Semiharmonic bicyclic graphs

Classification of harmonic and semiharmonic graphs according to their cyclomatic number became of interest recently. All finite harmonic graphs with up to four independent cycles, as well as all finite semiharmonic graphs with at most one cycle were determined. Here, we determine all finite semiharmonic bicyclic graphs. Besides that, we present several methods for constructing semiharmonic graphs from existing ones, and we apply one of these constructions to show that the number of semiharmonic graphs with fixed cyclomatic number $k$ is infinite for every $k$.     

Semiharmonic trees and monocyclic graphs

A graph G is defined to be semiharmonic if there is a constant μ (necessarily a natural number) such that, for every vertex v, the number of walks of length 3 starting in v equals μd_G(v) where d_G(v) is the degree of v. We determine all finite semiharmonic trees and monocyclic graphs.     

Isotone Maps as Maps of Congruences. II. Concrete Maps

Let L be a lattice and let L ₁, L ₂ be sublattices of L. Let be a congruence relation of L ₁. We extend to L by taking the smallest congruence......     

联系区间映射与圆周映射的函数方程

在解释区间映射和圆周映射的数量普适性现象的理论中，有关的重整化群函数方程及其解起着关键作用。本文研究具有广泛意义的联系这两种映射的函数方程得到的主要结果是它存在无穷多个Ｃ￣∞解，且可用构造性方法给出，其参数的范围比［９］中的Ｄ大。最后还提出一些值得进一步研究的问题。     

Computing Harmonic Maps and Conformal Maps on Point Clouds

We use a narrow-band approach to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a point cloud approximation, we simply use the standard cubic lattice to approximate its $\epsilon$-neighborhood. Then the harmonic map of the surface can be approximated by discrete harmonic maps on lattices. The conformal map, or the surface uniformization, is achieved by minimizing the Dirichlet energy of the harmonic map while deforming the target surface of constant curvature. We propose algorithms and numerical examples for closed surfaces and topological disks. To the best of the authors' knowledge, our approach provides the first meshless method for computing harmonic maps and uniformizations of higher genus surfaces.     

Intrinsic Reducibilities

Let . We show that for many reducibilities, the requirement that a relation be intrinsically reducible to the α‐th jump of a countable mode A has a syntactic equivalent. Furthermore, we show that many reducibilities coincide in such a situation.     

On Thermodynamics of Rational Maps. II: Non-Recurrent Maps

The pressure function p(t) of a non-recurrent map is real analyticon some interval (0,t_*) with t_* strictly greater than the dimensionof the Julia set. The proof is an adaptation of the well knowntower techniques to the complex dynamics situation. In general,p(t) need not be analytic on the whole positive axis.     

Parabolic Rational Maps

The paper studies the dynamics of rational maps with indifferentparabolic points by comparing their dynamical properties withthose of their ‘jump transformation’ which is uniformlyexpanding on a non-compact set with infinite Markov partition.It establishes the spectral properties of a two-variables operator-valuedfunction associated to the jump transformation and exploitstheir dynamical relevance to allow the analytic properties ofthe pressure, the escape rate from a neighbourhood of the Juliaset and the asymptotic distribution of pre-images to be studied.     

Asymmetric Combinatorially-Regular Maps

It is shown that for every g≥3, there exists a combinatorially regular map M of type (3, 7) on a closed orientable surface of genus g, such that M has trivial symmetry group. Such maps are constructed from Schreier coset graphs corresponding to permutation representations of the (2, 3, 7) triangle group. 1991 Mathematics Subject Classification: 57M15.     

Subelliptic Biharmonic Maps

We study subelliptic biharmonic maps, i.e., smooth maps ?:M→N from a compact strictly pseudoconvex CR manifold M into a Riemannian manifold N which are critical points of the energy functional $E_{2,b} (\phi ) = \frac{1}{2} \int_{M} \| \tau_{b} (\phi ) \|^{2} \theta \wedge (d \theta)^{n}$ . We show that ?:M→N is a subelliptic biharmonic map if and only if its vertical lift ?°π:C(M)→N to the (total space of the) canonical circle bundle $S^{1} \to C(M) \stackrel{\pi}{\longrightarrow} M$ is a biharmonic map with respect to the Fefferman metric F _θ on C(M).     

幂保持加法映射

本文得到了域上n×n矩阵代数的幂保持加法映射的刻画,同时刻画了对称矩阵的幂保持加法映射.     

保谱乘法映射

设X,Y为Banach空间,证明了B（X）到B（Y）的保谱乘法满射φ具有形式φ（T）＝ATA-1,其中A为X到Y上的同构．     

Factoring Factor Maps

A noninjective bounded-to-one factor map from an irreducibleshift of finite type onto a sofic system can be factored asa composition of other such maps in only finitely many ways(up to isomorphism). This generalizes to factor maps from systemswith canonical coordinates to finitely presented dynamical systems.     

关于三商映射

三商映射是完备映射和开映射的共同推广。本文综述三商映射的理论，论术这三商映射，开映射，紧覆盖映射，诱导完备映之间的一些转换关系，提出了几个供进一步研究的问题。     

p阶Feigenbaum映射

A continuous map f from the unit closed interval into itself is called a p-order Feigenbaum's map if fp(λx) = λf(x),f(O)=1 and f|[λ,1] is univallecular. In this paper, some characterizations of p order Feigenbaum's maps are discussed and the existence for both types of such maps is proven.     

Subadditive Separating Maps

Let X and Y denote compact Hausdorff spaces and let K = R (real numbers) or C(complex numbers). C(X) and C(Y) denote the spaces of K-valued continuous functions on X and Y, respectively. A map H : C(X) C(Y) is separating if fg = 0 implies that HfHg = 0. Results about automatic continuity and the form of additive and linear separating maps have been developed in [1], [2], [3], [4], [5], [7], [8], and [10]. In this article similar results are developed for subadditive separating maps. We show (Theorem 5.11) that certain biseparating, subadditive bijections H are automatically continuous.     

Hemi-slant Riemannian Maps

In this note, we characterize global Lipschitz Nemytskii operators in the Riesz-bounded variation space with variable exponent, and in the course of the proof, we also show that this space is a Banach algebra.