This paper presents a study of Pell’s equation, one of the most important Diophantine equations in number theory. It reviews the historical development of the equation, its basic properties, and classical solution methods based on continued fractions. The paper also discusses its applications in algebraic number theory, quadratic forms, and Diophantine analysis. Several worked examples are included to illustrate the solution process. In addition, a statistical perspective is presented to examine the distribution of solvable Pell-type equations for selected values of D.

Nanotechnology is a modern technology and has many applications that include the manufacture of molecules or particles in the range of the nanoscale. Nanotechnology from the Greek word nano, meaning "dwarf". Nanoparticles are defined as single particles whose dimensions do not exceed 100 nanometers. The unique properties and features of nanoparticles are due to their small size, in addition to their chemical composition and surface structure. Different materials at the nanoscale lead to the development of new properties in industrial products, resulting in a real and impressive increase in industrial and medical applications. In this review, we will learn about this technology, its history, and the characteristics and shapes of nanoparticles. The focus will be on the application of nanotechnology in medicine, particularly in engineering living tissues with nanoscale scaffolds that simulate the functions of the extracellular matrix (ECM) to promote tissue recovery, replacement, and regeneration. It turns out that stem cells attached to a scaffold are more successful in adapting to their environment and performing the task of regeneration. The nerve endings in the body are attached to the scaffolding by weaving between the openings. This will cause them to act as a bridge to connect the cut sections. Over time, the scaffolds will dissolve and exit the body safely, leaving intact nerves in place. Some of the successfully used scaffolds are briefly identified, such as bone scaffolds, cardiac muscle scaffolds, and spinal cord engineering.

Energy storage technologies (EST) are becoming the primary facilitator of electric vehicle (EV) performance, efficiency, and sustainability as transportation electrification advances. Under the aegis of five interrelated research dimensions, the paper thoroughly examines the role, development, and enhancement of energy storage systems (ESS) in the EV ecosystem. With special attention to the evolution of traditional hybrid and plug-in hybrid into the noticeably more advanced battery-electric and fuel-cell platforms, the development, classification, and comparison of EV technologies are evaluated at the outset. Evaluation indicates that fuel cell electric vehicles (FCEVs) and hybrid architectures are pushing the operational envelope for applications that need more load and range. With the recent development of battery-electric vehicles (BEVs) and the current lithium-ion technology standard, short- and medium-range electric vehicles now have a commercially viable route. The popularity of the ESS as an essential component of EVs is further investigated, as is its role in energy management, regenerative braking, and power delivery systems. Certain energy, power density, charge rate, and life-cycle efficiency have been described for storage technologies in electrochemical, hybrid, chemical, electrical, and mechanical configurations. The third section evaluates ESTs using performance metrics like energy density, power density, round trip efficiency, thermal stability, and cost per kilowatthour while addressing technology trade-offs.

Toxoplasmosis is a worldwide contagious disease of humans and other warm-blooded animals, including birds. Toxoplasma gondii (T. gondii) is an obligate intracellular protozoan parasite responsible for Toxoplasmosis disease, which is clinically manifested chiefly in pregnant women and people with weakened immune systems. Clinical complications include abortion and stillbirths, encephalitis, pneumonia, brain and eye damage, and neonatal mortality. The genus Toxoplasma was first proposed in 1908 by Nicolle and Manceaux following the identification of asexual stages of similar parasites in the tissues of birds and mammals, and merozoites in the blood of North African rodents, Ctenodactylus gundi. At about the same time, Splendore independently described Toxoplasma in laboratory rabbits in Sao Paulo, Brazil, and Darling probably found it in man in Panama in the same year. Although several species were named, during the 1930s, it was shown that these were identical to the type species T. gondii. During the 1960, scientists provided evidence for the coccidian nature of the parasite. Then, between 1960 and 1970, the heterogeneous life cycle was elucidated by the discovery of sexual stages in the small intestine of cats, which followed the induction of infection in intermediate hosts by inoculation with cat feces. This review seeks to study the parasite and its responsibility to cause disease, condition prevalence, clinical manifestations accompanied by infection, and treatment protocols.

