scholarly journals GRADED INFINITE ORDER JET MANIFOLDS

2007 ◽  
Vol 04 (08) ◽  
pp. 1335-1362 ◽  
Author(s):  
G. SARDANASHVILY
Keyword(s):  
Differential Calculus ◽  
Infinite Order ◽  
Smooth Manifolds ◽  
Variational Bicomplex ◽  
Relevant Material

The relevant material on differential calculus on graded infinite order jet manifolds and its cohomology is summarized. This mathematics provides the adequate formulation of Lagrangian theories of even and odd variables on smooth manifolds in terms of the Grassmann-graded variational bicomplex.

scholarly journals On the Canonical Connection for Smooth Envelopes

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
Giovanni Moreno
Keyword(s):  
Differential Calculus ◽  
Smooth Manifolds ◽  
Canonical Connection ◽  
Enveloping Algebra

AbstractA notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds, which were proposed in the last decades. Such an operation is indispensable in order to perform differential calculus. A derivation of the enveloping algebra can be restricted to the original one, but it is a delicate question if the the viceversa can be done as well. In a physical language, this would correspond to the existence of a canonical connection. In this paper, we show an example of an algebra which always possesses such a connection.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

On students’ understanding of the differential calculus of functions of two variables

2015 ◽  
Vol 38 ◽  
pp. 57-86 ◽  
Author(s):  
Rafael Martínez-Planell ◽  
Maria Trigueros Gaisman ◽  
Daniel McGee
Keyword(s):  
Differential Calculus ◽  
Functions Of Two Variables
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