Booking Space

Unifies the field of optimization with a few geometric principles. The number of books that can legitimately be called classics in their fields is small indeed, but David Luenberger's Optimization by Vector Space Methods certainly qualifies. Not only does Luenberger clearly demonstrate that a large segment of the field of optimization can be effectively unified by a few geometric principles of linear vector space theory, but his methods have found applications quite removed from the engineering problems to which they were first applied. Nearly 30 years after its initial publication, this book is still among the most frequently cited sources in books and articles on financial optimization. The book uses functional analysis the study of linear vector spaces to impose simple, intuitive interpretations on complex, infinite-dimensional problems. The early chapters offer an introduction to functional analysis, with applications to optimization. Topics addressed include linear space, Hilbert space, least-squares estimation, dual spaces, and linear operators and adjoints. Later chapters deal explicitly with optimization theory, discussing Optimization of functionals Global theory of constrained optimization Local theory of constrained optimization Iterative methods of optimization. End-of-chapter problems constitute a major component of this book and come in two basic varieties. The first consists of miscellaneous mathematical problems and proofs that extend and supplement the theoretical material in the text; the second, optimization problems, illustrates further areas of application and helps the reader formulate and solve practical problems. For professionals andgraduate students in engineering, mathematics, operations research, economics, and business and finance, Optimization by Vector Space Methods is an indispensable source of problem-solving tools.

Though human fascination with polyhedra can be traced back to the time of Pythagoras, only in the twentieth century have architects begun to fully appreciate and exploit their advantages as elements of structure and design. In Beyond the Cube, J. Franois Gabriel and a team of leading space frame experts from around the world examine the practical as well as theoretical aspects of space frames. They discuss some of the most memorable examples and practitioners of twentieth-century space frame design: Louis Kahn and the Yale University Art Gallery, Buckminster Fuller's geodesic domes, Philip Johnson's radically different approach to space frames in the Crystal Cathedral, and I. M. Pei's Javits Convention and Exhibition Center, among others. In an extended discussion on the theory of polyhedra, Beyond the Cube explores the ways in which coupling cube to tetrahedron produces an array of other polyhedra that enable the expansion of design sources beyond the cube. The book examines the geometric laws that govern many of these shapes prisms, antiprisms, domes, and folded plate structures, as well as space frames and surveys the symbolic meanings ascribed to many polyhedra. Structural aspects of polyhedra are examined from two points of view, that of the structural engineer and that of the designer using CAD for the purpose of visualization and formal transformations. The book concludes with a look toward the future of polyhedra in architecture, including tensegrity structures, in which structural elements under compression are not in direct contact with each other; space labyrinths, made of a continuous surface dividing space into two parts; and quasicrystals,three-dimensional manifestations of higher-dimensional polyhedra. The final chapter examines the architectural spaces found within space frames, including "hexmods," "star beams," and the many other spaces that have yet to be named.

Ambient space - The ambient space, in mathematics, is the space surrounding a mathematical object. For example, a line may be studied in insolation, or it may be studied as an object in two-dimensional space -- in which case the ambient space is the plane, or as an object in three-dimensional space -- in which case the ambient space is three dimensional.

Hausdorff space - In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which points can be separated by neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the Hausdorff condition is the most frequently used and discussed .

Space partitioning - In mathematics, space partitioning is the process of dividing a space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divides a space into non-overlapping regions.

ProPhoto RGB color space - The ProPhoto RGB color space is an RGB color space, developed by Kodak, that offers an especially large gamut designed for use with photographic output in mind. The ProPhoto RGB color space encompasses over 90% of the visible colors specified by the CIE L*a*b* color space, making ProPhoto even larger than the Adobe Wide Gamut RGB color space.

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