategy for SLW which has been delivered by this project will go a long way towards minimising production costs in an environment characterised by rapidly rising input costs. SLW has the potential to permanently debilitate the national cotton industry by influencing market sentiment and quality perceptions. Field validation of the SLW population sampling models and management options in the Dawson irrigation area cotton and southern Queensland during 2006-07 documents the robustness of the entomological research outcomes achieved through this project.