J.-L. Loday introduced the concept of coherent unit actions on a regular operad and showed that such actions give Hopf algebra structures on the free algebras. Hopf algebras obtained this way include the Hopf algebras of shuffles, quasi-shuffles and planar rooted trees. We characterize coherent unit actions on binary quadratic regular operads in terms of linear equations of the generators of th...

Let V be a G-module where G is a complex reductive group. Let Z := V//G denote the categorical quotient and let π : V → Z be the morphism dual to the inclusion O(V ) ⊂ O(V ). Let φ : Z → Z be an algebraic automorphism. Then one can ask if there is an algebraic map Φ: V → V which lifts φ, i.e., π(Φ(v)) = φ(π(v)) for all v ∈ V . In Kuttler [Kut11] the case is treated where V = rg is a multiple of...

We investigate and compare two dual formulations of the American option pricing problem based on two decompositions of supermartingales: the additive dual of Haugh and Kogan (Oper. Res. 52:258–270, 2004) and Rogers (Math. Finance 12:271–286, 2002) and the multiplicative dual of Jamshidian (Minimax optimality of Bermudan and American claims and their MonteCarlo upper bound approximation. NIB Cap...

We present an elementary proof of an important result of Y. Brenier ([Br1], [Br2]), namely that vector fields in R satisfying a nondegeneracy condition admit the polar factorization (∗) u(x) = ∇ψ(s(x)), where ψ is a convex function and s is a measure-preserving mapping. Brenier solves a minimization problem using Monge-Kantorovich theory, whereas we turn our attention to a dual problem, whose E...

‎we present an application of the dual gabor frames to image‎ ‎processing‎. ‎our algorithm is based on finding some dual gabor‎ ‎frame generators which reconstructs accurately the elements of the‎ ‎underlying hilbert space‎. ‎the advantages of these duals‎ ‎constructed by a polynomial of gabor frame generators are compared‎ ‎with their canonical dual‎.

We argue that the string theory dual to a certain sector of the four-dimensional Yang-Mills theory at large-N is the A-model wrapping N Lagrangian Dbranes on the twistor space of the complex two-dimensional projective space, with a certain flux and Wilson loop background, by finding that the targetspace beta function of this A-model coincides with the large-N beta function of the Yang-Mills the...

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in p + 1 dimensions, there is a uniquely associated “dual” solution of the vacuum Einstein equations in p + 2 dimensions. The dual geometry has an intrinsically flat timelike boundary segment Σc whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a “n...

Let V →֒ H →֒ V ∗ be a normal triple of spaces with dense and continuous embeddings, where V is a reflexive Banach space, H is a Hilbert space, identified with its dual by means of the inner product in H , and V ∗ is the dual of V . Let W = (Wt)t≥0 be an r-dimensional Brownian motion carried by a stochastic basis (Ω,F , (Ft)t≥0, P ). In this paper, we study the approximation of the solution to th...

We consider nonquasiclassical solutions to the quantum Yang– Baxter equation and the corresponding quantum cogroups Fun(SL(S)) constructed earlier in [G]. We give a criterion of the existence of a dual quasitriangular structure in the algebra Fun(SL(S)) and describe a large class of such objects related to the Temperley–Lieb algebra satisfying this criterion. We show also that this dual quasitr...