scholarly journals Another note on the inequality between geometric and p ‐generalized arithmetic mean

2021 ◽  
Author(s):  
Christoph Thäle
Keyword(s):  
Arithmetic Mean ◽  
Generalized Arithmetic

scholarly journals Hydrotropic Pulping of Miscanthus to Obtain Pulp

2019 ◽  
pp. 483-493
Author(s):  
Igor N. Pavlov ◽  
Alexey A. Kukhlenko ◽  
Yulia V. Sevastyanova
Keyword(s):  
Lignin Content ◽  
Arithmetic Mean ◽  
Pulp Yield ◽  
Residual Lignin ◽  
Optimum Conditions ◽  
Time Effects ◽  
Miscanthus Sacchariflorus ◽  
Optimization Parameter ◽  
Special Paper ◽  
Generalized Arithmetic

The hydrotropic pulping of crushed straw of Miscanthus sacchariflorus Andersson to produce pulp was studied herein. A concentrated sodium benzoate solution was used as the reagent. Established regularities of the pulping temperature and time effects on delignification quality attributes such as pulp yield and residual lignin content in the pulp. The generalized arithmetic-mean optimization parameter enabled hydrotropic pulping optimum conditions to be identified to obtain hard pulp fit. Experimentally displayed the possibility of using cellulose for the manufacture of special paper grades

On Statistics of Log-Ratio of Arithmetic Mean to Geometric Mean for Nakagami-m Fading Power

2012 ◽  
Vol E95-B (2) ◽  
pp. 647-650
Author(s):  
Ning WANG ◽  
Julian CHENG ◽  
Chintha TELLAMBURA
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Log Ratio

scholarly journals A Deterministic Rapid Intensification Aid

2011 ◽  
Vol 26 (4) ◽  
pp. 579-585 ◽  
Author(s):  
Charles R. Sampson ◽  
John Kaplan ◽  
John A. Knaff ◽  
Mark DeMaria ◽  
Chris A. Sisko
Keyword(s):  
Real Time ◽  
Arithmetic Mean ◽  
Forecast Errors ◽  
Rapid Intensification ◽  
Intensity Forecast ◽  
Probability Threshold ◽  
Forecast Time ◽  
National Hurricane Center ◽  
Made In

Abstract Rapid intensification (RI) is difficult to forecast, but some progress has been made in developing probabilistic guidance for predicting these events. One such method is the RI index. The RI index is a probabilistic text product available to National Hurricane Center (NHC) forecasters in real time. The RI index gives the probabilities of three intensification rates [25, 30, and 35 kt (24 h)−1; or 12.9, 15.4, and 18.0 m s−1 (24 h)−1] for the 24-h period commencing at the initial forecast time. In this study the authors attempt to develop a deterministic intensity forecast aid from the RI index and, then, implement it as part of a consensus intensity forecast (arithmetic mean of several deterministic intensity forecasts used in operations) that has been shown to generally have lower mean forecast errors than any of its members. The RI aid is constructed using the highest available RI index intensification rate available for probabilities at or above a given probability (i.e., a probability threshold). Results indicate that the higher the probability threshold is, the better the RI aid performs. The RI aid appears to outperform the consensus aids at about the 50% probability threshold. The RI aid also improves forecast errors of operational consensus aids starting with a probability threshold of 30% and reduces negative biases in the forecasts. The authors suggest a 40% threshold for producing the RI aid initially. The 40% threshold is available for approximately 8% of all verifying forecasts, produces approximately 4% reduction in mean forecast errors for the intensity consensus aids, and corrects the negative biases by approximately 15%–20%. In operations, the threshold could be moved up to maximize gains in skill (reducing availability) or moved down to maximize availability (reducing gains in skill).

