Search results for "Combinatorics"
showing 10 items of 1770 documents
Table of Periodic Properties of Fullerenes Based on Structural Parameters.
2004
The periodic table (PT) of the elements suggests that hydrogen could be the origin of everything else. The construction principle is an evolutionary process that is formally similar to those of Darwin and Oparin. The Kekulé structure count and permanence of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q and r. Let p be the number of edges common to two pentagons, q the number of vertices common to three pentagons, and r the number of pairs of nonadjacent pentagon edges shared between two other pentagons. Principal component analysis (PCA) of the structural parameters and cluster analysis (CA) of the fullerenes perm…
Locally convex quasi *-algebras with sufficiently many *-representations
2012
AbstractThe main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra (A[τ],A0) attains sufficiently many (τ,tw)-continuous ⁎-representations in L†(D,H), to separate its points. Having achieved this, a usual notion of bounded elements on A[τ] rises. On the other hand, a natural order exists on (A[τ],A0) related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras.
The cartesian closed bicategory of generalised species of structures
2007
AbstractThe concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised analytic functors, is also put forward. These definitions encompass most notions of combinatorial species considered in the literature — including of course Joyal's original notion — together with their associated substitution operation. Our first main result exhibits the substitution calculus of generalised species as arising from a Kleisli bicategory for a pseudo-comonad on profunctors. Our secon…
On the proper homotopy invariance of the Tucker property
2006
A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.
Optimization Under Fuzzy Max-t-Norm Relation Constraints
2019
Fuzzy relation equations and inequalities play an important role in many tools of fuzzy modelling and have been extensively studied. In many practical applications they are used as constraints in optimization. Algorithms for specific objective functions have been proposed by many authors. In this paper we introduce a method to convert a system of fuzzy relation constraints with max-t-norm composition to a linear constraint system by adding integer variables. A numerical example is provided to illustrate the proposed method.
Ornamenti un Simetrijas: Ornamentālo Rakstu Zīmju Valoda (intervija ar Modri Tenisonu)
2010
Ornaments and Symmetry: Language of Signs of Ornamental Tracery (see interview with Modris Tenisons http://www.blip.tv/file/3173653) In his first interview Modris Tenisons explains language of ornamentalistic signs for national ornamental belts using his discovered law of sieve displacement, which gives base duality element in ornamentalistic signs, and routine how to generate 240 elements of signs from 10 “seeds of chaos” sufficient to produce all ornametal belts of first order. He tells also about his discoverd 16 sign alphabet, that does the same. Pirmajā mutvārdu liecinājumā Modris Tenisons stāsta par ornamentālo rakstu zīmju veidošanās likumsakarībām sakrustojot divu krāsu diegus audum…
Polyomino coloring and complex numbers
2008
AbstractUsually polyominoes are represented as subsets of the lattice Z2. In this paper we study a representation of polyominoes by Gaussian integers. Polyomino {(x1,y1),(x2,y2),…,(xs,ys)}⊂Z2 is represented by the set {(x1+iy1),(x2+iy2),…,(xs+iys)}⊂Z[i]. Then we consider functions of type f:P→G from the set P of all polyominoes to an abelian group G, given by f(x,y)≡(x+iy)m(modv), where v is prime in Z[i],1≤m<N(v) (N(v) is the norm of v). Using the arithmetic of the ring Z[i] we find necessary and sufficient conditions for such a function to be a coloring map.
Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
2020
We provide a quantitative lower bound to the Cheeger constant of a set $\Omega$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide examples which show that these quantitative estimates are sharp.
Strong chromatic index of products of graphs
2007
Graphs and Algorithms
Exact results for accepting probabilities of quantum automata
2001
One of the properties of Kondacs-Watrous model of quantum finite automata (QFA) is that the probability of the correct answer for a QFA cannot be amplified arbitrarily. In this paper, we determine the maximum probabilities achieved by QFAs for several languages. In particular, we show that any language that is not recognized by an RFA (reversible finite automaton) can be recognized by a QFA with probability at most 0.7726...