Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In Noether's original presentation of her celebrated theorem of 1918, allowances were made for the dependence of the coefficient functions of the differential operator which generated the infinitesimal transformation of the Action Integral upon the derivatives of the dependent variable(s), the so-called generalized, or dynamical, symmetries. A similar allowance is to be found in the variables of the boundary function, often termed a gauge function by those who have not read the original paper. This generality was lost after texts such as those of Courant and Hilbert or Lovelock and Rund confined attention to only point transformations. In recent decades, this diminution of the power of Noether's Theorem has been partly countered, in particular, in the review of Sarlet and Cantrijn. In this Special Issue, we emphasize the generality of Noether's Theorem in its original form and explore the applicability of even more general coefficient functions by allowing for nonlocal terms. We also look at the application of these more general symmetries to problems in which parameters or parametric functions have a more general dependence upon the independent variables.

Symmetry.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This reprint is dedicated to Professor Delfim F. M. Torres for his 50th birthday. Professor Delfim F. M. Torres is a recognized researcher, particularly in the calculus of variations, optimal control, and mathematical biology. In this reprint, several studies in his research fields are presented.

Symmetry (Physics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Symmetry (Physics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Symmetry is an intriguing phenomenon manifesting itself in art, nature, and the mind. This Special Issue book features 19 articles about discrete geometric and combinatorial polyhedral structures, with symmetry as the unifying theme. These articles present an attractive mix of topics and have appeared in two related Special Issues of Symmetry, on "Polyhedra" in 2012/2013 and on "Polyhedral Structures" in 2016/2017. Specific topic areas covered include polyhedra, tilings, and crystallography; abstract polyhedra, maps on surfaces, and graphs; and polyhedral structures, arts, and architectural design.

Polyhedra. --- Symmetry (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Symmetry --- Symétrie