A Theory of the Asymptotic Function

2018 ◽  
pp. 101-110
Keyword(s):  
Asymptotic Function

scholarly journals An embedding of Schwartz distributions in the algebra of asymptotic functions

1998 ◽  
Vol 21 (3) ◽  
pp. 417-428 ◽  
Author(s):  
Michael Oberguggenberger ◽  
Todor Todorov
Keyword(s):  
Differential Algebra ◽  
Generalized Functions ◽  
Schwartz Distributions ◽  
Asymptotic Functions ◽  
Space Of Distributions ◽  
Asymptotic Function

We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper “asymptotic function,” similar to but different from J. F Colombeau's algebras of new generalized functions.

Numerical Simulation of Sheet Metal Forming Processes Using a New Yield Criterion

2007 ◽  
Vol 344 ◽  
pp. 833-840 ◽  
Author(s):  
Dan Sorin Comsa ◽  
Dorel Banabic
Keyword(s):  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Equivalent Stress ◽  
Constitutive Models ◽  
Cold Forming ◽  
Material Parameters ◽  
Numerical Tests ◽  
Hardening Law ◽  
Asymptotic Function ◽  
New Formulation

The paper is focused on the development of a new phenomenological yield criterion able to describe the inelastic response of sheet metals subjected to cold forming. The model consists in two components: the equivalent stress and the hardening law. The equivalent stress is a function incorporating 8 material parameters. Due to these parameters, the new formulation is able to describe four normalized yield stresses (y0, y45, y90, yb) and four coefficients of plastic anisotropy (r0, r45, r90, rb). The hardening law is defined as a linearly asymptotic function containing 4 material parameters. The numerical tests presented in the last section of the paper prove the capability of the elastoplastic constitutive models based on the new yield criterion to model the earing as well as the wrinkling phenomena accompanying the deep-drawing process.

Mechanics of browsing in dense food patches: effects of plant and animal morphology on intake rate

1992 ◽  
Vol 70 (9) ◽  
pp. 1743-1752 ◽  
Author(s):  
Lisa A. Shipley ◽  
Donald E. Spalinger
Keyword(s):  
Functional Response ◽  
Rangifer Tarandus ◽  
Asymptotic Relation ◽  
Acer Rubrum ◽  
Neutral Detergent Fiber ◽  
Intake Rate ◽  
Red Maple ◽  
Bite Size ◽  
Snowshoe Hares ◽  
Asymptotic Function

There appear to be two dominant forms of the functional response of vertebrate herbivores, corresponding to animals foraging in spatially concentrated or spatially dispersed food patches. We examine the factors contributing to the functional response of herbivores feeding on spatially concentrated browses. Specifically, we tested the hypothesis that the instantaneous intake rate of four boreal browsers (moose, Alces alces, woodland caribou, Rangifer tarandus caribou, white-tailed deer, Odocoileus virginianus, and snowshoe hares, Lepus americanus) feeding on red maple (Acer rubrum) browse is an asymptotic function of the size of bite obtainable by the herbivore. Based on this functional response model, we also hypothesized that (i) cropping rate of the herbivores would decline curvilinearly with bite size, (ii) intake rate would decline with increasing fibrousness (measured, as the neutral detergent fiber of the foods consumed), and (iii) maximum intake rate would scale as the 2/3 power of herbivore body mass (BM). Intake rates of all animals increased 2- to 10-fold with increasing bite size of stems and leaves, and conformed to the hypothesized asymptotic relation. Similarly, cropping rate declined curvilinearly with increasing bite size, and intake rate declined with increasing fibrousness of foods consumed. Maximum intake rate scaled with BM0.76, not significantly different from the hypothesized exponent of 0.67. These data support the hypothesis that bite size affects intake rate by controlling the ratio of cropping and chewing, and that the asymptotic intake rate of herbivores is related to the food processing capability of the mouth.

scholarly journals Base water potential for germination of radiata pine and buddleia seeds adjusts in response to time, seed-bed water potential and supra-optimal temperatures

2010 ◽  
Vol 14 ◽  
pp. 113-118
Author(s):  
M. Bloomberg ◽  
M.S. Watt
Keyword(s):  
Water Potential ◽  
Pinus Radiata ◽  
Radiata Pine ◽  
Time Model ◽  
Bed Temperature ◽  
Proposed Model ◽  
Ecological Implications ◽  
Asymptotic Function ◽  
Buddleia Davidii ◽  
Base Water Potential

Hydrothermal germination models are mathematical models which predict germination time of seeds for a specified seed-bed temperature (T) and water potential (Ψ). In this paper, the commonly observed decline in seed germination at supra-optimal temperatures is investigated by fitting a hydrothermal time model to germination data from two unrelated plant species (Buddleia davidii and Pinus radiata). For both these species, reduced germination rates and germination percentages above optimum temperatures (20°C and 25°C for P. radiata and B. davidii, respectively) were successfully modelled by an upward shift in the seeds' base water potential (Ψb) during germination. The upwards shift in Ψb was shown to be an asymptotic function of time to germination, but with the rate increased by higher temperatures and moister seed-bed conditions. The physiological and ecological implications of this proposed model of the observed decline in germination at supraoptimal temperatures are discussed. Keywords: hydrothermal, model, Pinus radiata, Buddleia davidii

