It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the int...

Defuzzification is the process of converting a fuzzy quantity to precise quantity, just as fuzzification is the conversion of a precise quantity to a fuzzy quantity. Various types of defuzzification methods, are available for conversion of fuzzy to non-fuzzy. In this paper, defuzzification functions in intuitionistic fuzzy environment such as triangular, trapezoidal, L-trapezoidal, R-trapezoida...

This article presents the longue durée social history of a medieval fish weir. It reveals significant role fishing and weirs in construction reconstruction structures cultural identities. focuses on an enigmatic annual ceremony – Horngarth or Penny Hedge at Whitby, North Yorkshire. The begins by arguing that descends from intertidal weir, before exploring possible contexts which weir originated...

trapezoidal channels are frequently used in irrigation networks and other free surface water conveyance systems. the computation of the critical flow depth is one of the primary importance in the design process. it is usually determined by using design charts of iteration techniques. however, researchers have recently proposed formulas that directly provide approximate solutions. this paper pre...

P-normGeneralizedTrapezoidalIntuitionisticFuzzyNumberisthemostgeneralizedformofFuzzy aswellasIntuitionisticFuzzyNumber.Ithasahugeapplicationwhilesolvingvariousproblemsin impreciseenvironment.Inthispapertheauthorshavediscussedsomebasicarithmeticoperationsof p-normGeneralizedTrapezoidalIntuitionisticFuzzyNumbersusingtwodifferentmethods(extensio...

We show that the class of level-k control languages, as defined by Weir, is properly included in the class of 2 k−1-multiple context-free languages for each k ≥ 2. The proof of inclusion uses a representation of the set of derivation trees for a level-k control language in terms of a second-order abstract categorial grammar. 1.1 Introduction Weir (1992a) introduced a hierarchy of language class...

Thin-plate weirs are commonly used as measuring devices in flumes and channels, enabling an accurate discharge measurement with simple instruments. The calibration formulae of such devices rely upon some empirical coefficients and there is a need to obtain new accurate physical data to complement the existing evidence. In the present study, the discharge calibration of a large 901 V-notch thin ...

Tubular channel angular pressing (TCAP) is a recently invented novel severe plastic deformation technique for producing UFG tubes. Plastic deformation analysis using the finite element method (FEM) was carried out to investigate the effects of trapezoidal channel geometry on strain inhomogeneity index (SII), strain level and required load compared to previously used channel geometries. The resu...

This paper is concerned with monitoring the hourly event-based river suspended sediment concentration (SSC) due to storms in Jiasian diversion weir in southern Taiwan. The weir is built for supplying 0.3 million tons of water per day averagely for civil and industrial use. Information of suspended sediments fluxes of rivers is crucial for monitoring the quality of water. The issue of water qual...

We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name “modal interval trapezoidal fuzzy numbers”. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to...