scholarly journals Lacunas and local algebraicity of volume functions

2018 ◽  
Author(s):  
V. A. Vassiliev
Keyword(s):  
Volume Functions

Common volume functions and diffraction line profiles of polyhedral domains

2012 ◽  
Vol 45 (6) ◽  
pp. 1162-1172 ◽  
Author(s):  
Alberto Leonardi ◽  
Matteo Leoni ◽  
Stefano Siboni ◽  
Paolo Scardi
Keyword(s):  
Diffraction Pattern ◽  
Excellent Agreement ◽  
Numerical Algorithm ◽  
Theoretical Description ◽  
Fast Computation ◽  
Line Profiles ◽  
Cubic Materials ◽  
Equilibrium Shapes ◽  
The Common ◽  
Volume Functions

A general numerical algorithm is proposed for the fast computation of the common volume function (CVF) of any polyhedral object, from which the diffraction pattern of a corresponding powder can be obtained. The theoretical description of the algorithm is supported by examples ranging from simple equilibrium shapes in cubic materials (Wulff polyhedra) to more exotic non-convex shapes, such as tripods or hollow cubes. Excellent agreement is shown between patterns simulated using the CVF and the corresponding ones calculated from the atomic positionsviathe Debye scattering equation.

scholarly journals Field and Computer Application of Mesavage and Girard Form Class Volume Tables

1998 ◽  
Vol 22 (2) ◽  
pp. 81-87 ◽  
Author(s):  
Robert C. Parker
Keyword(s):  
Regression Model ◽  
Iterative Procedure ◽  
Computer Applications ◽  
Tree Size ◽  
Computer Application ◽  
Form Class ◽  
Single Tree ◽  
Standing Trees ◽  
Taper Equation ◽  
Volume Functions

Abstract Mesavage and Girard form class volume tables for estimating board foot volume of standing trees remain the most widely used volume tables in the East and South even though newer, more versatile and sophisticated volume functions are available. The volume tables are being misused by foresters because the merchantability standards of the average, upper-log taper table used to derive the volume tables does not show that merchantable top diameters and form class applications require appropriate sampling and accurate measurement of form on selected trees. The original upper-log tapers, developed from averages of actual tree measurements and ocular estimates, were fitted to a regression model to smooth the inconsistencies of the table values. The resulting Mesavage and Girard "taper equation" is used to obtain upper stem diameters for trees of known Girard form class, dbh, and merchantable height. The taper equation shows that top-limit diameter increases with both tree size (dbh and height) and Girard form class, and any attempt to apply form class volume tables to a fixed-top diameter on inventory trees would produce erroneous cruise volumes. The derived taper equation can be used in an iterative procedure during computer applications to obtain single tree volumes as the sum of log segment volumes for segments of user-defined length. A hierarchy of suggested form class application options is presented along with suggestion sampling, measurement, and stratification procedures. South. J. Appl. For. 22(2):81-87.

Tree and stand volume functions for Eucalyptus saligna

1992 ◽  
Vol 47 (1-4) ◽  
pp. 211-223 ◽  
Author(s):  
B.D. Shiver ◽  
G.H. Brister
Keyword(s):  
Eucalyptus Saligna ◽  
Stand Volume ◽  
Volume Functions

scholarly journals Minimum sample size for fitting compatible taper-volume functions for three pine species in Chihuahua

2020 ◽  
Vol 27 (1) ◽  
pp. 143-163
Author(s):  
Juan M. Villela-Suárez ◽  
◽  
Oscar A. Aguirre-Calderón ◽  
Eduardo J. Treviño-Garza ◽  
Marco A. González-Tagle ◽  
...  
Keyword(s):  
Sample Size ◽  
Goodness Of Fit ◽  
Small Samples ◽  
Stem Volume ◽  
Minimum Sample Size ◽  
Forest Regions ◽  
Minimum Number ◽  
Minimum Sample ◽  
Volume Models ◽  
Volume Functions

Introduction: The choice of sample size is an important decision in the development of volume models and taper functions. Objective: To calculate the minimum sample size required for fitting compatible taper-volume functions for Pinus arizonica Engelm., P. durangensis Martínez and P. engelmannii Carr. in Chihuahua. Materials and methods: The methodology was divided into three phases: (i) fitting of a linear regression model to the diameter-height data of 50 trees of each species in the three forest regions; (ii) calculation of the minimum sample size required, and (iii) comparison of the goodness of fit of the taper-volume function using both sample sizes. Results and discussion: The minimum number of trees calculated ranged from 53 (Pinus durangensis) to 88 (P. engelmannii) and it is located in the interval reported in studies carried out to estimate the optimal sample size for the development of taper functions. No significant differences were observed in the goodness of fit (α = 0.05) in terms of the R 2 and the root mean square error, using the full sample size and the calculated minimum sample size; no significant effect was observed in the stem volume estimates. Conclusion: The use of small samples in the fit of taper-volume models generates accurate estimates if adequate representation of the study population is ensured.

New techniques for comparing the volume functions of historical texts

1989 ◽  
Vol 47 (1) ◽  
pp. 2302-2311
Author(s):  
V. V. Kalashnikov ◽  
S. T. Rachev ◽  
A. T. Fomenko
Keyword(s):  
New Techniques ◽  
Historical Texts ◽  
Volume Functions

A Proceedure for Systematically Fitting Local Volume Functions Using Orthogonal Polynomials

1970 ◽  
Vol 46 (3) ◽  
pp. 225-228
Author(s):  
L. C. Wensel ◽  
J. Van Roessel
Keyword(s):  
Computer Program ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Polynomial Equations ◽  
Computational Process ◽  
End Points ◽  
Local Volume ◽  
Best Fit ◽  
Volume Functions

The proposed technique is designed to fit orthogonal polynomial equations to existing local volume tables. This method has the advantage of being able to find the "best" fit of up to 8 powers (terms) such that (1) the function will yield volumes that increase with increasing diameter, and (2) will keep the end points of the curves within range. The computer program is designed so that it can be used with little or no knowledge of the computational process involved.

Gear Transmission Density Maximization

2011 ◽  
Author(s):  
Alexander L. Kapelevich ◽  
Viacheslav M. Ananiev
Keyword(s):  
Gear Tooth ◽  
Load Capacity ◽  
Gear Ratio ◽  
Gear Transmission ◽  
Gear Trains ◽  
Reduced Costs ◽  
Gear Drives ◽  
Internal Gear ◽  
Ratio Optimization ◽  
Volume Functions

Maximization of the gear transmission density presents an important task. It allows to increase the output torque within given dimensional constrains that is critical, for instance, in racing gearboxes, or to reduce size and weight of aerospace gear drives. It can also lead to reduced costs for automotive and consumer product gear trains, etc. There are several ways to increase gear drive load capacity, including advanced design, materials, and technologies. This paper presents an approach that allows optimizing gearbox kinematic arrangement and gear tooth geometry to achieve high gear transmission density. It introduces dimensionless gearbox volume functions, which can be minimized by the internal gear ratio optimization. Different gearbox arrangements are analyzed to define a minimum of the volume functions. Application of the asymmetric gear tooth profiles power density maximization is also considered.

Sign in / Sign up

Export Citation Format

Share Document