We classify the holomorphic structures of the tangent vertical bundle Θ of the twistor fibration of a quaternionic manifold (M,Q) of dimension 4n ≥ 8. In particular, we show that any self-dual quaternionic connection D of (M,Q) induces an holomorphic structure ∂̄ on Θ. We construct a Penrose transform which identifies solutions of the Penrose operator P on (M,Q) defined by D with the space of ∂̄-...

Let Y → M be a fibred manifold with m-dimensional base and n-dimensional fibres. If m > 2 and n > 3, we classify all linear connections A(Γ,Λ,Θ) : T Y → J(T Y → Y ) in T Y → Y (i.e., classical linear connections on Y ) depending canonically on a system (Γ,Λ,Θ) consisting of a general connection Γ : Y → JY in Y → M , a torsion free classical linear connection Λ : T M → J(T M → M) on M and a line...

An (m, n, k, λa, λc) optical orthogonal signature pattern code (OOSPC) is a family C of m × n (0, 1)-matrices of Hamming weight k satisfying two correlation properties. OOSPCs find application in transmitting two-dimensional image through multicore fiber in CDMA networks. Let Θ(m, n, k, λa, λc) denote the largest possible number of codewords among all (m, n, k, λa, λc)-OOSPCs. An (m, n, k, λa, ...

We show that any contact form whose Fefferman metric admits a nonzero parallel vector field is pseudo-Einstein of constant pseudohermitian scalar curvature. As an application we compute the curvature groups H(C(M),Γ) of the Fefferman space C(M) of a strictly pseudoconvex real hypersurface M ⊂ C. 1. Statement of results Let M be a strictly pseudoconvex CR manifold of CR dimension n and θ a conta...

and Applied Analysis 3 Lemma 2.3. Besides the properties of the argument functions, the Hamiltonian structure of the problem is essential for us to obtain variational periodic and antiperiodic halfeigenvalues, see Lemma 3.2. After introducing the rotation number function, we can easily obtain the ordering of these variational periodic half-eigenvalues, see 3.38 . For regular self-adjoint linear...

Consider a random instance I of k-SAT with n variables and m clauses. Suppose that θ, c > 0 are any fixed real numbers. Let k = k(n) ≥ ( 1 2 + θ ) log2 n. We prove that lim n→∞ Pr(I is satifiable) = { 1 m ≤ ( 1− c √ n ) 2kn ln 2 0 m ≥ ( 1 + c √ n ) 2kn ln 2.

We present a fractional superspace formulation of the centerless parasuper-Virasoro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms of the superline. We work on the fractional superline parametrized by t and θ, with t a real coordinate and θ a paragrassmann variable of order M a...

The almost Mathieu operator is the discrete Schrödinger operator Hα,β,θ on `2(Z) defined via (Hα,β,θf)(k) = f(k+1)+f(k−1)+β cos(2παk+θ)f(k). We derive explicit estimates for the eigenvalues at the edge of the spectrum of the finite-dimensional almost Mathieu operator H α,β,θ. We furthermore show that the (properly rescaled) m-th Hermite function φm is an approximate eigenvector of H α,β,θ, and ...

We consider the problem of learning skill templates for a parameterized reinforcement learning problem class T. That is, we assume that a task, i.e., an instance of the problem class, is defined by a task parameter vector τ ∈ T ⊆ R n and an associated interpretation. Likewise, a skill is considered as a parameterized policy with parameter vector θ ∈ R m. A parameterized skill [1] is a mapping Θ...