On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

Motzkin decomposition of closed convex sets via truncation

A nonempty set F is called Motzkin decomposable when it can be expressed as the Minkowski sum of a compact convex set C with a closed convex cone D. In that case, the sets C and D are called compact and conic components of F. This paper provides new characterizations of the Motzkin decomposable sets involving truncations of F (i.e., intersections of FF with closed halfspaces), when F contains no lines, and truncations of the intersection F̂ of F with the orthogonal complement of the lineality of F, otherwise. In particular, it is shown that a nonempty closed convex set F is Motzkin decomposable if and only if there exists a hyperplane H parallel to the lineality of F such that one of the truncations of F̂ induced by H is compact whereas the other one is a union of closed halflines emanating from H. Thus, any Motzkin decomposable set F can be expressed as F=C+D, where the compact component C is a truncation of F̂. These Motzkin decompositions are said to be of type T when F contains no lines, i.e., when C is a truncation of F. The minimality of this type of decompositions is also discussed.

A new surface joining technique for the design of shoe lasts

The footwear industry is a traditional craft sector, where technological advances are difficult to implement owing to the complexity of the processes being carried out, and the level of precision demanded by most of them. The shoe last joining operation is one clear example, where two halves from different lasts are put together, following a specifically traditional process, to create a new one. Existing surface joining techniques analysed in this paper are not well adapted to shoe last design and production processes, which makes their implementation in the industry difficult. This paper presents an alternative surface joining technique, inspired by the traditional work of lastmakers. This way, lastmakers will be able to easily adapt to the new tool and make the most out of their know-how. The technique is based on the use of curve networks that are created on the surfaces to be joined, instead of using discrete data. Finally, a series of joining tests are presented, in which real lasts were successfully joined using a commercial last design software. The method has shown to be valid, efficient, and feasible within the sector.

Cálculo del asiento elástico tridimensional de cimentaciones de rigidez variable en terrenos con una capa rígida inclinada

Las fórmulas basadas en la teoría de la elasticidad son ampliamente utilizadas para el cálculo de asientos de cimentaciones, ya que la totalidad de la normativa geotécnica recomienda su empleo. No obstante, estos métodos no cubren todas las situaciones geotécnicamente posibles ya que frecuentemente las condiciones geológicas son complejas. En este trabajo se analiza la influencia de la presencia de una capa rígida inclinada en los asientos elásticos de una cimentación superficial. Para ello se han resuelto 273 modelos tridimensionales no lineales de elementos finitos, variando los parámetros clave del problema: la inclinación y la profundidad de la capa rígida y la rigidez de la cimentación. Finalmente, se ha realizado un análisis estadístico de los resultados de los modelos y se ha propuesto una fórmula que puede ser utilizada en el cálculo de asientos por métodos elásticos, para tener en consideración la presencia de una capa rígida inclinada en profundidad.

A demand-driven analysis of tourist accommodation price: A quantile regression of room bookings

Tourist accommodation expenditure is a widely investigated topic as it represents a major contribution to the total tourist expenditure. The identification of the determinant factors is commonly based on supply-driven applications while little research has been made on important travel characteristics. This paper proposes a demand-driven analysis of tourist accommodation price by focusing on data generated from room bookings. The investigation focuses on modeling the relationship between key travel characteristics and the price paid to book the accommodation. To accommodate the distributional characteristics of the expenditure variable, the analysis is based on the estimation of a quantile regression model. The findings support the econometric approach used and enable the elaboration of relevant managerial implications.