Let X → B be an orientable sphere bundle. Its Gysin sequence exhibits H∗(X) as an extension of H∗(B)-modules. We prove that the class of this extension is the image of a canonical class that we define in the Hochschild 3-cohomology of H∗(B), corresponding to a component of its A∞ -structure, and generalizing the Massey triple product. We identify two cases where this class vanishes, so that the...

Let ̃ SL(2, F) be the metaplectic two-fold cover of SL(2, F), the special linear group in two variables over a local field F of characteristic 0. The inverse image T̃ of a maximal torus T in ̃ SL(2, F) is an abelian extension of T by ±1. We consider the question of whether this extension is trivial. More generally we find the minimal subgroup A of the circle for which the extension is split when c...

The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, anisotropic—isotropic or invariant split. Related stress elasticity tensors in reference current configurations are worked out. A new kinematic model derived based on tangent Poisson’s rat...

We introduce the Split-C language, a parallel extension of C intended for high performance programming on distributed memory multiprocessors, and demonstrate the use of the language in optimizing parallel programs. Split-C provides a global address space with a clear concept of locality and unusual assignment operators. These are used as tools to reduce the frequency and cost of remote access. ...

During overground or treadmill walking, the stance phase and cycle durations are reduced as speed increases, whereas swing phase duration remains relatively invariant. When the speed of the left and right sides is unequal, as is the case during split-belt locomotion or when walking along a circular path, adjustments in stance and swing phases are observed, which could alter the phase/cycle dura...

Suppose E/F is a quadratic extension of number fields and GU(2, 2) is the quasi-split unitary similitude group attached to E/F . We prove functoriality from globally generic cuspidal representations of GU(2, 2)(AF ) to automorphic representations of GL6(AF ) corresponding to the twisted exterior square map on the dual side. For a split quadratic algebra E/F , the twisted exterior square map red...

In this paper, we are interested in the enumeration of minimal dominating sets in graphs. A polynomial delay algorithm with polynomial space in split graphs is presented. We then introduce a notion of maximal extension (a set of edges added to the graph) that keeps invariant the set of minimal dominating sets, and show that graphs with extensions as split graphs are exactly the ones having chor...

We study differential splitting fields of quaternion algebras with derivations. A algebra over a field k is always split by quadratic extension k. However, need not be any algebraic use solutions certain Riccati equations to provide bounds on the transcendence degree algebra.

In this paper we introduce two general identities relating Eisenstein series on split classical groups, as well double covers of symplectic groups. The first identity can be viewed an extension the doubling construction introduced in [CFGK19] . second is a generalization descent studied [GRS11]

We introduce the notion of 3-Hom-Lie-Rinehart algebras and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we consider extensions algebra characterize first space in terms group automorphisms an A-split abelian extension equivalence classes extensions. Finally, study formal deformations algebras.