Interestingly, he found that no minimising total order of subsets of existed for his problem, contrasting with both the Kruskal–Katona theorem and Theorem 1.4. A second motivation concerns vertex-isoperimetric problems for graphs. The vertex boundary of a set of vertices of a graph is the set ...
graded collateral connections (CC) according to the angiographic visibility: CC0: no continuous connection between donor and recipient artery, CC1: continuous, thread-like connections ( ≥0.4 mm), and CC2: continuous, small side branch-like size of the collateral throughout its course (>1 mm)...
Spleen size, total number of splenocytes and individual subsets in WT and nude rats.doi:10.1371/JOURNAL.PONE.0059602.G005Gu LijuanXiong XiaoxingWei DingtaiGao XuwenKrams SheriZhao HengPLOS ONE
Find a bijection between the set X of subsets of A with an odd number of elements and the set Y of subsets of A with an even number of elements: precisely define Let S be a set containing n elements. Show that S has 2n subsets. How many different relations are the...
The AbC™ Total Antibody Compensation Bead Kit provides a consistent, accurate, and simple-to-use technique for the setting of flow cytometry compensation when using fluorochrome-conjugated mouse, rat, hamster, or rabbit antibodies with any laser in flow cytometry.• Broadest multispecies ...
How many solutions exist of the equation x_1 + x_2 + x_3 + x_4 + x_5 = 12, where each x_i is a positive integer? How many numbers greater than one thousand can be made using the digits 1, 0, 3, 4, and 5 without repetition? How...
Since v is an arbitrary vertex, every vertex of G is in a γt-set with one of its neighbors, the condition holds for all subsets S with |S|=1. Next assume that S={u,v}. Without loss of generality, we many assume that two pebbles are placed on u and one pebble is placed on ...
A complete metric measure space that fulfills the doubling property is proper, meaning that all closed and bounded subsets are compact, see [2, Proposition 3.1]. Following the concept of Heinonen and Koskela [23], we call a Borel function\(g: {\mathcal {X}}\rightarrow [0, \infty ]\...
significant natural resource consumption [3]. In developed economies, the way populations consume resources has been identified as a primary driver of environmental degradation within those populations [23]. They also noted that population growth was no longer the sole driver of environmental ...
In these problems, each time a new job is added to the sequence a setup time proportional to the length of the already processed jobs is required. As a result, the makespan is no longer sequence independent. The authors showed that a forward implementation of the S-B algorithm can handle ...