Moduli stabilisation and the statistics of axion physics in the landscape

String theory realisations of the QCD axion are often said to belong to the anthropic window where the decay constant is around the GUT scale and the initial misalignment angle has to be tuned close to zero. In this paper we revisit this statement by studying the statistics of axion physics in the string landscape. We take moduli stabilisation properly into account since the stabilisation of the saxions is crucial to determine the physical properties of the corresponding axionic partners. We focus on the model-independent case of closed string axions in type IIB flux compactifications and find that their decay constants and mass spectrum feature a logarithmic, instead of a power-law, distribution. In the regime where the effective field theory is under control, most of these closed string axions are ultra-light axion-like particles, while axions associated to blow-up modes can naturally play the role of the QCD axion. Hence, the number of type IIB flux vacua with a closed string QCD axion with an intermediate scale decay constant and a natural value of the misalignment angle is only logarithmically suppressed. In a recent paper we found that this correlates also with a logarithmic distribution of the supersymmetry breaking scale, providing the intriguing indication that most, if not all, of the phenomenologically interesting quantities in the string landscape might feature a logarithmic distribution.

Reliability tests in the operation of military vehicles

Reliability studies in the operation of military vehicles are not carried out extensively. This is due to the guidelines of superiors regarding the keeping of operational records in military units. As a result, this work attempts to determine the reliability of military vehicles. This work includes reliability tests of military vehicles operated in military units in the second phase of operation, i.e. in the operation interval, where the extent of change in the intensity of damage is the least in the function of mileage. The study used a sample of 37 vehicles for which all operational events relevant to reliability determination were recorded during a two-year observation period. Using recorded operational data, an empirical reliability function of the vehicles included in the test sample was determined. Based on reliability tests of the reliability function as a function of mileage to damage, they show that second-phase vehicles used in military units have a logarithmic distribution of reliability as a function of mileage.

Study of a unit power-logarithmic distribution

This article proposes a new unit distribution based on the power-logarithmic scheme. The corresponding cumulative distribution function is defined by a special ratio of power and logarithmic functions that is dependent on one parameter. We show that this function benefits from great flexibility characterized by a large selection of convex and concave shapes. The other key functions are determined and studied. In particular, we show that the probability density function may take on different decreasing or U shapes, and the hazard rate function has a wide panel of U shapes. These functional capabilities are rare for a one-parameter unit distribution. In addition, we prove certain stochastic order results, provide the expression of the quantile function via the Lambert function, some interesting distributional results, and give simple expressions for the ordinary moments, mean, variance, skewness, kurtosis, moment generating function and incomplete moments. Subsequently, a basic statistical approach is described, to show how the new distribution can be applied in a data analysis scenario. Finally, complementary mathematical findings are presented, yielding new integrals linked to the Euler constant via some well-known moments properties.

Hydraulic resistances of suspended flows in bedrooms with a moving bottom

The results of some existing theoretical and experimental studies of hydraulic resistances of open flows in moving channels are considered. Possible reasons for the inconsistency of the results of various studies of hydraulic resistance in open channels with increased roughness are indicated. The analysis of mass field data on the Darcy (Shezi) coefficient of canals in alluvial soils and a sandy mobile bed is carried out. It was confirmed that the channels of these categories are characterized by a mixed zone of hydraulic resistance, and regularities were revealed that take into account the features of the real resistance zone of earthen channels. Based on the analysis of the smoothly varying flow of open flows and the corresponding theory of the boundary layer and the law of the logarithmic distribution of velocities, the calculated dependencies are obtained, making it possible to determine the resistance of open flows concerning natural conditions.

Moduli stabilisation and the statistics of SUSY breaking in the landscape

The statistics of the supersymmetry breaking scale in the string landscape has been extensively studied in the past finding either a power-law behaviour induced by uniform distributions of F-terms or a logarithmic distribution motivated by dynamical supersymmetry breaking. These studies focused mainly on type IIB flux compactifications but did not systematically incorporate the Kähler moduli. In this paper we point out that the inclusion of the Kähler moduli is crucial to understand the distribution of the supersymmetry breaking scale in the landscape since in general one obtains unstable vacua when the F-terms of the dilaton and the complex structure moduli are larger than the F- terms of the Kähler moduli. After taking Kähler moduli stabilisation into account, we find that the distribution of the gravitino mass and the soft terms is power-law only in KKLT and perturbatively stabilised vacua which therefore favour high scale supersymmetry. On the other hand, LVS vacua feature a logarithmic distribution of soft terms and thus a preference for lower scales of supersymmetry breaking. Whether the landscape of type IIB flux vacua predicts a logarithmic or power-law distribution of the supersymmetry breaking scale thus depends on the relative preponderance of LVS and KKLT vacua.

