Descripción: Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: Fil:Braberman, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: A recursive reformulation of Sierpinski's construction of an absolutely normal number was provided. The reformulation produced a computable absolute normal number in base 2, which was normal in any scale considered. The construction was adapted to define numbers in any other bases and distinct numbers were obtained for different bases.

Descripción: A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum clique-independent set of G, respectively. A graph G is clique-perfect if these two numbers are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. In this paper, we present a partial result in this direction; that is, we characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs. © 2007 Elsevier B.V. All rights reserved.

Descripción: Fil:Durán, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: Fil:Burzyn, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees. © 2010 Elsevier B.V. All rights reserved.

Descripción: We applied a methodology capable of resolving the optical rotatory power into atomic contributions. The individual atomic contributions to the optical rotatory power and molecular chirality of the methylhydroperoxide are obtained via a canonical transformation of the Hamiltonian by which the electric dipolar moment operator is transformed to the acceleration gauge formalism and the magnetic dipolar moment operator to the torque formalism. The gross atomic isotropic contributions have been evaluated for the carbon, the nonequivalent oxygen, and the nonequivalent hydrogen atoms of methylhydroperoxide, employing a very large Gaussian basis set which is close to the Hartree-Fock limit. © 2008 American Institute of Physics.

Descripción: An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting density matrix contains explicit time odd components in the form of collective flows. As a specific application we consider the dynamics of the expansion in connection with heavy ion experiments. Lattice gas and classical molecular dynamics simulations are shown. © 2007 American Institute of Physics.

Descripción: The present work investigates several questions from a recent survey of Miller and Nies related to Chaitin's Ω numbers and their dependence on the underlying universal machine. Furthermore, the notion ΩU [X] = ∑p : U (p) ↓ ∈ X 2- | p | is studied for various sets X and universal machines U. A universal machine U is constructed such that for all x, ΩU [{ x }] = 21 - H (x). For such a universal machine there exists a co-r.e. set X such that ΩU [X] is neither left-r.e. nor Martin-Löf random. Furthermore, one of the open problems of Miller and Nies is answered completely by showing that there is a sequence Un of universal machines such that the truth-table degrees of the ΩUn form an antichain. Finally, it is shown that the members of hyperimmune-free Turing degree of a given Π1 0-class are not low for Ω unless this class contains a recursive set. © 2006 Elsevier Inc. All rights reserved.

Descripción: In an unpublished manuscript, Alan Turing gave a computable construction to show that absolutely normal real numbers between 0 and 1 have Lebesgue measure 1; furthermore, he gave an algorithm for computing instances in this set. We complete his manuscript by giving full proofs and correcting minor errors. While doing this, we recreate Turing's ideas as accurately as possible. One of his original lemmas remained unproved, but we have replaced it with a weaker lemma that still allows us to maintain Turing's proof idea and obtain his result. © 2007 Elsevier Ltd. All rights reserved.

Descripción: The set of 1:1 and 2:1 complexes of XOOX′ (X, X′ H, CH 3) with lithium cation has been studied to determine if they are suitable candidates for chiral discrimination in an isotropic medium via nuclear magnetic resonance spectroscopy. Conventional nuclear magnetic resonance is unable to distinguish between enantiomers in the absence of a chiral solvent. The criterion for experimental detection is valuated by the isotropic part of nuclear shielding polarisability tensors, related to a pseudoscalar of opposite sign for two enantiomers. The study includes calculations at coupled Hartree-Fock and density functional theory schemes for 17O nucleus in each compound. Additional calculations for 1H are also included for some compounds. A huge static homogeneous electric field, perpendicular to the magnetic field of the spectromer, as big as ≈1.7 108 V m -1 should be applied to observe a shift of ≈1 ppm for 17O magnetic shielding in the proposed set of complexes. © 2011 American Institute of Physics.

Descripción: We present an algorithm to compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with a fixed structure. Using this representation, we also show an algorithm to compute polynomial inequality conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present symbolic procedures to describe the set of isolated totally mixed Nash equilibria of an arbitrary game and to compute, under certain general assumptions, the exact number of these equilibria. The complexity of all these algorithms is polynomial in the number of players, the number of each player's strategies and the generic number of totally mixed Nash equilibria of a game with the considered structure. © 2009 Elsevier Ltd. All rights reserved.

