Related papers: A novel operation associated with Gauss' arithmeti…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
New forms of Born-Infeld, D-brane and M theory five-brane actions are found which are quadratic in the abelian field strength. The gauge fields couple both to a background or induced metric and a new auxiliary metric, whose elimination…
To every $C^*$ correspondence over a $C^*$-algebra one can associate a Cuntz-Pimsner algebra generalizing crossed product constructions, graph $C^*$-algebras, and a host of other classes of operator algebras. Cuntz-Pimsner algebras come…
The tau function corresponding to the affine ring of a certain plane algebraic curve, called (n,s)-curve, embedded in the universal Grassmann manifold is studied. It is neatly expressed by the multivariate sigma function. This expression is…
A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve…
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
We obtain identities and relationships between the modular $j$-function, the generating functions for the classical partition function and the Andrews $spt$-function, and two functions related to unimodal sequences and a new partition…
We present a refinement, by selfimprovement, of the arithmetic geometric inequality.
We define a new equivalence between algebras for n-globular operads which is suggested in [Cottrell 2015], and show that it is a generalization of ordinary equivalence between categories.
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…
Two fundamental approaches to information averaging are based on linear and logarithmic combination, yielding the arithmetic average (AA) and geometric average (GA) of the fusing initials, respectively. In the context of target tracking,…
We begin by introducing an algebraic structure with three constants and one ternary operation to which we call mobi algebra. This structure has been designed to capture the most relevant properties of the unit interval that are needed in…
Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form…
The seminal work of Kubo and Ando from 1980 provided us with an axiomatic approach to means of positive operators. As most of their axioms are algebraic in nature, this approach has a clear algebraic flavor. On the other hand, it is highly…
Matrix geometric means between two positive definite matrices can be defined from distinct perspectives - as solutions to certain nonlinear systems of equations, as points along geodesics in Riemannian geometry, and as solutions to certain…
It is often noted that many of the basic concepts of differential geometry, such as the definition of connection, are purely algebraic in nature. Here, we review and extend existing work on fully algebraic formulations of differential…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…