The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Origins and efficiency of the electric industry regulation in Spain, 1910-1936

The aim of this paper is to discover the origins of utility regulation in Spain, and to analyse, from a microeconomic perspective, its characteristics and the impact of regulation on consumers and utilities. Madrid and the Madrilenian utilities are taken as a case study. The electric industry in the period studied was a natural monopoly2. Each of the three phases of production, generation, transmission and distribution, had natural monopoly characteristics. Therefore, the most efficient form to generate, transmit and distribute electricity was the monopoly because one firm can produce a quantity at a lower cost than the sum of costs incurred by two or more firms. A problem arises because when a firm is the single provider it can charge prices above the marginal cost, at monopoly prices. When a monopolist reduces the quantity produced, price increases, causing the consumer to demand less than the economic efficiency level, incurring a loss of consumer surplus. The loss of the consumer surplus is not completely gained by the monopolist, causing a loss of social surplus, a deadweight loss. The main objective of regulation is going to be to reduce to a minimum the deadweight loss. Regulation is also needed because when the monopolist fixes prices at marginal cost equal marginal revenue there would be an incentive for firms to enter the market creating inefficiency. The Madrilenian industry has been chosen because of the availability of statistical information on costs and production. The complex industry structure and the atomised demand add interest to the analysis. This study will also provide some light on the tariff regulation of the period which has been poorly studied and will complement the literature on the US electric utilities regulation where a different type of regulation was implemented.

Repeated Interaction and the Revelation of the Monitor's Type: A Principal-Monitor-Agent Problem

This paper studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the effort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when replacement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of bene…tting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.

Test methods: anabolics.

In the International Olympic Committee (IOC) accredited laboratories, specific methods have been developed to detect anabolic steroids in athletes' urine. The technique of choice to achieve this is gas-chromatography coupled with mass spectrometry (GC-MS). In order to improve the efficiency of anti-doping programmes, the laboratories have defined new analytical strategies. The final sensitivity of the analytical procedure can be improved by choosing new technologies for use in detection, such as tandem mass spectrometry (MS-MS) or high resolution mass spectrometry (HRMS). A better sample preparation using immuno-affinity chromatography (IAC) is also a good tool for improving sensitivity. These techniques are suitable for the detection of synthetic anabolic steroids whose structure is not found naturally in the human body. The more and more evident use, on a large scale, of substances chemically similar to the endogenous steroids obliges both the laboratory and the sports authorities to use the steroid profile of the athlete in comparison with reference ranges from a population or with intraindividual reference values.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

A tale of two logits, compositional data analysis and zero observations

The application of compositional data analysis through log ratio trans-formations corresponds to a multinomial logit model for the shares themselves.This model is characterized by the property of Independence of Irrelevant Alter-natives (IIA). IIA states that the odds ratio in this case the ratio of shares is invariant to the addition or deletion of outcomes to the problem. It is exactlythis invariance of the ratio that underlies the commonly used zero replacementprocedure in compositional data analysis. In this paper we investigate using thenested logit model that does not embody IIA and an associated zero replacementprocedure and compare its performance with that of the more usual approach ofusing the multinomial logit model. Our comparisons exploit a data set that com-bines voting data by electoral division with corresponding census data for eachdivision for the 2001 Federal election in Australia

Explaining Fiscal Balances with a Simultaneous Equation Model of Revenue and Expenditure : A Case Study of Swiss Cantons Using Panel Data

Empirical literature on the analysis of the efficiency of measures for reducing persistent government deficits has mainly focused on the direct explanation of deficit. By contrast, this paper aims at modeling government revenue and expenditure within a simultaneous framework and deriving the fiscal balance (surplus or deficit) equation as the difference between the two variables. This setting enables one to not only judge how relevant the explanatory variables are in explaining the fiscal balance but also understand their impact on revenue and/or expenditure. Our empirical results, obtained by using a panel data set on Swiss Cantons for the period 1980-2002, confirm the relevance of the approach followed here, by providing unambiguous evidence of a simultaneous relationship between revenue and expenditure. They also reveal strong dynamic components in revenue, expenditure, and fiscal balance. Among the significant determinants of public fiscal balance we not only find the usual business cycle elements, but also and more importantly institutional factors such as the number of administrative units, and the ease with which people can resort to political (direct democracy) instruments, such as public initiatives and referendum.

