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关键词： Graph   The second largest signless Laplacian eigenvalue   Maximum degree   Second maximum degree   Nordhaus-Gaddum-type  

摘要： Let G be a simple graph of order n with m edges. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G) = D(G) + A(G). Let q1 = q2 = center dot center dot center dot = qn be the signless Laplacian eigenvalues of graph G and also let. =.(G) (1 =. = n) be the largest positive integer such that q. = 2m/ n. Denote by G the complement graph of graph G. If G Kn, Kn, Kn- 1. K1, K1, n- 1, Kn - e, K2. (n 2) K1, then we prove that q2(G) + q2(G) = n - 1. Moreover, if G K1, n- 1, Kn- 1. K1, Kn - e, K2. (n - 2) K1, then (nu) over tilde +. >= 3.

关键词： Multiplicity of solutions   fractional     (     p   1           p   2         …           p   k     )     -Laplacian system   Nehari manifold  

摘要： This paper is devoted to study the existence and multiplicity of solutions to fractional ( p 1 , p 2 , horizontal ellipsis , p k ) -Laplacian system by analyzing the relationship between the Nehari manifold and fibering maps.

摘要： In this paper, we study some potential-theoretic aspects of the eikonal and infinity Laplace operator on a Finsler manifold M. Our main result shows that the forward completeness of M can be detected in terms of Liouville properties and maximum principles at infinity for subsolutions of suitable inequalities, including Delta(N)(infinity) u >= g(u). Also, an infinity-capacity criterion and a viscosity version of Ekeland principle are proved to be equivalent to the forward completeness of M. Part of the proof hinges on a new boundary-to-interior Lipschitz estimate for solutions of Delta(N)(infinity) u = g(u) on relatively compact sets, that implies a uniform Lipschitz estimate for certain entire, bounded solutions without requiring the completeness of M. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Paramagnetic resonance  

摘要： Dimethylammonium magnesium formate, [(CH3)2NH2][Mg(HCOO)(3)] or DMAMgF, is a model used to study high temperature hybrid perovskite-like dielectrics. This compound displays an order-disorder phase transition at about 260 K. Using multifrequency electron spin resonance in continuous wave and pulsed modes, we herein present the quantum dynamics of the Mn2+ ion probe in DMAMgF. In the high temperature paraelectric phase, we observe a large distribution of the zero field splitting that is attributed to the high local disorder and further supported by density functional theory computations. In the low temperature ferroelastic phase, a single structure phase is detected and shown to contain two magnetic structures. The complex electron paramagnetic resonance signals were identified by means of the Rabi oscillation method combined with the crystal field kernel density estimation.

关键词： Laplacian eigenfunctions   dual geometry   product formulas   triple product   quantum chaos   harmonic analysis on graphs  

摘要： We discuss the geometry of Laplacian eigenfunctions -Delta phi = lambda phi on compact manifolds (M, g) and combinatorial graphs G = (V, E). The "dual" geometry of Laplacian eigenfunctions is well understood on T-d (identified with Z(d)) and R-n (which is self-dual). The dual geometry is of tremendous role in various fields of pure and applied mathematics. The purpose of our paper is to point out a notion of similarity between eigenfunctions that allows to reconstruct that geometry. Our measure of "similarity" alpha(phi(lambda), phi(mu)) between eigenfunctions phi(lambda) and phi(mu) is given by a global average of local correlations alpha(phi(lambda), phi(mu))(2) = parallel to phi(lambda)phi(mu)parallel to(-2)(L2) integral(M)(integral(M) p(t,x,y) (phi(lambda)(y) - phi(lambda)(x)) phi(mu)(y) - phi(mu)(x)dy)(2) dx, where p(t, x, y) is the classical heat kernel and e(-t lambda) + e(-t mu) = 1. This notion recovers all classical notions of duality but is equally applicable to other (rough) geometries and graphs, many numerical examples in different continuous and discrete settings illustrate the result.

关键词： Excited states  

摘要： We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.

关键词： Sodium chloride  

摘要： The lowest band in the charge-transfer-to-solvent ultraviolet absorption spectrum of aqueous chloride ion is studied by experiment and computation. Interestingly, the experiments indicate that at concentrations up to at least 0.25 M, where calculations indicate ion pairing to be significant, there is no notable effect of ionic strength on the spectrum. The experimental spectra are fitted to aid comparison with computations. Classical molecular dynamic simulations are carried out on dilute aqueous Cl-, Na+, and NaCl, producing radial distribution functions in reasonable agreement with experiment and, for NaCl, clear evidence of ion pairing. Clusters are extracted from the simulations for quantum mechanical excited state calculations. Accurate ab initio coupled-cluster benchmark calculations on a small number of representative clusters are carried out and used to identify and validate an efficient protocol based on time-dependent density functional theory. The latter is used to carry out quantum mechanical calculations on thousands of clusters. The resulting computed spectrum is in excellent agreement with experiment for the peak position, with little influence from ion pairing, but is in qualitative disagreement on the width, being only about half as wide. It is concluded that simulation by classical molecular dynamics fails to provide an adequate variety of structures to explain the experimental CTTS spectrum of aqueous Cl-.