The third real de Rham cohomology of compact homogeneous spaces is studied. Given $$M=G/K$$ with G semisimple, we first show that each bi-invariant symmetric bilinear form Q on $${\mathfrak {g}} $$ such $$Q|_{{\mathfrak {k}} \times {\mathfrak }=0$$ naturally defines a G-invariant closed 3-form $$H_Q$$ M, which plays the role so called Cartan $$Q([\cdot ,\cdot ],\cdot )$$ Lie group G. Indeed, ev...

Three novel and significant contributions are made in this paper Firstly, non-recursive formulation of Haar connection coefficients, pioneered by the present authors is presented, which can be computed very efficiently and avoid stack and memory overflows. Secondly, the generalized approach for state analysis of singular bilinear time-invariant (TI) and time-varying (TV) systems is presented; v...

We study bilinear embedding models for the task of multirelational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can provide good prediction performance. The main goal of this paper is to explore the expressiveness of and the connections between various bilinear models propo...

A class of bilinear differential operators is introduced through assigning appropriate signs and used to create bilinear differential equations which generalize Hirota bilinear equations. The resulting bilinear differential equations are characterized by a special kind of Bell polynomials and the linear superposition principle is applied to the construction of their linear subspaces of solution...

In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarević operators. By exhibiting a generalized “taxi-cab” metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlying contractive bilinear IFS. We present an explicit formula for the box-counting dimension of the ...