Robert W. Easton

THE END The world as we know has come to an end. There is destruction and chaos as far as the eye can see. Are you prepared? THE END COMES IN MANY FORMS, WHICH ONE SPEAKS TO YOU? Author Valerie Lioudis has assembled an original anthology of stories from a group of today's hottest writers. Inside there are tales of extinction level events, survival in a broken wasteland, a bar at the end of it all, and so much more. This is a collection of new views on the Earth's demise and humanity's will to survive despite it. With stories from L. Douglas Hogan, Derek Shupert, Kevin J. Kennedy, Veronica Smith, Stefan Lear, Robert W. Easton, Jack Appell, Austin James, Ellen A. Easton, William Stuart, Michael Gillette, T. D. Ricketts and Valerie Lioudis this wildly diverse and entertaining collection is sure to entertain you with each word. TOCEnd of the Line by Valerie LioudisStill Here Somehow by William Stuart The PitForsaken Gravitas by Robert W. EastonUnderground by Jack AppellThe Picnic by Ellen A. EastonSpaceship Earth by Michael GillettCountdown by Veronica SmithLycan Rising by Derek ShupertThe Cataclysm by L. Douglas HoganSatan's Apocalypse by Kevin J. KennedyWasteland Wanderer by T. D. RickettsThe Pit by William StuartFlare-up by Austin JamesBury Em' Deep by Stefan Lear

A queen trapped in a castle during a siege is torn between duty to the king she cares about, and love for the knight sworn to them both. Faylin knows she is not the type to entice a man. She's too broad, too exotic, too strong willed. But more importantly, she is a sorceress in a land where magic is mistrusted. When she married King Cheston, she thought that she had finally found a place in which to grow roots. At least until Gancett, a former suitor, laid siege to her new husband's castle. As a handsome new warrior rides to their defense, she feels torn between duty to the husband she barely knows, and her heart's desire she sees in a man she just met. Cannelyr has been unlucky in love, and is recovering from his last romantic disaster. When his King calls for aid, he gathers his forces and rides into the siege, joining forces with the beleaguered ruler. When he first sees Queen Faylin, he resists his hearts calling and doubles down on his duty to his king. But when Cheston is injured, he is forced to help manage the fortress at the queen's side. Has Cannelyr's bad luck in love struck a new low, or will it finally turn around for them both?

This book is for those interested in dynamical systems. It assumes a solid undergraduate training in mathematics. Geometrical methods are developed to study the process of iteration, which involves taking the output of a function and feeding it back as input. Iteration processes are used to produce fractals and wavelets, and to numerically approximate solutions to ordinary and partical differential equations. Each iteration procedure generates a discrete dynamical system. These systems are at the heart of many numerical algorithms. Essentially all mathematical models of evolving physical systems can be viewed as discrete dynamical systems. This book attempts to present the fundamental ideas of discrete dynamical systems as clearly and geometrically as possible. Illustrative examples of dynamical systems are presented in the first chapter. The second chapter gives a review of the typology of metric spaces. The third presents basic results and establishes a philosophy of dynamics which is strongly influenced by the work of Charles Conley. The stable manifold and local structural stability theorems are presented in the fourth chapter. Invariant sets and isolating blocks are defined in the fifth. The sixth develops what is called the Conley Index in the context of discrete dynamics, and the final chpater covers measure-preserving and symplectic maps. The book would be suitable for use as a main text for a graduate course in dynamical systems, and as a reference for engineers and scientists.