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

scholarly journals On the Beckenbach–Gini–Lehmer Means and Means Mappings

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1569
Author(s):  
Janusz Matkowski ◽  
Małgorzata Wróbel
Keyword(s):  
Functional Equation ◽  
Arithmetic Mean ◽  
Several Variables ◽  
Equality Of Means

Beckenbacg–Gini–Lehmer type means and mean-type mappings generated by functions of several variables, for which the arithmetic mean is invariant, are introduced. Equality of means of that type, their homogeneity, and convergence of the iterates of the respective mean-type mappings are considered. An application to solving a functional equation is given.

scholarly journals Faecal contamination of drinking water during collection and household storage: the need to extend protection to the point of use

2003 ◽  
Vol 1 (3) ◽  
pp. 109-115 ◽  
Author(s):  
Thomas F. Clasen ◽  
Andrew Bastable
Keyword(s):  
Drinking Water ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Faecal Contamination ◽  
Household Level ◽  
Safe Water ◽  
Female Head ◽  
Point Of Use ◽  
Thermotolerant Coliforms ◽  
And Storage

Paired water samples were collected and analysed for thermotolerant coliforms (TTC) from 20 sources (17 developed or rehabilitated by Oxfam and 3 others) and from the stored household water supplies of 100 households (5 from each source) in 13 towns and villages in the Kailahun District of Sierra Leone. In addition, the female head of the 85 households drawing water from Oxfam improved sources was interviewed and information recorded on demographics, hygiene instruction and practices, sanitation facilities and water collection and storage practices. At the non-improved sources, the arithmetic mean TTC load was 407/100 ml at the point of distribution, rising to a mean count of 882/100 ml at the household level. Water from the improved sources met WHO guidelines, with no faecal contamination. At the household level, however, even this safe water was subject to frequent and extensive faecal contamination; 92.9% of stored household samples contained some level of TTC, 76.5% contained more than the 10 TTC per 100 ml threshold set by the Sphere Project for emergency conditions. The arithmetic mean TTC count for all samples from the sampled households was 244 TTC per 100 ml (geometric mean was 77). These results are consistent with other studies that demonstrate substantial levels of faecal contamination of even safe water during collection, storage and access in the home. They point to the need to extend drinking water quality beyond the point of distribution to the point of consumption. The options for such extended protection, including improved collection and storage methods and household-based water treatment, are discussed.

A Neutral Model With Fluctuating Population Size and Its Effective Size

Genetics ◽  
2002 ◽  
Vol 161 (1) ◽  
pp. 381-388
Author(s):  
Masaru Iizuka ◽  
Hidenori Tachida ◽  
Hirotsugu Matsuda
Keyword(s):  
Asymptotic Behavior ◽  
Population Size ◽  
Diffusion Model ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Effective Size ◽  
Neutral Model ◽  
Average Heterozygosity ◽  
Special Case ◽  
Concrete Model

Abstract We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.

An existence theorem for Robin's equation

1972 ◽  
Vol 72 (3) ◽  
pp. 489-498 ◽  
Author(s):  
R. Cade
Keyword(s):  
Integral Equation ◽  
Existence Theorem ◽  
Electric Charge ◽  
Gaussian Curvature ◽  
Closed Surface ◽  
Arithmetic Mean ◽  
Main Argument

AbstractAn existence theorem is proved for Robin's integral equation for the density of electric charge on a closed surface, under the assumptions that the surface is convex, smooth and twice continuously differentiable. The technique is essentially Neumann's method of the arithmetic mean, used by Robin himself to show that the solution, assumed to exist, can be successively approximated by a sequence. In order to facilitate the main argument of the proof, it is assumed initially that the Gaussian curvature is everywhere positive, but this restriction is subsequently removed.

scholarly journals GALOIS THEORY OF THE CANONICAL THETA STRUCTURE

2011 ◽  
Vol 07 (01) ◽  
pp. 173-202
Author(s):  
ROBERT CARLS
Keyword(s):  
Galois Theory ◽  
Theoretical Foundation ◽  
Abelian Varieties ◽  
Geometric Mean ◽  
Null Point ◽  
Point Counting ◽  
Characteristic 2 ◽  
Theoretic Characterization ◽  
Generalized Arithmetic

In this article, we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain p-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application, we prove some 2-adic theta identities which describe the set of canonical theta null points of the canonical lifts of ordinary abelian varieties in characteristic 2. The latter theta relations are suitable for explicit canonical lifting. Using the theory of canonical theta null points, we are able to give a theoretical foundation to Mestre's point counting algorithm which is based on the computation of the generalized arithmetic geometric mean sequence.

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