Related papers: Reduction theorems for Noether's problem
A toric polyhedron is a reduced closed subscheme of a toric variety that are partial unions of the orbits of the torus action. We prove vanishing theorems for toric polyhedra. We also give a proof of the $E_1$-degeneration of Hodge to de…
The first and second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of…
The present paper completes the computation of the separating Noether numbers for the groups with order strictly less than $32$. Most of the results are proved for the case of a general (possibly finite) base field containing an element…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
Reductions of N-wave type equations related to simple Lie algebras and the hierarchy of their Hamiltonian structures are studied. The reduction group G_R is realized as a subgroup of the Weyl group of the corresponding algebra. Some of the…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
We give an elementary proof of Noether's first Theorem while stressing the magical fact that the global quasi-symmetry only needs to hold for one fixed integration region. We provide sufficient conditions for gauging a global…
In this paper, within the framework of the consistent approach recently introduced for approximate Lie symmetries of differential equations, we consider approximate Noether symmetries of variational problems involving small terms. Then, we…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.
In the process of calculating Noether's conservation laws, two sets of integration by parts are performed. Here it is shown why the boundary terms from the first set of integration by parts vanish.
We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.
We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers.
For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
The not-quite-Hamiltonian theory of singular reduction and reconstruction is described. This includes the notions of both regular and collective Hamiltonian reduction and reconstruction.
We prove a theorem concerning the Noether symmetries for the area minimizing Lagrangian under the constraint of a constant volume in an n-dimensional Riemannian space. We illustrate the application of the theorem by a number of examples.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
This note presents a uniform treatment of normality and three of its variants---topological, weak and seminormality---for Noetherian schemes. The key is to define these notions for pairs $(Z, X)$ consisting of a (not necessarily reduced)…
Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.