Search results for " Algebra"
showing 10 items of 2082 documents
Two-view “cylindrical decomposition” of binary images
2001
This paper describes the discrete cylindrical algebraic decomposition (DCAD) construction along two orthogonal views of binary images. The combination of two information is used to avoid ambiguities for image recognition purposes. This algorithm associates an object connectivity graph to each connected component, allowing a complete description of the structuring information. Moreover, an easy and compact representation of the scene is achieved by using strings in a five letter alphabet. Examples on complex digital images are also provided. © 2001 Elsevier Science Inc.
A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms
2017
Abstract The realification of the ( 2 n + 1 ) -dimensional complex Heisenberg Lie algebra is a ( 4 n + 2 ) -dimensional real nilpotent Lie algebra with a 2-dimensional commutator ideal coinciding with the centre, and admitting the compact algebra sp ( n ) of derivations. We investigate, in general, whether a real nilpotent Lie algebra with 2-dimensional commutator ideal coinciding with the centre admits a compact Lie algebra of derivations. This also gives us the occasion to revisit a series of classic results, with the expressed aim of attracting the interest of a broader audience.
Minimal flavour seesaw models
2009
26 pages, 8 figures.-- ArXiv pre-print available at: http://arxiv.org/abs/0906.1461
Diffraction by m-bonacci gratings
2015
We present a simple diffraction experiment with m-bonacci gratings as a new interesting generalization of the Fibonacci ones. Diffraction by these nonconventional structures is proposed as a motivational strategy to introduce students to basic research activities. The Fraunhofer diffraction patterns are obtained with the standard equipment present in most undergraduate physics labs and are compared with those obtained with regular periodic gratings. We show that m-bonacci gratings produce discrete Fraunhofer patterns characterized by a set of diffraction peaks which positions are related to the concept of a generalized golden mean. A very good agreement is obtained between experimental and …
Suffix Automata and Standard Sturmian Words
2007
Blumer et al. showed (cf. [3,2]) that the suffix automaton of a word w must have at least |w|+1 states and at most 2|w|-1 states. In this paper we characterize the language L of all binary words w whose minimal suffix automaton S(w) has exactly |w| + 1 states; they are precisely all prefixes of standard Sturmian words. In particular, we give an explicit construction of suffix automaton of words that are palindromic prefixes of standard words. Moreover, we establish a necessary and sufficient condition on S(w) which ensures that if w ∈ L and a ∈ {0, 1} then wa ∈ L. By using such a condition, we show how to construct the automaton S(wa) from S(w). More generally, we provide a simple construct…
The diamond partial order for strong Rickart rings
2016
The diamond partial order has been first introduced for matrices, and then discussed also in the general context of *-regular rings. We extend this notion to Rickart rings, and state various properties of the diamond order living on the so-called strong Rickart rings. In particular, it is compared with the weak space preorder and the star order; also existence of certain meets and joins under diamond order is discussed.
Feasibility of finite and infinite paths in data dependent programs
2005
This paper considers the feasibility of finite and infinite paths in programs in two simple programming languages. The language LBASE allows to express the dependencies of real time systems on integer data, the language LTIM can model quantitative timing constraints in r.t.s. specifications. It is proven that the problem of whether a given LBASE or LTIM program has an infinite feasible path (i.e. whether it can exhibit an infinite behaviour) is decidable. The possibilities to characterise the sets of all feasible finite and infinite paths in LBASE and LTIM programs are also discussed. The infinite feasible path existence problem is proven decidable also for the language LTIBA which has both…
Computational issues of an electromagnetics transient meshless method
2019
In this paper we refer to the computational issues in solving Maxwell’ s curl equations without using any connectivity among the points in which the problem domain is discretized. The adopted procedure is able to approximate the electric and magnetic vector fields making use of the derivatives of a kernel function at points arranged in the computational domain. In order to improve the numerical accuracy, dealing with irregular data distribution or data located near the boundary, a suitable strategy is considered. The computational core of the overall process requires elementary linear algebra operations. In the paper the method is presented and the discussion is revolved to the computationa…
Binary jumbled string matching for highly run-length compressible texts
2012
The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s. Previous solutions created an index of size O(n) in a pre-processing step, which was then used to answer queries in constant time. The fastest algorithms for construction of this index have running time $O(n^2/\log n)$ [Burcsi et al., FUN 2010; Moosa and Rahman, IPL 2010], or $O(n^2/\log^2 n)$ in the word-RAM model [Moosa and Rahman, JDA 2012]. We propose an index constructed directly from the run-length encoding of $s$. The construction time of our index i…
Nondeterministic operations on finite relational structures
1998
Abstract This article builds on a tutorial introduction to universal algebra for language theory (Courcelle, Theoret. Comput. Sci. 163 (1996) 1–54) and extends it in two directions. First, nondeterministic operations are considered, i.e., operations which give a set of results instead of a single one. Most of their properties concerning recognizability and equational definability carry over from the ordinary case with minor modifications. Second, inductive sets of evaluations are studied in greater detail. It seems that they are handled most naturally in the framework presented here. We consider the analogues of top-down and bottom-up tree transducers. Again, most of their closure propertie…