Harmonic Maps into Homogeneous Spaces According to a Darboux Homogeneous Derivative

Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work covers all type of invariant geometry in homogeneous space

Bounds for Invariance Pressure

This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields an explicit formula. Further applications to linear control systems on Lie groups and to inner control sets are discussed.Comment: 16 page

Leibniz algebras of Heisenberg type

We introduce and provide a classification theorem for the class of Heisenberg-Fock Leibniz algebras. This category of algebras is formed by those Leibniz algebras L whose corresponding Lie algebras are Heisenberg algebras Hn and whose Hn-modules I, where I denotes the ideal generated by the squares of elements of L, are isomorphic to Fock modules. We also consider the three-dimensional Heisenberg algebra H3 and study three classes of Leibniz algebras with H3 as corresponding Lie algebra, by taking certain generalizations of the Fock module. Moreover, we describe the class of Leibniz algebras with Hn as corresponding Lie algebra and such that the action I × Hn ! I gives rise to a minimal faithful representation of Hn. The classification of this family of Leibniz algebras for the case of n = 3 is given

Enlarging instruction streams

The stream fetch engine is a high-performance fetch architecture based on the concept of an instruction stream. We call a sequence of instructions from the target of a taken branch to the next taken branch, potentially containing multiple basic blocks, a stream. The long length of instruction streams makes it possible for the stream fetch engine to provide a high fetch bandwidth and to hide the branch predictor access latency, leading to performance results close to a trace cache at a lower implementation cost and complexity. Therefore, enlarging instruction streams is an excellent way to improve the stream fetch engine. In this paper, we present several hardware and software mechanisms focused on enlarging those streams that finalize at particular branch types. However, our results point out that focusing on particular branch types is not a good strategy due to Amdahl's law. Consequently, we propose the multiple-stream predictor, a novel mechanism that deals with all branch types by combining single streams into long virtual streams. This proposal tolerates the prediction table access latency without requiring the complexity caused by additional hardware mechanisms like prediction overriding. Moreover, it provides high-performance results which are comparable to state-of-the-art fetch architectures but with a simpler design that consumes less energy.Peer ReviewedPostprint (published version