Determinants of school efficiency : The case of primary schools in the State of Geneva, Switzerland

The public primary school system in the State of Geneva, Switzerland, is characterized by centrally evaluated pupil performance measured with the use of standardized tests. As a result, consistent data are collected among the system. The 2010-2011 dataset is used to develop a two-stage data envelopment analysis (DEA) of school efficiency. In the first stage, DEA is employed to calculate an individual efficiency score for each school. It shows that, on average, each school could reduce its inputs by 7% whilst maintaining the same quality of pupil performance. The cause of inefficiency lies in perfectible management. In the second stage, efficiency is regressed on school characteristics and environmental variables;external factors outside of the control of headteachers. The model is tested for multicollinearity, heteroskedasticity and endogeneity. Four variables are identified as statistically significant. School efficiency is negatively influenced by (1) the provision of special education, (2) the proportion of disadvantaged pupils enrolled at the school and (3) operations being held on multiple sites, but positively influenced by school size (captured by the number of pupils). The proportion of allophone pupils; schools located in urban areas and the provision of reception classes for immigrant pupils are not significant. Although the significant variables influencing school efficiency are outside of the control of headteachers, it is still possible to either boost the positive impact or curb the negative impact. Dans le canton de Genève (Suisse), les écoles publiques primaires sont caractérisées par un financement assuré par les collectivités publiques (canton et communes) et par une évaluation des élèves à l'aide d'épreuves standardisées à trois moments distincts de leur scolarité. Cela permet de réunir des informations statistiques consistantes. La base de données de l'année 2010-2011 est utilisée dans une analyse en deux étapes de l'efficience des écoles. Dans une première étape, la méthode d'analyse des données par enveloppement (DEA) est utilisée pour calculer un score d'efficience pour chaque école. Cette analyse démontre que l'efficience moyenne des écoles s'élève à 93%. Chaque école pourrait, en moyenne, réduire ses ressources de 7% tout en conservant constants les résultats des élèves aux épreuves standardisées. La source de l'inefficience réside dans un management des écoles perfectible. Dans une seconde étape, les scores d'efficience sont régressés sur les caractéristiques des écoles et sur des variables environnementales. Ces variables ne sont pas sous le contrôle (ou l'influence) des directeurs d'école. Le modèle est testé pour la multicolinéartié, l'hétéroscédasticité et l'endogénéité. Quatre variables sont statistiquement significatives. L'efficience des écoles est influencée négativement par (1) le fait d'offrir un enseignement spécialisé en classe séparée, (2) la proporition d'élèves défavorisés et (3) le fait d'opérer sur plusieurs sites différents. L'efficience des écoles est influencée positivement par la taille de l'école, mesurée par le nombre d'élèves. La proporition d'élèves allophones, le fait d'être situé dans une zone urbaine et d'offrir des classes d'accueil pour les élèves immigrants constituent autant de variables non significatives. Le fait que les variables qui influencent l'efficience des écoles ne soient pas sous le contrôle des directeurs ne signifie pas qu'il faille céder au fatalisme. Différentes pistes sont proposées pour permettre soit de réduire l'impact négatif soit de tirer parti de l'impact positif des variables significatives.

