Families of multiweights and pseudostars

Let ${\cal T}=(T,w)$ be a weighted finite tree with leaves $1,..., n$.For any $I :=\{i_1,..., i_k \} \subset \{1,...,n\}$,let $D_I ({\cal T})$ be the weight of the minimal subtree of $T$ connecting $i_1,..., i_k$; the $D_{I} ({\cal T})$ are called $k$-weights of ${\cal T}$. Given a family of real numbers parametrized by the $k$-subsets of $\{1,..., n\}$, $\{D_I\}_{I \in {\{1,...,n\} \choose k}}$, we say that a weighted tree ${\cal T}=(T,w)$ with leaves $1,..., n$ realizes the family if $D_I({\cal T})=D_I$ for any $I$. In [P-S] Pachter and Speyer proved that, if $3 \leq k \leq (n+1)/2$ and $\{D_I\}_{I \in {\{1,...,n\} \choose k}}$ is a family of positive real numbers, then there exists at most one positive-weighted essential tree ${\cal T}$ with leaves $1,...,n$ that realizes the family (where "essential" means that there are no vertices of degree $2$). We say that a tree $P$ is a pseudostar of kind $(n,k)$ if the cardinality of the leaf set is $n$ and any edge of $P$ divides the leaf set into two sets such that at least one of them has cardinality $\geq k$. Here we show that, if $3 \leq k \leq n-1$ and $\{D_I\}_{I \in {\{1,...,n\} \choose k}}$ is a family of real numbers realized by some weighted tree, then there is exactly one weighted essential pseudostar ${\cal P}=(P,w)$ of kind $(n,k)$ with leaves $1,...,n$ and without internal edges of weight $0$, that realizes the family; moreover we describe how any other weighted tree realizing the family can be obtained from ${\cal P}$. Finally we examine the range of the total weight of the weighted trees realizing a fixed family.Comment: 13 pages. arXiv admin note: substantial text overlap with arXiv:1404.679

Thick composite magnetoelectric films by electrophoretic deposition

Electrophoretic deposition (EPD) from colloidal suspensions was utilized for the preparation of composite magneto-dielectric films on a conductive substrate. The present process is developed as a convenient forming process for the development of devices based on thick magneto-dielectric films [1]. The deposition parameters - using EPD - such as colloidal parameters, deposition voltage and deposition time and the post process parameters, such as drying velocity and sintering will be controlled. This work aims to control the fillers/matrix ratio during the deposition and obtain a good adhesion, compaction and functionality of the composite film after the heat treatment. Measurements results for the current transients during constant-voltage deposition and the correlated deposited mass are presented [2, 3].1] A.O. Karilainen, P.M.T. Ikonen, C.R. Simovski, S.A. Tretyakov, A.N. Lagarkov, S.A. Maklakov, K.N. Rozanov, and S.N. Starostenko, Experimental studies on antenna miniaturisation using magneto-dielectric and dielectric materials, IET Microw. Antennas Propag., vol. 5, no. 4, pp. 495–502, 2011. 2] C. Baldisserri, D. Gardini and C. Galassi, An analysis of current transients during electrophoretic deposition (EPD) from colloidal TiO2 suspensions, Journal of Colloid and Interface Science 347 (2010) 102–111 3] H. Farnoush, J.A. Mohandesi, D. H. Fatmehsari and F. Moztarzadeh, A kinetic study on the electrophoretic deposition of hydroxyapatite–titania nanocomposite based on a statistical approach, Ceramics International 38 (2012), 6753-676

Structure analysis of cobalt ferrite/titania composite

Magnetodielectric bulk composite of a magnetic phase and a dielectric one were tailored to tune the macroscopic properties of permittivity and permeability. The designing of heterostructure formed by magnetic and dielectric counterparts offers a versatile route for the production of isotropic composite material with unusual electromagnetic properties. This study investigates the microstructure of sintered titania (TO)/cobalt ferrite (CFO) composites related to compositional modifications. The crystalline structure was studied through the comparison of theXRD patterns withthe EDS analysis and the results of the image analysis done on the electron micrographs. The image analysis wasfundamental to verifythe XRD and EDS interpretations, and to measure the effective volume contentof the phasesafter heat treatment.Several TO/CFO ratios from 0.7 to 11.8were analyzed. The formation oftheternary compound (FCTO) was foundonly in the composite with the TO/CFO ratio equal or bigger than 3

Processing of (BaSr)Fe12O19 for antenna miniaturization

Hexaferrites of M-type at high-frequency are investigated, owing to their higher ferro-magnetic resonances as compared to traditional magnetic materials, thus ensuring a less dispersive behavior of the material at microwaves frequencies. Here we present the experimental work concerned with the ceramic process for the production of the barium-strontium hexaferrite (BSFO). The critical issue in the production of this material is to obtain a fully dense and homogeneous microstructure. These aspects have been addressed by introducing powder grinding processes, and by varying the cold consolidation conditions of the powders. A number of samples of the material have been produced, both for morphological and microstructural characterization and a demonstrator antenna, onto which conductive patches were applied, and the radiating properties of which were tested. Barium-strontium hexaferrite as supporting material for antennas - while allowing substantial device miniaturization – displays relatively high dielectric and magnetic losses