Change of Variable in Riemann Integration

1961 ◽  
Vol 45 (351) ◽  
pp. 17 ◽  
Author(s):  
H. Kestelman
Keyword(s):  
Change Of Variable ◽  
Riemann Integration

Applications of Squeeze Theorem to Limiting Processes Involving Riemann Integration

2021 ◽  
Vol 52 (3) ◽  
pp. 224-226
Author(s):  
Brian Becsi ◽  
Solomon Huang ◽  
Verenalei Schoenfeld ◽  
Bogdan D. Suceavă ◽  
Ashley Thune-Aguayo
Keyword(s):  
Riemann Integration

Improved correlation dimension estimates through change of variable

1992 ◽  
Vol 163 (4) ◽  
pp. 269-274 ◽  
Author(s):  
M. Lefranc ◽  
D. Hennequin ◽  
P. Glorieux
Keyword(s):  
Correlation Dimension ◽  
Change Of Variable

scholarly journals r-Dependence in Two-Point Orientation Coherence Functions

2000 ◽  
Vol 34 (4) ◽  
pp. 233-241
Author(s):  
Peter R. Morris
Keyword(s):  
Correlation Function ◽  
Weight Function ◽  
Bessel Functions ◽  
Unit Weight ◽  
Experimental Procedure ◽  
Change Of Variable

Functions are derived, which are orthonormal on the range r=0, 1, with weight function corresponding to the distribution of r in a typical experimental procedure for measurement of the two-point orientation–coherence (or orientation–correlation) function. These are obtained by making an appropriate change of variable in spherical Bessel functions, orthonormal on the range r=0, 1, with unit weight function. The effects of weight function and change of variable on the functions are considered.

ON THE VALUATION OF DERIVATIVES WITH SNAPSHOT RESET FEATURES

2008 ◽  
Vol 11 (08) ◽  
pp. 905-941 ◽  
Author(s):  
ERIC C. K. YU ◽  
WILLIAM T. SHAW
Keyword(s):  
Convertible Bonds ◽  
Convertible Bond ◽  
Put Options ◽  
Risk Characteristics ◽  
Black Scholes ◽  
Barrier Type ◽  
Simple Change ◽  
Discontinuous Nature ◽  
Change Of Variable ◽  
Digital Options

We propose a general approach that requires only a simple change of variable that keeps the valuation of call and put options (convertible bonds) with strike (conversion) price resets two-dimensional in the classical Black–Scholes setting. A link between reset derivatives, compound options and "discrete barrier" type options, when there is one reset is then discussed, from which we analyze the risk characteristics of reset derivatives, which can be significantly different from their vanilla counterparts. We also generalize the prototype reset structure and show that the delta and gamma of a convertible bond with reset can both be negative. Finally, we show that the "waviness" property found in the delta and gamma of some reset derivatives is due to the discontinuous nature of the reset structure, which is closely linked to digital options.

Riemann Integration

2020 ◽  
pp. 151-188
Author(s):  
Daniel W. Cunningham
Keyword(s):  
Riemann Integration

Note on Newtonian Force-Fields

1949 ◽  
Vol 1 (2) ◽  
pp. 199-208 ◽  
Author(s):  
Garrett Birkhoff ◽  
Lindley Burton
Keyword(s):  
Force Fields ◽  
Volume Density ◽  
Newtonian Force ◽  
Riemann Integration

Although the behaviour of Newtonian potentials inside n-dimensional distributions of mass or charge has been discussed in the sense of Lebesgue-Stieltjes integrals by various authors, the discussion of various important theorems seems to have been made only in the sense of Riemann integration, and assuming the Hälder conditions (or at least piecewise continuity) for the volume density p. We shall generalize these theorems below.

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