On the Fibonacci k-numbers

We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers were found by studying the recursive application of two geometrical transformations used in the well-known four-triangle longest-edge (4TLE) partition. Many properties of these numbers are deduce directly from elementary matrix algebra.     

Thermodynamics of the interaction between hydroxypropyl-α-cyclodextrin and alkanols in aqueous solutions

The interactions of hydroxypropyl-α-cyclodextrin (HP-α-CD) with 1-alkanols and with some α,ω-alkanediols have been studied by calorimetric titration at 298.15 K. This technique enables the determination of the enthalpy and association constant for the complex formation, from which Gibbs energy and entropy can be derived. The results are compared to those reported for the complex formation between the native α-cyclodextrin (α-CD) and 1-alkanols or α,ω-alkanediols in the literature. Thermodynamic parameters corresponding to the transfer process of the alkanol from the native to the modified α-CD are also calculated. The results clearly show that the hydrophobic interactions are important in this process, but there are other effects like the size of the alkanol that are also of some importance.     

Urban rapid transit network capacity expansion

This paper examines a multi-period capacity expansion problem for rapid transit network design. The capacity expansion is realized through the location of train alignments and stations in an urban traffic context by selecting the time periods. The model maximizes the public transportation demand using a limited budget and designing lines for each period. The location problem incorporates the user decisions about mode and route. The network capacity expansion is a long-term planning problem because the network is built over several periods, in which the data (demand, resource price, etc.) are changing like the real problem changes. This complex problem cannot be solved by branch and bound, and for this reason, a heuristic approach has been defined in order to solve it. Both methods have been experimented in test networks.     

On two fragments with negation and without implication of the logic of residuated lattices

The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H_BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this notion of fragment is axiomatized by the rules of the sequent calculus for the connectives involved. We also prove that these deductive systems are non-protoalgebraic, while the Gentzen systems are algebraizable with equivalent algebraic semantics the varieties of pseudocomplemented (commutative integral bounded) semilatticed and latticed monoids, respectively. All the logical systems considered are decidable.     

Integrable perturbations of the N-dimensional isotropic oscillator

Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h₆-coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N−1) ‘Rosochatius’ terms that preserve the complete integrability of all these models.     

Asymptotic Lipschitz Regularity for Tug-of-War Games with Varying Probabilities

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ? ?ⁿ. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in Ω ×Ω via couplings.

     

On the Weak Order Ideal Associated to Linear Codes

In this work we study a weak order ideal associated with the coset leaders of a non-binary linear code. This set allows the incrementally computation of the coset leaders and the definitions of the set of leader codewords. This set of codewords has some nice properties related to the monotonicity of the weight compatible order on the generalized support of a vector in \(\mathbb {F}_q^n\) which allows to describe a test set, a trial set and the set of zero neighbours of a linear code in terms of the leader codewords.     

A sparse counterpart of Reichel and Gragg’s package QRUP

We describe how to maintain the triangular factor of a sparse QR factorization when columns are added and deleted and Q cannot be stored for sparsity reasons. The updating procedures could be thought of as a sparse counterpart of Reichel and Gragg’s package QRUP. They allow us to solve a sequence of sparse linear least squares subproblems in which each matrix B_k is an independent subset of the columns of a fixed matrix A, and B_k+1 is obtained by adding or deleting one column. Like Coleman and Hulbert [T. Coleman, L. Hulbert, A direct active set algorithm for large sparse quadratic programs with simple bounds, Math. Program. 45 (1989) 373-406], we adapt the sparse direct methodology of Björck and Oreborn of the late 1980s, but without forming A^TA, which may be only positive semidefinite. Our Matlab 5 implementation works with a suitable row and column numbering within a static triangular sparsity pattern that is computed in advance by symbolic factorization of A^TA and preserved with placeholders.