Correction to: CCZ equivalence of power functions

The aim of the article is to develop a method for calculating water losses from irrigation channels in determining the permeability of rock in the zone of filtration flow on the basis of the law of infiltration A.N. Kostyakov using the results of studies of free filtration from pits and foundation pits in loess loams. Pressure movement of water in irrigation canals is subject to the laws of two-phase flow, in which – in contrast to the Darcy law for the zone of saturation plays an important role, the volume and its change in time. The filtration rate (VF) increases with increasing rock moisture (θ) along the S-curve, while the pressure gradient (I = dh/dz) decreases. The dependences of these parameters on the pressure are represented by power functions, and their product CDP = VFI does not change in time and can serve as a characteristic of the filtration flow under the channel. When installing paired piezometers near the water chore line in the channel and determining the graph I(t) by the value of the twophase flow constant CDP, it is possible to calculate the filtration rate at a number of times and the water losses during unsteady filtration. Water losses from the channels at equilibrium humidity increases with increasing head according to the formula A.N. Kostyakova, in which the water permeability of rocks is characterized by a steady filtration rate at a head of 1.0 m, and the gradient is the function of pressure. The application of the proposed method of calculating losses in the design of irrigation systems will increase the reliability of the justification of the volume of anti-filtration measures and the forecast of the groundwater level.

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Constructing 'Proper' ROCs Using Weighted Power Functions

SSRN Electronic Journal ◽

10.2139/ssrn.2184051 ◽

2012 ◽

Author(s):

Douglas Mossman ◽

Hongying Peng

Keyword(s):

Power Functions

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Study of the Composite Materials Optimal Structure Containing a Hollow Aluminum and Silica Microsphere Dependence on Humidity

Micro and Nanosystems ◽

10.2174/1876402912999201109204218 ◽

2020 ◽

Vol 12 ◽

Author(s):

Alexandra Atyaksheva ◽

Yermek Sarsikeyev ◽

Anastasia Atyaksheva ◽

Olga Galtseva ◽

Alexander Rogachev

Keyword(s):

Composite Material ◽

Composite Materials ◽

Strength Function ◽

Theory And Practice ◽

Optimal Structure ◽

Optimal Size ◽

Structure And Properties ◽

Power Functions ◽

Silica Microsphere ◽

Heat Engineering

Aims:: The main goals of this research are exploration of energy-efficient building materials when replacing natural materials with industrial waste and development of the theory and practice of obtaining light and ultra-light gravel materials based on mineral binders and waste dump ash and slag mixtures of hydraulic removal. Background.: Experimental data on the conditions of formation of gravel materials containing hollow aluminum and silica microsphere with opportunity of receipt of optimum structure and properties depending on humidity with the using of various binders are presented in this article. This article dwells on the scientific study of opportunity physical-mechanical properties of composite materials optimization are considered. Objective.: Composite material contains hollow aluminum and silica microsphere. Method.: The study is based on the application of the method of separation of power and heat engineering functions. The method is based on the use of the factor structure optimality, which takes into account the primary and secondary stress fields of the structural gravel material. This indicates the possibility of obtaining gravel material with the most uniform distribution of nano - and microparticles in the gravel material and the formation of stable matrices with minimization of stress concentrations. Experiments show that the thickness of the cement shell, which performs power functions, is directly related to the size of the raw granules. At the same time, the thickness of the cement crust, regardless of the type of binder, with increasing moisture content has a higher rate of formation for granules of larger diameter. Results.: The conditions for the formation of gravel composite materials containing a hollow aluminosilicate microsphere are studied. The optimal structure and properties of the gravel composite material were obtained. The dependence of the strength function on humidity and the type of binder has been investigated. The optimal size and shape of binary form of gravel material containing a hollow aluminosilicate microsphere with a minimum thickness of a cement shell and a maximum strength function was obtained. Conclusion.: Received structure allows to separate power and heat engineering functions in material and to minimize the content of the excited environment centers.

