The algebra of stream processing functions

A dataflow network consists of nodes that communicate by passing data over unbounded FIFO channels. For dataflow networks containing only deterministic nodes, Kahn has presented a simple and elegant semantic model. However, the straight-forward generalization of this model to nondeterministic networks is not compositional. In the literature are two compositional models which in addition are fully abstract, i.e. they have added the least amount of extra information to attain compositionality. We relate these two model to each other, thereby showing that they are isomorphic. We give comments on the relation of the models to other compositional models, which are not fully abstract.KeywordsData ItemCommunication EventInfinite SequenceOutput ChannelInput ChannelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The primary objective of this work is to develop computing capabilities to enable computational prototyping as a complementary and parallel path to the hardware product development process. The evolution of a systems approach, capturing aspects of information generation, processing, visualization, transfer, and reuse, within a sharable, multimedia, electronic environment, is crucial to the integrated design process of the future. We discuss a general computing environment to support the multi-level (process-device-material) simulations of xerographic subsystems. This environment features: distributed computing, concurrent processing, network sharable information and tools, a visual programming interface, dynamic computing and visualization, and interactive steering. We describe the implementation of the testbed environment and the mathematical simulations, from first principles, of the charging, imaging, and development subsystems. Generic algorithms developed for these subsystems are discussed. Interactive steering of dynamical solutions and browsing of visual data are emphasized. A model for multi-level simulation is proposed to support the decision making process. A visual programming interface is used to encapsulate the simulation and visualization tools as modules which can then be visually assembled into dataflow networks on Unix workstations. Mathematical formulations, parallel computing on clusters of workstations, and their use in interactive sessions are detailed.

A complete description is given of the analytic structure of maximal dimension in the spectra of a wide class of concrete function algebras generated by analytic functions.A connection is also given with point derivations on such algebras.I. Introduction.Let B be a function algebra acting on its spectrum (maximal ideal space) Sp B, with Shilov boundary TB.According to a wellknown result of Rossi [15], the functions in B obey a weak maximum modulus principle on Sp B -TB.One of the principal themes in the theory of function algebras is the "explanation" of this analytic-type behavior by the existence of analytic structure in Sp B. More precisely, let us say that an analytic variety (of dimension n) in Sp B is a pair (X, r) where X is an analytic variety (of pure dimension n), r: X -► Sp B is a continuous map, and b ° r is analytic for each b e B. Then the question is: what are the nontrivial analytic varieties in SpS?Although Stolzenberg's example [16] shows that one does not have the existence of nontrivial analytic structure in all situations, a number of global and local conditions which imply the existence of analytic structure have been found by Gleason [11], Browder [8], Clayton [9] and others.A different approach, due to Bishop [3], which depends upon the existence of functions in B with finite fibers, leads to the construction of 1-dimensional analytic structure in Sp B. Bishop's ideas have been expanded and exploited by Stolzenberg [17], Bjork [5],[6], Alexander [1], [2], the author [20], and others, and have proven very useful in dealing with questions of approximation.In this paper, we shall be concerned with the classification of high-dimensional analytic structure.For a fairly wide class of concrete function algebras, those which contain a sufficiently rich collection of analytic functions, we are able to completely describe the analytic structure of maximal dimension which

In software verification it is often required to prove statements about heterogeneous domains containing elements of various sorts, such as counters, stacks, lists, trees and queues. Any domain with counters, stacks, lists, and trees (but not queues) can be easily seen a special case of the term algebra, and hence a decision procedure for term algebras can be applied to decide the first-order theory of such a domain. We present a quantifier-elimination procedure for the first-order theory of term algebra extended with queues. The complete axiomatization and decidability of this theory can be immediately derived from the procedure.

Recently, Beattie, Bulacu ,and Torrecillas proved Radford's formula for the fourth power of the antipode for a co-Frobenius Hopf algebra.In this note, we show that this formula can be proved for any regular multiplier Hopf algebra with integrals (algebraic quantum groups). This, of course, not only includes the case of a finite-dimensional Hopf algebra, but also that of any Hopf algebra with integrals (co-Frobenius Hopf algebras). Moreover, it turns out that the proof in this more general situation, in fact, follows in a few lines from well-known formulas obtained earlier in the theory of regular multiplier Hopf algebras with integrals.We discuss these formulas and their importance in this theory. We also mention their generalizations, in particular to the (in a certain sense) more general theory of locally compact quantum groups. Doing so, and also because the proof of the main result itself is very short, the present note becomes largely of an expository nature.

