Equivalence of the ellipticity conditions for geometric variational problems

We exploit the so called atomic condition, recently defined by De Philippis, De Rosa, and Ghiraldin in [Comm. Pure Appl. Math.] and proved to be necessary and sufficient for the validity of the anisotropic counterpart of the Allard rectifiability theorem. In particular, we address an open question of this seminal work, showing that the atomic condition implies the strict Almgren geometric ellipticity condition

Space, mass and ornament in the Gothic-Renaissance transition in Spain

La introducción en España de las nuevas formas y sintaxis renacentistas a lo largo del siglo xvi no se produjo con un abandono radical e inmediato de los viejos usos góticos, de validez comprobada en trascendentales cuestiones del diseño arquitectónico. La renovación de la producción fue heterogénea y en cierto modo particular de cada artífice, según su formación previa y el grado de contacto, coherencia y compromiso con las novedades italianas, generando un panorama híbrido y plural en la arquitectura del quinientos hispano. Atendiendo a significativos textos y documentos gráficos de la época, se pretende rastrear los cambios, e inercias, en el proceso de diseño arquitectónico durante esta larga etapa de transición, estructurando el análisis a partir de tres categorías sustanciales, interdependientes y autónomas a la vez: espacio, masa y ornato.During the sixteenth century the new Renaissance forms were introduced in Spain, but the Gothic procedures continued to be used due to their proven validity for the architectural design. The renovation of the architecture was heterogeneous and different for each master, according to his previous training and his knowledge of the new Italian forms. This involved a hybrid and plural context in the Spanish architecture of the 16th century. The changes and continuities of the architectural design process during this transitory stage are investigated in this paper, based on significant texts and graphic documents of this period. The analysis is structured based on three substantial architectural categories, which are simultaneously interdependent and autonomous: space, mass and ornamen

One numerical procedure for two risk factors modeling

We propose a numerical procedure for the pricing of financial contracts whose contingent claims are exposed to two sources of risk: the stock price and the short interest rate. More precisely, in our pricing framework we assume that the stock price dynamics is described by the Cox, Ross Rubinstein (CRR, 1979) binomial model under a stochastic risk free rate, whose dynamics evolves over time accordingly to the Black, Derman and Toy (BDT, 1990) one-factor model. To this aim, we set the hypothesis that the instantaneous correlation between the trajectories of the future stock price (conditional on the current value of the short rate) and of the future short rate is zero. We then apply the resulting stock price dynamics to evaluate the price of a simple contract, i.e. of a stock option. Finally, we compare the derived price to the price of the same option under different pricing models, as the traditional Black and Scholes (1973) model. We expect that, the difference in the two prices is not sensibly large. We conclude showing in which cases it should be helpful to adopt the described model for pricing purposes.option pricing; stochastic short rate model; binomial tree

Truth and Reconciliation Commissions: A Needed Force in Alaska?

Truth and Reconciliation Commissions are official, temporary bodies used for communities to come to terms with past violence, promote education and awareness of historic trauma, and to provide recognition and closure for victims and successors. By bringing past issues to light, such commissions promote healing and allow these communities to move forward. Although the Commission on Truth and Reconciliation in South Africa after the Apartheid-era is best known, several similar commissions have been established throughout the globe and within the United States. This paper compares commissions from South Africa, El Salvador, South Korea, and Canada with those that have been established in the United States to examine whether such a commission would be useful in Alaska to address current social problems in the state

Demand methods of price management: An empirical research

One factor which companies often take as a reference point for their pricing decisions is demand. This, however, is often done only partially, with priority being given to quantitative factors rather than qualitative factors. In this context, the aim of this study was to supply companies with a tool to facilitate and enhance price management in areas related to demand. In order to achieve this objective, the following procedure was implemented. Firstly, an extensive review of existing literature was carried out. This has made it possible to identify a set of factors which can influence consumer behaviour with respect to prices, and which should therefore be taken into account when making pricing decisions. The factors identified were then grouped into several categories (variables related to price, variables related to the product, variables related to the characteristics and the behaviour of the consumer, and variables related to the context of the purchase), in order to offer an overall, linked view. An empirical study was then carried out, interviewing price managers in a selection of companies from Andalusia (Spain). The objective was to gather data on their methods of price management, and to evaluate the practical usefulness of the sets of factors identified. The results of the study have made it possible to draw some interesting conclusions on price management. One of these is the importance which companies attach to pricing decisions. These decisions were taken in all cases by higher management teams. However, on analysing the factors which intervene in pricing decisions, it has been observed that their number is limited. In general, cost is still the major factor, while demandrelated aspects, in particular qualitative aspects, play a secondary role. On investigating the reasons for the priority given to quantitative rather than qualitative data, interviewees basically gave two answers. On the one hand, quantitative information (costs and sales) is easier to obtain, use and interpret than qualitative information (motivation, perception and attitude). On the other hand, most companies, and in particular the smaller ones, have no budget available for qualitative market studies. There may be a third reason for this behaviour, which was not explicitly mentioned at first by interviewees. This is the lack of knowledge regarding qualitative demand factors: their nature, their meaning, their usefulness and the way in which they can be incorporated into pricing decisions. This study is a first step towards solving this deficiency, since it proposes a chart which contains numerous restrictions in an integrated, organised fashion. Logically, it would be impractical to take them all into account simultaneously. This is where the work of each company begins, using market studies to establish priorities between the different factors