This paper presents algebraic identities and algebraic query optimization for a parametric model for temporal databases. The parametric model has several features not present in the classical model. In this model a key is explicitly designated with a relation and an operator is available to change the key. The algebra for the parametric model is three-sorted; it includes relational expressions ...

In this paper a fundamental duality is established between algebraic cycles and algebraic cocycles on a smooth projective variety. The proof makes use of a new Chow moving lemma for families. If X is a smooth projective variety of dimension n, our duality map induces isomorphisms LH(X) → Ln−sH2n−k(X) for 2s ≤ k which carry over via natural transformations to the Poincaré duality isomorphism H(X...

We define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove “algebraic” analogs of classical results. Using a modified version of Quillen’s small object argument, we show that every cofibrantly generated model structure in the usual sense underlies a cofibrantly generated algebraic mo...

We prove that the coefficients of certain weight −1/2 harmonic Maass forms are “traces” of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight −2 harmonic weak Maass forms to spaces of weight −1/2 vectorvalued harmonic weak Maass forms on Mp2(Z), a result which is of independent interest. We then prove a general theorem which guarantees (...

What is a qualitative calculus? Many qualitative spatial and temporal calculi arise from a set of JEPD (jointly exhaustive and pairwise disjoint) relations: a stock example is Allen’s calculus, which is based on thirteen basic relations between intervals on the time line. This paper examines the construction of such a formalism from a general point of view, in order to make apparent the formal ...

In this project, we have extended previous work on the formalization of the process algebra CCS in HOL4. We have added full supports on weak bisimulation equivalence and observation congruence (rooted weak equivalence), with related definitions, theorems and algebraic laws. Some deep lemmas were also formally proved in this project, including Deng Lemma, Hennessy Lemma and several versions of t...

We propose a generalisation of concurrent Kleene algebra [5] that can take account of probabilistic effects in the presence of concurrency. The algebra is proved sound with respect to a model of automata modulo a variant of rooted η-simulation equivalence. Applicability is demonstrated by algebraic treatments of two examples: algebraic may testing and Rabin’s solution to the choice coordination...

Ω is weak-geodetically closed whenever Ω is weak-geodetically closed with respect to w for any w ∈ X. ∗A manuscript for algebraic combinatorics workshop 7/2-4 in National Hsinchu University of Education, an extension of 2007 International Conference on Graph Theory and Combinatorics & Fourth Cross-strait Conference on Graph Theory and Combinatorics. †Department of Applied Mathematics, National ...

The primary object of this paper is to prove the conjecture of [HL08a] explaining how to recover the weak dimension of a ring from its derived category. In the process, we develop a theory of weak dimension, which we call ghost dimension, for the generalized rings, known as ring spectra, that arise in algebraic topology.