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Numerical analysis of heat flow in oxy-ethylene flame cutting of steel plate

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405416654183 ◽

2016 ◽

Vol 232 (4) ◽

pp. 742-751 ◽

Cited By ~ 3

Author(s):

Kang-Yul Bae ◽

Young-Soo Yang ◽

Myung-Su Yi ◽

Chang-Woo Park

Keyword(s):

Numerical Simulation ◽

Heat Flow ◽

Heat Affected Zone ◽

Steel Plate ◽

Cutting Parameters ◽

Cutting Process ◽

Heat Sources ◽

Power Functions ◽

Severe Problem ◽

Ethylene Flame

To manufacture a steel structure, in the first step, raw steel plate needs to be cut into proper sizes. Oxy-fuel flame is widely used in the cutting process due to its flexibility with respect to accessibility, plate thickness, cost, and material handling. However, the deformation caused by the cutting process frequently becomes a severe problem for the next process in the production of steel product. To decrease the deformation, the thermo-elasto-plastic behavior of the steel plate in the cutting process should be analyzed in advance. In this study, heat sources in oxy-ethylene flame cutting of steel plate were modeled first, and the heat flow in the steel plate was then analyzed by the models of the heat sources using a numerical simulation based on the finite element method. To verify the analysis by the numerical simulation including the models, a series of experiments were performed, and the temperature histories at several points on the steel plate during the cutting process were measured. Moreover, the predicted sizes of the heat-affected zone by the numerical simulations according to the variation in the cutting parameters were compared to the experimental results. The power functions of the relationship between the sizes of the heat-affected zone and cutting parameters were obtained by the recursion analysis using the correlation between the results and parameters. The results of the numerical simulation showed good agreement with those of the experiments, indicating that the proposed models of the heat sources and thermal analysis were feasible to analyze the heat flow in the steel plate during the cutting process.

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Fishing Power Functions in Aggregate Bioeconomic Models

Marine Resource Economics ◽

10.1086/mre.2.1.42628878 ◽

1985 ◽

Vol 2 (1) ◽

pp. 87-107 ◽

Cited By ~ 7

Author(s):

Timothy G. Taylor ◽

Fred J. Prochaska

Keyword(s):

Power Functions ◽

Bioeconomic Models

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Modeling the Compaction Characteristics of Fine-Grained Soils Blended with Tire-Derived Aggregates

Sustainability ◽

10.3390/su13147737 ◽

2021 ◽

Vol 13 (14) ◽

pp. 7737

Author(s):

Amin Soltani ◽

Mahdieh Azimi ◽

Brendan C. O’Kelly

Keyword(s):

Energy Levels ◽

Model Development ◽

Dry Mass ◽

Unit Weight ◽

Power Functions ◽

Compaction Characteristics ◽

Practical Applications ◽

Fine Grained ◽

Practical Procedure ◽

Fine Grained Soil

This study aims at modeling the compaction characteristics of fine-grained soils blended with sand-sized (0.075–4.75 mm) recycled tire-derived aggregates (TDAs). Model development and calibration were performed using a large and diverse database of 100 soil–TDA compaction tests (with the TDA-to-soil dry mass ratio ≤ 30%) assembled from the literature. Following a comprehensive statistical analysis, it is demonstrated that the optimum moisture content (OMC) and maximum dry unit weight (MDUW) for soil–TDA blends (across different soil types, TDA particle sizes and compaction energy levels) can be expressed as universal power functions of the OMC and MDUW of the unamended soil, along with the soil to soil–TDA specific gravity ratio. Employing the Bland–Altman analysis, the 95% upper and lower (water content) agreement limits between the predicted and measured OMC values were, respectively, obtained as +1.09% and −1.23%, both of which can be considered negligible for practical applications. For the MDUW predictions, these limits were calculated as +0.67 and −0.71 kN/m3, which (like the OMC) can be deemed acceptable for prediction purposes. Having established the OMC and MDUW of the unamended fine-grained soil, the empirical models proposed in this study offer a practical procedure towards predicting the compaction characteristics of the soil–TDA blends without the hurdles of performing separate laboratory compaction tests, and thus can be employed in practice for preliminary design assessments and/or soil–TDA optimization studies.

