For analytic functions the remainder term of Gaussian quadrature rules can be expressed as a contour integral with kernel Kn. In this paper the kernel is studied on elliptic contours for a great variety of symmetric weight functions including especially Gegenbauer weight functions. First a new series representation of the kernel is developed and analyzed. Then the location of the maximum modulu...

reported grain yield increased 3.9 and 7.4% cycle 1, respectively, over two cycles of selection in barley Increasing kernel weight has been proposed as a method to increase (Hordeum vulgare L.). Durum wheat (Triticum turflour extraction in spring wheat (Triticum aestivum L.). Recurrent selection was initiated to increase kernel weight while maintaining gidum L. var. durum) grain yield improved ...

In intraspecific F1 diallel hybrids of Gossypium barbadense L., the inheritance study traits plant height, boll weight, productivity, and 1000-seed with combining ability analysis took place in 2020–2022 at Institute Genetics Plant Experimental Biology, Academy Sciences, Uzbekistan. These polygenic traits’ showed different ways fine-fiber cotton hybrids. The height trait’s overdominance interme...

We consider a family of pseudo differential operators {∆ + a∆; a ∈ (0, 1]} on R for every d ≥ 1 that evolves continuously from ∆ to ∆ + ∆, where α ∈ (0, 2). It gives rise to a family of Lévy processes {X, a ∈ (0, 1]} in R, where X is the sum of a Brownian motion and an independent symmetric α-stable process with weight a. We establish sharp two-sided estimates for the heat kernel of ∆ + a∆ with...

We consider a family of pseudo differential operators {∆ + a∆; a ∈ (0, 1]} on R for every d ≥ 1 that evolves continuously from ∆ to ∆ + ∆, where α ∈ (0, 2). It gives rise to a family of Lévy processes {Xa, a ∈ (0, 1]} in R, where X is the sum of a Brownian motion and an independent symmetric α-stable process with weight a. We establish sharp two-sided estimates for the heat kernel of ∆ + a∆ wit...