Estimation of fuzzy memberships from histograms

Based on the conclusions drawn in the bijective transformation between possibility and probability, a method is proposed to estimate the fuzzy membership function for pattern recognition purposes. A rational function approximation to the probability density function is obtained from the histogram of a finite (and sometimes very small) number of samples. This function is normalized such that the highest ordinate is one. The parameters representing the rational function are used for classifying the pattern samples based on a max-min decision rule. The method is illustrated with examples.     

Structure and properties of a near-α titanium alloy after β solution treatment and aging at 625 °

The microstructure, tensile properties, and fractographic features of a near alpha titanium alloy, IMI 829 (Ti-6.lAl-3.2Zr-3.3Sn-lNb-0.5Mo-0.32Si) have been studied after aging at 625 ° for 24 hours following solution treatment in the beta phase field at 1050 ° and cooling at various rates (furnace, air, oil, or water). Transmission electron microscopy studies revealed that aging at 625 ° for 24 hours of this alloy had led to the precipitation of only one kind of silcide with a hexagonal structure (c = 0.36 nm andα = 0.70 nm). The precipitates are ellipsoidal in shape and their size depends on the cooling rate given to the alloy after beta solution treatment. Extremely fine precipitation of Ti₃Al phase has also been observed in the furnace cooled and aged condition. There is a significant improvement in both yield and ultimate tensile strengths after aging of both the oilquenched and water-quenched specimens whereas it is minimal in the case of furnace-cooled and air-cooled specimens. Aging the alloy has also resulted in a drastic reduction in both percentage elongation and percentage reduction in area for all the conditions investigated. While the fracture surfaces of the unaged specimens showed characteristic dimples, a large number of facets appeared in the fractographs of the aged specimens. formerly with Banaras Hindu University, is with the National Metallurgical Laboratory, Jamshedpur, India.     

Torsional oscillations of a finite inhomogeneous piezoelectric cylindrical shell

Torsional wave motion of a finite right circular cylindrical shell of inhomogeneous piezoelectric material of (622) crystal class under time dependent electric potential on the boundary is investigated. The inhomogeneity is restricted to the variations of density and other physical constants of the medium as expf((r)) where f is a suitable function of the radial distance. Two related problems, investigated by the author, in the papers [1, 2] are shown to be particular cases of the present problem.     

Water resources utilization in an irrigation project in India

Quantitative information on the adequacy of current operating procedures and available water resources in a typical major irrigation project in India (the Mahi Right Bank Canal project in Gujarat, India) is provided by comparing monthly and seasonal irrigation demands with canal releases and groundwater draught over a four‐year period. A strategy based on water conservation and the use of groundwater in the monsoon season for the full exploitation of reservoir potential in the subsequent seasons is proposed.     

An intermittently used n-unit complex system

In this paper we study an n-unit warm standby system which is needed intermittently with need and no-need periods occurring alternately. The life time of a unit while online and duration of a no-need period are generally distributed random variables while all the others are exponentially distributed. Identifying certain regeneration points, we obtain an expression for the distribution function of the time to the first disappointment.     

A complex three-unit system

A three-unit standby redundant system has been studied. All the random variables involved are discrete. The life time of a unit while online is an arbitrarily distributed random variable. Also it is assumed that the probability of the repair completion is a constant. Using the regeneration point technique, the availability of the system is derived.