A forceful study of an elite group of men chosen to form the U. S. Marines' only medium bomber group during WWII. Verterans recall their service flying combat missions against enemy garrisons on Bougainville and New Ireland, and later in the dramatic rocket and ground-strafing attacks in the Philippines. Detailed list of individual squadron aircraft and personnel losses, and all known PBJs assigned to units overseas.

Sighted Sub, Sank Same examines the United States Naval air campaign against German U-boats prowling for allied merchant shipping traversing the waters of the Atlantic, Caribbean, and Mediterranean; an economic war waged to cut the lifeline of food and armaments sailing across the Atlantic from North America. This battle of the Atlantic evolved into a far-ranging conflict beyond the North Atlantic and the eastern seaboard of the United States. It covered the frigid waters off Iceland down to the warm waters of Florida, through the Caribbean Sea, across the ocean to the Bay of Biscay, the Mediterranean Sea, down to Africa, and across the South Atlantic to Brazil's southern tip. Nazi Germany's efforts to deny supplies from reaching Europe came at a high price, losing 783 U-boats and approximately 30,000 men between 1939 and 1945 with land and carrier-based naval air units sinking 83 German submarines of the 159 sunk by American aircraft. German allies saw their submarines targeted as well in the Atlantic with Imperial Japanese submarine I-52 and the Italian Archimede falling victim to American naval aircraft armed with depth bombs or acoustic homing torpedoes. This story of the United States Navy's use of air power to hunt down and destroy German submarines unfolds in dramatic detail in Sighted Sub, Sank Same. The book contains over 200 colour and black and white photographs allowing for a visual imagery of the campaign while personal interviews, interrogation reports, personal correspondence, and after-action reports weave a fascinating history about the naval air campaign in the Atlantic, Caribbean, and Mediterranean Theaters during World War II.

This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case'. Creating a coherent picture of numerous investigations and scattered notions of the past 50 years, this work carefully introduces spectral flow, the Witten index and the spectral shift function and describes their relationship. After the introduction, Chapter 2 carefully reviews Double Operator Integrals, Chapter 3 describes the class of so-called p-relative trace class perturbations, followed by the construction of Krein's spectral shift function in Chapter 4. Chapter 5 reviews the analytic approach to spectral flow, culminating in Chapter 6 in the main abstract result of the book, namely the so-called principal trace formula. Chapter 7 completes the work with illustrations of the main results using explicit computations on two examples: the Dirac operator in Rd, and a differential operator on an interval. Throughout, attention is paid to the history of the subject and earlier references are provided accordingly. The book is aimed at experts in index theory as well as newcomers to the field.