Powers in the Lucas sequence when the index is divisible by three

In this paper the m-powers with m ≥ 2 included in the Lucas sequences when the index satisfies some conditions are foun

On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

- DELEGATION AND ENDOGENOUS MERGERS IN OLIGOPOLY

In this paper we consider the interactions between the use of strategic delegation and mergers in the context of a Cournot oligopoly with linear demand and cost functions. It is assumed that, after the merging process is completed, the owner of every independent firm decides its managerial incentive for his manager. In the context of endogenous mergers through acquisitions, we show that the incentive to merge, under delegation, is considerably increased with respect to the setting without delegation. In fact, we prove that the level of welfare in the setting with delgation is, in some cases, lower than the corresponding under non delegation.Strategic delegation, endoqenous mergers, cournot oligopoly

A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry

We develop a systematic algorithm for constructing an N-fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we construct a new multi-parameter family of N-fold supersymmetric models, which shall be referred to as "type C". We investigate various aspects of these type C models in detail. It turns out that in certain cases these systems exhibit a novel phenomenon, namely, partial breaking of N-fold supersymmetry.Comment: RevTeX 4, 28 pages, no figure

Las matemáticas del amor

Es indiscutible que las matemáticas resultan imprescindibles en la mayoría de las áreas científicas y son el fundamento de numerosos avances de la técnica. En este trabajo se pone de manifiesto como esta ciencia también puede explicar, ayudar y modelar problemas de tipo puramente social y humano. Concretamente veremos como puede aplicarse al estudio de las relaciones de pareja. Áreas como la estadística, la teoría de juegos, la geometría o las ecuaciones diferenciales entre otras, son válidas para ello

Spatiotemporal Stacked Sequential Learning for Pedestrian Detection

Pedestrian classifiers decide which image windows contain a pedestrian. In practice, such classifiers provide a relatively high response at neighbor windows overlapping a pedestrian, while the responses around potential false positives are expected to be lower. An analogous reasoning applies for image sequences. If there is a pedestrian located within a frame, the same pedestrian is expected to appear close to the same location in neighbor frames. Therefore, such a location has chances of receiving high classification scores during several frames, while false positives are expected to be more spurious. In this paper we propose to exploit such correlations for improving the accuracy of base pedestrian classifiers. In particular, we propose to use two-stage classifiers which not only rely on the image descriptors required by the base classifiers but also on the response of such base classifiers in a given spatiotemporal neighborhood. More specifically, we train pedestrian classifiers using a stacked sequential learning (SSL) paradigm. We use a new pedestrian dataset we have acquired from a car to evaluate our proposal at different frame rates. We also test on a well known dataset: Caltech. The obtained results show that our SSL proposal boosts detection accuracy significantly with a minimal impact on the computational cost. Interestingly, SSL improves more the accuracy at the most dangerous situations, i.e. when a pedestrian is close to the camera.Comment: 8 pages, 5 figure, 1 tabl

Understanding the relevance of national culture in international business research: a quantitative analysis

This review is a comprehensive quantitative analysis of the International Business literature whose focus is on national culture. The analysis relies on a broad range of bibliometric techniques as productivity rankings, citation analysis (individual and cumulative), study of collaborative research patterns, and analysis of the knowledge base. It provides insights on (I) faculty and institutional research productivity and performance; (II) articles, institutions, and scholars’ influence in the contents of the field and its research agenda; and (III) national and international collaborative research trends. The study also explores the body of literature that has exerted the greatest impact on the researched set of selected articles.info:eu-repo/semantics/publishedVersio