The paper continues a study of extensional formulas and their representation by normal forms. The notion of extensional formula is extended to the case when extensionality is considered with respect to a binary reflexive relation. It has been proved that extensional formulas can be represented by normal forms of infinite type and “approximated” by normal forms of finite type. All proofs are giv...

Relational databases have had great industrial success in computer science, their power evidenced by theoretical analysis and widespread adoption. Often, automated theorem provers do not take advantage of database query engines and therefore do not routinely leverage that source of power. Extensional Reasoning is a novel approach to automated theorem proving where the system automatically trans...

Complex fluids containing long polymer chains exhibit measurably large resistance to stretching or extensional flows, due to additional stresses generated by the extensional deformation of the underlying fluid microstructure. Understanding and quantifying the response of such elastic fluids to extensional flows is necessary for optimizing fluid composition for technological applications like in...

Schema integration as part of the database design as well as of the database integration process has to deal with extensional relationships among classes of the di erent schemata to be integrated. As a rule, the extensional relationships must be speci ed by the database designer. Partially, some relationships may also be derived from other relationships. Most existing schema integration approac...

Several recent techniques and tools for Ontology-based Data Access (OBDA) make use of the so-called extensional constraints (a.k.a. ABox dependencies). So far, extensional constraints have been mainly considered in a setting where data are represented in an ABox, instead of external data sources connected to the ontology through declarative mappings. Moreover, the issue of how to generate exten...

We show that visualization and analysis of capillary-driven thinning and pinch-off dynamics of the columnar neck in an asymmetric liquid bridge created by dripping-onto-substrate can be used for characterizing the extensional rheology of complex fluids. Using a particular example of dilute, aqueous PEO solutions, we show the measurement of both the extensional relaxation time and extensional vi...

In this study, we characterize the shear and extensional rheology of dilute to semidilute solutions of cellulose in the ionic liquid 1-ethyl-3-methylimidazolium acetate (EMIAc). In steady shear flow, the semidilute solutions exhibit shear thinning, and the high-frequency complex modulus measured in small amplitude oscillatory shear flow exhibits the characteristic scaling expected for solutions...

reluctance towards implementation of precision agriculture (pa) seems to be based on lackof consideration to education, extension, and research sectors. the objective of this study isto identify educational, extensional, and research requirements in application of the pasystem. the research population included all the experts in qazvin province who are familiarwith pa concepts and pa’s equipmen...

This historical review takes a few selected issues from the rheological studies of extensional flow that fill the literature, starting with extracts from the seminal papers of Trouton (Proc. Roy. Soc. A77 (1906) 426-440) and Fano (Archivio di fisiologio, 5 (1908) 365-370). Work in the first half of the twentieth century on spinnability and extensional viscosity measurement is highlighted, follo...

This paper studies confluence properties of extensional and non-extensional λ-calculi with explicit substitutions, where extensionality is interpreted by η-expansion. For that, we propose a general scheme for explicit substitutions which describes those abstract properties that are sufficient to guarantee confluence. Our general scheme makes it possible to treat at the same time many well-known...