Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.

The purpose of this note is to state a collection of results, all related to questions of uniqueness of smooth neighborhoods of finite complexes as imbedded (nicely) in differentiable manifolds. The reported results will appear in subsequent papers, the first of which is [l ]. The approach taken is always via the theory of simple homotopy types (due to J. H. C. Whitehead), and the main theorem ...

In his essay, the author reflects on death of ‘beauty’ within context present state nature (the phenomenon forest and its problems), modern art transformations visual art) language demise dialects, destruction by contemporary ideologies). The fact that is not merely a subjective category purely matter individual taste means we can rationally discuss renewal (nature), talent, craftsmanship dilig...

Concurrence and further entanglement quantifiers can be computed explicitly for channels of rank two if representable by just two Kraus operators. Almost all details are available for the subclass of rank two 1-qubit channels. There is a simple geometric picture beyond, explaining nicely the role of anti-linearity.

Isocyanides are important building blocks in organic synthesis; however, their synthesis is time and resource consuming often unpleasant due to smelly nature. Diversification of isocyanides can be accomplished by de novo or from already existing isocyanides. In this work, we report for the first-time isocyanide diversification based on nucleophilic aromatic substitution suitable precursor The m...

Received ; accepted – 2 – ABSTRACT We evaluate the dependence of the cluster correlation length r c on the mean intercluster separation D c , for three models with critical matter density, vanishing vacuum energy (Λ = 0) and COBE normalized: a tilted CDM (tCDM) model (n = 0.8) and two blue mixed models with two light massive neutrinos yielding Ω h = 0.26 and 0.14 (MDM1 and MDM2, respectively). ...

Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness,...

As a rule, an energy method is widely adopted for b-spline curve smoothing, but this method has the disadvantages such as massive calculation, computation complexity and low efficiency. Compared with the energy method, multi-resolution smoothing approaches nicely overcome these obstacles. Presently, some researches have been conducted on multi-resolution smoothing, but these efforts mainly aime...

Problem Set 1 is due next Wednesday. 2 Overview Today we will do the following. • Prove the Elias-Bassalygo-Johnson Bound introduced in the previous lecture. Recall that the proof consists of the two lemmas described roughly below – List decodable codes have poor rate. – Good error correcting codes are nicely decodable. • Introduce some algebraic codes along with some helpful idea from algebra....

PURPOSE This article proposes a simple model that describes the quantitative relationship between unaided visual acuity and blur attributed to refractive errors. METHODS The standard model for describing the relationship between visual acuity and blur, as published by Raasch, is used as a starting point to develop a simpler model based on heuristic arguments. The basis of Raasch's data is aug...