Line arrangements and configurations of points with an unexpected geometric property

Geometric Graphs and Arrangements

Preface The body of this text is written. It remains to find some words to explain what to expect in this book. A first attempt of characterizing the content could be: In words: The questions posed and partly answered in this book are from the intersection of graph theory and discrete geometry. The reader will meet some graph theory with a geometric flavor and some combinatorial geometry of the...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Extremal Configurations and Levels in Pseudoline Arrangements

Geometric Arrangements: Substructures and Algorithms

In this thesis we study a variety of problems in computational and combinatorial geometry, which involve arrangements of geometric objects in the plane and in higher dimensions. Some of these problems involve the design and analysis of algorithms on arrangements and related structures, while others establish combinatorial bounds on the complexity of various substructures in arrangements. Inform...

Worldlines and body points associated with an extensive property

Material structure of bodies that is usually assumed a-priory in continuum mechanics is constructed on the basis of a balance of a given extensive property on spacetime. Body points are identified with worldlines—the integral lines of the flux of the property. The geometric setting assumes that spacetime has only the structure of a differentiable manifold and no particular frame is assumed to b...