Semi-classical scalar products in the generalised SU(2) model

In these notes we review the field-theoretical approach to the computation of the scalar product of multi-magnon states in the Sutherland limit where the magnon rapidities condense into one or several macroscopic arrays. We formulate a systematic procedure for computing the 1/M expansion of the on-shell/off-shell scalar product of M-magnon states in the generalised integrable model with SU(2)-invariant rational R-matrix. The coefficients of the expansion are obtained as multiple contour integrals in the rapidity plane.Comment: 13 pages, 3 figures. Based on a talk delivered at the X. International Workshop "Lie Theory and Its Applications in Physics", (LT-10), Varna, Bulgaria, 17-23 June 201

Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetric t-J Model

We construct the Drinfeld twists (factorizing $F$-matrices) for the supersymmetric t-J model. Working in the basis provided by the $F$-matrix (i.e. the so-called $F$-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the $gl(2|1)$ invariant t-J model.Comment: 23 pages, no figure, Latex file, minor misprints are correcte

Utilización de Leucaena leucocephala en el levante de ovinos africanos en el Piedemonte Llanero, Colombia

The objective of this project was to evaluate the leucaena (Leucahena lecucephala) as a supplement in sheep grazing. Using 12 males African (Sudanese), average weight of 14.45 kg, with a base diet of braquiaria (B. decumbens), the sheeps were randomly distributed entirely to the three replications and four treatments: T1 (control): braquiaria, T2: braquiaria plus 1% of live animal weight of dry matter of leucaena (DML), T3 braquiaria, 1.5 % of DML and T4: braquiaria plus 2.0% of DML. The sheep remained in bands divided with electric fence and were rotated daily. The sheeps were weigthed every seven days during the two months. In four sheeps, with a weight of 15 kg were housed in metabolic cages, were given the same treatments to assess the digestibility in vivo. At the braquiaria and leucaena were analyzed for estimate dry matter, protein, fat, Crude fiber, and ash, neutral detergent fiber (NDF) and acid detergent fiber (ADF) The collected excreta were also analized to determinate the same nutrients of the forages. With this information were calculated digestibility coefficients (COD) and total digestible nutrients (TDN). The protein content in leucaena is 19.3%, while that of grass is 8.5% 2.29 times that of the legume compared with grass. The digestibility of DM and protein were higher (P>0.05) in T3 and T4, compared with the other two treatments. The total weight gains and daily were higher (P>0.05) for T3 and T2 followed by T4 that are higher (P> 0.05) at T1. The DM intakes were higher (P>0.05) T1 and T4 and T3 compared with T2. The best feed conversion (P>0.05) on DM intake was T3 followed by T2, T4 and T1. Undoubtedly, using leucaena fed to ruminants as a supplement to a grass is advantageous because its nutrient content allows it to offer a balanced diet without detriment to its productive indices, especially in areas where forages are of low quality.El objetivo de este proyecto fue evaluar la L. lecucephala como suplemento en ovinos de levante en pastoreo. Se utilizaron 12 machos tipo africano (sudaneses), peso promedio de 14.45 Kg, con una dieta base de B. decumbens, los ovinos se distribuyeron completamente al azar tres repeticiones y cuatro tratamientos: T1: (testigo) braquiaria, T2: braquiaria más el 1% del peso vivo del animal, en materia seca de leucaena (MSL), T3: braquiaria, 1.5% de MSL y T4: braquiaria más el 2.0% de MSL. Los ovinos se mantuvieron en franjas divididas con cerca eléctrica y diariamente se rotaban. Los pesajes se tomaron cada 7 días durante los dos meses. Para las pruebas de digestibilidad, se utilizaron cuatro ovinos machos, peso promedio de 15 kilos y se estabularon en jaulas metabólicas, se les suministraron los mismos tratamientos para evaluar la digestibilidad in vivo. Al pasto braquiaria y a la leucaena se les realizaron análisis proximal (materia seca proteína, grasa, fibra cruda, cenizas) y determinación de fibra detergente neutro (FDN) y fibra detergente ácido (FDA). A las excretas recolectadas también se realizaron los mismos análisis de los forrajes, se calcularon los coeficientes de digestibilidad (COD) y los nutrientes digestibles totales (NDT). El contenido de proteína de la leucaena es de 19.3%, mientras que la del pasto es de 8.5%, es 2.29 veces más la de la leguminosa comparada con la del pasto. Las digestibilidades de MS y proteína fueron superiores (P>0.05) en los tratamientos T3 y T4, con relación a los otros dos. Las ganancias de peso total y diaria fueron superiores (P>0.05) para T3 seguido de T4 y T2 que son mayores (P>0.05) a T1. Los consumos de MS fueron más elevados (P>0.05) en T1 y T4 con relación a T3 y T2. La mejor conversión alimenticia (P>0.05) sobre el consumo de MS fue para T3 seguido de T2, T4 y T1. Indudablemente, utilizar la leucaena para la alimentación de rumiantes como suplemento de una gramínea es ventajoso porque su contenido nutricional le permite ofrecer una dieta balanceada al animal sin detrimento de sus índices productivos, sobre todo en zonas donde los forrajes son de baja calidad

