JOURNAL OF EDUCATION AND SCIENCE

This paper extends the classification of three-dimensional connected topological proper loops , for which the multiplication group is a six-dimensional decomposable solvable Lie group. Building upon the significant results presented in [1], which established class two central nilpotency for these loops, we derive explicit matrix representations for the associated Lie algebras. These representations are critical for completing the classification, as they facilitate verification of structural compatibility with the conditions dictated by the Lie bracket. We identify distinct families of matrix Lie groups, including groups characterized by one-dimensional centers and groups with two-dimensional centers. Additionally, we clarify the correspondence between these groups and their derived Lie algebras. Our findings address an existing gap in the literature by providing a systematic framework for examining the interrelationships between topological loops and their corresponding Lie groups.

When a specific method is chosen for a solution, representing or encoding a mathematical model, others seek to make this method ambiguous through what we can call (multiple encoding) to conceal the solution and make it more secret. This is exactly what we did in this research, as we placed a special movement exclusively on the columns of the first main e-abacus diagram, which we called ( ) on the condition that the first and last columns of the original diagram are not affected at all, due to our actual need for them in representing the diagram later. In addition, the mechanism was implemented in the form of a graph, and a computer program was also created to solve the problem more quickly. It is expected that the application of this technology will have industrial potential aimed at improving production in terms of quality and quantity.

A detailed study was conducted on various specimens of Alcea and Althaea, including Althaea hirsuta, Althaea ludwigii, Althaea officinalis, and Alcea kurdica, Alcea rosa cultivars (white, pink, violet, and red hollyhocks, depending on the flower color. Each specimen exhibited distinct morphological characteristics in petiole structure, midrib anatomy, leaf border features, and epidermal cell patterns. Trichome Diversity and Leaf Anatomy. The specimens displayed a variety of trichomes, including non-glandular (unicellular and multicellular), glandular (capitate and short-stalked), and peltate types. Additionally, druse crystals were observed in the petiole and midrib of all specimens, suggesting a possible role in structural support or defense mechanisms. Epidermal Cell and Stomatal Characteristics. The anticlinal walls of the epidermal cells varied from straight to undulate, with polygonal cell morphologies dominating across all samples. Stomatal analysis revealed the presence of paracytic and anisocytic types on both abaxial and adaxial leaf surfaces, with some instances of conjugate stomata, indicating adaptations to different environmental conditions. Variations among Cultivars and Wild Species. The Alcea rosa cultivars exhibited subtle differences in trichome density and leaf margin structure compared to wild species like Alcea kurdica and Althaea spp., which had more pronounced midrib shapes and petiole cross-sections. These morphological distinctions could be useful for taxonomic identification and understanding ecological adaptations. This study highlights the structural diversity within Alcea and Althaea, providing insights into their classification and potential functional adaptations.

This study applies k-means clustering to group countries based on key economic and health indicators: Gross National Income per capita (GNIP), health expenditure, life expectancy, birth and death rates, and urbanization. The elbow method identified k = 3 as the optimal number of clusters, indicating a significant drop in within-cluster sum of squares (from 5000 to 2000). The results reveal three distinct development groupings. A small cluster of 13 high-performing countries stands out with strong economic (GNIP = 0.658) and health outcomes (Life Expectancy = 0.856), along with low birth (0.116) and death rates (0.113). This group also shows strong internal similarity (silhouette width = 0.58). The remaining countries fall into two broader clusters. The first includes 320 countries with moderate development, higher urbanization (UrbanP = 0.712), and relatively high health spending (healthE = 0.219), but lower GNIP (0.066). The second cluster of 277 countries faces greater challenges, marked by low life expectancy (0.414), high birth rates (0.670), and weak economic indicators (GNIP = 0.067). Both larger clusters show moderate cohesion (silhouette widths = 0.29 and 0.32). These findings highlight the stratified and multidimensional nature of global development, offering a data-driven framework to inform policy decisions and tailor interventions to the unique characteristics of each cluster.

The present study focused on the wastewater from three hospitals in Erbil: Hawler Teaching Hospital, Rezgary Teaching Hospital, and Rozhawa Emergency Hospital. Wastewater samples were collected monthly (December 2024 to February 2025) for some parameters related to water quality, fungal counts, and detections. The study aims to determine the risk of hospital wastewater in terms of contaminated disposal water and to investigate the types of fungi present in it. The results showed that wastewater was characterized by neutral to slightly alkaline. Electrical conductivity (EC) and biochemical oxygen demand (BOD5) values were high and exceeded local and international discharge guidelines. Related to nutrient content, both phosphate (PO4) and nitrate (NO3) were high in all sampling sites. A total of 13 fungal genera were identified, suggesting that hospital wastewater provides a conducive environment for fungal growth. The highest number of fungi and the most isolates were detected at Razgary Teaching Hospital, where 8300 (CFU/mL-1) and 16 species of fungi were identified out of a total of 19 species, coinciding with the highest temperature and lowest phosphate concentration compared to other hospitals. The most common fungal species detected in all studied hospitals were: Aspergillus niger, Candida albicans, Geotrichum candidum, Mucor sp., and Penicillium sp. The results highlighted that the risk of polluted hospital wastewater poses a threat to both public health and the environment. Therefore, it is necessary to build sewage treatment units and monitor the quality of the discharged water.

