For simplicity, we use the following convention: X denotes a BCI-algebra, X1 denotes a non empty subset of X, A, I denote ideals of X, x, y, z denote elements of X, and a denotes an element of A. The following four propositions are true: (1) For all elements x, y, z, u ofX such that x ≤ y holds u\(z\x) ≤ u\(z\y). (2) For all elements x, y, z, u of X holds x \ (y \ z) \ (x \ (y \ u)) ≤ z \ u. (3...

Section 1 contains a review of Gaussian mixture BP and particle BP, as well as a detailed explanation of our strategy for learning edge potentials for these approaches from training data. Section 2 provides parameter settings and experiment details for particle BP and discrete BP, in the synthetic image denoising and depth reconstruction experiments. Section 3 contains a comparison of two diffe...

ZENK expression in vocal nuclei is associated with singing behavior. Area X is an important nucleus for learning and stabilizing birdsong. ZENK expression is higher in Area X compared to that in other vocal nuclei when birds are singing. To reveal the relationship between the ZENK expression in Area X and song crystallization, immunohistochemistry was used to detect ZENK protein expression in A...

For a Banach space X we shall denote the set of all closed subspaces of X by G(X). In some kinds of problems it turned out to be useful to endow G(X) with a topology. The main purpose of the present paper is to survey results on two the most common topologies on G(X). The organization of this paper is as follows. In section 2 we introduce some definitions and notation. In sections 3 and 4 we in...

In this paper, we study the regularity of solutions of the quasilinear equation where X = ( X , ; . . , X , , , ) is a system of real smooth vector fields, A i j , B E Cw(Q x R m + l ) . Assume that X satisfies the Hormander condition and ( A , , ( x , z , c ) ) is positive definite. We prove that if u E S2@(Q) (see Section 2) is a solution of the above equation, then u E Cw(Q). Introduction In...

We calculate the pp → t ¯ tγ + X → W γ + X cross section at SSC energies. Approximately 40% of the total cross section originates from photon bremsstrahlung off the final state jet in t ¯ tj production. Without cuts restricting the hadronic activity, the t ¯ tγ rate is a factor 10 (2) larger than the tree level W γ cross section for a top quark mass of 110 GeV (200 GeV). Imposing a jet veto cut...

The method used consists first of constructing a divided-difference table from the normalized x values and the given values of y and its derivatives with respect to x. The Newton form of q x ð Þ is then obtained from this table, as described in Huddleston (1974) and Krogh (1970), with the modification described in Section 8.2. The Newton form of the polynomial is then converted to Chebyshev-ser...

Let X → Pn be a 2n-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over Pn. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space Def(X) of deformations of X. We extend his result by proving that if the Lagrangian fibration admits a section, then there is a codimension two family of deformations which also pr...