On the number of spanning trees in graphs with multiple edges

In this paper, we consider a class of nonlinear matrix equation of the type \(X+\sum _{i=1}^mA_i^{*}X^{-q}A_i-\sum _{j=1}^nB_{j}^{*}X^{-r}B_j=Q\), where \(0<q,\,r\le 1\) and Q is positive definite. Based on the Schauder fixed point theorem and Bhaskar–Lakshmikantham coupled fixed point theorem, we derive some sufficient conditions for the existence and uniqueness of the positive definite solution to such equations. An iterative method is provided to compute the unique positive definite solution. A perturbation estimation and the explicit expression of Rice condition number of the unique positive definite solution are also established. The theoretical results are illustrated by numerical examples.     

Quantitative Uncertainty Principles for the Canonical Fourier—Bessel Transform

Acta Mathematica Sinica, English Series - The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential supports...     

Spectral theory of certain unbounded Jacobi matrices

Using the conjugate operator method of Mourre we study the spectral theory of a class of unbounded Jacobi matrices. We especially focus on the case where the off-diagonal entries an=nα(1+o(1)) and diagonal ones bn=λnα(1+o(1)) with α>0, λ∈R.     

On the Spectral Properties of the Spin-Boson Hamiltonians

We analyze the spectral properties of the spin-boson model, describing a two level atom coupled to a boson field. We show that a limiting absorption principle holds, and there is no singularly continuous spectrum for this Hamiltonian outside some small neighborhoods of the eigenvalues of the spin matrix. For this, we construct a conjugate operator for a special class of self-adjoint operators.     

Synthesis,structural characterization,Hirshfeld surface analysis,spectroscopic and ferroelectric properties studies of 4-methylbenzylammonium sulfate

Single crystals of 4-methylbenzylammonium sulfate were grown in an aqueous solution at room temperature. The grown compound is characterized by spectroscopic, thermal, and dielectric studies and its structure was determined by single-crystal X-ray diffraction analysis. Its crystal structure is described as a three-dimensional network where the sulfate anions (HSO₄^?) are interconnected through H-bonds to form anionic layers between which the 4-methylbenzylammonium cations are located. The hydrogen bonding network connecting the different components is given. Hirshfeld surface analysis was performed to visualize, explore and quantify intermolecular interactions in the crystal lattice. This analysis revealed the presence of H…C/H…C, C…O/O…C intermolecular interactions and O…O, H…H short contacts in the crystal. X-ray, structural and electrical results are correlated. The kind of the observed conduction is protonic by translocation. Differential scanning calorimetry (DSC) shows that this material presents a reversible phase transition at 390 K, confirmed by the dielectric permittivity study.     

Mourre's theory for some unbounded Jacobi matrices

We show a Mourre estimate for a class of unbounded Jacobi matrices. In particular, we deduce the absolute continuity of the spectrum of such matrices. We further conclude some propagation theorems for them.