This reference work covers the classical, transitional and modern periods. Editors and contributors cover an international scope of Arabic literature in many countries.

Encyclopedia of Arabic Literature

In this letter, a general orthogonal-modulation model to develop new modulations and to identify some widely used modulation schemes is proposed. Based on this general framework, an optimum scheme for non-Gaussian channels under a given set of constraints can be derived. In software radios, the modulation should be changed by tracking this optimum scheme. The proposed model is based on orthonormal vectors, which are obtained by multidimensional rotations. Several widely used modulation schemes are renamed by their consecutive multidimensional rotation angles within the proposed framework. New modulation examples in continuous-wave interference and impulse interference channels are given to illustrate the corresponding local optima.

A general orthogonal modulation model for software radios

The IBM MathML Expression Editor is a two-dimensional mathematical editor for expressions encoded using MathML content and presentation elements. It allows a user to interact with the visual presentation of an expression, while simultaneously creating the underlying content structure of the expression. This paper describes the internal expression framework used by the editor to represent the content and presentation structures, the layout mechanisms used to transform content into presentation, the structural navigation conventions used to select subexpressions, the editing templates used to support visual input of MathML content expressions, and the customization framework that allows for a fully extensible set of content operators, including complete support for MathML 2.0 content elements as well as user-defined function symbols and operators.

Coordinating mathematical content and presentation markup in interactive mathematical documents

Satellite attitude control using a novel Constrained Magnetic Linear Quadratic Regulator

The aim of this paper is to describe an introductory mathematics course for primary student teachers and to explain the philosophy behind it. The paper is structured as follows: It starts with a general plea for placing the mathematical training of any category of students into their professional context. Then the context of primary education in Germany, with its strong emphasis on the principle of learning by discovery, is sketched.

The Alpha and Omega of Teacher Education: Organizing Mathematical Activities

1 linear Functions.- 1.1 Linear Functions.- 1.2 Local Linearity.- 1.3 Matrices.- 1.4 More Linearity.- 2 Linear Geometry.- 2.1 Linear Geometry in the Plane.- 2.2 Vectors and Lines in the Plane.- 2.3 Linear Geometry in Space.- 2.4 An Introduction to Linear Perspective.- 3 Systems of Linear Equations.- 3.1 Systems of Linear Equations.- 3.2 Gaussian Elimination.- 3.3 Gauss-Jordan Elimination.- 3.4 Matrix Rank and Systems of Linear Equations.- 3.5 The Simplex Algorithm.- 4 Basic Matrix Algebra.- 4.1 The Matrix Product: A Closer Look.- 4.2 Fibonacci Numbers and Difference Equations.- 4.3 The Determinant.- 4.4 Properties and Applications of the Determinant.- 4.5 The LU-Decomposition.- 5 Key Concepts of Linear Algebra in Rn.- 5.1 Linear Combinations and Subspaces.- 5.2 Linear Independence.- 5.3 Basis and Dimension.- 6 More Vector Geometry.- 6.1 The Dot Product.- 6.2 Angles and Projections.- 6.3 The Cross Product.- 7 Eigenvalues and Eigenvectors of Matrices.- 7.1 Eigenvalues and Eigenvectors.- 7.2 Eigenspaces and Diagonalizability.- 7.3 Symmetric Matrices and Probability Matrices.- 8 Matrices as Linear Transformations.- 8.1 Linear Transformations.- 8.2 Using Linear Transformations.- 8.3 Change of Basis.- 9 Orthogonality and Least-Squares Problems.- 9.1 Orthogonality and the Gram-Schmidt Process.- 9.2 Orthogonal Projections.- 9.3 Least-Squares Approximations.- Answers to Odd-Numbered Problems.

Linear Functions and Matrix Theory

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Linear Functions and Matrix Theory