Formal description, compression and transformation of digital pictures II. Picture algebra and geometry

In an earlier paper (Part I) we described the construction of Hermite code for multiple grey-level pictures using the concepts of vector spaces over Galois Fields. In this paper a new algebra is worked out for Hermite codes to devise algorithms for various transformations such as translation, reflection, rotation, expansion and replication of the original picture. Also other operations such as concatenation, complementation, superposition, Jordan-sum and selective segmentation are considered. It is shown that the Hermite code of a picture is very powerful and serves as a mathematical signature of the picture. The Hermite code will have extensive applications in picture processing, pattern recognition and artificial intelligence.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

A decision method for elementary algebra and geometry

"This report...was written while the project was a part of Douglas Aircraft Co., inc."

A treatise of algebra, in three parts : containing I. The fundamental rules and operations. II. The composition and resolution of equations of all degrees; and the different affections of their roots. III. The application of algebra and geometry to each other : to which is added, an appendix, concerning the general properties of geometrical lines /

Mode of access: Internet.

Outline studies in arithmetic, algebra and geometry,

Cover-title.

Lectures on fundamental concepts of algebra and geometry,

Mode of access: Internet.

A treatise of algebra, in three parts. Containing I. The fundamental rules and operations; II. The composition and resolution of equations of all degrees, and the different affections of their roots; III. The application of algebra and geometry to each other. To which is added an appendix concerning the general properties of geometrical lines.

Appendix in Latin.

A treatise on infinitesimal calculus, containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics.

Vol. 3 and 4 form the author's Treatise on analytical mechanics.

The basic concepts of mathematics; a companion to current textbooks on algebra and analytic geometry.

pt.1. Algebra.

Practical mathematics; being the essentials of arithmetic, geometry, algebra and trigonometry.

Mode of access: Internet.

Practical mathematics : being the essentials of arithmetic, geometry, algebra and trigonometry /

Mode of access: Internet.

An introduction to algebra : with notes and observations : designed for the use of schools and places of public education : to which is added an appendix on the application of algebra to geometry /

Mode of access: Internet.

Bonnycastle's introduction to algebra : containing the indeterminate and diophantine analysis, and the application of algebra to geometry.

At head of title: Dean's stereotype edition.

The differential and integral calculus : containing differentiation, integration, development, series, differential equations, differences, summation, equations of differences, calculus of variations, definite integrals,--with applications to algebra, plane geometry, solid geometry, and mechanics. Also, Elementary illustrations of the differential and integral calculus /

First issued in 25 parts, July 15, 1836, to June 1, 1842.

A collection of problems, designed to facilitate the application of algebra to geometry, and of the principles of natural philosophy to practical questions.

Mode of access: Internet.