Given a graph $G$, the exponential distance matrix is defined entry-wise by letting $(u,v)$-entry be $q^{\text{dist}(u,v)}$, where $\text{dist}(u,v)$ between vertices $u$ and $v$ with convention that if are in different components, then $q^{\text{dist}(u,v)}=0$. In this paper, we will establish several properties of characteristic polynomial (spectrum) for matrix, give some families graphs whic...

The absorption spectra of chloramphenicol aqueous solution were obtained experimentally. isomers and the effect on formation H-bonded complexes calculated interpreted using quantum chemistry methods. Calculation results showed that spectrum by position bands their nature is largely determined nitrobenzene fragment with little participation propanol dichloroacetamide fragments chloramphenicol. p...

This paper deals with singular Schrödinger operators of the form−d2dx2+∑k∈Zγkδ(⋅−zk),γk∈R, in L2(ℓ−,ℓ+), where δ(⋅−zk) is Dirac delta-function supported at zk∈(ℓ−,ℓ+) and (ℓ−,ℓ+) a bounded interval. It will be shown that interaction strengths γk points zk can chosen such way essential spectrum part discrete this self-adjoint operator coincide prescribed sets on real line.