Related papers: Some basic properties of G-Calculus and its applic…
Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this paper we define a notion of $N$-metric exterior algebra, which depends on $N$ matrices of structure constants.…
The quasisymmetic Macdonald polynomials $G_{\gamma}(X; q, t)$ were recently introduced by the first and second authors with Haglund, Mason, and Williams in [3] to refine the symmetric Macdonald polynomials $P_{\lambda}(X; q, t)$ with the…
In this paper we continue the development of the differential calculus started by Aragona-Ferandez-Juriaans. Guided by the topology introduced recently by those authors we introduce the notion of membranes and extend the definition of…
We have developed a new tool for numerical work in General Relativity: GRworkbench. While past tools have been ad hoc, GRworkbench closely follows the framework of Differential Geometry to provide a robust and general way of computing on…
This is an essay on potential theory for geometric plurisubharmonic functions. It begins with a given closed subset G of the Grassmann bundle $G(p,TX)$ of tangent $p$-planes to a riemannian manifold $X$. This determines a nonlinear partial…
Explicit general constructions of paragrassmann calculus with one and many variables are given. Relations of the paragrassmann calculus to quantum groups are outlined and possible physics applications are briefly discussed. This paper is…
We define a new type of valuation of a ring that combines the notion of Krull valuation with that of multiplicative seminorm. This definition partially restores the broken symmetry between archimedean and non-archimedean valuations. This…
This paper is an invitation to the study and use of general theory of non-gaussian $r-$congruences in the theory of numbers. In this work we classify the two kinds of $r-$congruences that exist (namely the trivial and non-trivial types) and…
We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero, provides a classical non-linear,…
A few new indices to characterize the scientific output of scientists are defined in the paper. These indices are compared with -index and its alternative indices using some proven assertions. The gd-indices are introduced as extensions of…
The differential calculus on `non-standard' $h$-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.
Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre…
R. B. Melrose's b-calculus provides a framework for dealing with problems of partial differential equations that arise in singular or degenerate geometric situations. This article is a somewhat informal short course introducing many of the…
A new calculus on fractal curves, such as the von Koch curve, is formulated. We define a Riemann-like integral along a fractal curve F, called F-alpha-integral, where alpha is the dimension of F. A derivative along the fractal curve called…
In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the…
We outline an alternative approach to the geometric notion of a saddle point for real-valued functions of two variables. It is argued that this is more natural compared to the usual treatment of this topic in standard texts on Calculus.
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.