Wemake improvements to the current upper bounds on pairwise distance preservers and additive spanners. A distance preserver is a sparse subgraph that exactly preserves all distances in a given pair set P . We show that every undirected unweighted graph has a distance preserver on O(max{n|P |, n|P |}) edges, and we conjecture that O(n|P |+ n) is possible. An additive subset spanner is a sparse s...

A two-photon polymerization initiator is a kind of nonlinear optical material. With the demand for more efficient initiators in additive manufacturing, there are and related studies. In this paper, four conjugate-extended with different alkane chain lengths were designed synthesized, single-photon, two-photon, photodegradation experiments carried out. Additive manufacturing illustrated that mol...

The method of minimum evolution reconstructs a phylogenetic tree T for n taxa given dissimilarity data d. In principle, for every tree W with these n leaves an estimate for the total length of W is made, and T is selected as the W that yields the minimum total length. Suppose that the ordinary least-squares formula S(W)(d) is used to estimate the total length of W. A theorem of Rzhetsky and Nei...

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

—This paper studies the frequency estimation of twodimensional (2-D) harmonics in presence of multiplicative and additive noise. We construct a cyclic covariance matrix using a class of cyclic covariance of the 2-D harmonics. Exploiting the shift-invariance structure of the signal subspace, we extend ESPRIT to estimate the frequency pairs of 2-D harmonics in multiplicative and additive noise. ...

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

In phylogenetic analysis, a standard problem is to approximate a given metric by an additive metric. Here it is shown that, given a metric D defined on some finite set X and a non-expansive map f : X → R, the one-parameter family of the Gromov transforms D of D relative to f and ∆ that starts with D for large values of ∆ and ends with an additive metric for ∆ = 0 consists exclusively of metrics...

We propose to study a problem that arises naturally from both Topological Numbering of Directed Acyclic Graphs, and Additive Coloring (also known as Lucky Labeling). Let D be a digraph and f a labeling of its vertices with positive integers; denote by S(v) the sum of labels over all neighbors of each vertex v. The labeling f is called topological additive numbering if S(u) < S(v) for each arc (...