A wide variety of media can be used in learning, including distance learning, such as print, lectures, conference sections, tutors, pictures, video, sound, and computers. Any one instance of distance learning will make choices among these media, perhaps using several.

Multimedia in Learning

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Complex biological systems and cellular networks may underlie most genotype to phenotype relationships. Here, we review basic concepts in network biology, discussing different types of interactome networks and the insights that can come from analyzing them. We elaborate on why interactome networks are important to consider in biology, how they can be mapped and integrated with each other, what global properties are starting to emerge from interactome network models, and how these properties may relate to human disease.

Interactome networks and human disease

Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

Boundary value problems

Fundamental theory: Holomorphic functions and domains of holomorphy Implicit functions and analytic sets The Poincare, Cousin, and Runge problems Pseudoconvex domains and pseudoconcave sets Holomorphic mappings Theory of analytic spaces: Ramified domains Analytic sets and holomorphic functions Analytic spaces Normal pseudoconvex spaces Bibliography Index.

Function theory in several complex variables

In this article the jump problem for monogenic functions (Clifford holomorphicity) on the boundary of a Jordan domain in Euclidean spaces is investigated. We shall establish some criteria that imply the uniqueness of the solution in terms of a natural analogue of removable singularities in the plane to ℝn+1 (n ≥ 2). Sufficient conditions to extend monogenically continuous Clifford algebra valued functions across a hypersurface are proved.

Jump problem and removable singularities for monogenic functions

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil–Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

Integration over non-rectifiable curves and Riemann boundary value problems

Several studies have focused on identifying the significant behavioral predictors of learning performances in web-based courses by examining the log data variables of learning management systems, i...

Emotions, Motivation, Cognitive–Metacognitive Strategies, and Behavior as Predictors of Learning Performance in Blended Learning:

The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel–Pompeiu and the Clifford–Cauchy formula have been obtained by using a (2 × 2) circulant matrix formulation. In the meantime, the basic setting has been established for so-called quaternionic Hermitean Clifford analysis, a theory centred around the simultaneous null solutions, called q-Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford–Cauchy integral formula, by following a (4 × 4) circulant matrix approach.

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Juan Bory-Reyes

Papers

Jump problem and removable singularities for monogenic functions

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

Integration over non-rectifiable curves and Riemann boundary value problems

Emotions, Motivation, Cognitive–Metacognitive Strategies, and Behavior as Predictors of Learning Performance in Blended Learning:

Cauchy Integral Formulae in Quaternionic Hermitean Clifford Analysis