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Kronecker product bases and their applications in approximation theory

Research Abstract

The Kronecker product is widely utilized to construct higher-dimensional spaces from lower-dimensional ones, making it an indispensable tool for efficiently analyzing multi-dimensional systems across various fields. This paper investigates the representation of analytic functions within hyper-elliptical regions through infinite series expansions involving sequences of Kronecker product bases of polynomials. Additionally, we examine the growth order and type and T ρ-property of series composed of Kronecker product bases that represent entire functions. We also delve into the convergence properties of Kronecker product bases associated with special functions, including Bessel, Chebyshev, Bernoulli, Euler, and Gontcharoff polynomials. The obtained results extend and enhance the existing findings of such representations in hyper-spherical regions.

Research Authors
Mohra Zayed, Gamal Hassan
Research Date
Research Department
Research Journal
Electronic Research Archive
Research Year
2025

A geospatial decision-support framework for managed aquifer recharge in hyper-arid environments: Wadi El-Nakhil Basin, Eastern Desert, Egypt

Research Abstract

Groundwater recharge sustains freshwater resources in arid and hyper-arid environments, where replenishment is largely restricted to episodic flash floods. However, identifying locations where such short-lived runoff can be effectively and safely captured for Managed Aquifer Recharge (MAR) remains a major planning challenge. This study developed an integrated hydro-geospatial framework for screening and prioritizing candidate sites for Managed Aquifer Recharge (MAR) investigation in Wadi El-Nakhil Basin, Eastern Desert, Egypt. Remote sensing, Geographic Information Systems, the Analytic Hierarchy Process (AHP), and Weighted Linear Combination were used to integrate eighteen geological, hydrogeological, topographic, hydrological, and environmental criteria into a Groundwater Recharge Potential Index (GRPI). The mapped GRPI classes comprised Very High (15.33%), High (31.04%), Moderate (27.80%), Low (16.50%), and Very Low (9.33%) relative screening suitability. Nine candidate locations were identified for further MAR investigation. The AHP weighting showed high internal consistency (CR = 0.006787). Monte Carlo analysis examined variation in criterion weights under prescribed perturbations. Comparison with eight control wells indicated agreement with groundwater productivity, although spatially independent performance was not established. Gravity-fed recharge wells, permeable gabion check dams, and subsurface infiltration galleries are discussed as conceptual options requiring site-specific hydraulic, water-quality, operational, and economic assessment. The assessment identifies spatial priorities for MAR investigation in a basin where episodic water supply and heterogeneous subsurface conditions complicate site selection. Its contribution is a basin-specific screening assessment linking candidate locations to the field information required for feasibility evaluation. Recharge rates, available storage, recoverable water volumes, and operational performance remain to be established through site investigation and pilot testing.

Research Authors
Eltaher M. Shams, Rashad Sawires, Tadahiro Kishida
Research Date
Research Department
Research Journal
Scientific African
Research Member
Research Pages
e03703
Research Publisher
Elsevier
Research Rank
Web of Science Q1
Research Vol
34
Research Website
https://www.sciencedirect.com/science/article/pii/S2468227626005284
Research Year
2026

Morphological Insights into Multinucleated Giant Cell Populations and Testicular Alterations Induced by DBP and DEHP in Prepubertal Mice

