Statistical Mechanics Analysis of the Continuous Number Partitioning Problem

The number partitioning problem consists of partitioning a sequence of positive numbers ${a_1,a_2,..., a_N}$ into two disjoint sets, ${\cal A}$ and ${\cal B}$, such that the absolute value of the difference of the sums of $a_j$ over the two sets is minimized. We use statistical mechanics tools to study analytically the Linear Programming relaxation of this NP-complete integer programming. In particular, we calculate the probability distribution of the difference between the cardinalities of ${\cal A}$ and ${\cal B}$ and show that this difference is not self-averaging.Comment: 9 pages, 1 figur

Connection between the Affine and Conformal Affine Toda Models and their Hirota's Solution

It is shown that the Affine Toda models (AT) constitute a ``gauge fixed'' version of the Conformal Affine Toda model (CAT). This result enables one to map every solution of the AT models into an infinite number of solutions of the corresponding CAT models, each one associated to a point of the orbit of the conformal group. The Hirota's $\tau$-function are introduced and soliton solutions for the AT and CAT models associated to $\hat {SL}(r+1)$ and $\hat {SP}(r)$ are constructed.Comment: 11 pages, LaTe

Intrinsec Value of Drugs

A nova versão das Boas Práticas de Distribuição de Medicamentos foi aprovada ao nível da Comunidade Europeia e decorre atualmente a sua implementação ao nível dos diversos países...

Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson currents of KP hierarchy are being associated with sites of the corresponding chain by successive actions of discrete symmetry.Comment: 12 pgs, LaTeX, IFT-P.041/9

Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies

We give the correct prescriptions for the terms involving the inverse of the derivative of the delta function, in the Hamiltonian structures of the AKNS and DNLS systems, in order for the Jacobi identities to hold. We also establish that the sl(2) AKNS and DNLS systems are tri-Hamiltonians and construct two compatible Hamiltonian structures for the sl(3) AKNS system. We also give a derivation of the recursion operator for the sl(n+1) DNLS system.Comment: 10 pages, LaTe

Higher Grading Conformal Affine Toda Teory and (Generalized) Sine-Gordon/Massive Thirring Duality

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local Lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of $\hat{sl}(n) (n=2,3)$ is presented explicitly.Comment: 28 pages, JHEP styl

On Non-Linear W-Infinity Symmetry of Generalized Liouville and Conformal Toda Models

Invariance under non-linear ${\sf {\hat W}}_{\infty}$ algebra is shown for the two-boson Liouville type of model and its algebraic generalizations, the extended conformal Toda models. The realization of the corresponding generators in terms of two boson currents within KP hierarchy is presented.Comment: 10 pgs, LaTeX, IFT-P.038/9

Hirota's Solitons in the Affine and the Conformal Affine Toda Models

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the Affine Toda model valid for all underlying Lie groups. Embedding of the Affine Toda model in the Conformal Affine Toda model plays a crucial role in this analysis.Comment: 36 pages, LaTe

A New Deformation of W-Infinity and Applications to the Two-loop WZNW and Conformal Affine Toda Models

We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra $w_{\infty}$ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth $W_{\infty}$ invariance of these models.Comment: 8 page

Evaluation of the impact of initial red wine composition on changes in color and anthocyanin content during bottle storage

Sixteen commercial red wines, selected to cover a different range of color and total polyphenols index (TPI), were stored at 25 °C during 6 months under controlled and different oxygen additions (0, 1.1, 3.1, 10.6 and 30.4 mg L-1) during the bottling process. Changes in color and the anthocyanic composition were evaluated using transmittance spectra and UPLC-MS-UV/Vis respectively. Results reveal a general pattern in the evolution of wines. However, different patterns of evolution related to initial wine composition, especially to TPI, were observed. Wines with higher TPI had a lower evolution, whereas wines with lower TPI showed a higher evolution and greater variability in behavior. In general, oxygen seemed to accelerate all changes observed during aging although the oxygen effect was more limited than the effect of the storage time. These results are relevant for wine experts and help explain the evolution of wine at the bottling stage