The Barbero-Immirzi (BI) connection, as usually introduced out of a spin connection, is a global object though it does not transform properly as a genuine connection with respect to generic spin transformations, unless quite specific and suitable gauges are imposed. We shall here investigate whether and under which global conditions a (properly transforming and hence global ) SU(2)-connection c...

The Barbero-Immirzi (BI) connection, as usually introduced out of a spin connection, is a global object though it does not transform properly as a genuine connection with respect to generic spin transformations, unless quite specific and suitable gauges are imposed. We shall here investigate whether and under which global conditions a (properly transforming and hence global ) SU(2)-connection c...

We show that with every separable calssical Stäckel system of Benenti type on a Riemannian space one can associate, by a proper deformation of the metric tensor, a multi-parameter family of non-Hamiltonian systems on the same space, sharing the same trajectories and related to the seed system by appropriate reciprocal transformations. These system are known as bi-cofactor systems and are integr...

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{...

In this paper we introduce Bit-Interleaved pragmatic spacetime codes (BI-PSTC) and evaluate their performance over correlated fading channels taken into account by a Block Fading Channel (BFC) model. More precisely, the BitInterleaved pragmatic space-time codes (BI-PSTC) proposed here are obtained with the serial concatenation of a convolutional encoder, a bit-interleaver and a space-time mappe...

We know that I(̺,M) and uncertainty δ2(M)̺ coincides on pure state, i.e, when ̺ is a pure state, then the inequalities (2) and (6) in lemma 1, 2 both become equality. let us recall the “Local Uncertainty Relations” (LURs), introduced by Hofmann and Takeuchi [4]. Let Ai be observables on Alice’s space of a bipartite system. If they do not share a common eigenstate, there is a number CA > 0 such tha...

The Induced Dimension Reduction method [12] was proposed in 1980 as an iterative method for solving large nonsymmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared) [9]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized, [11]). All three methods are based on efficient short recurrences. An important similarity between the m...

The Induced Dimension Reduction method [12] was proposed in 1980 as an iterative method for solving large nonsymmetric linear systems of equations. IDR can be considered as the predecessor of methods like CGS (Conjugate Gradient Squared) [9]) and Bi-CGSTAB (Bi-Conjugate Gradients STABilized, [11]). All three methods are based on efficient short recurrences. An important similarity between the m...

In this article we prove that for any hyperbolic Riemann surface M of infinite analytic type, the little Bers space Q0(M) is isomorphic to c0. As a consequence of this result, if M is such a Riemann surface, then its asymptotic Teichmüller space AT (M) is bi-Lipschitz equivalent to a bounded open subset of the Banach space l∞/c0. Further, if M and N are two such Riemann surfaces, their asymptot...

Graph neural network (GNN) has shown superior performance in dealing with structured graphs, which attracted considerable research attention recently. Most of the existing GNNs are designed Euclidean spaces; however, real-world spatial data can be non-Euclidean surfaces (e.g., hyperbolic spaces). For example, biologists may inspect geometric shape a protein surface to determine its interaction ...