Search results for "topological"
showing 10 items of 420 documents
Fractal Dimension of Transdermal-Delivery Drug Models: 4-Alkylanilines
2008
Abstract The pathways that exist in porous membranes used to deliver drugs form fractal percolating paths. For a homologous series of 4-alkylanilines, the fractal dimension D is calculated as a model for transdermal-delivery drugs. Program TOPO is used for the calculation of the solvent-accessible surface AS, which is denoted by the centre of a probe, which is allowed to roll on the outside while maintaining contact with the bare molecular surface S. AS depends on the probe radius R. For 4-alkylanilines, the quadrupole moment Θ is doubled. The hydrophobic contribution to AS is doubled while its hydrophilic part remains constant. D increases 11%. Geometric descriptor and topological index re…
Characteristic Topological Features of Promoter Capture Hi-C Interaction Networks
2020
Current Hi-C technologies for chromosome conformation capture allow to understand a broad spectrum of functional interactions between genome elements. Although significant progress has been made into analysis of Hi-C data to identify the biologically significant features, many questions still remain open. In this paper we describe analysis methods of Hi-C (specifically PCHi-C) interaction networks that are strictly focused on topological properties of these networks. The main questions we are trying to answer are: (1) can topological properties of interaction networks for different cell types alone be sufficient to distinguish between these types, and what the most important of such propert…
THE TOPOLOGY OF BASIN BOUNDARIES IN A CLASS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS
1996
We will develop new methods to determine the topology of the basin boundary in a class of three-dimensional dynamical systems. One approach is to approximate the basin boundary by backward integration. Unfortunately, there are dynamical systems where it is hard to approximate the basin boundary by a numerical backward integration algorithm. We will introduce topological methods which will provide new information about the structure of the basin boundary. The topological invariants which we will use can be numerically computed.
Topological Insulators from a Chemist’s Perspective
2012
Topology and chemistry are deeply entangled subjects, whichmanifests in the way chemists like to think and approachproblems. Although not at first glance, topology allows thecategorizationoffundamentalinherentpropertiesofthehugenumber of different chemical compounds, carving out theunique features of a class of materials of different complexity,a topic which Turro worked out in his treatise on geometricaland topological thinking in chemistry.
Separation conditions on controlled Moran constructions
2017
It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions with this respect.
Spectral Properties of Partial *-Algebras
2010
We continue our study of topological partial *algebras focusing our attention to some basic spectral properties. The special case of partial *-algebras of operators is examined first, in order to find sufficient hints for the study of the abstract case. The outcome consists in the selection of a class of topological partial *-algebras (partial GC*-algebras) that behave well from the spectral point of view and that allow, under certain conditions, a faithful realization as a partial O*-algebra.
Remarks on the semivariation of vector measures with respect to Banach spaces.
2007
Suppose that and . It is shown that any Lp(µ)-valued measure has finite L2(v)-semivariation with respect to the tensor norm for 1 ≤ p < ∞ and finite Lq(v)-semivariation with respect to the tensor norm whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor norm for any 1 ≤ q < 2. It is also shown that the measure m (A) = χA has infinite Lq-semivariation with respect to the tensor norm if q < p.
Hypergraph functor and attachment
2010
Using an arbitrary variety of algebras, the paper introduces a fuzzified version of the notion of attachment in a complete lattice of Guido, to provide a common framework for the concept of hypergraph functor considered by different authors in the literature. The new notion also gives rise to a category of variable-basis topological spaces which is a proper supercategory of the respective category of Rodabaugh.
On Certain Metrizable Locally Convex Spaces
1986
Publisher Summary This chapter discusses on certain metrizable locally convex spaces. The linear spaces used are defined over the field IK of real or complex numbers. The word "space" will mean "Hausdorff locally convex space". This chapter presents a proposition which states if U be a neighborhood of the origin in a space E. If A is a barrel in E which is not a neighborhood of the origin and F is a closed subspace of finite codimension in E’ [σ(E’,E)], then U° ∩ F does not contain A° ∩ F. Suppose that U° ∩ F contain A° ∩ F. Then A° ∩ F is equicontinuous hence W is also equicontinuous. Since W° is contained in A, it follows that A is a neighborhood of the origin, a contradiction.
On closures of discrete sets
2018
The depth of a topological space $X$ ($g(X)$) is defined as the supremum of the cardinalities of closures of discrete subsets of $X$. Solving a problem of Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the supremum of the cardinalities of the free sequences in $X$.