Geometrical formulation for variational electromagnetics

1990 ◽  
Vol 137 (6) ◽  
pp. 321-330 ◽  
Author(s):  
D. Baldomir ◽  
P. Hammond
Keyword(s):  
Geometrical Formulation

scholarly journals Types of Derivatives: Concepts and Applications (II)

2017 ◽  
Vol 9 (1) ◽  
pp. 50
Author(s):  
Salma A. Khalil ◽  
Mohammed A. Basheer ◽  
Tarig A. Abdelhaleem
Keyword(s):  
Differential Geometry ◽  
Fluid Mechanics ◽  
Exterior Calculus ◽  
Geometrical Formulation

The notion of differential geometry is known to have played a fundamental role in unifying aspects of the physics of particles and fields, and have completely transformed the study of classical mechanics.In this paper we applied the definitions and concepts which we defined and derived in part (I) of our paper: Types of Derivatives: Concepts and Applications to problems arising in Geometry and Fluid Mechanics using exterior calculus. We analyzed this problem, using the geometrical formulation which is global and free of coordinates.

A Fuzzy Approach Using Euclidean Geometrical Formulation for Classifying SAR Images

2013 ◽  
Vol 3 (4) ◽  
pp. 27-35
Author(s):  
Biagio Cammaroto ◽  
Matteo Cacciola ◽  
Mario Versaci
Keyword(s):  
Scientific Literature ◽  
Geometric Approach ◽  
Classification Problem ◽  
Coastal Protection ◽  
Sar Images ◽  
Good Tool ◽  
Geophysical Application ◽  
Geometrical Formulation ◽  
Standard Techniques

Synthetic Aperture Radar (SAR) is a good tool to investigate problems in many geophysical application as classification of ground terrain types and coastal protection. In scientific literature, many analytical and/or numerical techniques have been taken into account to solve the classification problem at hand, especially in all of applications in which it is necessary to classify portion of images with uncertainty and imprecision. In fact, according to the conventional classification approaches, the assignment of a class to each portion of an image could be particularly inadequate for all those portions that span more than a class (for example the coastal areas of the shoreline). This article is devoted to present a fuzzy-geometric approach based on fuzzy subsethood operator to classify SAR images for coastal protection applications. The obtained results were compared, in terms of accuracy, with standard techniques of classification.

scholarly journals Geometrical Formulation for Adjoint-Symmetries of Partial Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1547
Author(s):  
Stephen C. Anco ◽  
Bao Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Fields ◽  
Evolution Equations ◽  
Applied Mathematics ◽  
Tangent Vector ◽  
Solution Space ◽  
Partial Differential ◽  
Geometrical Meaning ◽  
Geometrical Formulation

A geometrical formulation for adjoint-symmetries as one-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution space of a PDE. Two applications of this formulation are presented. Additionally, for systems of evolution equations, adjoint-symmetries are shown to have another geometrical formulation given by one-forms that are invariant under the flow generated by the system on the solution space. This result is generalized to systems of evolution equations with spatial constraints, where adjoint-symmetry one-forms are shown to be invariant up to a functional multiplier of a normal one-form associated with the constraint equations. All of the results are applicable to the PDE systems of interest in applied mathematics and mathematical physics.

scholarly journals Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

2010 ◽  
Vol 374 (48) ◽  
pp. 4801-4803 ◽  
Author(s):  
Paolo Facchi ◽  
Ravi Kulkarni ◽  
V.I. Man'ko ◽  
Giuseppe Marmo ◽  
E.C.G. Sudarshan ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Geometrical Formulation

scholarly journals Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1332
Author(s):  
Florio M. Ciaglia ◽  
Jürgen Jost ◽  
Lorenz Schwachhöfer
Keyword(s):  
Statistical Models ◽  
Estimation Theory ◽  
Parametric Estimation ◽  
Mathematical Framework ◽  
Quantum Case ◽  
C Algebras ◽  
Finite Dimensional ◽  
Geometrical Formulation

A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.

scholarly journals A geometrical formulation of the μ-lower bound problem

2009 ◽  
Vol 3 (4) ◽  
pp. 465-472 ◽  
Author(s):  
J. Kim ◽  
I. Postlethwaite ◽  
D.G. Bates
Keyword(s):  
Lower Bound ◽  
Geometrical Formulation

scholarly journals TOWARDS A DEFINITION OF QUANTUM INTEGRABILITY

2009 ◽  
Vol 06 (01) ◽  
pp. 129-172 ◽  
Author(s):  
JESÚS CLEMENTE-GALLARDO ◽  
GIUSEPPE MARMO
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Complete Integrability ◽  
Infinite Dimensional ◽  
Quantum Integrability ◽  
Classical Systems ◽  
Definition Of ◽  
Geometrical Formulation ◽  
Quantum Framework

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarilly isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.

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