Predicting the Logarithmic Distribution Factors for Coprecipitation into an Organic Salt: Selection of Rare Earths into a Mixed Oxalate

Thermodynamic modelling of a leaching system that involves concurrent precipitation depends on an understanding of how the metals distribute into the precipitate before an assessment of solubility can be made. It has been suggested in the past that a pair of rare earths (A and B) in solution will separate from each other by oxalate precipitation according to a logarithmic distribution coefficient (λ), determined by the kinetics of the precipitation. By contrast, the present study hypothesises that λ may be approximated from thermodynamic terms, including the solubility product (KSp) of each rare earth oxalate and the stability constant (β1) for the mono-oxalato complex of each rare earth. The proposed model was used to calculate λ between pairs of rare earths. An experimental study was conducted to determine λ between selected pairs using homogenous precipitation through the hydrolysis of an oxalic acid ester, with fairly close agreement to the values under the proposed model. Though this model requires more thorough testing, as well as application to other organic salts, it may provide insight into distribution factors of a precipitate formed by a sequence of organic complexes.

LEI DE NEWCOMB BENFORD E AUDITORIA CONTÁBIL: UMA REVISÃO SISTEMÁTICA DE LITERATURA

Lei de Newcomb Benford - LNB, foi concebida pelo astrônomo e matemático Simon Newcomb, em 1881. Seus estudos demonstraram que a ocorrência de um número natural, de modo espontâneo ou aleatório, não se dava na proporção esperada de 1/9, mas segundo uma distribuição logarítmica. Desde então, esta lei vem sendo testada em muitas áreas do conhecimento. Em finanças corporativas, os estudiosos têm testado a lei para investigar fraudes em dados contábeis. Contudo, ainda não há consenso sobre a eficácia da LNB nesse âmbito. Assim, o objetivo deste artigo é identificar os argumentos favoráveis e contrários, bem como os métodos de pesquisa e os principais achados das pesquisas sobre a aplicação da LNB como ferramenta de auditoria. Para tanto, aplicou-se uma Revisão Sistemática de Literatura, seguindo os passos de Levy e Ellis (2006). Deste modo, além de informações sobre autoria, modelos utilizados pelos autores para suportar suas conclusões e seus principais achados, apresentam-se lacunas de pesquisa, e as implicações para o futuro da pesquisa são discutidas.Palavras-chave: Lei de Newcomb Benford. Revisão sistemática. Auditoria contábil.ABSTRACTNewcomb Benford’s Law - LNB, was conceived by the astronomer and mathematician Simon Newcomb, in 1881. His studies showed that the occurrence of a natural number, spontaneously or randomly, did not occur in the expected proportion of 1/9, but according to a logarithmic distribution. Since then, this law has been tested in many areas of knowledge. In corporate finance, scholars have tested the law to investigate fraud in accounting data. However, there is still no consensus on the effectiveness of LNB in this area. Thus, the objective of this article is to identify the arguments for and against, as well as the research methods and the main findings of research on the application of LNB as an audit tool. For that, a Systematic Literature Review was applied, following the steps of Levy and Ellis (2006). Thus, in addition to information on authorship, models used by the authors to support their conclusions and main findings, research gaps are presented, and the implications for the future of research are discussed.Keywords: Newcomb Benford’s law. Systematic review. Accounting audit..

Hydraulic characteristics of the aeration basin in a ski-jump-step spillway

The ski-jump-step spillway was designed using a ski-jump and an aeration basin to effectively pre-aerate flow in a stepped spillway. A new experimental study of the hydraulic characteristics of aeration basins was conducted to better understanding their pre-aeration properties and mechanisms. The plunge-pool patterns of aeration basins were classified into partially aerated, fully aerated, and vortex expelled, with increasing unit discharge. Relations between the distributions of the time-averaged pressure and the air concentration of the plunge-pools suggested that the ski-jump jet impact and the recirculating vortices are the main causes of plunge-pool air entrainment. Based on the export cross-section of the aeration basins, the bottom air concentrations remained greater than 3.0%. The sidewall air concentrations were greater than 7.5% and followed a logarithmic distribution in the vertical direction, demonstrating that the export flow attains a completely aerated state without any blackwater zones. In addition, increasing the aeration basin length was found to prevent the occurrence of a vortex expelled plunge-pool, thus promoting the appropriate pre-aeration effect under large unit discharges.

Detecting Anomalous Data in Household Surveys: Evidence for Argentina

This paper advances in the detection of anomalous data in income reports of Argentina. In particular, income declared by households surveyed in the Encuesta Permanente de Hogares (EPH, Permanent Household Survey in English) -for the period 2003-2017- and in the Encuesta Anual de Hogares Urbanos (EAHU, Annual Urban Household Survey in English) -for the period 2010-2014- are analyzed. A widely known technique in forensic accounting and auditing, such as Benford’s law -also known as the first digit law- is used. If the analyzed data were generated naturally-free of manipulation- it should follow the logarithmic distribution of Benford. The Chi-square test and the absolute mean deviation (MAD) are used for verification. The results suggest that the income reported in the EPH does not follow the Benford distribution and the degree of compliance with this law decreases significantly between 2007-2015 coinciding with the intervention period of the Instituto Nacional de Estadísticas y Censos (INDEC, National Institute of Statistics and Censuses in English).