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We are interested in determining the bound of the average of the degrees of the irreducible characters whose degrees are not divisible by some prime p that guarantees a finite group G of odd order is p-nilpotent. There was found to be a bound which depends on the prime p. By further restricting the average by fixing a subfield k of the complex numbers and then computing the average of the degrees of the irreducible characters whose degrees are not divisible by p and have values in k, then a bound was obtained which depends on both p and k. Examples are provided which show best possible bounds. [ABSTRACT FROM AUTHOR]

The study and conservation of biological diversity is one of the global contemporary environmental problems of world significance. The goal of the study is to propose a method for identifying promising plants based on iteration of average values. For this purpose, nine trial plots were laid in the steppe, forest-steppe, and mountain zones of the Northwestern Caucasus in protective and forest stands. Based on well-known methods, the height, trunk diameter, crown radius, abundance of fruiting, weight and selection value of nuts were studied. We studied the change in the average values of the indicators at different numbers of iterations. A method for identifying promising individuals based on the values of the average of iterations 4 and 5 was proposed. The proposed method was compared with the known method based on the values of the sum (difference) of the mean and double standard deviation. With a statistically normal distribution of indicators, the known and proposed methods give close values in the direction of increase or decrease in the indicator. Using the known method with a statistical distribution that differs from normal in some cases gives meaningless values. The proposed method based on the average value of iterations 4 and 5 in the direction of increase or decrease in the studied indicator allows one to use it to select objects with a statistical distribution that differs from normal. [ABSTRACT FROM AUTHOR]

Averages became a distinctive form of information in early modern European culture, first in commercial arithmetic, then in natural philosophy, demography, political economy, and eventually in eclectic social analysis. Averaging, in the modern sense of calculating an arithmetic mean by adding up the individual values of cases in a set and then dividing that total by the number of cases, provided an empirical and heuristic resource for understanding planetary orbits, fertility and mortality rates, experimental results in natural philosophy, fiscal resources, the return on stock market investments, the relative profitability of crops, incomes and the cost of living, and even the trivia of daily life. Averaging created a new class of fact—precisely typifying information that varied. By the Enlightenment, averages had become a respectable, readily deployed, form of fact, giving unity to the variety of experience and knowledge. Averages became a metaphor of credibility and normality. [ABSTRACT FROM AUTHOR]

The probability parameter is calculated for the system of neutral K0 K ¯ 0 mesons based on the results previously obtained by the author and the result of the Gell-Mann and Pais classical work consistent with them. [ABSTRACT FROM AUTHOR]

Between the thirteenth and seventeenth centuries, Averages played an important (and neglected) role within Venetian maritime trade and shipping, as they functioned both as risk management tools and as a mechanism for the absorption of transaction costs. The essay will trace these normative developments across the phase of economic growth in the Middle Ages, and analyse how these were structurally transformed in the seventeenth century under the pressure of new maritime operators which contributed to the early modern crisis of the Venetian maritime sector. This touches on several elements of the shifting Venetian economy about which we still know very little: the internal balance of interests between different economic sectors; and within the maritime sector itself - shipowners, merchants, investors; and presents a novel interpretation of the resilience of Venetian maritime working capital well into the eighteenth century. [ABSTRACT FROM AUTHOR]

The variation of river water runoff is a normal phenomenon, given the close link between runoff and atmospheric precipitation, both components of the water balance. The variation of the flow over a period of time can be calculated using several simple and complex indicators, among which the most important are the absolute and relative deviation, the standard deviation (deviation) and the coefficient of variation. In the Căliman Mountains, no analysis of the variation of river water flow has been made so far, this work being the first of its kind. Following this work, it was observed that the variation of water flow from these rivers in the period 1950-2010 depended strongly on the variation of climatic elements (precipitation and temperatures), but also on the characteristics of river basins, both annually and seasonally.

Faces are highly informative social stimuli, yet before any information can be accessed, the face must first be detected in the visual field. A detection template that serves this purpose must be able to accommodate the wide variety of face images we encounter, but how this generality could be achieved remains unknown. In this study, we investigate whether statistical averages of previously encountered faces can form the basis of a general face detection template. We provide converging evidence from a range of methods—human similarity judgements and PCA-based image analysis of face averages (Experiment 1–3), human detection behaviour for faces embedded in complex scenes (Experiment 4 and 5), and simulations with a template-matching algorithm (Experiment 6 and 7)—to examine the formation, stability and robustness of statistical image averages as cognitive templates for human face detection. We integrate these findings with existing knowledge of face identification, ensemble coding, and the development of face perception. [ABSTRACT FROM AUTHOR]