We extend the Larson–Sweedler theorem to group-cograded multiplier Hopf algebras introduced in Abd El-hafez et al. (2004), by showing that a group-cograded multiplier bialgebra with finite-dimensional unital components is a group-cograded multiplier Hopf algebra if and only if it possesses a nondegenerate left cointegral. We also generalize the theory of multiplier Hopf algebras of discrete type in Van Daele and Zhang (1999) to group-cograded multiplier Hopf algebras. Our results are applicable to Hopf group-coalgebras in the sense of Turaev (2000). Finally, we study regular multiplier Hopf algebras of η -discrete type.

We discuss the enumeration theory for ags in Eulerian partially ordered sets, emphasizing the two main geometric and algebraic examples, face posets of convex polytopes and regular CW -spheres, and Bruhat intervals in Coxeter groups. We review the two algebraic approaches to ag enumeration { one essentially as a quotient of the algebra of noncommutative symmetric functions and the other as a subalgebra of the algebra of quasisymmetric functions { and their relation via duality of Hopf algebras. One result is a direct expression for the Kazhdan-Lusztig polynomial of a Bruhat interval in terms of a new invariant, the complete cd-index. Finally, we summarize the theory of combinatorial Hopf algebras, which gives a unifying framework for the quasisymmetric generating functions developed here.

Let Hp(m), 0 < p ^ oo, be the Hardy spaces on a quotient K of the Bohr group. In this paper we completely determine the isometries of Hp{m), p Φ 2, onto itself. Our result is a generalization of a recent work of Muhly who determined the isometries of Hp(m) onto itself under the assumption that the dual group of K is countable, and it may be regarded as a partial answer to a question posed by Muhly. 1* Introduction* Many results have been obtained concerning isometries of Hardy spaces in the theory of uniform algebras. The most fundamental result in this direction is due to de Leeuw, Rudin, and Wermer [2], which states that an automorphism of the classical Hardy space H°°{T) is induced via composition with the unit circle T of a fractional linear transformation of the unit disc onto itself. Their work was carried on independent of Nagasawa [13], who also described the isometries of ίί oo(Tr) onto itself. On the other hand, Arens [1] completely determined the automorphisms of the uniform algebra of analytic functions on a compact abelian group K whose dual group Γ is archimedean ordered (cf. [11]). This result was extended by Muhly [11] to the uniform algebra of analytic functions induced by a flow which has no periodic orbits. Moreover Muhly [12] has recently given, among other things, the following interesting generalization of this result of Arens to the case of isometries of Hardy spaces Hp(m), p Φ 2, on K: Under the assumption that Γ is countable, every isometry of Hp(m), p Φ 2, is induced via composition with an affine map of K such that the adjoint of the additive factor of this map preserves the order of Γ. The purpose of this paper is to remove the assumption on Γ. This result provide a partial positive answer to the following question posed by Muhly in [12; §5]: Is it possible to describe the isometries of ergodic Hardy spaces

We lay down the foundations of the theory of Poisson vertex algebras aimed at its applications to integrability of Hamiltonian partial differential equations. Such an equation is called integrable if it can be included in an infinite hierarchy of compatible Hamiltonian equations, which admit an infinite sequence of linearly independent integrals of motion in involution. The construction of a hierarchy and its integrals of motion is achieved by making use of the so called Lenard scheme. We find simple conditions which guarantee that the scheme produces an infinite sequence of closed 1-forms $$\omega_j, j \in {\mathbb {Z}}_+$$ , of the variational complex Ω. If these forms are exact, i.e., ω j are variational derivatives of some local functionals ∫ h j , then the latter are integrals of motion in involution of the hierarchy formed by the corresponding Hamiltonian vector fields. We show that the complex Ω is exact, provided that the algebra of functions is $$\fancyscript {V}$$ is “normal”; in particular, for arbitrary $$\fancyscript {V}$$ , any closed form in Ω becomes exact if we add to $$\fancyscript {V}$$ a finite number of antiderivatives. We demonstrate on the examples of the KdV, HD and CNW hierarchies how the Lenard scheme works. We also discover a new integrable hierarchy, which we call the CNW hierarchy of HD type. Developing the ideas of Dorfman, we extend the Lenard scheme to arbitrary Dirac structures, and demonstrate its applicability on the examples of the NLS, pKdV and KN hierarchies.