Abstract

Background: The "iron allergy hypothesis" suggests insufficient iron stores drive T-helper 2 polarisation and promote IgE sensitisation. We studied the association between serum ferritin and total IgE categories among Libyan children with recurrent wheeze. Methods: This cross-sectional study was conducted at Ali Omar Asker Hospital (Tripoli, Libya) from January 2023 to February 2026.Investigated 150 children aged 2-16 years diagnosed with recurrent wheezing. Serum ferritin and total IgE levels were classified as normal, low, or high based on laboratory ranges. Statistical analysis was performed using Pearson’s Chi-square, Fisher’s exact and Spearman’s rank correlation tests. Results: Among the 150 children, 23.8% had low ferritin, 76.2%were normal, and none were high. Overall, 54.7% had high IgE levels. The results showed IgE levels were nearly the same in both the normal and low ferritin groups (55.6% vs. 54.8%). This difference was not significant (χ² = 0.089, p = 0.912). Also, Spearman’s test confirmed no correlation between the two measures (rho = 0.012, p = 0.883).In subgroups, boys had a significantly higher rate of high IgE than girls (62.5% compared to 43.5%; p = 0.032). Regarding age, high IgE was found in 47.7% of children aged 2-6 years, 56.9% aged 7-11 years, and 58.5% aged 12-16 years. However, these variations were not statistically significant (p = 0.645). Finally, patient atopy and family history showed no significant links to ferritin or IgE levels.

Conclusion: Our study found no association between serum ferritin and total IgE levels in Libyan children with recurrent wheeze. However, the finding of male predominance in elevated IgE warrants more investigation. Further studies are needed to clarify nutrition-immunity interactions in pediatric respiratory diseases.

Toxoplasmosis is a worldwide contagious disease of humans and other warm-blooded animals, including birds. Toxoplasma gondii (T. gondii) is an obligate intracellular protozoan parasite responsible for Toxoplasmosis disease, which is clinically manifested chiefly in pregnant women and people with weakened immune systems. Clinical complications include abortion and stillbirths, encephalitis, pneumonia, brain and eye damage, and neonatal mortality. The genus Toxoplasma was first proposed in 1908 by Nicolle and Manceaux following the identification of asexual stages of similar parasites in the tissues of birds and mammals, and merozoites in the blood of North African rodents, Ctenodactylus gundi. At about the same time, Splendore independently described Toxoplasma in laboratory rabbits in Sao Paulo, Brazil, and Darling probably found it in man in Panama in the same year. Although several species were named, during the 1930s, it was shown that these were identical to the type species T. gondii. During the 1960, scientists provided evidence for the coccidian nature of the parasite. Then, between 1960 and 1970, the heterogeneous life cycle was elucidated by the discovery of sexual stages in the small intestine of cats, which followed the induction of infection in intermediate hosts by inoculation with cat feces. This review seeks to study the parasite and its responsibility to cause disease, condition prevalence, clinical manifestations accompanied by infection, and treatment protocols.

Nanotechnology is a modern technology and has many applications that include the manufacture of molecules or particles in the range of the nanoscale. Nanotechnology from the Greek word nano, meaning "dwarf". Nanoparticles are defined as single particles whose dimensions do not exceed 100 nanometers. The unique properties and features of nanoparticles are due to their small size, in addition to their chemical composition and surface structure. Different materials at the nanoscale lead to the development of new properties in industrial products, resulting in a real and impressive increase in industrial and medical applications. In this review, we will learn about this technology, its history, and the characteristics and shapes of nanoparticles. The focus will be on the application of nanotechnology in medicine, particularly in engineering living tissues with nanoscale scaffolds that simulate the functions of the extracellular matrix (ECM) to promote tissue recovery, replacement, and regeneration. It turns out that stem cells attached to a scaffold are more successful in adapting to their environment and performing the task of regeneration. The nerve endings in the body are attached to the scaffolding by weaving between the openings. This will cause them to act as a bridge to connect the cut sections. Over time, the scaffolds will dissolve and exit the body safely, leaving intact nerves in place. Some of the successfully used scaffolds are briefly identified, such as bone scaffolds, cardiac muscle scaffolds, and spinal cord engineering.