Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Bimodules over nest algebras and Deddens'

We generalise Dedden's Theorem for nest algebras to nest algebra bimodules. We define an object which extends the Jacobson radical of a nest algebra, and characterose it generalising a theorem of Erdos.

Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $phi$ and $psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $phi (X)= [M_2^*psi (Y)M_1]^{-w^*}$ and $psi (Y)=[M_2phi (X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.

Jordan isomorphism of purely infinite C*-algebras

We prove that every unital bounded linear mapping from a unital purely infinite C*-algebra of real rank zero into a unital Banach algebra which preserves elements of square zero is a Jordan homomorphism. This entails a description of unital surjective spectral isometries as the Jordan isomorphisms in this setting.

Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson’s space.

On the weak amenability of β(X)

We investigate the weak amenability of the Banach algebra ß(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

Handling Inconsistency In Distributed Software Requirements Specifications Based On Prioritized Merging

Developing a desirable framework for handling inconsistencies in software requirements specifications is a challenging problem. It has been widely recognized that the relative priority of requirements can help developers to make some necessary trade-off decisions for resolving con- flicts. However, for most distributed development such as viewpoints-based approaches, different stakeholders may assign different levels of priority to the same shared requirements statement from their own perspectives. The disagreement in the local levels of priority assigned to the same shared requirements statement often puts developers into a dilemma during the inconsistency handling process. The main contribution of this paper is to present a prioritized merging-based framework for handling inconsistency in distributed software requirements specifications. Given a set of distributed inconsistent requirements collections with the local prioritization, we first construct a requirements specification with a prioritization from an overall perspective. We provide two approaches to constructing a requirements specification with the global prioritization, including a merging-based construction and a priority vector-based construction. Following this, we derive proposals for handling inconsistencies from the globally prioritized requirements specification in terms of prioritized merging. Moreover, from the overall perspective, these proposals may be viewed as the most appropriate to modifying the given inconsistent requirements specification in the sense of the ordering relation over all the consistent subsets of the requirements specification. Finally, we consider applying negotiation-based techniques to viewpoints so as to identify an acceptable common proposal from these proposals.

A Low Complexity Video Watermarking in H.264 Compressed Domain

In this paper, a new blind and readable H.264 compressed domain watermarking scheme is proposed in which the embedding/extracting is performed using the syntactic elements of the compressed bit stream. As a result, it is not necessary to fully decode a compressed video stream both in the embedding and extracting processes. The method also presents an inexpensive spatiotemporal analysis that selects the appropriate submacroblocks for embedding, increasing watermark robustness while reducing its impact on visual quality. Meanwhile, the proposed method prevents bit-rate increase and restricts it within an acceptable limit by selecting appropriate quantized residuals for watermark insertion. Regarding watermarking demands such as imperceptibility, bit-rate control, and appropriate level of security, a priority matrix is defined which can be adjusted based on the application requirements. The resulted flexibility expands the usability of the proposed method.

Recovering Social Networks from Individual Attributes

One of the most important challenges of network analysis remains the scarcity of reliable information on existing connection structures. This work explores theoretical and empirical methods of inferring directed networks from nodes attributes and from functions of these attributes that are computed for connected nodes. We discuss the conditions, under which an underlying connection structure can be (probabilistically) recovered, and propose a Bayesian recovery algorithm. In an empirical application, we test the algorithm on the data from the European School Survey Project on Alcohol and Other Drugs.

Modulated transverse off-plane dust-lattice wave packets in hexagonal two-dimensional dusty plasma crystals

The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. Transverse (off-plane) dust grain oscillatory motion is considered in the form of a backward propagating wave packet whose linear and nonlinear characteristics are investigated. An evolution equation is obtained for the slowly varying amplitude of the first (fundamental) harmonic by making use of a two-dimensional lattice multiple scales technique. An analysis based on the continuum approximation (spatially extended excitations compared to the lattice spacing) shows that wave packets will be modulationally stable and that dark-type envelope solitons (density holes) may occur in the long wavelength region. Evidence is provided of modulational instability and of the occurrence of bright-type envelopes (pulses) at shorter wavelengths. The role of second neighbor interactions is also investigated and is shown to be rather weak in determining the modulational stability region. The effect of dissipation, assumed negligible in the algebra throughout the article, is briefly discussed.