Related papers: Kirkman's hypothesis revisited

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…

The key tool of this paper is a new Carleman estimate for an arbitrary parabolic operator of the second order for the case of reversed time data. This estimate works on an arbitrary time interval. On the other hand, the previously known…

We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.

We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.

We present several results on the inverse problem and equivalent contactLagrangian systems. These problems naturally lead to consider smooth transformations on the z variable (i.e., reparametrizations of the action). We present the extended…

In this paper we prove a version of Lie-B\"acklund theorem for overdetermined systems of scalar PDEs, whose general solution depends on 1 function of 1 variable. This generalizes the case of involutive system of the second order on the…

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…

The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…

In this note we prove an equivariant version of a result of Cartan for equivariant simplicial cohomology with local coefficients.

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…

Reparametrization-invariant theories of point relativistic particle interaction with fields of arbitrary tensor dimension are considered. It has been shown that the equations of motion obtained by Kalman [G. Kalman, Phys. Rev. vol.123,…

We prove the converse of Yano's extrapolation theorem for translation invariant operators.

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

Reinhardt's conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite…

In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first…

From a new perspective, this paper rederives Lagrange's equations. By applying the chain rule of differentiation, the intrinsic relationship between the momentum theorem and the kinetic energy theorem is first established. Subsequently,…

Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…

An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this problem. A single location of the point source is used. Using a…