Many factors could impact spermatogenesis. The influence of silymarin on some sexual efficiency, Sertoli cell, Leydig cell, and Johnsen's score alterations in male quails exposed to thermal stress has been studied. Quail were placed into four groups of ten birds each: 1st group control, 2nd group heat-related stress at 42±2 ºC for 4 hours daily, 3rd group heat-related stress at 42±2 ºC for 4 hours daily with 200 mg/kg of silymarin orally. The 4th group received 200 mg/kg of silymarin orally. The heat-related stress group's results indicate a notable drop in sperm count and the percentage of viable sperm, testosterone hormone, luteinizing hormone, glutathione level, foam gland weight, diameter of seminiferous tubules, Sertoli cell, Leydig cell, and Johnsen's score and a rise in dead sperm percentage, abnormal sperm percentage, and MDA level relative to control values. Heat stress with the silymarin group existing a notable rise in sperm count, testosterone hormone, foam gland weight, glutathione level, diameter of seminiferous tubules, Sertoli cells, Leydig cells, and Johnsen's score and a decrease in MDA level compared with the heat stress group, the silymarin group displayed a notable rise in testosterone hormone and glutathione level versus the control group. This study concluded that silymarin has beneficial effects on male quail infertility due to heat stress.

In this study, we examine the high-pressure energy bandgap of several photocatalyst semiconductors (ZnO, MgO, CdO, WO3, CaO, SnO2, In2O3, ZrO2, ZnS, and TiO2) by applying the Angilella equation. This equation helps analyze the change in energy gap with pressure, relative to the variation in lattice constant. The Murnaghan equation of state (EOS) was used to calculate the pressure. The validity of the Angillela equation is confirmed only for cubic ZnO, wurtzite MgO, and rock salt CdO, but for other semiconductors(WO3, CaO, SnO2, In2O3, ZrO2, ZnS, and TiO2), it is found that the Angillela equation is not valid precisely. Our results indicate that the energy gap of these photocatalyst semiconductors behaves similarly to that of other semiconductors under high pressure, with an increase in energy gap as pressure rises. Additionally, our results reveal that the lattice constant decreases as pressure is applied for all photacatalyst semiconductors used in this work.

The most common modifiable cardiovascular disease (CVD) risk element is hypertension, and CVD has a wide variety of conditions that include coronary artery disease, heart failure, cerebrovascular accidents, myocardial infarction, atrial fibrillation and peripheral arterial disease, among chronic kidney disease or CKD and cognitive impairment. Hypertension is the leading cause of death and disability worldwide. This cross-sectional research carried out in Ramadi, Iraq, assessed 50 cases of hypertension and 25 healthy individuals to determine the demographic trends, biochemical indicators, and cardiovascular risk factors. The prevalence of hypertension was diagnosed higher in women (68%) than in men (32%), and most common in the age category of 50 60 (56%), as compared to the regional trends of ageing. There was a high hereditary connection whereby 68 per cent of the patients claimed a family history of hypertension. Blood pressure measures showed that systolic pressure (16.72 ± 1.70 mmHg vs. 11.50± 0.65 mmHg) and diastolic pressure (9.89± 1.15 mmHg vs. 7.68± 0.61 mmHg) highly increased in the patients compared with experiences of controls (P < 0.0001). Biochemical studies have revealed an increased amount of uric acid in hypertensive patients (5.28 ± 1.35 mg/dL vs. 3.94 ± 0.52 mg/dL) but not of urea. The results highlight how genetic, metabolic, and lifestyle influencing factors are interconnected in causing hypertension in western Iraq and the importance of monitoring uric acid levels, controlling lipids, and the need to have targeted community health promotion programs to aid in reducing cardiovascular risks.

The presence of a drive site within ligand structures plays a crucial role in enhancing their interaction with metal ions, resulting in highly efficient complex formation research. A new ligand, 2-(3-(4-nitrobenzoyl) thioureido) benzoic acid (NTB), was successfully synthesized via the reaction of 4-nitrobenzoyl isothiocyanate with anthranilic acid in a 1:1 molar ratio. The structure of the ligand was confirmed using elemental analysis, FT-IR, UV-Vis., and ¹H and ¹³C NMR spectroscopy. Then a series of metal complexes was synthesized by reacting NTB with divalent metal ions, including Hg²⁺, Cd²⁺, Zn²⁺, Cu²⁺, Ni²⁺, Co²⁺, and Mn2+. The analytical results suggest that all metal complexes adopt a tetrahedral geometry, except for the copper complex, which exhibits a square planar structure. The metal-to-ligand ratio in all complexes was determined to be 1:2, supporting the proposed [M(NTB)₂] formulation.