Section 32: Change of variable in partial differentiation

2004 ◽  
pp. 240-247
Keyword(s):  
Partial Differentiation ◽  
Change Of Variable

Myelomastocytic leukemia: myeloid neoplasm characterized by partial differentiation of mast cell-lineage cells

2002 ◽  
Vol 3 (2) ◽  
pp. 90-94 ◽  
Author(s):  
Peter Valent ◽  
Puchit Samorapoompichit ◽  
Wolfgang R Sperr ◽  
Hans-Peter Horny ◽  
Klaus Lechner
Keyword(s):  
Mast Cell ◽  
Cell Lineage ◽  
Partial Differentiation ◽  
Myeloid Neoplasm

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.

A New Kinematic Error Modelling and Identification Method of the Parallel Manipulator

2020 ◽  
Author(s):  
Weitao Li ◽  
Liping Wang
Keyword(s):  
Parallel Manipulators ◽  
Kinematic Error ◽  
Basic Error ◽  
Error Identification ◽  
Partial Differentiation ◽  
Differentiation Method ◽  
Modelling Method ◽  
Error Terms ◽  
Kinematic Error Model ◽  
Identification Model

Abstract Parallel manipulators have broad application prospects on hybrid machine tools. Kinematic error modelling and identification are two key processes to improve the accuracy of parallel manipulators. The traditional kinematic error modelling method adopts the partial differentiation of the ideal kinematic model. However, the partial differentiation method is pure mathematical calculation, which ignores physical meaning of error terms corresponding to each link. In the process of error identification, the Jacobian matrix obtained from the partial differentiation method is usually ill-conditioned, which leads to non-convergence of the identification process. In order to solve the above problems, this paper proposes a new kinematic error modelling method and an error identification model. Firstly, the basic error terms for single link are analyzed. Based on basic error terms, the kinematic error model is established by using the practical connection point of two adjacent links. Then, a new error identification model is derived from the kinematic error model. Finally, as a study case, a 3-DOF parallel tool head is used to verify the correctness of the proposed method. The numerical results show that the proposed method is effective and the accuracy of the 3-DOF parallel tool head improves significantly after compensation of error terms.

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.

Symbol for Partial Differentiation

Nature ◽  
1902 ◽  
Vol 66 (1707) ◽  
pp. 271-272
Author(s):  
JOHN PERRY
Keyword(s):  
Partial Differentiation
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