On the Odd Area of Planar Sets

نویسندگان

  • Assaf Oren
  • Igor Pak
  • Rom Pinchasi
چکیده

The main result in the paper is a construction of a simple (in fact, just a union of two squares) set T in the plane with the following property. For every > 0 there is a family F of an odd number of translates of T such that the area of those points in the plane that belong to an odd number of sets in F is smaller than .

برای دانلود 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

Optimization of the Kinematic Sensitivity and the Greatest Continuous Circle in the Constant-orientation Workspace of Planar Parallel Mechanisms

This paper presents the results of a comprehensive study on the efficiency of planar parallel mechanisms, considering their kinetostatic performance and also, their workspace. This aim is approached upon proceeding single- and multi-objective optimization procedures. Kinetostatic performances of ten different planar parallel mechanisms are analyzed by resorting to a recent index, kinematic sens...

متن کامل

A convex combinatorial property of compact sets in the plane and its roots in lattice theory

K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...

متن کامل

A two-dimensional numerical model of a planar solid oxide fuel cell

A two-dimensional CFD model of a planar solid oxide fuel cell (SOFC) has been developed.This model can predict the performance of SOFC at various operating and design conditions.The effect of Knudsen diffusion is accounted in the porous electrode (backing) and reaction zonelayers. The mathematical model solves conservation of electrons and ions and conservation ofspecies. The model is formulate...

متن کامل

Semifields, Relative Difference Sets, and Bent Functions

Recently, the interest in semifields has increased due to the discovery of several new families and progress in the classification problem. Commutative semifields play an important role since they are equivalent to certain planar functions (in the case of odd characteristic) and to modified planar functions in even characteristic. Similarly, commutative semifields are equivalent to relative dif...

متن کامل

Planar Graphs of Odd-girth at Least 9 Are Homomorphic to Petersen Graph

Let G be a graph and let c : V (G) → ({1,...,5} 2 ) be an assignment of 2-element subsets of the set {1, . . . , 5} to the vertices of G such that for every edge vw, the sets c(v) and c(w) are disjoint. We call such an assignment a (5, 2)-coloring. A graph is (5,2)-colorable if and only if it has a homomorphism to the Petersen graph. The odd-girth of a graph G is the length of the shortest odd ...

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

برای دانلود 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

عنوان ژورنال:
  • Discrete & Computational Geometry

دوره 55  شماره 

صفحات  -

تاریخ انتشار 2016