Descripción: A two-component theory for shielding calculations starting from a four-component Rayleigh-Schrodinger perturbation theory (RSPT) formalism is presented. Thus, a set of operators entering the RSPT expressions in terms of the Schrodinger molecular spectrum are derived by expanding such four-component expression as a power series in c-1. All formal expressions are retained, without neglecting any terms in the intermediate steps of the derivation.

Descripción: For a vector function u: ℝ→ ℝ N we consider the system, where G: ℝ N → ℝ is a C 1 function. We are interested in finding all possible T-periodic forcing terms p(t) for which there is at least one solution. In other words, we examine the range of the semilinear operator S: H 2 per → L 2([0, T],ℝ N) given by, where. Writing p(t) = p̄ + p̄(t), where, we present several resultsconcerning the topological structure of the set. © 2012 Texas State University-San Marcos.

Descripción: Nitrogen 14 quadrupole coupling constants for H2CN+ and HCN are predicted via ab initio self-consistent-field and configuration interaction theory. Effects of electron correlation, basis set completeness, and geometrical structure on the predicted electric field gradients are analyzed. The quadrupole coupling constant obtained for H2CN+ is one order of magnitude less than in HCN, providing an explanation for the experimental fact that the fine structure of the microwave spectrum of H 2CN+ has not been resolved. This research also allows a reliable prediction of the nuclear quadrupole moment of 14N, namely Q(14N)=2.00×10-26 cm2. © 1986 American Institute of Physics.

Descripción: The theory of dynamic frames is a promising approach to handle the so-called framing problem, that is, giving a precise characterizations of the locations in the heap that a procedure may modify. In this paper, we show that the machinery used for dynamic frames may be exploited even further. In particular, we use it to check that implementations of abstract data types maintain certain structural invariants that are very hard to express with usual means, including being acyclic (like non-circular linked lists and trees) and having a unique path between nodes (like in a tree). The idea is that regions in this formalism over-approximate the set of reachable objects. We can then maintain this structural invariants by including special preconditions in assignments, of the kind that can be verified by state-of-the-art SMT-based tools. To test this approach we modified the verifier for the Dafny programming language in a suitable way and were able to enforce these invariants in non-trivial examples. © 2011 Springer-Verlag.

Descripción: In this work we present Zeus, a Distributed Model-Checker that evolves from the tool Kronos [8] and that currently can handle backwards computation of TCTL-reachability properties [1] over timed-automata [2]. Zeus was developed following a software architecture centric approach. It introduces some interesting features such as a priori graph partitioning, a sophisticated machinery to reach optimum performance (communication piggybacking and delayed messaging) and dead-time utilization, where every processor uses time intervals of inactivity to perform auxiliary, time-consuming tasks that will later speed up the rest of the computation. Although some good results have been obtained, early experiments pinpointed the difficulties of getting speedups using a parallel asynchronous version. We also propose some paths to overcome those obstacles. We would like to thank Sergio Yovine for making Kronos libraries available to us. © 2002 Published by Elsevier Science B.V.

Descripción: We introduce the notion of a T-path within Petri nets, and propose to adopt the model of directed hypergraphs in order to determine properties of nets; in particular, we study the relationships between T-paths and firable sequences of transitions. Let us consider a Petri net P=〈P,T,A,M0〉 and the set of places with a positive marking in M0, i.e., P0=p|M0(p)>0. If we regard the net as a directed graph, the existence of a simple path from any place in P0 to a transition t is, of course, a necessary condition for the potential firability of t. This is sufficient only if the net is a state machine, where |•t|=|t•|=1 for all t∈T. In this paper we show that the existence of a T-path from any subset of P0 to a transition t is a more restrictive condition and is, again, a necessary condition for the potential firability of t. But, in this case: (a) if P is a conflict-free Petri net, this is also a sufficient condition, (b) if P is a general Petri net, t is potentially firable by increasing the number of tokens in P0. For conflict-free nets (CFPN) we consider the following problems: (a) determining the set of firable transitions, (b) determining the set of coverable places, (c) determining the set of live transitions, (d) deciding the boundedness of the net. For all these problems we provide algorithms requiring linear space and time, i.e., O(|P|+|T|+|A|), for a net P=〈P,T,A,M0〉. Previous results for this class of networks are given by Howell et al. (1987) [20], providing algorithms for solving problems in conflict-free nets in O(|P|×|T|) time and space. Given a Petri net and a marking M, the well-known coverability problem consists in finding a reachable marking M′ such that M′ ...ver más