Delta-function derivatives of arbitrary order in equal-time charge current commutator

1972 ◽  
Vol 3 (8) ◽  
pp. 332-334
Author(s):  
T. Pradhan
Keyword(s):  
Arbitrary Order ◽  
Delta Function ◽  
Equal Time ◽  
Current Commutator ◽  
Charge Current ◽  
Derivatives Of

scholarly journals CONSTRAINT ALGEBRAS IN GAUGE-INVARIANT SYSTEMS

1995 ◽  
Vol 10 (28) ◽  
pp. 4087-4105 ◽  
Author(s):  
KH. S. NIROV
Keyword(s):  
Wide Class ◽  
Arbitrary Function ◽  
Arbitrary Order ◽  
Local Symmetry ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Constraint Algebra ◽  
Derivatives Of

A Hamiltonian description is constructed for a wide class of mechanical systems having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order. The Poisson brackets of the Hamiltonian and constraints with each other and with an arbitrary function are explicitly obtained. The constraint algebra is proved to be of the first class.

Implications of dynamic patterns of Delta and Notch expression for cellular interactions during Drosophila development

Development ◽  
1993 ◽  
Vol 117 (2) ◽  
pp. 493-507 ◽  
Author(s):  
P.J. Kooh ◽  
R.G. Fehon ◽  
M.A. Muskavitch
Keyword(s):  
Cell Fate ◽  
Delta Function ◽  
Cellular Level ◽  
Cellular Interactions ◽  
Cell Fate Specification ◽  
Drosophila Development ◽  
Fate Specification ◽  
Endocytic Vesicles ◽  
Derivatives Of ◽  
Subcellular Level

Delta and Notch function are required for cell fate specification in numerous tissues during embryonic and postembryonic Drosophila development. Delta is expressed by all members of interacting cell populations within which fates are being specified and is subsequently down-regulated as cells stably adopt particular fates. Multiphasic expression in the derivatives of many germ layers implies successive requirements for Delta function in a number of tissues. At the cellular level, Delta and Notch expression are generally coincident within developing tissues. At the subcellular level, Delta and Notch are localized in apparent endocytic vesicles during down-regulation from the surfaces of interacting cells, implying an interaction consistent with their proposed roles as signal and receptor in cellular interactions during development.

scholarly journals Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Jianfei Wang
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Arbitrary Order ◽  
Complex Banach Space ◽  
Holomorphic Mappings ◽  
Partial Derivatives ◽  
Carathéodory Metric ◽  
Homogeneous Ball ◽  
Derivatives Of

LetBXbe the unit ball in a complex Banach spaceX. AssumeBXis homogeneous. The generalization of the Schwarz-Pick estimates of partial derivatives of arbitrary order is established for holomorphic mappings from the unit ballBntoBXassociated with the Carathéodory metric, which extend the corresponding Chen and Liu, Dai et al. results.

Schwarz—Pick Inequalities for Derivatives of Arbitrary Order

2003 ◽  
Vol 19 (2) ◽  
pp. 265-277 ◽  
Author(s):  
Avkhadiev ◽  
-J. Wirths
Keyword(s):  
Arbitrary Order ◽  
Derivatives Of

A Friedrichs inequality and an application

1984 ◽  
Vol 97 ◽  
pp. 185-191 ◽  
Author(s):  
Roger T. Lewis
Keyword(s):  
Differential Operators ◽  
Arbitrary Order ◽  
Type Inequality ◽  
Essential Spectra ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Partial Differential Operators ◽  
Even Order ◽  
Friedrichs Inequality ◽  
Derivatives Of

SynopsisAn inequality whose origins date to the work of G. H. Hardy is presented. This Hardy-type inequality applies to derivatives of arbitrary order of functions whose domain is a subset of ℝn. The Friedrichs inequality is a corollary. The result is then used to establish lower bounds on the essential spectra of even-order elliptic partial differential operators on unbounded domains.

scholarly journals Higher Order Automatic Differentiation with Dual Numbers

2020 ◽  
Author(s):  
László Szirmay-Kalos
Keyword(s):  
Gaussian Curvature ◽  
Automatic Differentiation ◽  
Arbitrary Order ◽  
Higher Order ◽  
Dual Numbers ◽  
Computer Implementation ◽  
Particular Solution ◽  
Derivatives Of ◽  
Curve Fairing ◽  
Curvature Computation

In engineering applications, we often need the derivatives of functions defined by a program. The approach chosen for derivative computation must be algebraic to allow computer implementation. A particular solution to obtain first derivatives is the application of dual numbers. This paper proposes simple and compact generalizations of this idea to obtain derivatives of arbitrary order for single or multi-variate functions and the automatic handling of 0/0 ambiguities in the calculations. We also provide the C++ code that takes advantage of operator overloading and recursion. The method is demonstrated by path animation, Gaussian curvature computation, and curve fairing.

Sign in / Sign up

Export Citation Format

Share Document