Related papers: Superposition rules for higher-order systems and t…

There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…

Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…

We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express…

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…

Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…

A novel procedure for the nonlinear superposition of two self-similar solutions of the heat conduction equation with power-law nonlinearity is introduced. It is shown how the boundary conditions of the superposed state conflicts with…

It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.

First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…

We generalize the Hamilton-Jacobi formulation for higher order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraint structure present in such systems.

The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…

It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…

In this paper we derive a new class of sum rules for products of the Bessel functions of first kind. Using standard algebraic manipulations we extend some of the well known properties of $J_n$. Some physical applications of the results are…

In this paper we introduce two new DSm fusion conditioning rules with example, and as a generalization of them a class of DSm fusion conditioning rules, and then extend them to a class of DSm conditioning rules.

We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…

The superposition principle of two qubit states is formulated as nonlinear addition rule of mean spinprojection onto three perpendicular directions. The explicit expression for the mean value determining the superposition state in term of…

We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…

Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…

Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. The symmetry group and its optimal system are given. Furthermore, preliminary classification of its group invariant solutions, symmetry reduction and…