The variation of river water runoff is a normal phenomenon, given the close link between runoff and atmospheric precipitation, both components of the water balance. The variation of the flow over a period of time can be calculated using several simple and complex indicators, among which the most important are the absolute and relative deviation, the standard deviation (deviation) and the coefficient of variation. In the Căliman Mountains, no analysis of the variation of river water flow has been made so far, this work being the first of its kind. Following this work, it was observed that the variation of water flow from these rivers in the period 1950-2010 depended strongly on the variation of climatic elements (precipitation and temperatures), but also on the characteristics of river basins, both annually and seasonally. [ABSTRACT FROM AUTHOR]

It is known that the j̃-metric, the half-Apollonian metric, and the scale-invariant Cassinian metric are not Gromov hyperbolic. These metrics are defined as a supremum of one-point metrics (i.e., metrics constructed using one boundary point), and the supremum is taken over all boundary points. The aim of this paper is to show that taking the average instead of the supremum yields a metric that is Gromov hyperbolic. Moreover, we show that the Gromov hyperbolicity constant of the resulting metric does not depend on the number of boundary points used in taking the average. We also provide an example to show that the average of Gromov hyperbolic metrics is not, in general, Gromov hyperbolic. [ABSTRACT FROM AUTHOR]

Summary: Low‐quality images are problematic for face identification, for example, when the police identify faces from CCTV images. Here, we test whether face averages, comprising multiple poor‐quality images, can improve both human and computer recognition. We created averages from multiple pixelated or nonpixelated images and compared accuracy using these images and exemplars. To provide a broad assessment of the potential benefits of this method, we tested human observers (n = 88; Experiment 1), and also computer recognition, using a smartphone application (Experiment 2) and a commercial one‐to‐many face recognition system used in forensic settings (Experiment 3). The third experiment used large image databases of 900 ambient images and 7,980 passport images. In all three experiments, we found a substantial increase in performance by averaging multiple pixelated images of a person's face. These results have implications for forensic settings in which faces are identified from poor‐quality images, such as CCTV. [ABSTRACT FROM AUTHOR]

While in molar mass determinations different averages are clearly distinguished, such differentiation is usually not performed when dealing with the composition of copolymers or polymer blends. The present article shows that the mol ratio calculated by nuclear magnetic resonance (NMR) usually provides neither a weight nor a number average. Only if the composition does not vary with molar mass, or if both copolymer units are of equal molar mass, a weight average mol ratio is obtained from NMR measurements. The frequent assumption that NMR yields a number average composition is incorrect, therefore. However, the mass fraction calculated from NMR corresponds to the weight average mass fraction. [ABSTRACT FROM AUTHOR]

Successive differences on a sequence of data help discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper is to mimic them to a sequence of regular samples of a function in a shift-invariant subspace allowing its stable recovery. A suitable expression for the functions in the shift-invariant subspace by an isomorphism with the L2(0,1) space is the key to identify the simple pattern followed by the dual Riesz bases involved in the derived formulas. The paper contains examples illustrating different non-exhaustive situations including also the two-dimensional case. [ABSTRACT FROM AUTHOR]

Let A f ( 1 , n ) be the normalized Fourier coefficients of a G L ( 3 ) Hecke–Maass cusp form f and let a g ( n ) be the normalized Fourier coefficients of a G L ( 2 ) cusp form g . Let λ ( n ) be either A f ( 1 , n ) or the triple divisor function d 3 ( n ) . It is proved that for any ϵ > 0 , any integer r ≥ 1 and r 5 / 2 X 1 / 4 + 7 δ / 2 ≤ H ≤ X with δ > 0 , 1 H ∑ h ≥ 1 W ( h H ) ∑ n ≥ 1 λ ( n ) a g ( r n + h ) V ( n X ) ≪ X 1 − δ + ϵ , where V and W are smooth compactly supported functions, and the implied constants depend only on the associated forms and ϵ . [ABSTRACT FROM AUTHOR]

We study when a union of saturated models is saturated in the framework of tame abstract elementary classes (AECs) with amalgamation. We prove: Theorem 0.1. If K is a tame AEC with amalgamation satisfying a natural definition of superstability (which follows from categoricity in a high-enough cardinal), then for all high-enough $$\lambda {:}$$ Our proofs use independence calculus and a generalization of averages to this non first-order context. [ABSTRACT FROM AUTHOR]

