In [10, 11] we proposed a technique to approximate Hybrid Automata (HA) with Polynomial HA. The idea was to replace functions appearing in formulae with their Taylor Polynomials. Here we extend this technique to HA with formulae admitting integral functions. We prove that we get over-approximations of the original HA. We study the conditions ensuring that: 1. the “distance” between the formulae...

Primary care physicians in developing countries frequently use Weech's formulae to estimate the expected weight and height of children using age as a variable. The present study was undertaken to assess the validity of Weech's formulae in diagnosing undernutrition. We collected anthropometric information from 294 consecutive children, aged 12-59 months, who visited a health centre. Age was calc...

To date, little research on pragmatic transfer has considered a multilingual situation where there is an interaction among three different languages spoken by one person. Of interest was whether pragmatic transfer of refusals among three languages spoken by the same person occurs from L1 and L2 to L3, L1 to L2 and then to L3 or from L1 and L1 (if there are more than one L1) to L2. This study ai...

Motivated by model-theoretic properties of the BernaysSchönfinkel-Ramsey (BSR) class, we present a family of semantic classes of FO formulae with finite or co-finite spectra over a relational vocabulary Σ. A class in this family is denoted EBSΣ(σ), where σ ⊆ Σ. Formulae in EBSΣ(σ) are preserved under substructures modulo a bounded core and modulo re-interpretation of predicates in Σ \ σ. We stu...

One initial goal for the DRMF is to seed our digital compendium with fundamental orthogonal polynomial formulae. We had used the data from the NIST Digital Library of Mathematical Functions (DLMF) as initial seed for our DRMF project. The DLMF input LTEX source already contains some semantic information encoded using a highly customized set of semantic LTEX macros. Those macros could be convert...

In reporting on the theorem prover SCOTT (Slaney, SCOTT: A Semantically Guided Theorem Prover, Proc. IJCAI, 1993) we suggested semantic constraint as as an appropriate mechanism for guiding proof searches in propositional systems where the rule of inference is condensed detachment|a generalisation of Modus Ponens. Such constrained condensed detachment is closely analogous to semantic resolution...

A generalisation of a perturbed version of the Ostrowski inequality for twice differentiable mappings is studied. It is shown that the error bounds are better than those obtained previously. Applications for general quadrature formulae are also given.

3-SAT formulae are deened as nite sets of clauses, each clause being a disjunction of 3 literals over a set of boolean variables. Experiments on solving random 3-SAT formulae have provided strong evidence of a phase transition phenomenon. Explicitly, almost every random 3-SAT formula is satissable when its ratio: number of variables to number of clauses, denoted by c, is less than a value of ab...

The structure of objects employed in the study of Natural Language Semantics has been increasingly being complicated to represent the items of information conveyed by utterances. The complexity becomes a source of troubles when we employ those theories in building linguistic applications such as speech translation system. To understand better how programs operating on semantic representations w...

Inductance has been identified as an emerging troublemaker of interconnects for the next generation high-speed digital VLSI design. As a result, accurate and fast inductance extraction is of crucial importance. Formulae-based partial inductance extraction method approaches have been widely adopted for inductance extraction due to its simplicity and efficiency. However, there are so many inducta...