Generalized Kronecker’s theorem and strong limit power functions

2011 ◽  
Author(s):  
Chuanyi Zhang
Keyword(s):  
Power Functions ◽  
Strong Limit ◽  
Kronecker’S Theorem ◽  
Limit Power

scholarly journals Uniform limit power-type function spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Chuanyi Zhang ◽  
Weiguo Liu
Keyword(s):  
Power Function ◽  
Function Spaces ◽  
Power Functions ◽  
Power Type ◽  
Uniform Limit ◽  
Type Function ◽  
Limit Power

To answer a question proposed by Mari in 1996, we propose𝒰ℒ𝒫α(ℝ+), the space of uniform limit power functions. We show that𝒰ℒ𝒫α(ℝ+)has properties similar to that of𝒜𝒫(ℝ+). We also proposed three other limit power function spaces.

Two new spaces of vector-valued limit power functions

2007 ◽  
Vol 44 (4) ◽  
pp. 423-443 ◽  
Author(s):  
Chuanyi Zhang ◽  
Chenhui Meng
Keyword(s):  
Fourier Series ◽  
Power Function ◽  
Hilbert Spaces ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Power Functions ◽  
Uniform Limit ◽  
Parseval’S Equality ◽  
Vector Valued ◽  
Limit Power

To answer a question in [24], we propose \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{U}\mathcal{L}\mathcal{P}(\mathbb{R}^ + ,H)$$ \end{document}, the space of uniform limit power functions and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{L}\mathcal{P}_2$$ \end{document}, the space of limit power functions. We show that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{U}\mathcal{L}\mathcal{P}(\mathbb{R}^ + ,H)$$ \end{document} and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{L}\mathcal{P}_2$$ \end{document} have properties respectively similar to that of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{A}\mathcal{P}(\mathbb{R}^ + ,H)$$ \end{document}, the space of almost periodic functions and to that of B2 , Besicovitch’s space. Finally, we point out that \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{L}\mathcal{P}_2$$ \end{document} is the largest among those Hilbert spaces in limit power function set whose members have associated Fourier series (in the sense of a new basis) and satisfy Parseval’s equality.

Methodology for determining water losses from irrigation canals

2020 ◽  
pp. 16-18
Author(s):  
Elena Makarycheva
Keyword(s):  
Filtration Rate ◽  
Darcy Law ◽  
Filtration Flow ◽  
Irrigation Canals ◽  
Power Functions ◽  
Two Phase ◽  
Water Losses ◽  
Irrigation Channels ◽  
Unsteady Filtration ◽  
S Curve

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.

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

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.

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

2016 ◽  
Vol 232 (4) ◽  
pp. 742-751 ◽  
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.

scholarly journals Fishing Power Functions in Aggregate Bioeconomic Models

1985 ◽  
Vol 2 (1) ◽  
pp. 87-107 ◽  
Author(s):  
Timothy G. Taylor ◽  
Fred J. Prochaska
Keyword(s):  
Power Functions ◽  
Bioeconomic Models
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