The discrete Green Theorem and some applications in discrete geometry

The discrete Green Theorem and some applications in discrete geometry

The discrete version of Green’s Theorem and bivariate difference calculus provide a general and unifying framework for the description and generation of incremental algorithms. It may be used to compute various statistics about regions bounded by a finite and closed polygonal path. More specifically, we illustrate its use for designing algorithms computing many statistics about polyominoes, reg...

the study of bright and surface discrete cavity solitons dynamics in saturable nonlinear media

امروزه سالیتون ها بعنوان امواج جایگزیده ای که تحت شرایط خاص بدون تغییر شکل در محیط منتشر می-شوند، زمینه مطالعات گسترده ای در حوزه اپتیک غیرخطی هستند. در این راستا توجه به پدیده پراش گسسته، که بعنوان عامل پهن شدگی باریکه نوری در آرایه ای از موجبرهای جفت شده، ظاهر می گردد، ضروری است، زیرا سالیتون های گسسته از خنثی شدن پراش گسسته در این سیستم ها بوسیله عوامل غیرخطی بوجود می آیند. گسستگی سیستم عامل...

Discrete Differential Geometry: Theory and Applications

Discrete Optimal Transport: Complexity, Geometry and Applications

Some minor examples on discrete geometry

Of course this is exaggerated, but really the question is about emerging quantum mechanics [3, 4, 5, 6]. i.e., about to accept the discretizacion of area as a first principle, then deriving from it the rules of quantum mechanics. Markopoulou and Smolin [3] have showed that QM emerges if some stochasticity principle is incorporated to the description. Here this small puzzle shows that such princ...