Speelman and McGann's (2013) examination of the uncritical way in which the mean is often used in psychological research raises questions both about the average's reliability and its validity. In the present paper, we argue that interrogating the validity of the mean involves, amongst other things, a better understanding of the person's experiences, the meaning of their actions, at the time that the behaviour of interest is carried out. Recently emerging approaches within Psychology and Cognitive Science have argued strongly that experience should play a more central role in our examination of behavioural data, but the relationship between experience and behaviour remains very poorly understood. We outline some of the history of the science on this fraught relationship, as well as arguing that contemporary methods for studying experience fall into one of two categories. Wide approaches tend to incorporate naturalistic behaviour settings, but sacrifice accuracy and reliability in behavioural measurement. Narrow approaches maintain controlled measurement of behaviour, but involve too specific a sampling of experience, which obscures crucial temporal characteristics. We therefore argue for a novel, mid-range sampling technique, that extends Hurlburt's Descriptive Experience Sampling, and adapts it for the controlled setting of the laboratory. This Controlled Descriptive Experience Sampling may be an appropriate tool to help calibrate both the mean and the meaning of an experimental situation with one another.

We address the problem of observing the solutions of a given Partial Differential Equation (PDE), submitted to unknown additive perturbations fulfilling another PDE, possibly of different nature. The problem under consideration is motivated by the issue of averaged control and observation. In the latter, one aims at determining the initial datum of a dynamics, submitted to unknown perturbations, by means of measurements done on the average of solutions with respect to the unknown parameters. We do it in two different cases. First, we assume that a given dynamics is perturbed in an additive manner by a state governed by a PDE, but not necessarily of the same type. In particular we consider the additive superposition of multi-physics solutions of wave and heat type, for instance. Assuming the PDEs under consideration have constant coefficients, we prove that, the by now well-known observability properties of PDE (mainly heat and wave equations) from open subsets of the domain where the dynamics evolves, are stable under these additive perturbations. The proof is rather systematic and easy to apply. It consists in composing all but one (the observable one) PDE operators so to reduce the problem to the consideration of a single equation and applying its known observability properties. The same proof leads to very interesting open problems for systems involving PDEs with variable coefficients where commutators lead to non-local lower order perturbations. We then consider a particular case of a PDE depending on a parameter in a continuous manner. We show that the average is governed by the superposition of two distinct solutions, corresponding to the extremal values of the parameter, and experiencing an extra regularizing effect. This allows showing that the averaged observability property holds, for the continuous average, but to the price of losing a finite number of derivatives. This opens a wide range of interesting problems to be explored. [ABSTRACT FROM AUTHOR]

Speelman and McGann's (2013) examination of the uncritical way in which the mean is often used in psychological research raises questions both about the average's reliability and its validity. In the present paper, we argue that interrogating the validity of the mean involves, amongst other things, a better understanding of the person's experiences, the meaning of their actions, at the time that the behavior of interest is carried out. Recently emerging approaches within Psychology and Cognitive Science have argued strongly that experience should play a more central role in our examination of behavioral data, but the relationship between experience and behavior remains very poorly understood. We outline some of the history of the science on this fraught relationship, as well as arguing that contemporary methods for studying experience fall into one of two categories. "Wide" approaches tend to incorporate naturalistic behavior settings, but sacrifice accuracy and reliability in behavioral measurement. "Narrow" approaches maintain controlled measurement of behavior, but involve too specific a sampling of experience, which obscures crucial temporal characteristics. We therefore argue for a novel, mid-range sampling technique, that extends Hurlburt's descriptive experience sampling, and adapts it for the controlled setting of the laboratory. This controlled descriptive experience sampling may be an appropriate tool to help calibrate both the mean and the meaning of an experimental situation with one another. [ABSTRACT FROM AUTHOR]

The Chemical Engineering curriculum at Polytechnique Montreal is structured to gradually provide more and more autonomy to the students. The third-year Unit Operations is taught using an outcomes-based approach and represents a turning point in the undergraduate curriculum where rubrics-based assessments overtake normative assessments. This begs the question: is it really necessary to divulge the average to students following assessments? Those from a more industrial background see the average as an unnecessary crutch for students, while the more academically inclined see it as a useful pedagogical tool to provide feedback and help students determine if they have attained their learning objectives. To settle this debate, we set into motion a yearlong study during which the average results to tests were withheld. Students were asked to predict their grade and the class average, and provide feedback on the assessment process. Results show that students are able to predict the average, but have difficulty predicting their individual performance (especially before a test, where more than 50% of students are off by a factor of more than 10%). Students award more importance to their personal sense of learning satisfaction than their position with respect to the average, and do not systematically use the average to plan study time (despite preferring to know it). Thus, it may be possible to substitute alternate frames of reference to the class average in an outcomes-based course, but this is not necessarily desirable and should at the very least be the subject of a more open discussion. [ABSTRACT FROM AUTHOR]

