The family of judicious partitioning problems, introduced by Bollobás and Scott to the field of extremal combinatorics, has been extensively studied from a structural point of view for over two decades. This rich realm of problems aims to counterbalance the objectives of classical partitioning problems such as Min Cut, Min Bisection and Max Cut. While these classical problems focus solely on th...

Let G = (V (G), E(G)) be a nontrivial connected graph of order n with an edge-coloring c : E(G) → {1, 2, . . . , q}, q ∈ N, where adjacent edges may be colored the same. A tree T in G is a rainbow tree if no two edges of T receive the same color. For a vertex set S ⊆ V (G), a tree connecting S in G is called an S-tree. The minimum number of colors that are needed in an edge-coloring of G such t...

In this study, nanoporous silica aerogel and silica aerogel-activated carbon composites have been synthesized using a water glass precursor by cost effective ambient pressure drying method. Equilibrium and kinetics of benzene and ethyl benzene adsorption on silica aerogel and its composites have been measured in a batch mode at tree weights of adsorbent. For the first time, the experimental dat...

Development of network quality speech coders at 16 kb/s and below is an active research area. This thesis focuses on the study of low-delay Code Excited Linear Predictive (CELP) and tree coders. A 16 kb/s stochastic tree coder based on the (M,L) search algorithm suggested by Iyengar and Kabal and a low-delay CELP coder proposed by AT&T (CCITT 16 kb/s standardization candidate) are examined. The...

A bstract We investigate the ground state of a (1+1)-dimensional conformal field theory (CFT) built with M species massless free Dirac fermions coupled at one boundary point via junction/interface. Each CFT represents wire finite length L . develop systematic strategy to compute Rényi entropies for generic bipartition between wires and entanglement negativity two non-complementary sets wires. B...

This research was sponsored in part by U S WEST and in part by the Defense Advanced Research Projects Agency (DOD), and monitored by the Space and Naval Warfare Systems Command under Contract N0003985-C-0163, ARPA Order No. 5167. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or ...

Let G be a connected graph with vertex set V (G), we define $\sigma _{2}(G)=\min \limits \{d(u)+d(v)$ for all non-adjacent vertices u,v ∈ (G)}. Km,m+k complete bipartite bipartition (Km,m+k) = A ∪ B, |A| m, |B| m + k. Denote by H to the obtained from adding (or not adding) some edges two end in A. $\mathcal H$ of graphs H. In this paper, prove that if is satisfying σ2(G) ≥|G|− k then has spanni...

In this paper, we show that each f -graph with more than 5 vertices has an unique minimum bipartition, and we also show the upper and lower bound of the balanced size of f -graphs.