The purpose of this paper is to discuss the relationship between the characteristic function of an E-valued meromorphic function f and and that of its derivative f ′. Consequently, for a finite order E-valued meromorphic function f with maximal deficiency sum, we obtain that T (r, f ′) ∼ (2 − δ(∞̂, f))T (r, f) as r → +∞. Results are obtained to extend the related results for meromorphic scalar v...

Let T be a node-weighted tree with n nodes, and let π(u, v) denote the path between two nodes u and v in T . We address two problems: (i) Path Maximum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight on π(u, v) can be found quickly. (ii) Path Maximum Sum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight sum subpath of π(u, v) ca...

Signed digit (SD) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. Such carry-free addition is primarily a three-step process; adding the equally weighted SDs to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the tra...

We say that a set A t-intersects a set B if A and B have at least t common elements. A family A of sets is said to be t-intersecting if each set in A t-intersects any other set in A. Families A1,A2, ...,Ak are said to be cross-t-intersecting if for any i and j in {1, 2, ..., k} with i 6= j, any set in Ai t-intersects any set in Aj . We prove that for any finite family F that has at least one se...

We study the problem of finding a length-constrained maximum-density path in a tree with weight and length on each edge. This problem was proposed in [R.R. Lin, W.H. Kuo, K.M. Chao, Finding a length-constrained maximum-density path in a tree, Journal of Combinatorial Optimization 9 (2005) 147–156] and solved in O(nU ) time when the edge lengths are positive integers, where n is the number of no...

signed digit (sd) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. such carry-free addition is primarily a three-step process; adding the equally weighted sds to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the transfers to...

Reconfigurable intelligent surfaces (RISs) represent a new technology that can shape the radio wave propagation and thus offers great variety of possible performance implementation gains. Motivated by this, we investigate achievable sum-rate optimization in broadcast channel (BC) presence RISs. We solve this problem exploiting well-known duality between Gaussian multiple-input multiple-output (...