The Stationary Phase Method for a Wave Packet in a Semiconductor Layered System. The applicability of the method

Using the formal analysis made by Bohm in his book, {\em "Quantum theory"}, Dover Publications Inc. New York (1979), to calculate approximately the phase time for a transmitted and the reflected wave packets through a potential barrier, we calculate the phase time for a semiconductor system formed by different mesoscopic layers. The transmitted and the reflected wave packets are analyzed and the applicability of this procedure, based on the stationary phase of a wave packet, is considered in different conditions. For the applicability of the stationary phase method an expression is obtained in the case of the transmitted wave depending only on the derivatives of the phase, up to third order. This condition indicates whether the parameters of the system allow to define the wave packet by its leading term. The case of a multiple barrier systems is shown as an illustration of the results. This formalism includes the use of the Transfer Matrix to describe the central stratum, whether it is formed by one layer (the single barrier case), or two barriers and an inner well (the DBRT system), but one can assume that this stratum can be comprise of any number or any kind of semiconductor layers.Comment: 15 pages, 4 figures although figure 4 has 5 graph

New allocation of Special Drawing Rights

El Fondo Monetario Internacional (FMI) realizó en agosto de 2021 una nueva asignación de derechos especiales de giro (DEG), por un importe equivalente a 650 mm de dólares estadounidenses. Se trata de una cuantía significativa, que triplica los saldos actuales. En particular, para España ha supuesto un incremento de un 16 % de las reservas exteriores, así como de los activos frente al FMI, que alcanzarían un 22 % de las reservas en el balance del Banco de España, en comparación con el 10 % actual. El objetivo de esta expansión de los DEG es dar apoyo a un grupo de países con mayores dificultades para combatir el impacto de la pandemia de COVID-19, a lo que se ha unido una mayor necesidad de divisas para obtener suministros básicos, con un cierre de los mercados de capitales internacionales. Es previsible que la nueva asignación dinamice la operativa en DEG, dados su elevado importe, la acuciante necesidad de fondos en algunos países y el aprendizaje respecto a la asignación de 2009. En este documento se explican las características del uso de los DEG como fuente efectiva de liquidez, con la conclusión de que el modo en que se hace efectiva la emisión de este instrumento es mediante las transacciones, y de que es la asignación el presupuesto formal de su existencia. Por tanto, el aspecto clave para su efectividad será la realidad de las transacciones que se hagan para obtener liquidez en el tráfico internacional. Con el objetivo de hacer un seguimiento de su uso, se sugiere una ratio de su liquidez. Por otro lado, en relación con la magnitud de la asignación, y puesto que se realiza en función de las cuotas de cada país miembro del FMI, se observa un «acaparamiento» por parte de los países desarrollados, frente a los que muestran más dificultades en el acceso a los mercados, que hará inevitable la adopción de medidas que favorezcan la recirculación de los DEG para alcanzar sus fines, de modo que se complementen eficazmente las reservas disponibles en el marco del comercio internacional.In August 2021, the International Monetary Fund (IMF) made a new allocation of Special Drawing Rights (SDRs) equivalent to $650 billion. This significant amount has tripled the total existing stock of SDRs. For Spain it involves an increase of 16% in foreign reserves, and an increase in receivables from the IMF, which amount to 22% of the reserves on the balance sheet of the Banco de España, as compared with 10% at present. The purpose of this expansion of SDRs is to support a group of countries that are having most difficulty fighting the impact of the COVID-19 pandemic. These countries have a greater need for foreign exchange to obtain basic supplies just when they are shut out of international capital markets. The new allocation is likely to boost SDR transactions given its large amount, the urgent need for funds in some countries and the experience of the 2009 allocation. This paper explains the characteristics of the use of SDRs as an effective source of liquidity, concluding that the way in which the issuance of this instrument is made effective is by means of transactions, allocation being the formal prerequisite for their existence. Accordingly, the key to their effectiveness will be the transactions actually carried out to obtain liquidity in international business. A liquidity ratio is proposed for monitoring their use. With regard to the magnitude of the allocation and, given that it is based on the quotas of each IMF member country, the developed countries have received the bulk of the allocation, as opposed to those countries having greater difficulty accessing the markets. Accordingly, measures will have to be taken to promote the passing on of SDRs so that their purpose can be achieved and they effectively supplement the reserves available within the framework of international trade

Catálogo de los sulfuros metálicos de Cataluña existentes en museos y colecciones de la región

Se presenta una recopilación de los ejemplares de sulfuros metálicos de Cataluña que se encuentran en museos y colecciones de la región. Consta de tres listas ordenadas, respectivamente, por museos y colecciones, especies minerales y localidades. Entrando por cualquiera de las tres se encuentra la correspondiente referencia a las otras dos, de tal manera quepuede hallarse fácilmente cualquier dato que se busque

