Invariance of Bajraktarevic mean with respect to quasi arithmetic means

2012 ◽  
Vol 80 (3-4) ◽  
pp. 441-455 ◽  
Author(s):  
JANUSZ MATKOWSKI
Keyword(s):  
Arithmetic Means ◽  
Bajraktarević Mean

scholarly journals Join Products K2,3 + Cn

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 925
Author(s):  
Michal Staš
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number ◽  
Arithmetic Means ◽  
Minimum Number ◽  
Edge Crossings

The crossing number cr ( G ) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main goal of the paper is to state the crossing number of the join product K 2 , 3 + C n for the complete bipartite graph K 2 , 3 , where C n is the cycle on n vertices. In the proofs, the idea of a minimum number of crossings between two distinct configurations in the various forms of arithmetic means will be extended. Finally, adding one more edge to the graph K 2 , 3 , we also offer the crossing number of the join product of one other graph with the cycle C n .

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 Indicators of Targeted Physical Fitness in Judo and Jujutsu—Preliminary Results of Research

2021 ◽  
Vol 18 (8) ◽  
pp. 4347
Author(s):  
Wojciech J. Cynarski ◽  
Jan Słopecki ◽  
Bartosz Dziadek ◽  
Peter Böschen ◽  
Paweł Piepiora
Keyword(s):  
Reaction Time ◽  
Visual Stimulation ◽  
Intrinsic Value ◽  
Reaction Times ◽  
Arithmetic Means ◽  
Simple Reaction ◽  
Martial Art ◽  
Student’S T ◽  
Pearson Correlations ◽  
Student’S T Test

(1) Study aim: This is a comparative study for judo and jujutsu practitioners. It has an intrinsic value. The aim of this study was to showcase a comparison of practitioners of judo and a similar martial art jujutsu with regard to manual abilities. The study applied the measurement of simple reaction time in response to a visual stimulus and handgrip measurement. (2) Materials and Methods: The group comprising N = 69 black belts from Poland and Germany (including 30 from judo and 39 from jujutsu) applied two trials: “grasping of Ditrich rod” and dynamometric handgrip measurement. The analysis of the results involved the calculations of arithmetic means, standard deviations, and Pearson correlations. Analysis of the differences (Mann–Whitney U test) and Student’s t-test were also applied to establish statistical differences. (3) Results: In the test involving handgrip measurement, the subjects from Poland (both those practicing judo and jujutsu) gained better results compared to their German counterparts. In the test involving grasping of Ditrich rod, a positive correlation was demonstrated in the group of German judokas between the age and reaction time of the subjects (rxy = 0.66, p < 0.05), as well as in the group of jujutsu subjects between body weight and the reaction time (rxy = 0.49, p < 0.05). A significant and strong correlation between handgrip and weight was also established for the group of German judokas (rxy = 0.75, p < 0.05). In Polish competitors, the correlations were only established between the age and handgrip measurements (rxy = 0.49, p < 0.05). (4) Conclusions: Simple reaction times in response to visual stimulation were shorter in the subjects practicing the martial art jujutsu. However, the statement regarding the advantage of the judokas in terms of handgrip force was not confirmed by the results.

scholarly journals SPAD Leaf Greenness Index: Green Mass Yield Indicator of Maize (Zea mays L.), Genetic and Agriculture Practice Relationship

Plants ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 830
Author(s):  
Piotr Szulc ◽  
Jan Bocianowski ◽  
Kamila Nowosad ◽  
Waldemar Zielewicz ◽  
Joanna Kobus-Cisowska
Keyword(s):  
Mineral Fertilizer ◽  
Group Method ◽  
Growth Stages ◽  
Arithmetic Means ◽  
Stay Green ◽  
Plant Nitrogen ◽  
Green Mass ◽  
The Impact ◽  
Leaf Greenness ◽  
Greenness Index

