Let M be a 4k-dimensional closed oriented smooth manifold. Let E be a complex vector bundle over M . For any complex number t , set 3t(E)= C | M + t E + t232(E)+ · · · , St(E)= C | M + t E + t2S2(E)+ · · · , where for any integer j ≥ 1, 3 j (E) is the j-th exterior power of E and S j (E) is the j-th symmetric power of E ; see [Atiyah 1967]. Set Ẽ = E −Crk(E). Let q = e iτ with τ ∈ H, the upper ...

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary symmetric polynomial or a complete homogeneous symmetric polynomial. Thus, we generalize the classical Pieri’s rule for symmetric polynomials/Grassmann varietie...

We show that the deformations of the de Rham cohomology of a closed simply connected KK ahler manifold are governed by the dual of real-valued cohomology of its free loop space. A currently very active eld in Mathematics is the theory of quantum cohomol-ogy, which provides a special kind of deformations of the multiplication structure on the de Rham cohomology of symplectic manifolds. The mathe...

We define a pseudo quasi-3 design as a symmetric design with the property that the derived and residual designs with respect to at least one block are quasi-symmetric. Quasi-symmetric designs can be used to construct optimal self complementary codes. In this article we give a construction of an infinite family of pseudo quasi-3 designs whose residual designs allow us to construct a family of co...

The pseudo-perturbative shifted l expansion technique PSLET is shown applicable in the non-Hermitian PT symmetric context. The construction of bound states for several PT symmetric potentials is presented, with special attention paid to V (r) = ir3 − α √ ir oscillators.

We establish rigorous scaling laws for the average bursting time for bubbling bifurcations of an invariant manifold, assuming the dynamics within the manifold to be uniformly hyperbolic. This type of global bifurcation appears in nearly synchronized systems, and is conjectured to be typical among those breaking the invariance of an asymptotically stable hyperbolic invariant manifold. We conside...

We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to A-connection, we construct Weyl projective tensor In this way, obtain new conditions for manifold be projectively flat. At end of paper, define η-Einstein manifolds θ-th kind and prove that they coincide

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

The object of this paper is to study (k, μ)-paracontact metric manifolds with qusi-conformal curvature tensor. It has been shown that, h-quasi conformally semi-symmetric and φ-quasi-conformally semi-symmetric (k, μ)-paracontact metric manifold with k 6= −1 cannot be an η-Einstein manifold.