تطوير المجموعات النجمية بالاستفادة من مفهوم الرؤية الدرجية

الموضوعات

علوم بحتة وطبيعية

روابط وملفات

التعريف والنوع

رقم الوثيقة

efae7917-f4c9-48a5-b7ef-ed23d880f91c

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

1958224_1.pdf

بيانات النشر

ترجمة العنوان

Development of starshaped sets by using staircase visibility

ألقاب المؤلفين

[{"name_ar":"رامي شاهين","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"عدنان ظريف ","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"نجود علي حسن","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

Arabic

المصدر والدورية

اسم المصدر

تطوير المجموعات النجمية بالاستفادة من مفهوم الرؤية الدرجية

المحتوى والصفحات

عدد الصفحات

0

ترجمة الملخص

In this dissertation we could specify the staircase kernel of a two-fold connected orthogonal polygon through using results of by Motwani et al (1990) and the Breen’s way (1992) about finding the staircase kernel of simply connected orthogonal polygon (that means we generalized Breen’s way (1992)). For that we classified simply connected orthogonal polygon in the classes according to the number of maximal staircase paths in its boundary or according to the kind of dents. Now, we offer the most important results that we have obtained :Theorem (1):Let be a two-fold connected closed orthogonal polygon .Assume that is starshaped via staircase paths. If the boundary of the bounded component of is a rectangle, then the kernel of is either one component or two or four ones. Theorem (2):Let be a two-fold connected closed orthogonal polygon. Assume that is starshaped via staircase paths. If the boundary of the bounded component of is union of two staircase paths one of them consists of two edges and the other consists of more than two edges, then the kernel of is either one component or two or three ones. Theorem (3):Let be a two-fold connected closed orthogonal polygon. Assume that is starshaped via staircase paths. If the boundary of the bounded component of is union of two staircase paths, every path consists of more than two edges, then the kernel of is either one component or two. Theorem (4):Let be a two-fold connected closed orthogonal polygon. Assume that is starshaped via staircase paths. If the boundary of the bounded component of contains two staircase paths, that have common edge and every path consists of more than two edges, then the kernel of is either one component or two. Theorem (5):Let be a two-fold connected closed orthogonal polygon .Assume that is starshaped via staircase paths. If the boundary of the bounded component of is union of three maximal staircase paths, every path consists of more than two edges, then the kernel of is one component. Theorem (6):Let be a two-fold connected orthogonal polygon. If the boundary of the bounded component of is union of four maximal staircase paths has no dents, and every path consists of more than two edges, then is not starshaped via staircase paths .Theorem (7):Let be a two-fold connected closed orthogonal polygon .Assume that is starshaped via staircase paths .If the boundary of the bounded component of contains north dents only, then there is not any component of in the southeast or the southwest of .Theorem (8):Let be a two-fold connected closed orthogonal polygon .Assume that is starshaped via staircase paths. If the boundary of the bounded component of contains north dents only, then the kernel of is either one component or two .Theorem (9):Let , be a two-fold connected orthogonal polygon .Assume that is starshaped via staircase paths .If the boundary of the bounded component of contains only one kind of dents east, west, south or north, then the kernel of is either one component or two .Theorem (10):Let , be a two-fold connected closed orthogonal polygon .Assume that is starshaped via staircase paths. If the boundary of the bounded component of contains only north and east dents then is composed of one component found in the northeast of . Theorem (11):Let be a two-fold connected closed orthogonal polygon. Assume that is starshaped via staircase paths. If the boundary of the bounded component of contains only one kind of horizontal dents (north or south) and one kind of vertical dents (east or west), then is only one component .Theorem (12):Let be a two-fold connected closed orthogonal polygon .Assume that is starshaped via staircase paths .If the boundary of the bounded component of contains two kinds of horizontaldents, say north and south, then is not starshaped via staircase paths. Theorem (13):Let be a two-fold connected closed orthogonal polygon. Assume that is starshaped via staircase paths .If the boundary of the bounded component of contains two kinds of vertical dents, say east and west, then is not starshaped via staircase paths. Theorem (14):Let be a two-fold connected orthogonal polygon .Assume that is starshaped via staircase paths. And let be the closed bounded component of where is a simple open orthogonalcurve, and let be an appropriately chosen simple closed or thogonalcurve in surrounds , then is either one component or two or three or four ones. Theorem (15):Let be a two-fold connected orthogonal polygon .Assume that is starshaped via staircase paths. And let be the closed bounded component of where is an open or thogonalcurve and not simple. Let be an appropriately chosen simple closed or thogonalcurve in surrounds , then is one component or two. Theorem (16):Let be a two-fold connected orthogonal polygon. Assume that is starshaped via staircase paths. And let be the closed bounded component of where is a closed or thogonalcurve and 166not simple. Let be an appropriately chosen simple closed or thogonalcurve in surrounds , then is either one component or two or three ones. Every one of theorems (1) to (13) is true when is closed set, then we obtain an analogue for every one of them .Now we can formulate the main result for specifying the staircase kernel of a two-fold connected orthogonal polygon when is closed set or not necessarily closed and not necessarily open set, and the bounded component of is an open or closed set and every staircase path in has maximal length. For that let when is an open set and when is a closed set where is an appropriate simple closed or thogonalcurve that surrounds .Main result Let , be a two-fold connected orthogonal polygon. Assume that is starshaped via staircase paths, is the bounded component of , and is the curve described above. Then we can find as follow:1. Finding the set where,()()()()-2. Omitting the two strips: the vertical and the horizontal that are determined by . So four parts of the plane will remain.3. For every remaining part of the four parts let be all the points of in this part.4. If is in the same side of the dents in and every point in sees every point in every staircase path in then is a component of .5. In the other cases, is not a component of .Result (1):According to the above main result: There is a way to say if the orthogonal polygon is not starshaped as follow:1. If every part of the four parts is not in the same side of the dents in then is not a component of .

إشراف وإعداد

الإشراف

رامي شاهين, عدنان ظريف

الإعداد

نجود علي حسن

الاقتباسات الببليوغرافية