The study presents the results of two field studies (Experiment I, Experiment II), whose aim was to assess the impact of agriculture factors on maize green mass and leaf greenness index (Soil and Plant Analysis Development, SPAD) in critical growth stages, as well as to determine the relationship between the SPAD index and the yield of green maize for ensiling. It was shown that thermal and humidity conditions in maize growing seasons determined the value of the SPAD leaf greenness index and the yield of maize harvested for silage. Row application of mineral fertilizer (N, NP) and selection of “stay-green” varieties guarantee a higher yield of maize green mass. Growing maize in direct sowing reduces chlorophyll content expressed in SPAD units, thereby reducing plant nitrogen condition, which significantly decreases the yield of biomass intended for silage. The SPAD leaf greenness index determined in critical stages of maize growth can be considered as a yield predictor of green mass for ensiling. The examined maize cultivars were divided into two groups on the basis of hierarchically grouping using the unweighted pair group method of arithmetic means. The first group comprised cultivars SY Cooky and Drim “stay-green,” while the second one included cultivars ES Paroli “stay-green” and ES Palazzo.

Generalized weighted quasi-arithmetic means

2010 ◽  
Vol 79 (3) ◽  
pp. 203-212 ◽  
Author(s):  
Janusz Matkowski
Keyword(s):  
Arithmetic Means

A Comparative Study on Engineering Student's Performance between the Single-Gender Classroom and Co-educational Classroom: A Case Study of Islamic University of Technology

2021 ◽  
Vol 1 (3) ◽  
pp. 20-24
Author(s):  
Faruq Bashir ◽  
Farouque Ahmed Haolader
Keyword(s):  
Comparative Study ◽  
Descriptive Analysis ◽  
Research Process ◽  
Male Students ◽  
Single Gender ◽  
Arithmetic Means ◽  
University Of Technology ◽  
Quasi Experimental ◽  
Group A ◽  
Group B

The purpose of this research was to conduct a comparative study to find out which setting performs better between students in the Co-educational Instruction setting and Students in the Single-gender Instruction set. In this research process, the researchers compared the performance of students who receive instruction in a single-gender classroom with the performance of other students who receive instruction in a co-educational classroom. The study population was 756 students of single and mixed-gender streams, classified into two groups (A & B). Out of this, one single-gender male class of 268 students (group A) and one COED class of 488 students (group B) were sampled from the Islamic University of Technology (IUT) in Bangladesh. The research adopted a quasi-experimental research design. The instruments used for data collection were the summative assessment of both groups' first and second-semester results that serve as test instruments. Frequency counts and the Arithmetic means were used for descriptive analysis. The independent sample t-test was used to test the hypotheses. Social learning theory emphasizes the importance of biological, social, and cultural impacts on human behavioral development and learning, especially on gender and genders specific traits and roles. Based on the analyses and interpretation of the data, the researcher found that male students perform better academically in single-gender classes, contrary to their academic performance when mixed with females in the same classes. Thus, single-gender instruction could be a more favorable environment for male students than a co-educational instruction environment.

Confidence intervals for a difference between lognormal means in cluster randomization trials

2014 ◽  
Vol 26 (2) ◽  
pp. 598-614 ◽  
Author(s):  
Julia Poirier ◽  
GY Zou ◽  
John Koval
Keyword(s):  
Confidence Intervals ◽  
Community Acquired Pneumonia ◽  
Small Sample ◽  
Cluster Randomization ◽  
Critical Pathway ◽  
Arithmetic Means ◽  
Multiple Parameters ◽  
The Difference ◽  
Using Data ◽  
Small Sample Sizes

Cluster randomization trials, in which intact social units are randomized to different interventions, have become popular in the last 25 years. Outcomes from these trials in many cases are positively skewed, following approximately lognormal distributions. When inference is focused on the difference between treatment arm arithmetic means, existent confidence interval procedures either make restricting assumptions or are complex to implement. We approach this problem by assuming log-transformed outcomes from each treatment arm follow a one-way random effects model. The treatment arm means are functions of multiple parameters for which separate confidence intervals are readily available, suggesting that the method of variance estimates recovery may be applied to obtain closed-form confidence intervals. A simulation study showed that this simple approach performs well in small sample sizes in terms of empirical coverage, relatively balanced tail errors, and interval widths as compared to existing methods. The methods are illustrated using data arising from a cluster randomization trial investigating a critical pathway for the treatment of community acquired pneumonia.

