On the Barnes double zeta and Gamma functions

We present a complete description of the analytic properties of the Barnes double zeta and Gamma functions. (C) 2009 Elsevier Inc. All rights reserved.

Wannier functions of isolated bands in one-dimensional crystals

We present a simple procedure to obtain the maximally localized Wannier function of isolated bands in one-dimensional crystals with or without inversion symmetry. First, we discuss the generality of dealing with real Wannier functions. Next, we use a transfer-matrix technique to obtain nonoptimal Bloch functions which are analytic in the wave number. This produces two classes of real Wannier functions. Then, the minimization of the variance of the Wannier functions is performed, by using the antiderivative of the Berry connection. In the case of centrosymmetric crystals, this procedure leads to the Wannier-Kohn functions. The asymptotic behavior of the Wannier functions is also analyzed. The maximally localized Wannier functions show the expected exponential and power-law decays. Instead, nonoptimal Wannier functions may show reduced exponential and anisotropic power-law decays. The theory is illustrated with numerical calculations of Wannier functions for conduction electrons in semiconductor superlattices.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

Topological K-equivalence of analytic function-germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 Elsevier B.V. All rights reserved.

Axial anomaly through analytic regularization

In this work we consider the two-point Green's functions in (1 + 1)-dimensional quantum electrodynamics and show that the correct implementation of analytic regularization gives a gauge invariant result for the vacuum polarization amplitude and the correct coefficient for the axial anomaly.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

Grid-based histogram arithmetic for the probabilistic analysis of functions

The selection of predefined analytic grids (partitions of the numeric ranges) to represent input and output functions as histograms has been proposed as a mechanism of approximation in order to control the tradeoff between accuracy and computation times in several áreas ranging from simulation to constraint solving. In particular, the application of interval methods for probabilistic function characterization has been shown to have advantages over other methods based on the simulation of random samples. However, standard interval arithmetic has always been used for the computation steps. In this paper, we introduce an alternative approximate arithmetic aimed at controlling the cost of the interval operations. Its distinctive feature is that grids are taken into account by the operators. We apply the technique in the context of probability density functions in order to improve the accuracy of the probability estimates. Results show that this approach has advantages over existing approaches in some particular situations, although computation times tend to increase significantly when analyzing large functions.

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Zeta functions and Eisenstein series on classical groups

We construct an Euler product from the Hecke eigenvalues of an automorphic form on a classical group and prove its analytic continuation to the whole complex plane when the group is a unitary group over a CM field and the eigenform is holomorphic. We also prove analytic continuation of an Eisenstein series on another unitary group, containing the group just mentioned defined with such an eigenform. As an application of our methods, we prove an explicit class number formula for a totally definite hermitian form over a CM field.

Analytic function theory.

Includes bibliographies.

Calculus, with analytic geometry.

Includes index.

An elementary treatise on curves, functions, and forces.

Available on demand as hard copy or computer file from Cornell University Library.

Practical analytic geometry with applications to aircraft /

"Answers": p. 273-277.

The Power of the Palestinian Landscape : An exploratory study of the functions of power using aerial image interpretation

The Palestinian region is changing rapidly, with both economic and cultural consequences. One way of approaching this very political process is thru the concept of landscape. By viewing the region as a multiprocessual, dynamic landscape the analysis allows for a holistic read where historical and contemporary projections, interpretations and notions of power are fused. This thesis draws on the scholarly fields of humanistic landscape research and aerial image interpretation as well as theories of orientalism and power. A case study of two regions of the West Bank is performed; interviews and observations provide localized knowledge that is then used in open-access image interpretation. By performing image interpretations this thesis explores the power embedded in mapping and the possible inclinations the development towards open-access geospatial analytic tools could have on the functions of power in the Palestinian landscape. By investigating the spatial configuration of the Palestinian landscape and tracing its roots this thesis finds four major themes that are particularly pivotal in the processual change of the Palestinian landscape: the Israeli/Palestinian time-space, the blurring of the conflict, the dynamics of the frontier region and the orientalist gaze.