A new method, namely Impact-synchronous Modal Analysis (ISMA), utilizing the modal extraction technique commonly used in Experimental Modal Analysis performed in the presence of the ambient forces, is proposed. In ISMA, the extraction is performed while the machine is running, utilized Impact-synchronous Time Averaging prior to performing the Fast Fourier Transform. The number of averages had a very important effect when applying ISMA on structures with dominant periodic responses of cyclic loads and ambient excitation. With a sufficient number of impacts, all the unaccounted forces were diminished, leaving only the response due to the impacts. This study demonstrated the effectiveness of averages taken in the determination of dynamic characteristics of a machine while in different rotating speeds. At low operating speeds that coincided with the lower natural modes, ISMA with a high number of impacts determined the dynamic characteristics of the system successfully. Meanwhile, at operating speeds that were away from any natural modes, ISMA with a moderate number of averages taken was sufficient to extract the modal parameters. Finally for high-speed machines, ISMA with a high number of impacts taken has limitations in extracting natural modes close to the operating speed. [ABSTRACT FROM AUTHOR]

We obtain an exact formula for the average of values of L-series over two independent odd characters. The average of any positive moment of values at s = 1 is then expressed in terms of finite cotangent sums subject to congruence conditions. As consequences, bounds on such cotangent sums, limit points for the average of first moment of L-series at s = 1 and the average size of positive moments of character sums related to the class number are deduced. [ABSTRACT FROM AUTHOR]

We discuss the use of monotonic set measures for the representation of uncertain information. We look at some important examples of measure-based uncertainty, specifically probability and possibility and necessity. Others types of uncertainty such as cardinality based and quasi-additive measures are discussed. We consider the problem of determining the representative value of a variable whose uncertain value is formalized using a monotonic set measure. We note the central role that averaging and particularly weighted averaging operations play in obtaining these representative values. We investigate the use of various integrals such as the Choquet and Sugeno for obtaining these required averages. We suggest ways of extending a measure defined on a set to the case of fuzzy sets and the power sets of the original set. We briefly consider the problem of question answering under uncertain knowledge. [ABSTRACT FROM AUTHOR]

In this paper we study geometry of Young diagrams for the special class of permutations called ( C, B, A)-permutations (or Arnold permutations). In particular we compute the averages of such Young diagrams and compare them with the averages of arbitrary Young diagrams. [ABSTRACT FROM AUTHOR]

Abstract: In this article we study two problems raised by a work of Conrey and Ghosh from 1989. Let be the k-th derivative of the Riemann zeta-function, and be factor in the functional equation of the Riemann zeta-function. We calculate the average values of and χ at the nontrivial zeros of . [Copyright &y& Elsevier]

Abstract: Synchronous averaging is one of the most powerful techniques for the extraction of periodic signals from a composite signal. It is based on averaging periodic sections, necessitating an a-priori knowledge of the period sought. It is one of the most effective signal processing tools applied to rotating machinery, and has been known and used for decades.It will be shown that synchronous average is actually just one of the many possible "synchronous filters" which could be used to extract the above periodic components performance. A novel signal analysis, geared to periodic signals will be introduced, with the potential of extracting more complex phenomena typical of some rotating machinery. Examples given are based on periodic oscillating transients, with various additive interferences. The possibility of additional signal processing approaches is also discussed. [Copyright &y& Elsevier]

There is a great potential opportunity to use portable physical activity monitoring devices as data collection tools for educational purposes. Using one such device, we designed and implemented a weeklong workshop with high school students to test the utility of such technology. During that intervention, students performed data investigations of physical activity that culminated in the design and implementation of their own studies. In this paper, we explore some of the mathematical thinking that took place through a series of vignettes of a pair of students engaged in analyzing some of their own activity data. A personal connection to the data appeared to aid these students in recognizing their own errors, and ultimately helped them move from a point-based analytical approach for making sense of the data to an aggregate one. From our observations of this designed learning experience, we conclude that physical activity data recording devices can afford students the opportunity to reason with personally relevant data in meaningful ways. [ABSTRACT FROM AUTHOR]

