آمار
| تعداد نشریات | 50 |
| تعداد شماره‌ها | 2,079 |
| تعداد مقالات | 19,525 |
| تعداد مشاهده مقاله | 22,889,315 |
| تعداد دریافت فایل اصل مقاله | 21,125,227 |
The Boolean Differential Calculus and Differential Equations | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 تیر 1401 | ||
| نوع مقاله: علمی مروری | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2022.65143.2201 | ||
| نویسنده | ||
سیدسیف‌اله موسی‌زاده 
| ||
| عضو هیئت علمی دانشکده علوم ریاضی دانشگاه کاشان | ||
| چکیده | ||
| The Boolean Differential Calculus is a powerful theory that based on definitions of differentials of Boolean variables, differentials of Boolean functions and their derivatives, and extended the Boolean algebra significantly. Definitions and theorems that the Boolean differential calculus based on them, allow us to model the changes of function values together with the changes of the values of variables and many other properties of Boolean functions. In this paper, first we describe the theory of the Boolean differential calculus and present several examples. Then, we introduce the Boolean differential equations. These equations contain the Boolean derivatives of an unknown Boolean function. We show that different from a Boolean equation, the solution of a Boolean differential equation is a set of Boolean functions, and therefore, Boolean differential equations allow us to describe and handle the sets of Boolean functions. In this paper, first we describe the theory of the Boolean differential calculus and present several examples. Then, we introduce the Boolean differential equations. These equations contain the Boolean derivatives of an unknown Boolean function. We show that different from a Boolean equation, the solution of a Boolean differential equation is a set of Boolean functions, and therefore, Boolean differential equations allow us to describe and handle the sets of Boolean functions. | ||
| کلیدواژه‌ها | ||
| Boolean algebra؛ logic function؛ Boolean differential calculus؛ Boolean differential equations | ||
|
آمار تعداد مشاهده مقاله: 74 |
||
