In string theory and in topological quantum field theory one encounters operators whose effect in correlation functions is simply to measure the topology of 2d spacetime. In particular these 'dilation'-type operators count the number of other operators via contact terms with the latter. While contact terms in general have a reputation for being convention-dependent, the ones considered here are...

The focus of this article is to develop mathematical morphology on hypergraphs. To this aim, we define lattice structures on hypergraphs on which we build mathematical morphology operators. We show some relations between these operators and the hypergraph structure, considering in particular transversals and duality notions. Then, as another contribution, we show how mathematical morphology can...

Recent advances in applied mathematics and signal processing have shown that, in order to obtain sparse representations of multi-dimensional functions and signals, one has to use representation elements distributed not only at various scales and locations – as in classical wavelet theory – but also at various directions. In this paper, we show that we obtain a construction having exactly these ...

We give near optimal bufferless routing algorithms for leveled networks. N packets with preselected paths are given, and once injected, the packets may not be buffered while in transit to their destination. For the preselected paths, the dilation D is the maximum path length, and the congestion C is the maximum number of times an edge is used. We give two bufferless routing algorithms for level...

Fix 0<r<1. The dilation theory for the quantum annulus QAr, consisting of those invertible Hilbert space operators T satisfying ‖T‖,‖T−1‖≤r−1, is determined. proof technique involves a geometric approach to that applies other well known theorems. compared, and contrasted, with canonical operator annuli.

R c(x)dx = 1. For any sufficiently large number K the space Lp([−K,K]) of all Lp-functions with support in the interval [−K,K] is an invariant space of Wc,α. It is known that Wc,α restricted to Lp([−K,K]) is a compact operator with eigenvalues α−k, k = 0, 1, . . . , and spectrum {α−k : k = 1, 2, . . .} ∪ {0}, which are independent of c and K. This result is better understood in the context of w...

Let H denote a separable, complex, Hilbert space and let L(H) denote the algebra of all bounded linear operators on H. Determining the structure of an arbitrary operator in L(H) has been one of the most studied topics in operator theory. In particular, the problem whether every operator T in L(H) has a nontrivial invariant subspace is still open. The most recent partial result in this direction...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

In this paper we use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that are nonlinear convolutions that can be expressed as supremum (resp. infimum) of fuzzy intersection (resp. union) norms. Our emphasis and differences with many previous works is the construction of pairs of fuzzy dilation (sup of fuzzy intersec...

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modal...