Sobre la presencia de gahnita ferrífera en Bossost (Vall D'Aran, Lérida)

[ES] Identificacióa de la gahnita ferrífera (creitonita) (Al, Fe)2 O4 (Zn, Fe, Mg), en mina "Victoria", (Vall d'Aran, Lérida).[FR] Sur la decouverte de le gahnite ferrifere (creitonite)(Al, Fe)2 O4 (Zn, Fe, Mg), dans la gîte "Mina Victoria", (Vall d'Aran, Lérida).Trabajo realizado, en parte, gracias a la ayuda para Fomento de la Investigación en la Universidad.Peer reviewe

Contribución al conocimiento de la arsenopirita de Liat (Vall d'Aran, Lleida)

Se estudian arsenopiritas procedentes de los yacimientos de Liat (Vall d'Aran, Lleida). La zona está constituida por materiales cambro-ordovícicos y las mineralizaciones se hallan emplazadas en niveles cuarcíticos metamorfizados. El conjunto roca de caja-mineralización aparece afectado por una serie de deformaciones a pequeña y gran escala. Las arsenopiritas presentan fenómenos de recristalización y formación de maclas centradas, contemporáneos del clímax metamórfico. Los esfuerzos deformativos posteriores dieron lugar a la génesis de maclas polisintéticas (201) y a la fracturación de los cristales. Las texturas y estructuras observadas permiten establecer para las fases minerales una historia paralela a la de la roca encajante.On étudie des arsenopyrites recueillies dans les gîtes de Liat (Vall d'Aran, Lleida). La zone est formée par des materiaux cambro-ordoviciens et les minéralisations se trouvent dans des niveaux quarzitiques métamorphisés. L'ensemble roche encaissante-minéralisation se trouve affectée par une série de deformations à petite et grande échelle. Les arsenopyrites montrent des phénomenes de récristalisation et formation de macles centrées, contemporaines du climax métamorphique. Les éfforts déformatifs posterieurs on donné lieu la genhe de macles polysintétiques (201) et A la fracturation des cristaux. Les textures et structures observées permettent d'établir une histoire parallele à celle de la roche encaissante

Determination of Network Configuration Considering Inventory Cost in a Supply Chain

AbstractIn this paper we show the importance of applying mathematical optimization when designing the distribution network in a supply chain, specifically in making decisions related location of facilities and inventory management, which are associated with different levels of planning but are closely related.The addressed problem is an extension of the classic capacitated facility location problem. The distinguishing features are: the inventory management, the presence of multiple plants, and the single source constraints in both echelons. A key issue is that demand at each distribution center is a function of the demands at the retailers assigned, which is a random variable whose value is not known at the time of designing the network. We focus on the mathematical modeling of the problem and the evaluation of the performance of the developed models, so, it can be observed the troubles that arise when modeling supply chains that consider different types of decisions

Superdiversity: New paths for social sciences in the upcoming future

Contemporary society has been characterized by its social complexity, which was boosted thanks to international migration flows, among other factors. This phenomenon brought us ‘superdiversity’ as a concept, which has been very well received by many social scientists, as well as criticized by others due to its similarities with previous notions such as diversity, multiculturalism, interculturalism or even intersectionality. However, this concept, with all the semantic breadth and defining ramifications that characterize it, has opened an interpretive door, and made possible an analytical framework that differs from the rest. As a result, we find superdiversity as a guiding research concept throughout all social sciences areas assuming a whole variety of approaches, without necessarily considering international migrations as a background variable. This monograph reflects this reality and is presented as a hybridization of more orthodox positions with other more flexible and interpretive ones.info:eu-repo/semantics/acceptedVersio

Evenly convex sets, and evenly quasiconvex functions, revisited

Since its appearance, even convexity has become a remarkable notion in convex analysis. In the fifties, W. Fenchel introduced the evenly convex sets as those sets solving linear systems containing strict inequalities. Later on, in the eighties, evenly quasiconvex functions were introduced as those whose sublevel sets are evenly convex. The significance of even convexity relies on the different areas where it enjoys applications, ranging from convex optimization to microeconomics. In this paper, we review some of the main properties of evenly convex sets and evenly quasiconvex functions, provide further characterizations of evenly convex sets, and present some new results for evenly quasiconvex functions.This research has been partially supported by MINECO of Spain and ERDF of EU, Grants PGC2018-097960-B-C22 and ECO2016-77200-P

Estudio morfológico, mediante luz reflejada, de piritas procedentes de la mina "Solitaria" (arres, Vall D'Aran, Lérida)

Se lleva a cabo el estudio y la interpretación de los diferentes tipos de cristales de pirita que se encuentran en el yacimiento Mina "Solitaria" (Arrés, Vall d'Aran) Lérida