Related papers: Lagrange Inversion Formula by Induction
We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm…
We prove a stochastic formula for the Gaussian relative entropy in the spirit of Borell's formula for the Laplace transform. As an application, we give unified and short proofs of a number of functional inequalities.
We prove inversion of adjunction for higher rational singularities.
In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…
We settle in the affirmative the Graham-Sloane conjecture.
Borell's formula is a stochastic variational formula for the log-Laplace transform of a function of a Gaussian vector. We establish an extension of this to the Riemannian setting and give a couple of applications, including a new proof of a…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
We discuss the problem of the existence of a regular invariant Lagrangian for a given system of invariant second-order differential equations on a Lie group $G$, using approaches based on the Helmholtz conditions. Although we deal with the…
We establish an explicit form of the Backlund transformation for the most known integrable systems.
We propose a simple model which possesses the chain fountain effect.
Inspired by the inductive proof of LYM-inequality given by P. Frankl, we provide an inductive proof of the Bollob\'{a}s two family theorem.
We derive a version of Lagrange's mean value theorem for quantum calculus. We disprove a version of Ostrowski inequality for quantum calculus appearing in the literature. We derive a correct statement and prove that our new inequality is…
We give a new proof of Chen-Lin result with Li-Zhang method.
We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.
A generalization of the law of total covariance is presented and proved.
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
We deal with a problem of the reconstruction of any holomorphic function $f$ on the unit ball of $\mathbb{C}^2$ from its restricions on a union of complex lines. We give an explicit formula of Lagrange interpolation's type that is…
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
In this paper, we prove a general simple relative trace formula. As an application, we prove a relative analogue of the Weyl law.
We present in this work a new and simple proof of the false centre theorem.