Total differentiation

1997 ◽  
Vol 76 (3) ◽  
pp. 133-135 ◽  
Keyword(s):  
Total Differentiation

Total Differentiation Under Jet Composition

2006 ◽  
Vol 13 (sup1) ◽  
pp. 102-109 ◽  
Author(s):  
Maido Rahula ◽  
Vitali Retšnoi
Keyword(s):  
Total Differentiation

scholarly journals Total Differentiation Under Jet Composition

2006 ◽  
Vol 13 (Supplement) ◽  
pp. 102
Author(s):  
Maido RAHULA ◽  
Vitali RETSNOI
Keyword(s):  
Total Differentiation

scholarly journals II. On a class of differential equations, including those which occur in dynamical problems

1856 ◽  
Vol 7 ◽  
pp. 4-7
Keyword(s):  
Differential Equations ◽  
General Theorem ◽  
Dynamical Equations ◽  
First Order ◽  
Independent Variable ◽  
Total Differentiation

This paper is intended to contain a discussion of some properties of a class of simultaneous differential equations of the first order, including as a particular case the form (which again includes the dynamical equations), x ' i = d Z/ dy i , y ' i = - d Z/ dx i . . . . . . . . (1) where x 1 ... x n , y 1 ... y n are two sets of n variables each, and accents denote total differentiation with respect to the independent variable t ; Z being any function of x 1 &c., y 1 which may also contain t explicitly. The part now laid before the Society is limited to the consideration of the above form. After deducing from known properties of functional determinants a general theorem to be used afterwards, the author establishes the following propositions.

NEAR-SURFACE LOCALIZATION AND SHAPE IDENTIFICATION OF A SCATTERER EMBEDDED IN A HALFPLANE USING SCALAR WAVES

2009 ◽  
Vol 17 (03) ◽  
pp. 277-308 ◽  
Author(s):  
CHANSEOK JEONG ◽  
SEONG-WON NA ◽  
LOUKAS F. KALLIVOKAS
Keyword(s):  
Shape Parameters ◽  
Shape Identification ◽  
Sh Waves ◽  
Near Surface ◽  
Fluid Velocities ◽  
True Shape ◽  
Surface Localization ◽  
Neumann Type ◽  
Scalar Waves ◽  
Total Differentiation

We discuss the inverse problem associated with the identification of the location and shape of a scatterer fully embedded in a homogeneous halfplane, using scant surficial measurements of its response to probing scalar waves. The typical applications arise in soils under shear (SH) waves (antiplane motion), or in acoustic fluids under pressure waves. Accordingly, we use measurements of either the Dirichlet-type (displacements), or of the Neumann-type (fluid velocities), to steer the localization and detection processes, targeting rigid and sound-hard objects, respectively. The computational approach for localizing single targets is based on partial-differential-equation-constrained optimization ideas, extending our recent work from the full-1 to the half-plane case. To improve on the ability of the optimizer to converge to the true shape and location we employ an amplitude-based misfit functional, and embed the inversion process within a frequency- and directionality-continuation scheme, which seem to alleviate solution multiplicity. We use the apparatus of total differentiation to resolve the target's evolving shape during inversion iterations over the shape parameters, à la.2,3 We report numerical results betraying algorithmic robustness for both the SH and acoustic cases, and for a variety of targets, ranging from circular and elliptical, to potato-, and kite-shaped scatterers.

Functions of Several Variables; Partial Differentiation; and Total Differentiation

2014 ◽  
pp. 339-377
Author(s):  
Klaus Weltner ◽  
Sebastian John ◽  
Wolfgang J. Weber ◽  
Peter Schuster ◽  
Jean Grosjean
Keyword(s):  
Partial Differentiation ◽  
Several Variables ◽  
Total Differentiation
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