We study the irrational factor function I( n) introduced by Atanassov and defined by $$ I(n) = \prod\nolimits_{\nu = 1}^k {p_\nu ^{1/\alpha _\nu } } $$ , where $$ n = \prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu } } $$ is the prime factorization of n. We show that the sequence { G( n)/ n} n≧1, where G( n) = Π I( ν)1/ n , is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I( n). [ABSTRACT FROM AUTHOR]

This article is the first of a two-part printed version of the Royal Statistical Society's Schools Lecture for 2004, on ‘Lies and Statistics’. [ABSTRACT FROM AUTHOR]

The statistical thinking exhibited by 14–19 year-old students during clinical interview sessions is described. The students’ thinking with regard to fundamental statistics concepts is reported in order to help inform instructional practice. [ABSTRACT FROM AUTHOR]

Background: Clinical investigators, although they are generally familiar with testing differences between averages, have difficulty testing differences between variabilities. Objective: To give examples of situations where variability is more relevant than averages and to describe simple methods for testing such data. Results: Examples include: (1) testing drugs with small therapeutic indices, (2) testing variability in drug response, (3) assessing pill diameters or pill weights, (4) comparing patient groups for variability in patient characteristics, (5) assessing the variability in duration of clinical treatment, (6) finding the best method for patient assessment. Various fields of research, particularly in clinical pharmacology, make use of test procedures that implicitly, address the variability in the data. Tests specially designed for testing variability in data include the χ²-test for one sample, the F-test for 2 samples and Bartlett's or Levene's test for 3 or more samples. Additional methods include(1) the comparison of confidence intervals, and (2) testing confidence intervals against prior defined intervals of therapeutic tolerance or equivalence. Many of these tests are available in Excel and other statistical software programs and one such program is described. Conclusions: In the analysis of clinical data the variability in the data is often more important than averages. Eight simple methods for assessment variability are described to illustrate the value and importance of putting more emphasis on and this parameter. [ABSTRACT FROM AUTHOR]

The averages of nonzero solutions of second-order ordinary differential equation x″+f(x)=0, x(0)=x(T)=0 are obtained if f(x)∈C1(R,R) and uf(u)>0 for u≠0. Generalization to nonlinear operators is also obtained. [Copyright &y& Elsevier]

The research in the field of potable water quality is characterized by a series of parameters, which defme water content from both physical and chemical point of views. They are mainly represented by: pH, conductivity and turbidimetry The aim of this paper was the monitoring of the potable water quality in Cluj - Napoca municipality, by characterizing the following quality indicators: pH, conductivity and turbidity. The study was realized during two experimental years, 2011, and 2012, and consisted from weekly prelevation of potable water from six points located in main districts of Cluj - Napoca (the same in each experimental year): Zorilor, Mărăşti, Grigorescu, Gheorgheni, Mănăştur, and city centre, and quantification of the pH, conductivity and turbidity in Laboratory of Environmental and Plant Protection of USAMV Cluj-Napoca. The methods were potentiometry, conductometry, and nefelometry. The results are presented as yearly averages. [ABSTRACT FROM AUTHOR]

This paper provides guidelines for determining average grain sizes with an optimal level of statistical adequacy and determine the best methods for estimating confidence intervals in grain size studies. I used Monte Carlo simulations and relative efficiency curves to test which central tendency measure (average) and which method of confidence interval estimation perform best depending on the lognormal shape and sample size. Results from synthetic populations were then compared and validated using actual grain size populations and random sampling methods. Overall, the geometric mean and the confidence intervals for the geometric mean provide the best balance between efficiency and robustness. The median is the best alternative when data contamination is an issue. Confidence intervals for the arithmetic mean in actual grain size populations are problematic regardless of the method used, especially for small sample sizes (n < 100). Lastly, we warn against the use of the area-weighted mean or the root mean square as both averages perform poorly. Image 1 • Guidelines for determining average grain sizes and reliable confidence intervals. • We use Monte Carlo simulations and relative efficiency curves. • The geometric mean provides the best balance between efficiency and robustness. • Confidence intervals for the arithmetic mean are problematic in real datasets. • Avoid the use of the area-weighted mean or the root mean square. [ABSTRACT FROM AUTHOR]

Databases may be compromised by asking a set of queries which return only statistical information and making inferences about a specific entry from the results of the set of queries. We present methods of constructing the set of queries to compromise a database where all the queries in the set return the maximum of a set of k elements, or all queries return the mean of a set of k elements. In the case of the mean query, all elements involved will be compromised. We also consider bounds on the number of queries required to compromise the database. [ABSTRACT FROM AUTHOR]