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Yayın A numerical approach for the design of matching networks consisting of brune sections based on fujisawa constraints(IEEE, 2018) Yıldız, Serkan; Aksen, Ahmet; Yarman, Bekir Sıddık BinboğaIn this study, the realization problem of matching network consisting of Brune sections is investigated. In the synthesis of a general impedance function with finite transmission zeros, each transmission zero extraction results in a Brune section involving a negative reactive element. Although coupled inductances can be used to remove negative elements, a direct mutual coupling free ladder design is aimed by properly incorporating the mid-shunt ladder realizability conditions of Fujisawa. For this purpose, impedance based Real Frequency Technique (RFT) is used to construct realizable impedance function and Fujisawa synthesis procedure is applied for mid-shunt ladder realization. An illustrative matching network design example is presented.Yayın Hierarchical b-Matching(Springer Science and Business Media Deutschland GmbH, 2021) Emek, Yuval; Kutten, Shay; Shalom, Mordechai; Zaks, ShmuelA matching of a graph is a subset of edges no two of which share a common vertex, and a maximum matching is a matching of maximum cardinality. In a b-matching every vertex v has an associated bound bv, and a maximum b-matching is a maximum set of edges, such that every vertex v appears in at most bv of them. We study an extension of this problem, termed Hierarchical b-Matching. In this extension, the vertices are arranged in a hierarchical manner. At the first level the vertices are partitioned into disjoint subsets, with a given bound for each subset. At the second level the set of these subsets is again partitioned into disjoint subsets, with a given bound for each subset, and so on. We seek for a maximum set of edges, that obey all bounds (that is, no vertex v participates in more than bv edges, then all the vertices in one subset do not participate in more that subset’s bound of edges, and so on hierarchically). This is a sub-problem of the matroid matching problem which is NP -hard in general. It corresponds to the special case where the matroid is restricted to be laminar and the weights are unity. A pseudo-polynomial algorithm for the weighted laminar matroid matching problem is presented in [8]. We propose a polynomial-time algorithm for Hierarchical b-matching, i.e. the unweighted laminar matroid matching problem, and discuss how our techniques can possibly be generalized to the weighted case.
