lexicographic ordering by spectral moments ($s$-order) among all trees is discussed in this‎ ‎paper‎. ‎for two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{t}_n^{p‎, ‎q}={t‎: ‎t$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. furthermore, ‎the last four trees‎, ‎in the $s$-order‎, ‎among $mathscr{t}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

the coupling of tetrazotised 1,8-diaminonaphthalene with 1,3-dicarbonyl compounds [acetylacetone,methylacetoacetate and acetoacetanilide] yielded a new series of tetradentate ligand systems. analytical, ir,1h nmr and mass spectral data indicate that the compounds exist in the intramolecularly hydrogen bondeddihydrazone form. dibasic tetradentate n2o2 coordination of these compounds in their [ml...

The coupling of tetrazotised 1,8-diaminonaphthalene with 1,3-dicarbonyl compounds [acetylacetone,methylacetoacetate and acetoacetanilide] yielded a new series of tetradentate ligand systems. Analytical, IR,1H NMR and mass spectral data indicate that the compounds exist in the intramolecularly hydrogen bondeddihydrazone form. Dibasic tetradentate N2O2 coordination of these compounds in their [ML...

Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $A(G)$ the adjacency matrix of $G$. The  signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of  graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

Voice clinicians require an objective, reliable, and relatively automatic method to assess voice change after medical, surgical, or behavioral intervention. This measure must be sensitive to a variety of voice qualities and severities, and preferably should reflect voice in continuous speech. The long-term average spectrum (LTAS) is a fast Fourier transform-generated power spectrum whose proper...