Related papers: Ram's theorem for Trisection
We consider a generalized angle in complex normed vector spaces. Its definition corresponds to the definition of the well known Euclidean angle in real inner product spaces. Not surprisingly it yields complex values as `angles'. This…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
This preprint concerns a mathematically rigorous treatment of an interesting physical phenomenon in relativity theory. We would like to draw the reader's attention particularly to the abstract mathematical formalism of relativity (which was…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a…
The Circumcentered Reflection Method (CRM) is a recently developed projection method for solving convex feasibility problems. It offers preferable convergence properties compared to classic methods such as the Douglas-Rachford and the…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
In this paper we discuss the problem of interpolation on straight lines by linear combinations of ridge functions with fixed directions. By using some geometry and/or systems of linear equations, we constructively prove that it is…
In this paper we show that it is possible to project onto the solutions of the $\mathfrak{grt}$ hexagon equation. We also consider in some sense generalized hexagon equations and other symmetry equations for multiple argument maps between…
We provide some new local obstructions to approximating tropical curves in smooth tropical surfaces. These obstructions are based on the relation between tropical and complex intersection theories which is also established here. We give two…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
The proper Euclidean geometry is considered to be metric space and described in terms of only metric and finite metric subspaces (sigma-immanent description). Constructing the geometry, one does not use topology and topological properties.…
We apply KAM theory to the equation of the forced relativistic pendulum to prove that all the solutions have bounded momentum. Subsequently, we detect the existence of quasiperiodic solutions in a generalized sense. This is achieved using a…
Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…
Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain Diophantine equations. We look at a number of such questions including the question of approximating arbitrary…
Several results from differential geometry of hypersurfaces in R^n are derived to form a tool box for the direct mapping method. The latter technique has been widely employed to solve problems with moving interfaces, and to study the…