Operator algebras of functions

A novel input-output model of water quality in water distribution systems is presented as a particle (water parcel) backtracking algorithm (PBA). The PBA is a simpler and more efficient version of that described by Zierolf et. al. in 1998 and is extended to allow storage tanks and multiple water sources and quality inputs. For simplicity the algorithm details are described for networks with a single water quality input at the water source, and the necessary extensions to allow multiple water sources and quality inputs are described separately. The PBA provides information that is not available using traditional simulation approaches: the various paths that water takes between a particular input source and output node, and their associated time delays and impact on output node water quality. Such information constitutes a complete description of the input-output behavior under typical assumptions of first-order chemical decay or production reactions. Thus the output behavior can be calculated for any source quality input, and the explicit mathematical form of the input-output behavior is useful information for certain applications such as feedback control. More generally, the PBA is a tool to understand flow-path-dependent water quality processes in distribution systems, since those paths and their characteristics are made explicit and thus available for analysis. The potential utility of input-output analysis is illustrated by several examples.

As pointed out by Hans Rott and others, there are two ways of reading AGM, the theory of Alchourrón, Gärdenfors and Makinson presented in a classic paper that has come to be regarded as the fons et origo of today’s formal study of belief revision [Alchourrón et al., 1985]. Under the “iterative” reading there is room for multiple sequential belief change, but under the “one-shot” reading the perspective is limited to one change. Roughly and informally, the “one-shot” reading recognizes doxastic situations of two kinds. First, there is status quo, the (generic but unique) anterior situation. Then a belief change takes place, landing the agent in a posterior situation. And this is the entire scenario! There is no inkling that there could be further belief changes and corresponding post-posterior situations. Iterative theories are richer and more interesting. But as they are more difficult to devise, one might begin by studying one-shot theories (to which from now on we will refer without scare quotes). In this paper, we suggest how one-shot AGM can be rendered within dynamic doxastic logic (DDL). This author’s first effort in this area was [Segerberg, 1994a], but only with van Linder, van der Hoek and Meyer [1995] did we get a faithful interpretation of AGM in a DDL language (that is, a model theoretical analysis of Gärdenfors’s characterization in [1988) of the three main doxastic operations: expansion, contraction, and revision of belief sets). However, in neither paper was the question of a complete axiomatization of the set of valid formulæ addressed; here, it is.

We propose a formal semantics for object data models. Our approach may be seen as a semantic approach to object-relational models. It is object-oriented because it captures the main concepts of objectoriented models namely : class, method, object identity, inheritance, collection types and persistence; it is relational because it maintain the main characteristics of the relational model, especially the clear separation between schema, instance and querying. Moreover, it is functional in the sense that it is based on a simple algebra of partial functions whose main role is to perform arithmetic computations, similar to commercial languages. Another important aspect of our approach is that it provides a rigorous mathematical treatment of null value.

Previous researchers in logic testing focused on shorts in MOS gate oxides that have zero-resistance. However, most shorts are resistive and may cause delay faults. In this paper, we propose a simple and realistic delay fault model for gate oxide shorts. A reasonably accurate method is proposed to compute delay change due to resistive shorts. We also enumerate all possible fault behaviors and present the relationship between input patterns and output behaviors, which is useful in ATPG.

The Embedded Machine is a virtual machine that mediates in real time the interaction between software processes and physical processes. It separates the compilation of embedded programs into two phases. The first, platform-independent compiler phase generates E code (code executed by the Embedded Machine), which supervises the timing ---not the scheduling--- of application tasks relative to external events, such as clock ticks and sensor interrupts. E~code is portable and exhibits, given an input behavior, predictable (i.e., deterministic) timing and output behavior. The second, platform-dependent compiler phase checks the time safety of the E code, that is, whether platform performance (determined by the hardware) and platform utilization (determined by the scheduler of the operating system) enable its timely execution. We have used the Embedded Machine to compile and execute high-performance control applications written in Giotto, such as the flight control system of an autonomous model helicopter.