Let \(E(G)\) and \(d_x\) denote the edge set and degree of a vertex \(x\) in \(G\), respectively. Recently, the elliptic Sombor index has been defined as \[ESO(G) = \sum_{xy \in E(G)} (d_x + d_y) \sqrt{d_x^2 + d_y^2}\,.\] A molecular tree is a tree in which the maximum degree does not exceed \(4\). In this paper, we establish sharp upper and lower bounds for the \(ESO\) index in the class of molecular trees with order \(n\) and exactly \(k\) vertices of maximum degree \(\Delta \geq 2\). Moreover, we completely characterize the extremal trees attaining these bounds. Our findings contribute to the structural analysis of molecular trees and further the understanding of the elliptic Sombor index in chemical graph theory.

Background:Teledermatology consists of a trained clinical photographer taking a series of digital images of a patient’s skin lesion. The images are remotely reviewed by a dermatologist to decide if additional in-office care is required. Objective: To analyze the scope and patterns of cutaneous cases received through social media websites. Patients and Methods: The research involved male and female patients of all ages—infants, children, and adults—who presented clinical photographs of dermatological lesions through WhatsApp. Results: The clinical information and photographs showed a varied range of dermatological disorders. Conclusion: Social media has revolutionized medical communication significantly, lowering distance-related barriers. All consultations, diagnoses, treatments, and follow-ups were provided for free, as a service to society. Alhamdulillah.

Zaslavsky (1991) characterized all single-element coextensions of graphic matroids in terms of a graphical structure called a biased graph. In this paper we characterize all orientations of a single-element coextension of a graphic matroid in terms of graphically defined orientations of its associated biased graph.

A series of novel 2-methyl-5-[2-(substituted)phenyl]-1,3,4-oxadiazole derivatives (6a–6i) was synthesized via a multi-step protocol starting from commercially available salicylic acid (1). The initial esterification of salicylic acid using thionyl chloride and ethanol at 80 °C for 12 h yielded ethyl 2-hydroxybenzoate (2), which was subsequently converted to 2-hydroxybenzohydrazide (3) upon treatment with hydrazine monohydrate in ethanol at 80 °C for 2 h. Acetylation of intermediate 3 with acetic anhydride afforded N’-acetyl-2-hydroxybenzoate (4), which was reacted with various halo compounds (4a–4i) to produce a series of N’-acetyl-2-(substituted)oxybenzohydrazides (5a–5i). These key intermediates were cyclized using triphenylphosphine, triethylamine, carbon tetrachloride, and acetonitrile at 100 °C for 1 h to furnish the final oxadiazole derivatives (6a–6i). The compounds were purified using appropriate chromatographic techniques and fully characterized by ¹H NMR, ¹³C NMR, FTIR, and mass spectrometry. Biological screening of the synthesized compounds revealed that several derivatives, particularly 6c, 6d, and 6g, exhibited promising antimicrobial and antioxidant activities. Notably, compound 6a demonstrated significant cytotoxicity against HeLa cancer cells. Molecular docking studies further supported the biological potential of the compounds, with 6e displaying a high docking score of –5.66 kcal/mol.

Shea butter is a natural moisturizer used to improve skin health. This study investigates its effects on skin barrier function, hy-dration, and lipid profile, using analytical chemistry methodologies. Trans-Epithelial Water Loss (TEWL), corneometry, im-pedance spectroscopy, and gas chromatography-mass spectrometry (GC-MS) were used to assess skin barrier function, hydra-tion, and lipid profile after shea butter application. Results show that TEWL decreased by 37.8% after 24 hours (p < 0.01), Skin hydration increased by 58% after 24 hours (p< 0.001). Impedance spectroscopy showed a 33% increase in skin imped-ance, GC-MS analysis revealed a balanced fatty acid composition in shea butter, ceramide profiling showed six subclasses, with Ceramide 1 and 2 being the most abundant. The results demonstrate shea butter's efficacy in improving skin barrier func-tion, hydration, and lipid profile. The rapid decrease in TEWL and increase in skin hydration suggest immediate effects on skin lipids. Shea butter's fatty acid composition contributes to its moisturizing and barrier-enhancing properties. This study provides evidence for the benefits of shea butter in maintaining healthy skin. Its natural moisturizing properties make it a valuable in-gredient in skincare products.

Urbanization and soil degradation have placed significant pressure on agricultural sustainability and food security, prompting the exploration of alternatives to soil. The potential of corncob as soilless substrate, an innovative growing media for sustainable urban agriculture, has been preliminary established. Hence, this study investigated the design-related properties of corncob necessary for developing crusher for producing corncob substrate using standard methods. Corncobs from yellow and white corn varieties were used for the study at five moisture levels (9.71, 11.01, 14.29, 17.58 and 21.87% w.b). The results indicate that moisture content rise increased the major axes, angle of repose, surface area and static coefficient of friction. Sphericity decreased for yellow corncob from 0.50 to 0.47 but increased for white corncob from 0.63 to 0.65. Solid and bulk densities decreased: yellow corncob from 0.365 to 0.290 g/cm³ and 0.325 to 0.225 g/cm³, respectively; white corncob from 0.395 to 0.340 g/cm³ and 0.345 to 0.270 g/cm³, respectively. Rupture strengths decreased from 1.12 to 0.80 N/mm² and 1.12 to 0.80 N/mm² for yellow and white corncobs, respectively. Valorization of corncob will create new economic opportunities and give farmers more value for their corn. Hence, this work is pivotal in achieving that with the empirical data provided for developing a corncob crusher for soilless substrate production.

Herein we have discussed various microscopic techniques for analysis of nanomaterials and biomaterials. We have discussed the origin of concept of magnification and resolution. The first attempt of magnification was done with the help of lenses. Thus, we have discussed various types of lenses and their properties. Then after various progress has taken place in the domain of magnification and today we are gifted with advanced microscopes. In this review article we have tried to classify the microscopic techniques into different categories as optical microscopes and acoustic microscopes. Also we have discussed the subtypes of optical microscope like simple microscope, compound microscope, Raman microscope, UV Visible microscope, Dark Field Microscope, Bright Field Microscope etc. Here we have discussed the historical aspects of developments in the microscopic techniques starting from the lens to the advanced Microscopic techniques etc. We have discussed the developmental stage, discovery of each microscope and then we discussed working principle of the instrument, its applications and advantages and limitations too. This review paper is useful for the researchers working in veterinary medicine, microbiology, health sciences, nanoscience and technology etc.