## Uber die magnetische Nachwirkung (Preisach, pp. 277-302) WITH Über eine Klasse von Lösungen der Diracschen Gleichung (pp. 250-260) in Zeitschrift für Physik, Volume 94, 1935

Berlin: Julius Springer, 1935. 1st Edition. FIRST EDITION, FULL VOLUME, OF THE PREISACH MODEL OF HYSTERESIS; BOUND WITH VOLKOV’S “EXACT SOLUTION TO THE DIRAC EQUATION FOR AN OTHERWISE FREE ELECTRON INTERACTING WITH AN ELECTROMAGNETIC PLANE WAVE” (Guo, Exact Wave Functions, 39). The origin of the Preisach model can be traced to this “landmark paper” (Mayergoyz, Mathematical Models of Hysteresis, 1).

The Preisach model is a well-known hysteresis identification method in which the hysteresis is modeled by linear combination of hysteresis operators. First introduced by Ferenc (Franz) Preisach in this paper, the widely accepted Preisach model of hysteresis “generalizes hysteresis loops as the parallel connection of independent relay hysterons" [a two-valued operator used to model hysteresis] (Wikipedia)

Hysteresis is a form of non-linearity with memory, an example being a magnet that may “have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past” (Wikipedia). In the Preisach model specifically, hysteresis is described starting from the hypothesis that a free-energy profile characterized by multiple local minima and metastable state can be decomposed into a set of many elementary bistable contribution. Each bistable unit can occupy one of two states, (+) and (-), and is characterized by tw0 reduced fields, the local coercive field and an interaction field” (Mayergoyz, The Science of Hysteresis, 101).

“Preisach’s approach was purely intuitive. It was based on a plausible hypotheses concerning the physical mechanisms of magnetization. For this reason, the Preisach model was first regarded as a physical model of hysteresis” (Mayergoyz). The model remains frequently in use is a wide variety of the sciences — from mathematics to engineering, mechanics, economics, and biology.

VOLKOV PAPER: First edition of Volkov’s solution (Volkov State) of the Dirac equation — an exact solution for the system of one electron in a plane electromagnetic wave. “The state of the charged particle, known as Volkov state, has been used extensively to explore numerous quantum phenomena such as Compton scattering, photo-ionization, bremsstrahlung processes and Kapitza-Dirac problem (scattering of an electron by a standing light wave), etc.” (Yuce, Free Electron in a Laser Field, Feb. 1, 2008). Item #1517

CONDITION & DETAILS: Complete volume. [vii], 819, . 8vo. (9 x 6.5; 225 x 163mm). Bound in clean black clothgilt-lettered at the spine. Very slightly rubbed at the edges. Tightly bound and very clean. The interior is clean and bright. Near fine condition.

Price: \$400.00