相关论文: On the Noether and the Cayley-Bacharach theorems w…

Let X be a very general complete intersection in complex projective space and we denote by $F_r(X)$ the variety of r-planes in X, for $r\geq 1$. We show that the Picard number of $F_r(X)$ is 1, as soon as $\dim F_r(X)\geq 2$, except when X…

In this paper,we deeply research Lagrange interpolation of n-variables and give an application of Cayley-Bacharach theorem for it. We pose the concept of sufficient intersection about s algebraic hypersurfaces in n-dimensional complex…

We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.

A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…

A gap in the mathematical logic in derivations in quantum field theory arises as consequence of variation before quantization. To close this gap the present paper introduces a mathematically rigorous variational calculus for operator…

We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of…

Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…

We prove a theorem on the intersection theory over a Noetherian local ring $R$, which gives a new proof of a classical theorem of Rees about degree functions. To obtain this, we define an intersection product on schemes that are proper and…

Noether's theorem is an elegant and powerful tool of classical mechanics, but it is of little to no consequence in discrete theories. Here we define and explore a discrete approach to covariant mechanics and show that within this framework…

Noether's theorem is one of the fundamental laws in physics, relating the symmetry of a physical system to its constant of motion and conservation law. On the other hand, there exist a variety of non-Hermitian parity-time (PT)-symmetric…

While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…

A general method using multipliers for finding the conserved integrals for any system of partial differential equations (PDEs) is reviewed and further developed in several ways. Multipliers are expressions whose (summed) product with a PDE…

The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…

We prove Noether's direct and inverse second theorems for Lagrangian systems on fiber bundles in the case of gauge symmetries depending on derivatives of dynamic variables of an arbitrary order. The appropriate notions of reducible gauge…

Noether's theorem is a cornerstone of analytical mechanics, making the link between symmetries and conserved quantities. In this article, I propose a simple, geometric derivation of this theorem that circumvents the usual difficulties that…

Combining monotonicity theory related to the parametric version of the Browder-Minty Theorem with fixed point arguments we obtain hybrid existence results for a system of two operator equations. Applications are given to a system of…

A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\epsilon$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\dot\epsilon$ in the variation of the action.…

We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to the varieties of zeros of the symbols of…

Fix a polarised Calabi-Yau threefold $(X,H)$. We reduce a version of the Bayer-Macr\`i-Toda conjecture for $(X,H)$, which ensures the existence of Bridgeland stability conditions on $X$, to verifying a Brill-Noether-type inequality for…

In this note we use the monodromy argument to prove a Noether-Lefschetz theorem for vector bundles.