A Quasiconvex Asymptotic Function with Applications in Optimization

2018 ◽  
Vol 180 (1) ◽  
pp. 170-186 ◽  
Author(s):  
Nicolas Hadjisavvas ◽  
Felipe Lara ◽  
Juan Enrique Martínez-Legaz
Keyword(s):  
Asymptotic Function

scholarly journals Effect of the Frictional Properties of Sunflower Seeds on the Efficiency of Pressing Equipment

2019 ◽  
pp. 571-578
Author(s):  
Mihail Berezin ◽  
Vitaly Borisov
Keyword(s):  
Practical Importance ◽  
Oil Yield ◽  
Hydrodynamic Resistance ◽  
Experimental Unit ◽  
Special Method ◽  
Related Factors ◽  
Friction Characteristics ◽  
Pressure Time ◽  
Asymptotic Function ◽  
Volume Characteristics

Introduction. The process of oil extraction from oilseeds is very complicated as it depends on a large number of related factors. The complex porous structure of pulp is a combination of three phases: dry solids, liquid (oil), and air. Therefore, the study of the process of pulp pressing requires a special method for determining the friction characteristics of the material. Study objects and methods. To determine the friction and volume characteristics of oilseeds, an original experimental unit was developed and manufactured. The study involved samples of the same mass weighted using a high-accuracy analytic balance (permissible error = ± 5%). The first stage of the experiment featured volume characteristics of ten samples. The second stage featured friction characteristics of the five first samples obtained during the first stage at different pressures. Results and discussion. The pressure time proved to have a more significant effect on the oil yield than the pressure volume, since the complex capillary structure of the pulp demonstrated a significant hydrodynamic resistance to oil outflow. The dependence of the oil yield on the pressure was described by an asymptotic function; the limit (asymptotic) value of the pressure was 48 MPa. At this pressure, the oil yield reached φ = 54 %. The dependence of the friction coefficient on the values of temperature, pressure, and sliding velocity was described by a power-law regression equation with the coefficient of accuracy of approximation R2 = 0.96. Conclusion. The obtained data are of practical importance and can be used to improve the efficiency of pressing equipment.

High speed RLC equivalent RC delay model using normalized asymptotic function for global VLSI interconnects

2021 ◽  
Vol 107 ◽  
pp. 104941
Author(s):  
Sunil Jadav ◽  
Shubham Tayal ◽  
Rajeevan Chandel ◽  
Munish Vashishath
Keyword(s):  
High Speed ◽  
Delay Model ◽  
Vlsi Interconnects ◽  
Asymptotic Function ◽  
Rc Delay

Maximum decomposition limits of forest litter types: a synthesis

1996 ◽  
Vol 74 (5) ◽  
pp. 659-672 ◽  
Author(s):  
Björn Berg ◽  
Maj-Britt Johansson ◽  
Gunnar Ekbohm ◽  
Charles McClaugherty ◽  
Flora Rutigliano ◽  
...  
Keyword(s):  
Litter Decomposition ◽  
Forest Litter ◽  
Limit Values ◽  
Limit Value ◽  
Needle Litter ◽  
Linear Relationships ◽  
Asymptotic Function ◽  
Linear Regressions ◽  
Negative Linear Relationship

We used long-term litter decomposition data to estimate final decomposition levels using an asymptotic function. The estimated final limit values for decomposition were compared with available chemical data for the different litter types. A total of 41 limit values were estimated from as many different decomposition studies, and 20 different litter types were incubated in eight different forest systems. The limit values estimated varied with litter type. They ranged from about 35 to about 100% decomposition and were linearly related to the initial litter concentrations of N, Mn, and Ca in the newly shed litter. For these three nutrients, there are causal relationships to lignin degradation and to the lignin-degrading microbial community. Using all available data, we made simple and multiple linear regressions and obtained a negative linear relationship between limit value and initial N concentration ([Formula: see text]; n = 41; p < 0.001). For needle litter alone, we obtained a better relationship ([Formula: see text]; n = 23; p < 0.001). Manganese concentrations in litter gave a positive relationship ([Formula: see text]; n = 25; p < 0.001), with a clear improvement when needle litter was tested for alone ([Formula: see text]; n = 16; p < 0.001). Calcium alone gave a barely significant relationship. When combining nutrients in multiple linear relationships we obtained high R2 values, indicating that the models were good. Thus for all sites and litter types, N, Mn, and Ca combined gave an [Formula: see text] value of 0.640 with n = 25 (p < 0.001). All needle litters combined gave an [Formula: see text] of 0.745 (n = 16; p < 0.001). The significance of this finding is discussed. Keywords: litter decomposition, limit values, maximum decomposition, nitrogen, manganese, calcium.

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