Let K and L be disjoint closed oriented submanifolds of the n-sphere S, with dimensions adding up to n − 1. We define a map from their join K ∗ L to S whose degree up to sign equals their linking number, and then use this to find the desired linking integral. AMS subject classifications: 57Q45; 57M25; 53C20 Here is our main result. Theorem. Let K and L be disjoint closed oriented smooth submani...

Let (P∆, ω) be a toric variety whose moment map image (with respect to the toric Kähler form ω) is the real convex polyhedron ∆ ⊂ MR. Also assume that the anti-canonical class of P∆ is represented by an integral reflexive convex polyhedron ∆0 ⊂ M and the unique interior point of ∆0 is the origin of M . Integral points m ∈ ∆0 correspond to holomorphic toric sections sm of the anticanonical bundl...

Abstract In this article, we introduce two notions of interpolative F -contractions with shrink map and map. We also study the existence E -fixed points by using these notations on a metric space endowed binary relation. As an application consequence main results, get some other interesting results like common fixed point result, result equipped graph, theorem for solution integral equations.

Using elementary counting methods, we calculate the universal invariant (also known as the LMO invariant) of a 3-manifold M , satisfying H1(M,Z) = Z, in terms of the Alexander polynomial of M . We show that +1 surgery on a knot in the 3-sphere induces an injective map from finite type invariants of integral homology 3-spheres to finite type invariants of knots. We also show that weight systems ...

Let (P∆, ω) be a toric variety whose moment map image (with respect to the toric Kähler form ω) is the real convex polyhedron ∆ ⊂ MR. Also assume that the anti-canonical class of P∆ is represented by an integral reflexive convex polyhedron ∆0 ⊂ M and the unique interior point of ∆0 is the origin of M . Integral points m ∈ ∆0 correspond to holomorphic toric sections sm of the anticanonical bundl...

Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, a new type of cyclic contraction mappings satisfying an implicit relation that involves a control function for a map in a metric space is ...

Reiner and Webb (preprint, 2002) compute the Sn-module structure for the complex of injective words. This paper refines their formula by providing a Hodge type decomposition. Along the way, this paper proves that the simplicial boundary map interacts in a nice fashion with the Eulerian idempotents. The Laplacian acting on the top chain group in the complex of injective words is also shown to eq...

We study the existence of solutions for a higher order differential inclusion with multipoint integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps. AMS Subject Classifications: 34A60, 34B15.

On the space L, of loops in the group of Hamiltonian symplecto-morphisms of a symplectic manifold, we define a closed Z-valued 1-form Ω. If Ω vanishes, the prequantization map can be extended to a group representation. On L one can define an action integral as an R/Z-valued function, and the cohomology class [Ω] is the obstruction to the lifting of that action integral to an R-valued function. ...

In this paper, we study the consistency of the regularized least square regression in a general reproducing kernel Hilbert spaces. We characterized the compactness of the inclusion map from a reproducing kernel Hilbert space to the space of continuous functions and showed that the capacity based analysis by uniform covering numbers may fail in a very general setting. We prove the consistency an...