Related papers: Generalized Lagrange Theorem

Generalized geometry finds many applications in the mathematical description of some aspects of string theory. In a nutshell, it explores various structures on a generalized tangent bundle associated to a given manifold. In particular,…

This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the invariant calculus of variations and the…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. The construction is achieved via a categorical approach that…

We discuss some variants of cone theorem for movable curves in any codimensions.

In our preceding article, we defined a generalized lambda function and showed that the genaralized lambda function and the modular invariant function generate the modular function field with respect to a principal congruence subgroup. In…

The generalized vector is defined on an $n$ dimensional manifold. Interior product, Lie derivative acting on generalized $p$-forms, $-1\le p\le n$ are introduced. Generalized commutator of two generalized vectors are defined. Adding a…

We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.

A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…

Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…

We prove an analog of Lagrange's Theorem for continued fractions on the Heisenberg group: points with an eventually periodic continued fraction expansion are those that satisfy a particular type of quadratic form, and vice-versa.

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations.…

In this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process. This concept is a natural extension of the classical concept…

The concept of weak Lie motion (weak Lie symmetry) is introduced through ${\cal{L}}_{\xi}{\cal{L}}_{\xi}g_{ab}=0,$ (${\cal{L}}_{\xi}{\cal{L}}_{\xi}f=0$). Applications are given which exhibit a reduction of the usual symmetry, e.g., in the…

Generalization bounds which assess the difference between the true risk and the empirical risk have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…

We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized…

Let p be a polynomial in one complex variable. Smale's mean value conjecture estimates |p'(z)| in terms of the gradient of a chord from (z, p(z)) to some stationary point on the graph of $p$. The conjecture does not immediately generalise…

Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…

We determine the Rolle function in Lagrange polynomial approximation using a suitable differential equation. We then propose a device for improving the Lagrange approximation by exploiting our knowledge of the Rolle function.

Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…