Slow relaxation in weakly open vertex-splitting rational polygons

The problem of splitting effects by vertex angles is discussed for nonintegrable rational polygonal billiards. A statistical analysis of the decay dynamics in weakly open polygons is given through the orbit survival probability. Two distinct channels for the late-time relaxation of type 1/t^delta are established. The primary channel, associated with the universal relaxation of ''regular'' orbits, with delta = 1, is common for both the closed and open, chaotic and nonchaotic billiards. The secondary relaxation channel, with delta > 1, is originated from ''irregular'' orbits and is due to the rationality of vertices.Comment: Key words: Dynamics of systems of particles, control of chaos, channels of relaxation. 21 pages, 4 figure

Classical and quantum decay of one dimensional finite wells with oscillating walls

To study the time decay laws (tdl) of quasibounded hamiltonian systems we have considered two finite potential wells with oscillating walls filled by non interacting particles. We show that the tdl can be qualitatively different for different movement of the oscillating wall at classical level according to the characteristic of trapped periodic orbits. However, the quantum dynamics do not show such differences.Comment: RevTeX, 15 pages, 14 PostScript figures, submitted to Phys. Rev.

Metallomic Signatures of Lung Cancer and Chronic Obstructive Pulmonary Disease

Lung cancer (LC) is the leading cause of cancer deaths, and chronic obstructive pulmonary disease (COPD) can increase LC risk. Metallomics may provide insights into both of these tobaccorelated diseases and their shared etiology. We conducted an observational study of 191 human serum samples, including those of healthy controls, LC patients, COPD patients, and patients with both COPD and LC.We found 18 elements (V, Al, As, Mn, Co, Cu, Zn, Cd, Se,W, Mo, Sb, Pb, Tl, Cr, Mg, Ni, and U) in these samples. In addition, we evaluated the elemental profiles of COPD cases of varying severity. The ratios and associations between the elements were also studied as possible signatures of the diseases. COPD severity and LC have a significant impact on the elemental composition of human serum. The severity of COPD was found to reduce the serum concentrations of As, Cd, and Tl and increased the serum concentrations of Mn and Sb compared with healthy control samples, while LC was found to increase Al, As, Mn, and Pb concentrations. This study provides new insights into the effects of LC and COPD on the human serum elemental profile that will pave the way for the potential use of elements as biomarkers for diagnosis and prognosis. It also sheds light on the potential link between the two diseases, i.e., the evolution of COPD to LC.This work has been supported by the project "Heteroatom-tagged proteomics and metabolomics to study lung cancer. Influence of gut microbiota” (Ref.: PY20_00366) (Project of Excellence, Regional Ministry of Economy, Knowledge, Business and University, Andalusia, Spain). The authors are also grateful for grants 651/2018 and 115/2020 from the Spanish Society of Pneumology and Surgery (SEPAR) and grant 08/2018 from the Association of Pneumology and Thoracic Surgery (Neumosur), which were used to facilitate recruitment at the hospitals and biobank registration. The authors also thank Instituto de Salud Carlos III (AES16/01783) and wish to express their gratitude for the unrestricted funding from the Menarini Group and AstraZeneca

Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation

We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.Comment: LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev.

Exact resolution of the Baxter equation for reggeized gluon interactions

The interaction of reggeized gluons in multi-colour QCD is considered in the Baxter-Sklyanin representation, where the wave function is expressed as a product of Baxter functions Q(lambda) and a pseudo-vacuum state. We find n solutions of the Baxter equation for a composite state of n gluons with poles of rank r in the upper lambda semi-plane and of rank n-1-r in the lower lambda semi-plane (0 leq r leq n-1). These solutions are related by n-2 linear equations with coefficients depending on coth (pi lambda). The poles cancel in the wave function, bilinear combination of holomorphic and anti-holomorphic Baxter functions, guaranteeing its normalizability. The quantization of the intercepts of the corresponding Regge singularities appears as a result of the physical requirements that the holomorphic energies for all solutions of the Baxter equation are the same and the total energies, calculated around two singularities lambda, lambda^* --> + i or -i, coincide. It results in simple properties of the zeroes of the Baxter functions. For illustration we calculate the parameters of the reggeon states constructed from three and four gluons. For the Odderon the ground state has conformal spin |m -m | = 1 and its intercept equals unity. The ground state of four reggeized gluons possesses conformal spin 2 and its intercept turns out to be higher than that for the BFKL Pomeron. We calculate the anomalous dimensions of the corresponding operators for arbitrary alpha_s/omega.Comment: LaTex, 42 pages, 8 .ps figures. Expanded and improved versio

Exact diagonalization of the generalized supersymmetric t-J model with boundaries

We study the generalized supersymmetric $t-J$ model with boundaries in three different gradings: FFB, BFF and FBF. Starting from the trigonometric R-matrix, and in the framework of the graded quantum inverse scattering method (QISM), we solve the eigenvalue problems for the supersymmetric $t-J$ model. A detailed calculations are presented to obtain the eigenvalues and Bethe ansatz equations of the supersymmetric $t-J$ model with boundaries in three different backgrounds.Comment: Latex file, 32 page