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91.
Let be a tree. We show that the null space of the adjacency matrix of has relevant information about the structure of . We introduce the Null Decomposition of trees, which is a decomposition into two different types of trees: N-trees and S-trees. N-trees are the trees that have a unique maximum (perfect) matching. S-trees are the trees with a unique maximum independent set. We obtain formulas for the independence number and the matching number of a tree using this decomposition. We also show how the number of maximum matchings and the number of maximum independent sets in a tree are related to its null decomposition. 相似文献
92.
What do the three names in the title have in common? The purpose of this paper is to relate them in a new and, hopefully, interesting way. Starting with the Fibonacci numeration system — also known as Zeckendorff's system — we will pose ourselves the problem of extending it in a natural way to represent all real numbers in (0,1). We will see that this natural extension leads to what is known as the ?-system restricted to the unit interval. The resulting complete system of numeration replicates the uniqueness of the binary system which, in our opinion, is responsible for the possibility of defining the Van der Corput sequence in (0,1), a very special sequence which besides being uniformly distributed has one of the lowest discrepancy, a measure of the goodness of the uniformity.Lastly, combining the Fibonacci system and the binary in a very special way we will obtain a singular function, more specifically, the inverse of one of the family of Riesz-Nágy. 相似文献
93.
Cristina Fernández-Córdoba Jaume Pujol Mercè Villanueva 《Designs, Codes and Cryptography》2010,56(1):43-59
A code C{{\mathcal C}} is
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive codes under an extended Gray map are called
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes. In this paper, the invariants for
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the rank and dimension of the kernel, are studied. Specifically, given the algebraic parameters of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the possible values of these two invariants, giving lower and upper bounds, are established. For each possible
rank r between these bounds, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code for each possible pair (r, k) is given. 相似文献
94.
We characterize all the quadratic polynomial differential systems having a polynomial inverse integrating factor and provide explicit normal forms for such systems and for their associated first integrals. We also prove that these families of quadratic systems have no limit cycles. 相似文献
95.
96.
97.
98.
Jaume Aguadé 《代数通讯》2013,41(3):1104-1116
We use ideas of J.-P. Serre to obtain a geometric classification of the integral p-adic rank two representations of the infinite dihedral group. 相似文献
99.
Joan C. Artés Jaume Llibre Dana Schlomiuk Nicolae Vulpe 《Journal of Fixed Point Theory and Applications》2013,14(2):555-618
In this work we classify, with respect to the geometric equivalence relation, the global configurations of singularities, finite and infinite, of quadratic differential systems possessing exactly three distinct finite simple singularities. This relation is finer than the topological equivalence relation which does not distinguish between a focus and a node or between a strong and a weak focus or between foci (or saddles) of different orders. Such distinctions are, however, important in the production of limit cycles close to the foci (or loops) in perturbations of the systems. The notion of geometric equivalence relation of configurations of singularities allows us to incorporate all these important geometric features which can be expressed in purely algebraic terms. The geometric classification of all configurations of singularities, finite and infinite, of quadratic systems was initiated in a work published in 2013 when the classification was done for systems with total multiplicity m f of finite singularities less than or equal to one. That work was continued in an article which is due to appear in 2014 where the geometric classification of configurations of singularities was done for the case m f = 2. In this article we go one step further and obtain the geometric classification of singularities, finite and infinite, for the subclass mentioned above. We obtain 147 geometrically distinct configurations of singularities for this family. We give here the global bifurcation diagram of configurations of singularities, both finite and infinite, with respect to the geometric equivalence relation, for this class of systems. The bifurcation set of this diagram is algebraic. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants, a fact which gives us an algorithm for determining the geometric configuration of singularities for any quadratic system in this particular class. 相似文献
100.