Related papers: Non-external Proofs of Lagrange Inversion Formula
The nonlinear Fourier transform discussed in these notes is the map from the potential of a one dimensional discrete Dirac operator to the transmission and reflection coefficients thereof. Emphasis is on this being a nonlinear variant of…
Non-relativistic potential models are considered of the pure power V(r)=sgn(q) r^q and logarithmic V(r)=ln(r) types. It is shown that, from the spectral viewpoint, these potentials are actually in a single family. The log spectra can be…
Although it is easy to prove the sufficient conditions for optimality of a linear program, the necessary conditions pose a pedagogical challenge. A widespread practice in deriving the necessary conditions is to invoke Farkas' lemma, but…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
Using explicit weakenings, we can define alpha-conversion by simple equations without any mention of free variables.
Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by…
We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be…
We give a formula for the inverse matrix to an infinite matrix with possibly noncommutative entries, generalizing the Newton interpolation formula and the Taylor formula.
A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding…
Lame equation arises from deriving Laplace equation in ellipsoidal coordinates; in other words, it's called ellipsoidal harmonic equation. Lame functions are applicable to diverse areas such as boundary value problems in ellipsoidal…
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
The non-standard Lagrangians (NSLs) for dissipative-like dynamical systems were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of…
In this paper some proof theory for propositional Lax Logic is developed. A cut free terminating sequent calculus is introduced for the logic, and based on that calculus it is shown that the logic has uniform interpolation. Furthermore, a…
The transformation of a Laguerre series $f (z) = \sum_{n=0}^{\infty} \lambda_{n}^{(\alpha)} L_{n}^{(\alpha)} (z)$ to a power series $f (z) = \sum_{n=0}^{\infty} \gamma_{n} z^{n}$ is discussed. Many nonanalytic functions can be expanded in…
The effective Lagrangian and power counting rules for non-relativistic gauge theories are derived via an expansion in $1/c$. It is shown that the $1/c$ expansion leads to an effective field theory which incorporates a multipole expansion.…
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…
A variational proof is provided of the existence and uniqueness of evolutions of regular Lagrangian systems.
The calculation of the standard model Lagrangian of classical field theory within the framework of noncommutative geometry is sketched using a variant with 18 parameters. Improvements compared with the traditional formulation are contrasted…