This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization.

"Mathematical Olympiad Treasures" aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience toapply techniques and strategies to real-worldproblems.

Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.

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A guide to the 3GPP-specified 5G physical layer with a focus on the new beam-based dimension in the radio system 5G New Radio: A Beam-based Air Interface is an authoritative guide to the newly 3GPP-specified 5G physical layer. The contributors--noted experts on the topic and creators of the actual standard--focus on the beam-based operation which is a new dimension in the radio system due to the millimeter wave deployments of 5G. The book contains information that complements the 3GPP specification and helps to connect the dots regarding key features. The book assumes a basic knowledge of multi-antenna technologies and covers the physical layer aspects related to beam operation, such as initial access, details of reference signal design, beam management, and DL and UL data channel transmission. The contributors also provide a brief overview of standardization efforts, IMT-2020 submission, 5G spectrum, and performance analysis of 5G components. This important text: Contains information on the 3GPP-specified 5G physical layer Highlights the beam-based operation Covers the physical layer aspects related to beam operation Includes contributions from experts who created the standard Written for students and development engineers working with 5G NR, 5G New Radio: A Beam-based Air Interface offers an expert analysis of the 3GPP-specified 5G physical layer.

This fascinating book holds an important key. Whether you're interested in the science of thinking and beliefs, how your own mind operates, how others control your thoughts, why things just don't work out for you, how you can create the life you've always wanted, how you can realize your true potential, how you can find peace, or, on a grander scale, how you can help make the world a better place, this book provides insights for all. Simply reading it will open your eyes to new worlds of possibilities. You'll change once you're exposed to the illusions most live under and by, and putting into practice any of these very simple teachings will open the door for you to achieve your highest potential. "Choices and Illusions" tells the story of one man's journey into the workings of the human mind and our reason for being. The adventure is every bit as exciting as the best scientific discoveries. Eldon Taylor's approach is pragmatic, and his conclusions are inspirational and soul enhancing. Along the journey, you'll hear fantastic stories of divine intervention, see why you think and do what you don't wish to do, and understand the very clear message that it's never too late to be happy and succeed, regardless of your past actions. Eldon says, "Many believe that self-help and self-improvement is about rags to riches, failure to success, and so forth, when indeed it's the beginning of a journey into self-discovery. Inside every human being is an eternal truth and a life purpose. Using our mind power is simply starting the engine on that path toward highest self-actualization."