相关论文: Iterated altans and their properties
Altanisation (formation of the altan of a parent structure) originated in the chemical literature as a formal device for constructing generalised coronenes from smaller structures. The altan of graph $G$, denoted $\mathfrak{a}(G, H)$,…
The regular embeddings of complete bipartite graphs $K_{n,n}$ in orientable surfaces are classified and enumerated, and their automorphism groups and combinatorial properties are determined. The method depends on earlier classifications in…
The structural investigations of nanomaterials motivated by their large variety and diverse set of applications have attracted considerable attention. In particular, the ever-improving machinery, both in laboratory and at large scale…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].
In this paper, it is established that quantum nilpotent algebras (also known as CGL extensions) are catenary, i.e., all saturated chains of inclusions of prime ideals between any two given prime ideals $P \subsetneq Q$ have the same length.…
Nanotubes show great promise for miniaturizing advanced technologies. Their exceptional physical properties are intimately related to their morphological and crystal structure. Circumferential faceting of multiwalled nanotubes reinforces…
Computational studies of basic models of strongly-correlated electron systems can provide guidance in the search for new materials as well as insight into the physical mechanisms responsible for their properties. Here, we illustrate this by…
This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…
In math.QA/0506507 I. Gelfand and the authors introduced and studied a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for a large class of layered (i.e. ranked) graphs.
The properties of bulk nanostructured materials are often controlled by atomic scale features like segregation along defects or composition gradients. Here we discuss about the complimentary use of TEM and APT to obtain a full description…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…
Research on graphene and other two-dimensional atomic crystals is intense and likely to remain one of the hottest topics in condensed matter physics and materials science for many years. Looking beyond this field, isolated atomic planes can…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…
Using empirical scheme, atomic structure of a new exotic class of silicon nanoclusters was elaborated upon the central icosahedral core (Si-IC) and pentagonal petals (Si-PP) growing from Si-IC vertexes. It was shown that Si-IC/Si-PP…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…
We introduce and study a category of algebras strongly connected with the structure of the Gelfand-Tsetlin subalgebras of the endomorphism algebras of Bott-Samelson bimodules. We develop a series of techniques that allow us to obtain…