The Wills functional from the theory of lattice point enumeration can be adapted to produce the following exponential inequality for zero mean Gaussian processes: Ee sup t (X t ?(1=2) 2 t) e E sup t X t : An application is a new proof of the deviation inequality for the supremum of a Gaussian process above its mean: P (sup t X t ? E sup t X t a) e ?(1=2)a 2 == 2 ; where a > 0 and 2 = sup t 2 t .

1 Quantales In this section we introduce the basic deenitions and results of the theory of quantales (a good reference is Ros]). Quantales were introduced by Mulvey ((Mul]) as an algebraic tool for studying representations of non-commutative C-algebras. Informally, a quantale is a complete lattice Q equipped with a product distributive over arbitrary sup's. The importance of quantales for Linea...

Let a poset P be called chain-complete when every chain, including the empty chain, has a sup in P. Many authors have investigated properties of posets satisfying some sort of chain-completeness condition (see [,11, [-31, [6], I-71, [17], [,181, ['191, [,211, [,221), and used them in a variety of applications. In this paper we study the notion of chain-completeness and demonstrate its usefulnes...

Let A be a von Neumann algebra acting in a separable complex Hilbert space H and let A be the set of all orthogonal projections (=idempotents) from A. A subset M ⊆ A is said to be ideal of projections if: a) p ≤ q where p ∈ A, q ∈ M ⇒ p ∈ M; b) p, q ∈ M and ‖pq‖ < 1 ⇒ p ∨ q ∈ M; c) sup{p : p ∈ M} = I. Put Mp := {q : q ∈ M, q ≤ p}, ∀p ∈ A . Note that A is the ideal of projections, 0 ∈ Mp, ∀p, an...

The topic of sets with fuzzy order relations valuated in complete lattices with additional structure has been quite active in the recent decade, and a number of papers have been published (see [3, 5, 6] among many others). Based on a quantale-valued order relation and subset membership, counterparts to common order-theoretic notions can be defined, like monotone mappings, adjunctions, joins and...

Iterative methods are considered for saddle point problems with a penalty term. A positive deenite preconditioner is constructed and it is proved that the condition number of the preconditioned system can be made independent of the discretization and the penalty parameters. Examples include the pure displacement problem in linear elasticity, the Timoshenko beam, and the Mindlin-Reissner plate. ...

We report the lattice site and symmetry of optically active Dy3+ and Tm3+ implanted Si. Local symmetry was determined by fitting crystal field parameters (CFPs), corresponding to various common symmetries, to the ground state splitting determined by photoluminescence measurements. These CFP values were then used to calculate the splitting of every J manifold. We find that ...

We propose new repair schemes for Reed-Solomon codes that use subspace polynomials and hence generalize previous works in the literature employ trace polynomials. The are over \mathbb F ql have redundancy r = n-k ≥ q m , 1 ≤...

and Applied Analysis 3 It is interesting to characterize the boundedness and compactness of the product operator on all kinds of function spaces. Even on the disk of , some properties are not easily managed; see some recent papers in 18, 25–28 . Building on those foundations, the present paper continues this line of research and discusses the operator in high dimension. The remainder is assembl...