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In this paper, we study the concept of nearness between L-fuzzy rough sets and the concepts of L-fuzzy rough grills and L-fuzzy rough δℱ-clusters on a Čech L-fuzzy rough proximity space (X,δℱ). Also, we investigate the relationship among L-fuzzy rough grills, L-fuzzy rough δℱ-clan and L-fuzzy rough δℱ-clusters. Moreover, we introduce the L-fuzzy rough LO-proximity spaces and study some of its basic properties. An adequate number of examples support the study. [ABSTRACT FROM AUTHOR]

The present investigation was conducted on 274 Kankrej cattle maintained at Livestock Research Station, Kodamdesar, Bikaner, calved between 2012 to 2022 with the objectives to study principal component analysis (PCA) and multiple linear regression analysis (MLRA) for prediction of lifetime performance of Kankrej cattle. Six early lactation traits (First lactation length- FLL, First lactation dry period-FDP, First lactation 305 days' milk yield- F305DMY, Second lactation length- SLL, Second lactation dry period- SDP, and Second lactation 305 days' milk yield- S305DMY) were used to analyze the lifetime milk yield upto 5th and 7th lactations. The MLR analysis revealed that the model containing F305DMY, SLL and S305DMY for upto 5th lactations' lifetime milk yield, and model containing F305DMY, FDP and SLL for upto 7th lactations' lifetime milk yield having R² = 68.3% and 68.5%, respectively, were found to be optimal models. PCA revealed that the first 2 principal components (FLL, F305DMY) explained more than 78% of the total variation for LTMY5 and more than 81% variation for LTMY7. In this study F305DMY was found most important early trait in prediction of lifetime production of Kankrej cattle on the basis of PCA and MLR analysis, out of which PCA was found to be better. Significant finding of this study may be helpful in developing selection methodology for Kankrej cattle after validation in a large population. [ABSTRACT FROM AUTHOR]

The object of this paper is to study a generalized Mittag-Leffler function and a modified general class of functions which is reducible to several special functions. convergent conditions of these functions are discussed. Some results pertaining to the generalized Mittag-Leffler function and generating relations involving these functions are derived. Further, fractional integrals involving these functions are achieved. Some illustrative exclusive cases of the results are presented. [ABSTRACT FROM AUTHOR]

In the present work, an in-house centrifugal casting setup was developed in the laboratory. Waste natural fillers such as soap nuts seeds, Aegle marmelos, and Terminalia chebula were used for the preparation of polyester based composite by using centrifugal casting technique. The influence of filler loading (3%, 6%, 9% and 12% by weight) on the physical-mechanical behaviour of hybrid composites has been performed. The moisture absorption tests were conducted according to the ASTM D 570-98 standards. Hybrid composites with varying composition of polyester, Aegle marmelos, Terminalia chebula, and soap nut seed were fabricated. It has been observed that the maximum water absorption was in the range of 0.23% to 2.12% (weight fraction), the maximum tensile strength 47.83 MPa, hardness 71VH and impact strength 5.8 Joule for the hybrid composite material with 12 wt% Aegle marmelos, 9 wt% Terminalia chebula, 6 wt% soap nuts seed. The minimum specific wear rate (0.00196 mm3/Nm) was obtained for the composition of 12 wt% soap nuts seed and 3 wt% Aegle marmelos.