scholarly journals A simple extension of Rolle’s theorem and its relation with multiple internal rates of return (IRR)

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Fernando Gómez Villarraga
Keyword(s):  
Geometric Interpretation ◽  
Simple Extension ◽  
Rates Of Return ◽  
Rolle’S Theorem

It has been stated a simple extension of the Rolle?s theorem. This extension permits to determine the amount of numbers  in which  in a given interval using the characteristics of the function  in that interval. The extension has been proved and the geometric interpretation is presented. Illustrative examples have been developed for each of the cases that can be obtained by applying the extension. The relation of this theorem with the problem of multiple internal rates of return (IRR) is presented.

scholarly journals A simple extension of Rolle’s theorem and its relation with multiple internal rates of return (IRR)

2020 ◽  
Vol 11 (2) ◽  
pp. 241-258
Author(s):  
Fernando Gómez Villarraga
Keyword(s):  
Geometric Interpretation ◽  
Simple Extension ◽  
Rates Of Return ◽  
Rolle’S Theorem

This paper presents a simple extension of Rolle’s Theorem. This extension allows determining the amount of numbers ξi in which f'(ξi) = 0 in a given interval, using the characteristics of the function f in that interval. The extension has been proved, and the geometric interpretation has been presented. Illustrative examples have also been developed for each case that can be obtained by applying the extension. Finally, the study examines the relation of this theorem with the problem of multiple internal rates of return (IRR).

Heteroscedastic Methods for Performing All Pairwise Comparisons of Regression Lines Associated With J Independent Groups

Methodology ◽  
2015 ◽  
Vol 11 (3) ◽  
pp. 110-115 ◽  
Author(s):  
Rand R. Wilcox ◽  
Jinxia Ma
Keyword(s):  
Least Squares ◽  
Pairwise Comparisons ◽  
Simple Extension ◽  
Type I ◽  
Type I Errors ◽  
Well Elderly ◽  
Using Data

Abstract. The paper compares methods that allow both within group and between group heteroscedasticity when performing all pairwise comparisons of the least squares lines associated with J independent groups. The methods are based on simple extension of results derived by Johansen (1980) and Welch (1938) in conjunction with the HC3 and HC4 estimators. The probability of one or more Type I errors is controlled using the improvement on the Bonferroni method derived by Hochberg (1988) . Results are illustrated using data from the Well Elderly 2 study, which motivated this paper.

Mathematical simulation of error functions of decision-making at tolerance control of measuring techniques availability

Metrologiya ◽  
2020 ◽  
pp. 3-15
Author(s):  
Rustam Z. Khayrullin ◽  
Alexey S. Kornev ◽  
Andrew A. Kostoglotov ◽  
Sergey V. Lazarenko
Keyword(s):  
Measurement Error ◽  
Geometric Interpretation ◽  
Measuring Instruments ◽  
Measured Quantity ◽  
Metrological Examination ◽  
Technical Documentation ◽  
Error Functions ◽  
Measuring Techniques ◽  
Tolerance Control ◽  
Laws Of Distribution

Analytical and computer models of false failure and undetected failure (error functions) were developed with tolerance control of the parameters of the components of the measuring technique. A geometric interpretation of the error functions as two-dimensional surfaces is given, which depend on the tolerance on the controlled parameter and the measurement error. The developed models are applicable both to theoretical laws of distribution, and to arbitrary laws of distribution of the measured quantity and measurement error. The results can be used in the development of metrological support of measuring equipment, the verification of measuring instruments, the metrological examination of technical documentation and the certification of measurement methods.

Historical Rates of Return on Investments in Flat Bonds

1968 ◽  
Vol 24 (6) ◽  
pp. 95-97 ◽  
Author(s):  
Elba F. Baskin ◽  
Gary M. Grooch
Keyword(s):  
Rates Of Return

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Pollution based real time control strategies for combined sewer systems

1997 ◽  
Vol 36 (8-9) ◽  
pp. 331-336 ◽  
Author(s):  
Gabriela Weinreich ◽  
Wolfgang Schilling ◽  
Ane Birkely ◽  
Tallak Moland
Keyword(s):  
Real Time ◽  
Control Strategies ◽  
Ammonia Nitrogen ◽  
Simple Extension ◽  
Real Time Control ◽  
Time Control ◽  
Sewer Systems ◽  
Receiving Waters ◽  
Tunnel System

This paper presents results from an application of a newly developed simulation tool for pollution based real time control (PBRTC) of urban drainage systems. The Oslo interceptor tunnel is used as a case study. The paper focuses on the reduction of total phosphorus Ptot and ammonia-nitrogen NH4-N overflow loads into the receiving waters by means of optimized operation of the tunnel system. With PBRTC the total reduction of the Ptot load is 48% and of the NH4-N load 51%. Compared to the volume based RTC scenario the reductions are 11% and 15%, respectively. These further reductions could be achieved with a relatively simple extension of the operation strategy.

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