The bicomplex quantum Coulomb potential problem

Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper provides an analytical solution of the quantum Coulomb potential problem formulated in terms of bicomplex numbers. We define the problem by introducing a bicomplex hamiltonian operator and extending the canonical commutation relations to the form [X_i,P_k] = i_1 hbar xi delta_{ik}, where xi is a bicomplex number. Following Pauli's algebraic method, we find the eigenvalues of the bicomplex hamiltonian. These eigenvalues are also obtained, along with appropriate eigenfunctions, by solving the extension of Schrodinger's time-independent differential equation. Examples of solutions are displayed. There is an orthonormal system of solutions that belongs to a bicomplex Hilbert space.Comment: Clarifications; some figures removed; version to appear in Can. J. Phy

Finite-Dimensional Bicomplex Hilbert Spaces

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including the spectral decomposition theorem. Applications to concepts relevant to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page

On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure

Lower Tropospheric Temperature Variability Over the USA: a GIS Approach

We use the high resolution North American Regional Analysis (NARR) dataset to build for the United States a Temperature Change Index (TCI) based on four contributing variables derived from the layer-averaged temperature and lapse rate of the 1000mb - 700mb layer (near-surface to 3000 meters) for the 1979-2008 period. The analysis uses Geographic Information Systems (GIS) methods to identify distinct regional patterns based on aggregate temperature trends and variability scores. The resulting index allows us to identify and compare regions that experience high (low) temperature trends and variability that are referred to as hot spots (cold spots). The upper Midwest emerges as the region that experiences the largest increases and variability, due to the large magnitude of variability and trends of all variables. In contrast, the lowest TCI scores are observed over southeastern regions and the Rocky Mountains. Regarding landscape characteristics, high TCI scores occur mostly over agricultural lands (thus implying the problem of temperature variability-dependant crop yields) while low scores generally prevail over forests. At a seasonal time scale, the largest and most contrasting TCI scores occur during the winter and, to a lesser extent, fall seasons. All variables used to build the TCI show well defined seasonal patterns and differences, especially between winter and summer. Our method, based on the use of thickness layers, provides a more complete analysis than methods based on monolevel data and confirms that temperature is a robust component of climate change in general and must be included in any study that deals with vulnerability assessment of climate change risks

Advances in Spatial Data Infrastructure, Acquisition, Analysis, Archiving and Dissemination

The authors review recent contributions to the state-of-thescience and benign proliferation of satellite remote sensing, spatial data infrastructure, near-real-time data acquisition, analysis on high performance computing platforms, sapient archiving, multi-modal dissemination and utilization for a wide array of scientific applications. The authors also address advances in Geoinformatics and its growing ubiquity, as evidenced by its inclusion as a focus area within the American Geophysical Union (AGU), European Geosciences Union (EGU), as well as by the evolution of the IEEE Geoscience and Remote Sensing Society's (GRSS) Data Archiving and Distribution Technical Committee (DAD TC)