Toeplitz matrix method and nonlinear integral equation of Hammerstein type

AbstractThe existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated

Reclaimed desert habitats favor entomopathogenic nematode and microarthropod abundance compared to ancient farmlands in the Nile Basin

Characterizing entomopathogenic nematode (EPN) biogeography with a goal of augmentation and conservation biological control requires fine-scale taxonomic resolution, because closely related EPN species can exhibit divergent phenotypes for key properties such as habitat adaptation and insect host specificity. Consequently, we employed high throughput genome sequencing (HTS) to identify and compare EPNs and natural enemies of EPNs in 58 citrus orchards in 2 ecoregions in Egypt (El Beheira and Al Qalyubia governorates). We designed improved primers targeting the ITS2 rDNA to discriminate EPN species and used pre-reported primers targeting D2-D3 region for soil microarthropods. Five EPN species (Heterorhabditis bacteriophora, H. indica, H. taysearae, Steinernema glaseri, and S. scapterisci) and one steinernematid not represented in Genbank databases were detected. This is the first report of S. scapterisci and possibly the unknown (perhaps undescribed) species in Egypt. Only heterorhabditid species, dominated by H. indica, were detected in the reclaimed, sandy desert soils of El Beheira governorate. In the fine textured, ancient farming lands of the Nile delta all six species were detected, but at lower frequency and abundance. Microarthropod family richness (P= 0.01) and abundance (P= 0.001) was higher in the reclaimed lands than in the Nile Delta. Soil clay content, pH and elevation explained significant variation in the mite community structure. Population density of H. indica, the only EPN found consistently and at high abundance in El-Beheira, was inversely related to abundance of species in the nematophagous mite family Rhodacaridae. © 2021 Exeley Inc.. All rights reserved

Existence and stability for fractional parabolic integro-partial differential equations with fractional Brownian motion and nonlocal condition

In this paper, a nonlinear fractional parabolic stochastic integro-partial differential equations with nonlocal effects driven by a fractional Brownian motion is considered. In particular, first we have formulated the suitable solution form for the fractional partial differential equations with nonlocal effects driven by fractional Brownian motion using a parabolic transform. Next, the existence and uniqueness of solutions are obtained for the fractional stochastic partial differential equations without any restrictions on the characteristic forms when the Hurst parameter of the fractional Brownian motion is less than half. Further, we investigate the stability of the solution for the considered problem. The required result is established by means of standard Picard’s iteration