"Provides a wide range of information on the composition, utilization, and evaluation of colorants and pigments in food, pharmaceuticals, and cosmetic products. Tabulates key data for food, drug, and cosmetic colorants by Color Index Numbers. Thoroughly describes the relationships between coloring reactions."

This book aims at presenting the field of Quantum Information Theory in an intuitive, didactic and self-contained way, taking into account several multidisciplinary aspects. Therefore, this books is particularly suited to students and researchers willing to grasp fundamental concepts in Quantum Computation and Quantum Information areas. The field of Quantum Information Theory has increased significantly over the last three decades. Many results from classical information theory were translated and extended to a scenario where quantum effects become important. Most of the results in this area allows for an asymptotically small probability of error to represent and transmit information efficiently. Claude E.Shannon was the first scientist to realize that error-free classical information transmission can be accomplished under certain conditions. More recently, the concept of error-free classical communication was translated to the quantum context. The so-called Quantum Zero-Error Information Theory completes and extends the Shannon Zero-Error Information Theory.

Classic undergraduate text explores wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, and the structure of simple and complex molecules. Numerous tables and figures.

This book offers a structured algebraic and geometric approach to the classification and construction of quantum codes for topological quantum computation. It combines key concepts in linear algebra, algebraic topology, hyperbolic geometry, group theory, quantum mechanics, and classical and quantum coding theory to help readers understand and develop quantum codes for topological quantum computation. One possible approach to building a quantum computer is based on surface codes, operated as stabilizer codes. The surface codes evolved from Kitaev's toric codes, as a means to developing models for topological order by using qubits distributed on the surface of a toroid. A significant advantage of surface codes is their relative tolerance to local errors. A second approach is based on color codes, which are topological stabilizer codes defined on a tessellation with geometrically local stabilizer generators. This book provides basic geometric concepts, like surface geometry, hyperbolic geometry and tessellation, as well as basic algebraic concepts, like stabilizer formalism, for the construction of the most promising classes of quantum error-correcting codes such as surfaces codes and color codes. The book is intended for senior undergraduate and graduate students in Electrical Engineering and Mathematics with an understanding of the basic concepts of linear algebra and quantum mechanics.

Everything around us - trees, buildings, food, light, water, air and even ourselves - is composed of minute particles, smaller than a nanometre (a billionth of a metre). Quantum physics is the science of these particles and without it none of our electronic devices, from smartphones to computers and microwave ovens, would exist. But quantum physics also pushes us to the very boundaries of what we know about science, reality and the structure of the universe. The world of quantum physics is an amazing place, where quantum particles can do weird and wonderful things, acting totally unlike the objects we experience in day-to-day life. How can atoms exist in two places at once? And just how can a cat be dead and alive at the same time? Find out more with this entertaining illustrated guide to the fascinating, mysterious world of quantum physics.

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory ofcolorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and the maximum number of colors. This feature pervades the theory, methods, algorithms, and applications of mixed hypergraph coloring. The book has broad appeal. It will be of interest to bothpure and applied mathematicians, particularly those in the areas of discrete mathematics, combinatorial optimization, operations research, computer science, software engineering, molecular biology, and related businesses and industries. It also makes a nice supplementary text for courses in graph theory and discrete mathematics. This is especially useful for students in combinatorics and optimization. Since the area is new, students will have the chance at this stage to obtain results that maybecome classic in the future.