A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such...

We perform the global stability analysis for a viral infection model with two types of immune response. The model is formulated as a system of delay differential equations. We determine the global dynamics in terms of the basic reproduction number using Lyapunov functionals. Our results on the global stability of the infected equilibrium answer the conjecture offered in the paper [K. Wang, W. W...

The newly adjusted energy-consistent nine-valence-electron pseudopotentials for K to Fr are used to calculate spectroscopic properties for the neutral and positively charged alkali dimers using coupled cluster and density functional theory. For the neutral dimers the static dipole polarizability was calculated. The coupled cluster results are all in excellent agreement with experimental values....

We introduce the space Sω1,ω2 of all C ∞ functions φ such that sup |α|≤m‖e1∂αφ‖∞ and sup |α|≤m‖e2∂αφ̂‖∞ are finite for all k ∈ N0, α ∈ Nn0 , where ω1 and ω2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space Sω1,ω2 without conditions on the derivatives. For functionals in the dual space S ′ ω1,ω2 , we prove a structure theo...

We prove a $\Gamma$-convergence result for class of Ginzburg-Landau type functionals with $\mathcal{N}$-well potentials, where $\mathcal{N}$ is closed and $(k-2)$-connected submanifold $\mathbb{R}^m$, in arbitrary dimension. This includes, instance, the Landau-de Gennes free energy nematic liquid crystals. The density minimisers, subject to Dirichlet boundary conditions, converges generalised s...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

The performance of density functional theory methods for the modeling of condensed aqueous systems is hard to predict and validation by ab initio molecular simulation of liquid water is absolutely necessary. In order to assess the reliability of these tests, the effect of temperature on the structure and dynamics of liquid water has been characterized with 16 simulations of 20 ps in the tempera...

We show in this paper that the Plancherel measure of the symmetric group S n converges weakly (as n ! 1) to a Gaussian random process in the innnite dimensional vector space. With respect to the law of large numbers for this group, found earlier in 1,2] this assertion is analogous to the central limit theorem. The idea of such a result was mentioned in 3]. In the course of preparation of the ar...

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

There are certain countably generated ?-algebras of sets in the real line which do not admit any non-zero, ?-finite, diffused (or, continuous) measure. Such can be obtained by use some special types infinite matrix known as Banach-Kuratowski and same may used deriving a generalized version Pelc Prikry?s theoremas shown Kharazishvili. Here, this paper, we develop an abstract formulation theorem ...