اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDiscrete Tomography of Planar Model Sets
114
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical quasicrystals. To this end, the class of cyclotomic model sets is introduced, and the corresponding consistency, reconstruction and uniqueness problems of the discrete tomography of these sets are discussed.
قيم البحث
اقرأ أيضاً
We show that the asymptotic dimension of a geodesic space that is homeomorphic to a subset in the plane is at most three. In particular, the asymptotic dimension of the plane and any planar graph is at most three.
The coincidence problem for planar patterns with $N$-fold symmetry is considered. For the N-fold symmetric module with $N<46$, all isometries of the plane are classified that result in coincidences of finite index. This is done by reformulating the p
roblem in terms of algebraic number fields and using prime factorization. The more complicated case $N ge 46$ is briefly discussed and N=46 is described explicitly. The results of the coincidence problem also solve the problem of colour lattices in two dimensions and its natural generalization to colour modules.
We consider the problem of distinguishing convex subsets of $n$-cyclotomic model sets $varLambda$ by (discrete parallel) X-rays in prescribed $varLambda$-directions. In this context, a `magic number $m_{varLambda}$ has the property that any two conve
x subsets of $varLambda$ can be distinguished by their X-rays in any set of $m_{varLambda}$ prescribed $varLambda$-directions. Recent calculations suggest that (with one exception in the case $n=4$) the least possible magic number for $n$-cyclotomic model sets might just be $N+1$, where $N=operatorname{lcm}(n,2)$.
A finite subset of a Euclidean space is called an $s$-distance set if there exist exactly $s$ values of the Euclidean distances between two distinct points in the set. In this paper, we prove that the maximum cardinality among all 5-distance sets in
$mathbb{R}^3$ is 20, and every $5$-distance set in $mathbb{R}^3$ with $20$ points is similar to the vertex set of a regular dodecahedron.
We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the un
assigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
