Integrable Kondo impurity in one-dimensional q-deformed t-J models

Integrable Kondo impurities in two cases of one-dimensional q-deformed t-J models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

The q-deformed supersymmetric t-J model with a boundary

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra U-q[sl(2\1)]. We. give the bosonization of the boundary states. We give an integral expression for the correlation functions of the boundary model, and derive the difference equations which they satisfy.

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Nine classes of integrable open boundary conditions, further extending the one-dimensional U-q (gl (212)) extended Hubbard model, have been constructed previously by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

Numerical modelling of tide-induced beach water table fluctuations

Field studies have shown that the elevation of the beach groundwater table varies with the tide and such variations affect significantly beach erosion or accretion. In this paper, we present a BEM (Boundary Element Method) model for simulating the tidal fluctuation of the beach groundwater table. The model solves the two-dimensional flow equation subject to free and moving boundary conditions, including the seepage dynamics at the beach face. The simulated seepage faces were found to agree with the predictions of a simple model (Turner, 1993). The advantage of the present model is, however, that it can be used with little modification to simulate more complicated cases, e.g., surface recharge from rainfall and drainage in the aquifer may be included (the latter is related to beach dewatering technique). The model also simulated well the field data of Nielsen (1990). In particular, the model replicated three distinct features of local water table fluctuations: steep rising phase versus flat falling phase, amplitude attenuation and phase lagging.

PREDICTION OF FAT-FREE MASS BY BIOELECTRICAL IMPEDANCE ANALYSIS IN OLDER ADULTS FROM DEVELOPING COUNTRIES: A CROSS-VALIDATION STUDY USING THE DEUTERIUM DILUTION METHOD

Objective: Several limitations of published bioelectrical impedance analysis (BIA) equations have been reported. The aims were to develop in a multiethnic, elderly population a new prediction equation and cross-validate it along with some published BIA equations for estimating fat-free mass using deuterium oxide dilution as the reference method. Design and setting: Cross-sectional study of elderly from five developing countries. Methods: Total body water (TBW) measured by deuterium dilution was used to determine fat-free mass (FFM) in 383 subjects. Anthropometric and BIA variables were also measured. Only 377 subjects were included for the analysis, randomly divided into development and cross-validation groups after stratified by gender. Stepwise model selection was used to generate the model and Bland Altman analysis was used to test agreement. Results: FFM = 2.95 - 3.89 (Gender) + 0.514 (Ht(2)/Z) + 0.090 (Waist) + 0.156 (Body weight). The model fit parameters were an R(2), total F-Ratio, and the SEE of 0.88, 314.3, and 3.3, respectively. None of the published BIA equations met the criteria for agreement. The new BIA equation underestimated FFM by just 0.3 kg in the cross-validation sample. The mean of the difference between FFM by TBW and the new BIA equation were not significantly different; 95% of the differences were between the limits of agreement of -6.3 to 6.9 kg of FFM. There was no significant association between the mean of the differences and their averages (r = 0.008 and p = 0.2). Conclusions: This new BIA equation offers a valid option compared with some of the current published BIA equations to estimate FFM in elderly subjects from five developing countries.

Use of lignin extracted from different plant sources as standards in the spectrophotometric acetyl bromide lignin method

A nongravimetric acetyl bromide lignin (ABL) method was evaluated to quantify lignin concentration in a variety of plant materials. The traditional approach to lignin quantification required extraction of lignin with acidic dioxane and its isolation from each plant sample to construct a standard curve via spectrophotometric analysis. Lignin concentration was then measured in pre-extracted plant cell walls. However, this presented a methodological complexity because extraction and isolation procedures are lengthy and tedious, particularly if there are many samples involved. This work was targeted to simplify lignin quantification. Our hypothesis was that any lignin, regardless of its botanical origin, could be used to construct a standard curve for the purpose of determining lignin concentration in a variety of plants. To test our hypothesis, lignins were isolated from a range of diverse plants and, along with three commercial lignins, standard curves were built and compared among them. Slopes and intercepts derived from these standard curves were close enough to allow utilization of a mean extinction coefficient in the regression equation to estimate : lignin concentration in any plant, independent of its botanical origin. Lignin quantification by use of a common regression equation obviates the steps of lignin extraction, isolation, and standard curve construction, which substantially expedites the ABL method. Acetyl bromide lignin method is a fast, convenient analytical procedure that may routinely be used to quantify lignin.

The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Exact solution for the Bariev model with boundary fields

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting K-matrices leading to four different types of boundary fields are obtained by solving the reflection equations. The models are exactly solved by means of the algebraic nested Bethe ansatz method and the four sets or Bethe ansatz equations as well as their corresponding energy expressions are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.