Search results for "complex analysis"

Correlation at low temperature I. Exponential decay

2003

Abstract The present paper generalizes the analysis in (Ann. H. Poincare 1 (2000) 59, Math. J. (AMS) 8 (1997) 123) of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general Hamiltonian function with pair interaction. The novelty, as compared to [2,20], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other extrema. Our derivation of exponential decay of correlations goes through the spectral analysis of a deformed Laplacian closely related to the Witten Laplacian studied in [2,20]. We prove that this Laplacian has a spectral gap above zero…

Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six

2017

We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases of the linear spaces generated by the real and imaginary parts of $G(a_1,\ldots,a_w;1)$ and present a table for expressing them as linear combinations of the elements of the bases.

Gravity, Non-Commutative Geometry and the Wodzicki Residue

1993

We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki residue Res$(D^{-n+2})$ is the integral of the second coefficient of the heat kernel expansion of $D^{2}$. We use this result to derive a gravity action for commutative geometry which is the usual Einstein Hilbert action and we also apply our results to a non-commutative extension which, is given by the tensor product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological co…

Low-temperature spectrum of correlation lengths of the XXZ chain in the antiferromagnetic massive regime

2015

We consider the spectrum of correlation lengths of the spin-$\frac{1}{2}$ XXZ chain in the antiferromagnetic massive regime. These are given as ratios of eigenvalues of the quantum transfer matrix of the model. The eigenvalues are determined by integrals over certain auxiliary functions and by their zeros. The auxiliary functions satisfy nonlinear integral equations. We analyse these nonlinear integral equations in the low-temperature limit. In this limit we can determine the auxiliary functions and the expressions for the eigenvalues as functions of a finite number of parameters which satisfy finite sets of algebraic equations, the so-called higher-level Bethe Ansatz equations. The behavio…

Determination of two-dimensional zero-magnetic-fieldI-Vexponent inBi2Sr2CaCu2O8+δ

2006

Determination of pesticide residues in fruit and vegetables.

1996

A review concerning the determination of pesticide residues in fruit and vegetables is presented. The basic principles and recent developments in the extraction and quantitation of pesticides are discussed. Consideration is given to solid phase and supercritical extraction techniques, automation and robotic systems, and immunoassay procedures.

Comparison among three boundary element methods for torsion problems: CPM, CVBEM, LEM

2011

This paper provides solutions for De Saint-Venant torsion problem on a beam with arbitrary and uniform cross-section. In particular three methods framed into complex analysis have been considered: Complex Polynomial Method (CPM), Complex Variable Boundary Element Method (CVBEM) and Line Element-less Method (LEM), recently proposed. CPM involves the expansion of a complex potential in Taylor series, computing the unknown coefficients by means of collocation points on the boundary. CVBEM takes advantage of Cauchy’s integral formula that returns the solution of Laplace equation when mixed boundary conditions on both real and imaginary parts of the complex potential are known. LEM introduces th…

Method to find the Minimum 1D Linear Gradient Model for Seismic Tomography

2016

The changes in the state of a geophysical medium before a strong earthquake can be found by studying of 3D seismic velocity images constructed for consecutive time windows. A preliminary step is to see changes with time in a minimum 1D model. In this paper we develop a method that finds the parameters of the minimum linear gradient model by applying a two-dimensional Taylor series of the observed data for the seismic ray and by performing least-square minimization for all seismic rays. This allows us to obtain the mean value of the discrete observed variable, close to zero value.

Effects of a mixture of vegetable and essential oils and fatty acid potassium salts on Tetranychus urticae and Phytoseiulus persimilis.

2008

Laboratory trials were carried out to evaluate the toxicity and the influence of a commercial mixture of vegetal, essential oils, and potassium salts of fatty acids (Acaridoil 13SL) on the population growth rate (r(i)--instantaneous rate of increase) of two mite species, the phytophagous Tetranychus urticae Koch and the predator Phytoseiulus persimilis Athias-Henriot. A residue of 1.3 mg/cm(2) of pesticide solution was harmless for Ph. persimilis eggs, while a moderate mortality of eggs and of larvae from treated eggs of T. urticae, was observed (53.8%). The pesticide also caused a delay in the postembryonic development of the tetranychid. Moreover, 83.4% mortality was reported for treated …

Complex, energy-independent, local potential reproducing an absorptive phase shift and a bound state

1994

The triton binding energy, and the partly real and partly complex neutron-deuteron doublet channel elastic scattering phase shifts, calculated by means of the exact three-body theory, are used as input in the fixed-[ital l] inverse scattering theory of Marchenko. The local potentials obtained hereby are independent of energy, and complex. Their strong imaginary part reflects the strong absorption in the doublet channel arising from the opening of the deuteron breakup channel. For total orbital angular momentum [ital l] different from zero the potentials are unique, reproducing the input phase shift in the whole energy region. For [ital l]=0 where there exists, in addition, a bound state we …