On the Decomposition of a Simple Closed Curve into Two Arcs

نویسندگان

  • Andrzej Trybulec
  • Yatsuka Nakamura
چکیده

(1) Let S1 be a finite non empty subset of R and e be a real number. If for every real number r such that r ∈ S1 holds r < e, then maxS1 < e. For simplicity, we follow the rules: C is a simple closed curve, A, A1, A2 are subsets of E2 T, p, p1, p2, q, q1, q2 are points of E2 T, and n is a natural number. Let us consider n. Observe that there exists a subset of En T which is trivial. One can prove the following propositions:

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Journal of Formalized Mathematics a Decomposition of Simple Closed Curves and an Order of Their Points

The goal of the article is to introduce an order on a simple closed curve. To do this, we x two points on the curve and devide it to two arcs. We prove that such a decomposition is unique. Other auxiliary theorems about arcs are proven for preparation of the proof of the above. For simplicity, we use the following convention: a, b, c, s, r are real numbers, n is a natural number, p, q are point...

متن کامل

On the Segmentation of a Simple Closed Curve

The main goal of the work was to introduce the concept of the segmentation of a simple closed curve into (arbitrary small) arcs. The existence of it has been proved by Yatsuka Nakamura [21]. The concept of the gap of a segmentation is also introduced. It is the smallest distance between disjoint segments in the segmentation. For this purpose, the relationship between segments of an arc [24] and...

متن کامل

On the Segmentation of a Simple Closed Curve1

The main goal of the work was to introduce the concept of the segmentation of a simple closed curve into (arbitrary small) arcs. The existence of it has been proved by Yatsuka Nakamura [21]. The concept of the gap of a segmentation is also introduced. It is the smallest distance between disjoint segments in the segmentation. For this purpose, the relationship between segments of an arc [24] and...

متن کامل

Benders decomposition algorithm for a green closed-loop supply chain under a build-to-order environment

Nowadays, researches pay more attention to environmental concerns consisted of various communities. This study proposes a multi-echelon, multi-period closed-loop supply chain (CLSC). A comprehensive model considers the selection of selection of technology and environmental effects. The supply chain is under a build-to-order (BTO) environment. So, there is not a final product inventory. Also, th...

متن کامل

Square Joints in Railway Track Waves

When rails are laid in a railway track, small gaps are left between the ends of adjoining rails to allow for the expansion of the rails when the temperature rises. Rail joints are provided to form a continuous rail path which are normally laid in standard lengths bolted together by fishplates. When two rail joints are exactly opposing each other, they are called square &#10&#10(side by side) jo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004