Search results for "combinatoric"

Molecular Classification of N-Aryloxazolidinone-5-carboxamides as Human Immunodeficiency Virus Protease Inhibitors

2015

Algorithms for classification and taxonomy are proposed in this chapter based information entropy (IE) and its production. The 38  N- aryloxazolidinone-5-carboxamides (NCAs), for human immunodeficiency virus (HIV) protease (PR) inhibition, are classified using seven characteristic chemical properties of different moieties: R 1/2 , R 3–6 on different phenyls and R 7 . Many classification algorithms are based on IE. When applying some procedures to moderate-sized sets, excessive number of results appear compatible with the data and suffer combinatorial explosion. However, after the equipartition conjecture (EC), one has a selection criterion among different variants that results from classifi…

Class Decomposition for Gastric Cancer Detection from Breath

2021

Lifting paths on quotient spaces

2009

Abstract Let X be a compactum and G an upper semi-continuous decomposition of X such that each element of G is the continuous image of an ordered compactum. If the quotient space X / G is the continuous image of an ordered compactum, under what conditions is X also the continuous image of an ordered compactum? Examples around the (non-metric) Hahn–Mazurkiewicz Theorem show that one must place severe conditions on G if one wishes to obtain positive results. We prove that the compactum X is the image of an ordered compactum when each g ∈ G has 0-dimensional boundary. We also consider the case when G has only countably many non-degenerate elements. These results extend earlier work of the firs…

Extremum degree sets of irregular oriented graphs and pseudodigraphs

2006

Presentations for the Mapping Class Groups of Nonorientable Surfaces

2014

On norm attaining polynomials

2003

We show that for every Banach space X the set of 2-homogeneous continuous polynomials whose canonical extension to X∗∗ attain their norm is a dense subset of the space of all 2-homogeneous continuous polynomials P(2X).

Invariant ordering of surface groups and 3-manifolds which fibre over $S^1$

2006

Spaces of typen on partially ordered sets

1989

This paper contains a generalized approach to incidence geometry on partially ordered sets. A difference to the usual geometrical concepts is that points may have different size. Our main result states that a large class of spaces allows lattice theoretic characterizations. Especially, a generalized version of the Veblen-Young axiom of projective geometry has a lattice theoretic equivalent, called then-generation property (which is a generalization of the ‘Verbindungssatz’). Modularity and distributivity of a lattice of subspaces are reflected in the underlying space. Finally we give specializations and examples.

Integer Complexity: Experimental and Analytical Results II

2015

We consider representing natural numbers by expressions using only 1’s, addition, multiplication and parentheses. Let \( \left\| n \right\| \) denote the minimum number of 1’s in the expressions representing \(n\). The logarithmic complexity \( \left\| n \right\| _{\log } \) is defined to be \({ \left\| n \right\| }/{\log _3 n}\). The values of \( \left\| n \right\| _{\log } \) are located in the segment \([3, 4.755]\), but almost nothing is known with certainty about the structure of this “spectrum” (are the values dense somewhere in the segment?, etc.). We establish a connection between this problem and another difficult problem: the seemingly “almost random” behaviour of digits in the ba…

Parabolic Equations Minimizing Linear Growth Functionals: L1-Theory

2004

Let Ω be a bounded set in ℝN with boundary of class C1. We are interested in the problem $$ \left\{ \begin{gathered} \frac{{\partial u}} {{\partial t}} = diva\left( {x,Du} \right)in Q = \left( {0,\infty } \right) \times \Omega , \hfill \\ u\left( {t,x} \right) = \phi \left( x \right)on S = \left( {0,\infty } \right) \times \partial \Omega , \hfill \\ u\left( {0,x} \right) = u_0 \left( x \right)in x \in \Omega \hfill \\ \end{gathered} \right. $$ (1) where ϕ ∈ L1(∂Ω), u0 ∈ L2(Ω) and a(x, ξ) = ∇ξ f(x, ξ, f being a function with linear growth in ‖ξ‖ as ‖ξ‖ → ∞. One of the classical examples is the nonparametric area integrand for which \( f(x,\xi ) = \sqrt {1 + \left\| \xi \right\|^2 } \). Prob…