相关论文: Existence and Optimality of $w$-Non-adjacent Forms…

Controlled and uniform assembly of "bottom-up" nanowire (NW) materials with high scalability has been one of the significant bottleneck challenges facing the potential integration of nanowires for both nano and macro electronic circuit…

The paper presents fundamental metrical theorems for a class of continued fraction-like expansions known as $\theta$-expansions. We first prove Khinchine's Weak Law of Large Numbers for the sum of digits, followed by the Diamond-Vaaler…

A recently developed finite element approach for fully numerical atomic structure calculations [S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019)] is extended to the description of atoms with spherically symmetric densities via…

We show there exists a constant $0<c_{0}<1$ such that the dimension of every measure on $[0,1]$, which makes the digits in the continued fraction expansion independent, is at most $1-c_{0}$. This extends a result of Kifer, Peres and Weiss…

The dimerized one-dimensional Hubbard model is studied in the framework of lattice density-functional theory (LDFT). The single-particle density matrix gamma_{ij} with respect to the lattice sites is considered as basic variable. The…

Currently, self-induced InAlN core-shell nanorods enjoy an advanced stage of accumulation of experimental data from their growth and characterization as well as a comprehensive understanding of their formation mechanism by the ab initio…

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…

A \emph{spanner} of a graph $G$ is a subgraph $H$ that approximately preserves shortest path distances in $G$. Spanners are commonly applied to compress computation on metric spaces corresponding to weighted input graphs. Classic spanner…

The shape dependence for the technologically important nickel oxide (NiO) nanocrystals on (001) strontium titanate substrates is investigated under the generalized Wulff-Kaichew (GWK) theorem framework. It is found that the shape of the NiO…

Let $(X,d)$ be a metric space and $f: X \rightarrow X$ be a homeomorphism. We say that a dynamical system $(X,f)$ is \emph{expansive}, with constant of expansivity $c \in \mathbb{R{^+}}$, if for all $x,y \in X$ , $x \neq y$, exists $n \in…

We provide a criterion for a vertex operator superalgebra homomorphism from an affine vertex algebra to another vertex superalgebra to be conformal, and an additional criterion that guarantees that this homomorphism is surjective. This…

In this note, we use the mass transference principle for rectangles, recently obtained by Wang and Wu (Math. Ann., 2021), to study the Hausdorff dimension of sets of "weighted $\Psi$-well-approximable" points in certain self-similar sets in…

We analyze the electronic structure of group III-V semiconductors obtained within full potential linearized augmented plane wave (FP-LAPW) method and arrive at a realistic and minimal tight-binding model, parameterized to provide an…

Let $C, W \subseteq \mathbb{Z}$. If $C + W = \mathbb{Z}$, then the set $C$ is called an additive complement to $W$ in $\mathbb{Z}$. If no proper subset of $C$ is an additive complement to $W$, then $C$ is called a minimal additive…

We investigate the Edge-Isoperimetric Problem (EIP) for sets with $n$ elements of the cubic lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. Minimizers $M_n$ of the edge perimeter are…

Let $A$ be an expanding $d\times d$ matrix with integer entries and ${\mathcal D}\subset {\mathbb Z}^d$ be a finite digit set. Then the pair $(A, {\mathcal D})$ defines a unique integral self-affine set $K=A^{-1}(K+{\mathcal D})$. In this…

We investigate the class of root systems R obtained by extending an irreducible root system by a torsion-free group G. In this context there is a Weyl group W and a group U with the presentation by conjugation. We show under additional…

We address the problem of determining the Hausdorff dimension of sets consisting of complex irrationals whose complex continued fraction digits satisfy prescribed restrictions and growth conditions. For the Hurwitz continued fraction, we…

Self-organized silicide nanowires are considered as main building blocks of future nanoelectronics and have been intensively investigated. In nanostructures, the lattice vibrational waves (phonons) deviate drastically from those in bulk…

Let $M$ be a smooth manifold equipped with a conformal structure, $E[w]$ the space of densities with the the conformal weight $w$ and $D_{w,w+\de}$ the space of differential operators from $E[w]$ to $E[w+\delta]$. Conformal quantization $Q$…