Related papers: Geometric Approach to the integral $\int \sec x\,d…
We survey the progress on the study of symplectic geometry past five decades. The survey focuses on the convexity properties of a moment map, the classification of symplectic actions, the symplectic embedding problems, and the theory of…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
This survey article is an introduction to Diophantine Geometry at a basic undergraduate level. It focuses on Diophantine Equations and the qualitative description of their solutions rather than detailed proofs.
We demonstrate a construction method based on a gain function that is defined on the incidence graph of an incidence geometry. Restricting to when the incidence geometry is a linear space, we show that the construction yields a generalized…
A novel approach is introduced to a very widely occurring problem, providing a complete, explicit resolution of it: minimisation of a convex quadratic under a general quadratic, equality or inequality, constraint. Completeness comes via…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
A collection of integer sequences is jointly ergodic if for every ergodic measure preserving system the multiple ergodic averages, with iterates given by this collection of sequences, converge in the mean to the product of the integrals. We…
Integration is the final key step when turning an infinitesimal argument into a result applicable to quantities of finite size. Conceptually, it is about combining infinitesimal contributions to a finite whole. We make a first step towards…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…
We have developed a general geometric treatment of the GCE valid for any stationary axisymmetric metric. The method is based on the remark that the world lines of objects rotating along spacely circular trajectories are in any case, for…
In this current study, the most apparent aspect is to submit a new geometric sequence space. We investigate its topological properties , inclusion relations, Geometric statistical convergence and Geometric property of Orlicz function and .…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
In this paper, using the theory of the so-called fractional calculus we show that it is possible to easily obtain the solutions for the confluent hypergeometric equation. Our approach is to be compared with the standard one (Frobenius)…
Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
We analyze properties of the 2-adic valuations of an integer sequence that originates from an explicit evaluation of a quartic integral. We also give a combinatorial interpretation of the valuations of this sequence. Connections with the…
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the…