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Completion Problems on Operator Matrices
Completion problems for operator matrices are concerned with the question of whether a partially specified operator matrix can be completed to form an operator of a desired type. The research devoted to this topic provides an excellent means to investigate the structure of operators. This book provides an overview of completion problems dealing with completions to different types of operators and can be considered as a natural extension of classical results concerned with matrix completions. The book assumes some basic familiarity with functional analysis and operator theory. It will be useful for graduate students and researchers interested in operator theory and the problem of matrix completions.
Algebraic Properties of Generalized Inverses
This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.
Characterization of Probability Distributions on Locally Compact Abelian Groups
It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By no...
Mathematical Reviews
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Algebraic Properties of Generalized Inverses
This book addresses selected topics in the theory of generalized inverses. Following a discussion of the "reverse order law" problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.--
The Rise of Metallurgy in Eurasia
The Rise of Metallurgy in Eurasia is a landmark study in the evolution of early metallurgy in the Balkans. It demonstrates that far from being a rare and elite practice, the earliest metallurgy in the world was a common and communal craft activity.
Teucrium Species: Biology and Applications
Teucrium species are an intersting object of research in the various aspects of science with multiple applications. With more than 300 species, Teucrium is one of the largest and well distributed genera of the Lamiaceae family. Known medicinal Teucrium species have a long traditional use as well as different potential applications in pharmacy, food and beverage industry. Teucrium species are very rich in a variety of secondary metabolites with significant biological activities. Based on that, the book contains 15 chapters which discusses recent advances in exploring the unique features of Teucrium species including morphology, systematics, taxonomy, biogeography, ethnobotany, phytochemistry,...
Fourier Transforms
The main purpose of this book is to provide a modern review about recent advances in Fourier transforms as the most powerful analytical tool for high-tech application in electrical, electronic, and computer engineering, as well as Fourier transform spectral techniques with a wide range of biological, biomedical, biotechnological, pharmaceutical, and nanotechnological applications. The confluence of Fourier transform methods with high tech opens new opportunities for detection and handling of atoms and molecules using nanodevices, with potential for a large variety of scientific and technological applications.
Carotenoids
Carotenoids are one of the most widespread pigment groups distributed in nature; more than 700 natural carotenoids have been described so far. These pigments are known for versatile roles they play in living organisms; however, their most pivotal function is involvement in scavenging of reactive oxygen species and photoprotection. In the same time, carotenoids as natural pigments with important biological activities, such as antioxidant and provitamin A activity, have a great potential in the food, feed and pharmaceutical industries. They can be either extracted from plants and algae or synthesized by various microorganisms, including bacteria, yeasts, filamentous fungi and microalgae.