WHY ARE PHARMACOKINETIC DATA SUMMARIZED BY ARITHMETIC MEANS?

2000 ◽  
Vol 10 (1) ◽  
pp. 55-71 ◽  
Author(s):  
Steven A. Julious ◽  
Camille A. M. Debarnot
Keyword(s):  
Pharmacokinetic Data ◽  
Arithmetic Means

scholarly journals Sharp transition between coalescence and non-coalescence of sessile drops

2014 ◽  
Vol 743 ◽  
Author(s):  
Stefan Karpitschka ◽  
Hans Riegler
Keyword(s):  
Contact Region ◽  
Threshold Value ◽  
System Control ◽  
Arithmetic Means ◽  
Liquid Body ◽  
Molecular Diffusivity ◽  
Experimental Resolution ◽  
Miscible Liquids ◽  
Phase Angles ◽  
Sessile Drops

AbstractUnexpectedly, under certain conditions, sessile drops from different but completely miscible liquids do not always coalesce instantaneously upon contact: the drop bodies remain separated in a temporary state of non-coalescence, connected through a thin liquid bridge. Here we investigate the transition between the states of instantaneous coalescence and temporary non-coalescence. Experiments reveal that it is barely influenced by viscosities and absolute surface tensions. The main system control parameters for the transition are the arithmetic means of the three-phase angles, $\overline{\Theta }_{a}$, and the surface tension differences $\Delta \gamma $ between the two liquids. These relevant parameters can be combined into a single system parameter, a specific Marangoni number $\widetilde{M}=3\Delta \gamma /(2\overline{\gamma }\overline{\Theta }_{a}^2)$. This $\widetilde{M}$ universally characterizes the coalescence transition behaviour as a function of both the physicochemical liquid properties and the shape of the liquid body in the contact region. The transition occurs at a certain threshold value $\widetilde{M}_t$ and is sharp within the experimental resolution. The experimentally observed threshold value of $\widetilde{M}_t\approx 2$ agrees quantitatively with values obtained by simulations assuming realistic material parameters. The simulations indicate that the absolute value of $\widetilde{M}_t$ very weakly depends on the molecular diffusivity.

scholarly journals DETERMINATION OF THE AVERAGE WALL TEMPERATURE OF THE PLATE IN A RECUPERATIVE HEAT EXCHANGER WITH A CORRUGATED MESH INSERT

2021 ◽  
Vol 11 (1) ◽  
pp. 46-55
Author(s):  
Arman B. KOSTUGANOV ◽  
Vitaly V. DEMIDOCHKIN
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Heat Exchange ◽  
Wall Temperature ◽  
Arithmetic Means ◽  
Average Value ◽  
Average Temperature ◽  
Coeffi Cients ◽  
Heat Transfer Coeffi ◽  
Recuperative Heat Exchanger

This article discusses the issue of determining the value the average wall temperature of the plate of a recuperative heat exchanger type “air-to-air” with a corrugated mesh insert based on the results processing the data of a physical experiment to determine the thermohydraulic characteristics such heat exchange surfaces. It has been established that the temperature fi eld of heat exchange surfaces of this type is nonuniform, depends on the conditions of heat exchange and hydraulic regimes of air fl ow. Therefore, the adoption of the arithmetic means value of the measured surface temperatures as the calculated average temperature of the heat exchanger wall entails signifi cant errors in the subsequent processing of experimental data and fi nal the values of the heat transfer coeffi cients, the values the Nusselt criterion and the criterion equations of heat transfer. It is proposed to determine the average value the wall temperature of the heat exchanger based on the results of measurements the wall’s temperatures, the estimate of the coordinates the center of distribution the results of measurements the wall temperatures, the equations of heat balance and heat transfer.

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