Research Abstract

Background: Phthalates are endocrine-disrupting chemicals associated
with reproductive toxicity. Aim: This study provides a comparative
evaluation of the effects of dibutyl phthalate (DBP) and di-(2-ethylhexyl)
phthalate (DEHP) on testicular injury in immature mice. Methods: Fortyeight
21-day-old Swiss albino male mice were allocated into eight groups:
control, corn oil vehicle, and DBP- or DEHP-treated groups receiving 100,
200, or 400 mg/kg body weight by oral gavage for 10 consecutive days.
Histological evaluation followed 7 and 10 days of exposure (postnatal days
28 and 31). Results: Both DBP and DEHP induced testicular injury,
including germ cell disorganization, cytoplasmic vacuolization, germ cell
loss, and multinucleated giant cell (MGC) formation. Morphometric
analysis demonstrated a significant reduction in seminiferous tubule
diameter in both treatment groups, with a greater decrease in DEHPexposed
animals at both time points. DBP-treated groups exhibited a high
incidence of MGCs, reaching 93.11% and 84.50% at 28 and 31 days,
respectively. In contrast, DEHP-treated groups showed a lower incidence of
MGCs, reaching 56.17% at 28 days, with complete absence at 31 days
despite more severe degeneration and germ cell depletion. Two distinct
MGC types were identified: a dark eosinophilic type with dense cytoplasm
and relatively regular nuclei, and a pale foamy type with vacuolated
cytoplasm and irregular condensed nuclei, suggesting germ cell symplasts
and macrophage-derived giant cells, respectively. Conclusion: Both DBP
and DEHP induced MGC formation, but their progression differed, with
prolonged MGC occurrence after DBP exposure and more severe germ cell
loss following DEHP exposure. Further mechanistic studies are warranted.

Research Authors
Heba Aboulqasem, Dalia Elzahraa Mostafa and Reda Ali
Research Date
Research Department
Research Journal
Assiut University Journal of Multidisciplinary Scientific Research (AUNJMSR)
Research Pages
817- 833
Research Publisher
Faculty of Science, Assiut University, Assiut, Egypt.
Research Vol
55 (3)
Research Year
2026

Mycotoxicity and Embryonic Development: III- Aflatoxin B1 Induces Hepatic and Renal Histopathological and Histomorphometric Alterations in Pregnant Mice

Research Abstract

Background: Aflatoxins, highly toxic compounds produced by
species of Aspergillus Flavus and Aspergillus parasiticus, are
known for their hepatonephric toxicity. There are no published
randomized controlled trials evaluating the effect of aflatoxin
exposure during pregnancy. Aim of the work: The current
study aims to evaluate the effect of AFB1 on hepatorenal
structure of pregnant mice. Methods: Female mice were daily fed on fodder contaminated with 5, 10 or 20 μg AFB1 seven days before mating and during pregnancy. Liver and kidney specimens were processed for histopathological and histomorphometric investigations. Results: 5 μg AFB1 treatments resulted in hepatonecrosis, inflammatory cells infiltration, vascular congestion and interstitial edema. 10 μg AFB1 group exerted hydropic and ballooning degeneration of hepatic cells, increased nuclear chromatin content, presence of trinucleated cells, dilation of blood sinusoids and areas of necrosis. In liver, 20 μg AFB1 group revealed marked vascular congestion and binucleated cells, with variable sized nuclei anisonucleosis and interstitial edema. Liver histomorphometry analyses revealed significant alterations in the central vein, nuclear and cytoplasmic area. Kidney treated with 5 μg AFB1 showed glomerular hypertrophy, tubular necrosis, congestion and Bowmn's space increase. Kidney treated with 10 μg AFB1 exhibited necrosis, damage in corpuscles & renal cast. Examination of kidney treated with 20 μg AFB1 revealed hemorrhage, necrosis, renal cast and glomerular hypertrophy. Kidney histomorphometry analyses revealed significant alterations in Bowman’s space, glomerular and corpuscle areas. Conclusion: AFB1 exerted hepatonephrotoxic negative impact in pregnant mice fed on contaminated fodder and caused many histopathological and histomorphometric alterations including necrosis, hydropic degeneration, edema, hemorrhage, blood congestion reflecting high risk toxicity of AFB1. It is suggested that accumulation of bioactivated AFB1 metabolites severely induced hepatonephrotoxicity in pregnant mice. Further studies are recommended.

Research Authors
Shorouk M. Mohammed, Karim S. Abdallah, Addel-Naser A. Zohri, and Reda A. Ali
Research Date
Research Department
Research Journal
Assiut University Journal of Multidisciplinary Scientific Research (AUNJMSR)
Research Pages
686- 723
Research Publisher
Faculty of Science, Assiut University, Assiut, Egypt.
Research Vol
55 (3)
Research Website
https://aunj.journals.ekb.eg
Research Year
2026
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