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Commutative semigroups whose endomorphisms are power functions

Semigroup Forum ◽

10.1007/s00233-021-10178-x ◽

2021 ◽

Author(s):

Ryszard Mazurek

Keyword(s):

Positive Integer ◽

Power Function ◽

Cyclic Group ◽

Commutative Semigroup ◽

Commutative Monoid ◽

Power Functions ◽

Commutative Semigroups ◽

Finite Cyclic Group

AbstractFor any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ f : S → S defined by $$f(x) = x^m$$ f ( x ) = x m is an endomorphism of S. We partly solve the Lesokhin–Oman problem of characterizing the commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid S is a power function if and only if S is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup S with an idempotent is a power function if and only if S is a finite cyclic semigroup. Furthermore, we prove that every endomorphism of a nontrivial commutative atomic monoid S with 0, preserving 0 and 1, is a power function if and only if either S is a finite cyclic group with zero adjoined or S is a cyclic nilsemigroup with identity adjoined. We also prove that every endomorphism of a 2-generated commutative semigroup S without idempotents is a power function if and only if S is a subsemigroup of the infinite cyclic semigroup.

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Influence of Temperature and Moisture Content on Thermal Performance of Green Roof Media

Energies ◽

10.3390/en14092421 ◽

2021 ◽

Vol 14 (9) ◽

pp. 2421

Author(s):

Bohan Shao ◽

Caterina Valeo ◽

Phalguni Mukhopadhyaya ◽

Jianxun He

Keyword(s):

Thermal Conductivity ◽

Moisture Content ◽

Green Roof ◽

Green Roofs ◽

Power Functions ◽

Thick Substrate ◽

Different Temperatures ◽

Test Cells ◽

Substrate Moisture ◽

Phase Transition Zone

The influence of moisture content on substrate thermal conductivity at different temperatures was investigated for four different commercially available substrates for green roofs. In the unfrozen state, as moisture content increased, thermal conductivity increased linearly. In the phase transition zone between +5 and −10 °C, as temperature decreased, thermal conductivity increased sharply during the transition from water to ice. When the substrate was frozen, thermal conductivity varied exponentially with substrate moisture content prior to freezing. Power functions were found between thermal conductivity and temperature. Two equally sized, green roof test cells were constructed and tested to compare various roof configurations including a bare roof, varying media thickness for a green roof, and vegetation. The results show that compared with the bare roof, there is a 75% reduction in the interior temperature’s amplitude for the green roof with 150 mm thick substrate. When a sedum mat was added, there was a 20% reduction in the amplitude of the inner temperature as compared with the cell without a sedum mat.

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Power comparison of Cochran-Armitage trend test against allelic and genotypic tests in large-scale case-control genetic association studies

Statistical Methods in Medical Research ◽

10.1177/0962280216683979 ◽

2016 ◽

Vol 27 (9) ◽

pp. 2657-2673 ◽

Cited By ~ 2

Author(s):

Mathieu Emily

Keyword(s):

Large Scale ◽

Association Studies ◽

Disease Model ◽

Trend Test ◽

Genome Wide Association Studies ◽

Power Functions ◽

Power Comparison ◽

Powerful Test ◽

Armitage Trend Test ◽

Mode Of Inheritance

The Cochran-Armitage trend test (CA) has become a standard procedure for association testing in large-scale genome-wide association studies (GWAS). However, when the disease model is unknown, there is no consensus on the most powerful test to be used between CA, allelic, and genotypic tests. In this article, we tackle the question of whether CA is best suited to single-locus scanning in GWAS and propose a power comparison of CA against allelic and genotypic tests. Our approach relies on the evaluation of the Taylor decompositions of non-centrality parameters, thus allowing an analytical comparison of the power functions of the tests. Compared to simulation-based comparison, our approach offers the advantage of simultaneously accounting for the multidimensionality of the set of features involved in power functions. Although power for CA depends on the sample size, the case-to-control ratio and the minor allelic frequency (MAF), our results first show that it is largely influenced by the mode of inheritance and a deviation from Hardy–Weinberg Equilibrium (HWE). Furthermore, when compared to other tests, CA is shown to be the most powerful test under a multiplicative disease model or when the single-nucleotide polymorphism largely deviates from HWE. In all other situations, CA lacks in power and differences can be substantial, especially for the recessive mode of inheritance. Finally, our results are illustrated by the comparison of the performances of the statistics in two genome scans.

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