Estimation of zero-sequence impedance of undergrounds cables for single-phase fault location in distribution systems with electric arc

This paper focus on the problem of locating single-phase faults in mixed distribution electric systems, with overhead lines and underground cables, using voltage and current measurements at the sending-end and sequence model of the network. Since calculating series impedance for underground cables is not as simple as in the case of overhead lines, the paper proposes a methodology to obtain an estimation of zero-sequence impedance of underground cables starting from previous single-faults occurred in the system, in which an electric arc occurred at the fault location. For this reason, the signal is previously pretreated to eliminate its peaks voltage and the analysis can be done working with a signal as close as a sinus wave as possible

Efficiency of Gumbel analyses for determining extreme daily precipitation in Switzerland

Gumbel analyses were carried out on rainfall time-series at 151 locations in Switzerland for 4 different periods of 30 years in order to estimate daily extreme precipitation for a return period of 100 years. Those estimations were compared with maximal daily values measured during the last 100 years (1911-2010) to test the efficiency of these analyses. This comparison shows that these analyses provide good results for 50 to 60% locations in this country from rainfall time-series 1961-1990 and 1980-2010. On the other hand, daily precipitation with a return period of 100 years is underestimated at most locations from time-series 1931-1960 and especially 1911-1940. Such underestimation results from the increase of maximal daily precipitation recorded from 1911 to 2010 at 90% locations in Switzerland.

When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’tincludes below detection limits and/or zero values, and since most of the geological dataresponds to lognormal distributions, these “zero data” represent a mathematicalchallenge for the interpretation.We need to start by recognizing that there are zero values in geology. For example theamount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-existswith nepheline. Another common essential zero is a North azimuth, however we canalways change that zero for the value of 360°. These are known as “Essential zeros”, butwhat can we do with “Rounded zeros” that are the result of below the detection limit ofthe equipment?Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimeswe need to differentiate between a sodic and a potassic alteration. Pre-classification intogroups requires a good knowledge of the distribution of the data and the geochemicalcharacteristics of the groups which is not always available. Considering the zero valuesequal to the limit of detection of the used equipment will generate spuriousdistributions, especially in ternary diagrams. Same situation will occur if we replace thezero values by a small amount using non-parametric or parametric techniques(imputation).The method that we are proposing takes into consideration the well known relationshipsbetween some elements. For example, in copper porphyry deposits, there is always agood direct correlation between the copper values and the molybdenum ones, but whilecopper will always be above the limit of detection, many of the molybdenum values willbe “rounded zeros”. So, we will take the lower quartile of the real molybdenum valuesand establish a regression equation with copper, and then we will estimate the“rounded” zero values of molybdenum by their corresponding copper values.The method could be applied to any type of data, provided we establish first theircorrelation dependency.One of the main advantages of this method is that we do not obtain a fixed value for the“rounded zeros”, but one that depends on the value of the other variable.Key words: compositional data analysis, treatment of zeros, essential zeros, roundedzeros, correlation dependency

Internal test sets studies in a group of antimalarials

Topological indices have been applied to build QSAR models for a set of 20 antimalarial cyclic peroxy cetals. In order to evaluate the reliability of the proposed linear models leave-n-out and Internal Test Sets (ITS) approaches have been considered. The proposed procedure resulted in a robust and consensued prediction equation and here it is shown why it is superior to the employed standard cross-validation algorithms involving multilinear regression models

Swain: Stata module to correct the SEM chi-square overidentification test in small sample sizes or complex models. Statistical Software Components S457617, Boston College Department of Economics.

Swain corrects the chi-square overidentification test (i.e., likelihood ratio test of fit) for structural equation models whethr with or without latent variables. The chi-square statistic is asymptotically correct; however, it does not behave as expected in small samples and/or when the model is complex (cf. Herzog, Boomsma, & Reinecke, 2007). Thus, particularly in situations where the ratio of sample size (n) to the number of parameters estimated (p) is relatively small (i.e., the p to n ratio is large), the chi-square test will tend to overreject correctly specified models. To obtain a closer approximation to the distribution of the chi-square statistic, Swain (1975) developed a correction; this scaling factor, which converges to 1 asymptotically, is multiplied with the chi-square statistic. The correction better approximates the chi-square distribution resulting in more appropriate Type 1 reject error rates (see Herzog & Boomsma, 2009; Herzog, et al., 2007).