Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups.

The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs.

Encompassing many of the main areas of the factorization theory, this book explores problems in which the underlying factored group is cyclic.

Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups. The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs. Encompassing many of the main areas of the factorization theory, this book explores problems in which the underlying factored group is cyclic.

Diode lasers use nearly microscopic chips of gallium-arsenide or other exotic semiconductor material to generate coherent light in a very small package. Their compact size, reliability, and low cost means that they find applications in all aspects of modern technology-most importantly they drive modern optical telecommunication systems.
Diode Lasers presents a comprehensive introduction to the principles and operation of diode lasers. It begins with a review of semiconductor physics and laser fundamentals, before describing the most basic homojunction laser. Later chapters describe more advanced laser types and their applications, and the book concludes with chapters describing the most recently developed and exotic laser designs. The author's intuitive style, coupled with an extensive set of worked examples and sample problems, make this the ideal introduction for undergraduate and graduate level students.

American hall-of-famer Tom Petty had a musical career that spanned four decades with Tom Petty and the Heartbreakers, and also notably included the co-founding of supergroup The Traveling Wilburys. As a songwriter and rock star, he was among the most successful of his time. His work appealed across socioeconomic boundaries to a diverse group of fans, and this collection of new essays explores this phenomenon. Other topics covered include Petty's writing process, his political stances, and the psychology behind his music.

Since the war of 2020, only the fearless or stupid would dare travel the trade route between southern America and Europe, the trail of ocean commonly called The Blood Current.

These waters are the prime target of the newly risen pirate regime, the sole law in the waters. The now weakened militaries can't stop them, not even the newly formed ASIS.

But when threat of a full scale war and nuclear threat rise from these waters, so does a rag-tag renegade group of pirates dead set on restoring order and claiming some sort of peace.

Josh Webbers leads the group as their captain. With intelligence and unmatched courage he leads his crew: Dusty Sandon, the famous 2020 sniper; Alby Weston, Demo expert; Hannah Thornburg, who works in intel acquisitions; Daniel McHarrow, the youngest known strategist; Levi Kirill; Cody Preston; and Rusty Kingser. But are they able to withstand the onslaught of pirates, or even the organized military regimes they're up against?