How Tight Is the Bollobás-Komlós Conjecture?

The bipartite case of the Bollobás and Komlós conjecture states that for every j₀, %>0 there is an !=!(j₀, %) >0 such that the following statement holds: If G is any graph with minimum degree at least n$\displaystyle {n \over 2}+%n then G contains as subgraphs all n vertex bipartite graphs, H, satisfying¶H)hj₀ \quad {\rm and} \quad b(H)h!n.$j (H)hj₀ \quad {\rm and} \quad b(H)h!n.¶Here b(H), the bandwidth of H, is the smallest b such that the vertices of H can be ordered as v₁, …, v_n such that v_i~_Hv_j implies |imj|hb.¶ This conjecture has been proved in [1]. Answering a question of E. Szemerédi [6] we show that this conjecture is tight in the sense that as %̂ then !̂. More precisely, we show that for any 0 such that that !(j₀, %)Д %.     

Resveratrol Hinders Postovulatory Aging by Modulating Oxidative Stress in Porcine Oocytes

Postovulatory aging of the mammalian oocytes causes deterioration of oocytes through several factors including oxidative stress. Keeping that in mind, we aimed to investigate the potential of a well-known antioxidant, resveratrol (RV), to evaluate the adverse effects of postovulatory aging in porcine oocytes. After in vitro maturation (IVM), a group of (25–30) oocytes (in three replicates) were exposed to 0, 1, 2, and 4 μmol/L of RV, respectively. The results revealed that the first polar body (PB1) extrusion rate of the oocytes significantly increased when the RV concentration reached up to 2 μmol/L (p < 0.05). Considering optimum RV concentration of 2 μmol/L, the potential of RV was evaluated in oocytes aged for 24 and 48 h. We used fluorescence microscopy to detect the relative level of reactive oxygen species (ROS), while GHS contents were measured through the enzymatic method. Our results revealed that aged groups (24 h and 48 h) treated with RV (2 μmol/L) showed higher (p < 0.05) ROS fluorescence intensity than the control group, but lower (p < 0.05) than untreated aged groups. The GSH content in untreated aged groups (24 h and 48 h) was lower (p < 0.05) than RV-treated groups, but both groups showed higher levels than the control. Similarly, the relative expression of the genes involved in antioxidant activity (CAT, GPXGSH-Px, and SOD1) in RV-treated groups was lower (p < 0.05) as compared to the control group but higher than that of untreated aged groups. Moreover, the relative mRNA expression of caspase-3 and Bax in RV-treated groups was higher (p < 0.05) than the control group but lower than untreated groups. Furthermore, the expression of Bcl-2 in the RV-treated group was significantly lower than control but higher than untreated aged groups. Taken together, our findings revealed that the RV can increase the expression of antioxidant genes by decreasing the level of ROS, and its potent antiapoptotic effects resisted against the decline in mitochondrial membrane potential in aged oocytes.     

Zinc-Based Metal-Organic Frameworks in Drug Delivery,Cell Imaging,and Sensing

The design and structural frameworks for targeted drug delivery of medicinal compounds and improved cell imaging have been developed with several advantages. However, metal-organic frameworks (MOFs) are supplemented tremendously for medical uses with efficient efficacy. These MOFs are considered as an absolutely new class of porous materials, extensively used in drug delivery systems, cell imaging, and detecting the analytes, especially for cancer biomarkers, due to their excellent biocompatibility, easy functionalization, high storage capacity, and excellent biodegradability. While Zn-metal centers in MOFs have been found by enhanced efficient detection and improved drug delivery, these Zn-based MOFs have appeared to be safe as elucidated by different cytotoxicity assays for targeted drug delivery. On the other hand, the MOF-based heterogeneous catalyst is durable and can regenerate multiple times without losing activity. Therefore, as functional carriers for drug delivery, cell imaging, and chemosensory, MOFs’ chemical composition and flexible porous structure allowed engineering to improve their medical formulation and functionality. This review summarizes the methodology for fabricating ultrasensitive and selective Zn-MOF-based sensors, as well as their application in early cancer diagnosis and therapy. This review also offers a systematic approach to understanding the development of MOFs as efficient drug carriers and provides new insights on their applications and limitations in utility with possible solutions.     

Essential Norm of Weighted Composition Operators From $$H^infty $$ H ∞ to nth Weighted Type Spaces

Mediterranean Journal of Mathematics - This work is concerned with the existence and uniqueness of positive solutions to a nonlinear boundary value problem with fractional q-derivative:...     

Synthesis,Crystal Structure and Comparative Study on the Removal of Cationic Dyes Using Different Amide and Amine Groups

Crystallography Reports - Two crystalline materials C18H16N3O3 (1) and C10H8N2⋅C8H7NO4 (2) have been synthesized under solvothermal conditions with different time and temperatures. The...     

Entropy generation in peristalsis with iron oxide

Journal of Thermal Analysis and Calorimetry - High-density polyethylene (HDPE) nanocomposites were prepared by a melting-compounding process with a polymethylsilsesquioxane (PMSQ) as nanofiller. In...     

A new 2D cadmium coordination polymer based on hydroxyl-substituted benzenedicarboxylic acid as an effective heterogeneous catalyst for Knoevenagel condensation

A self-assembled new 2D cadmium network, [Cd (BDC-OH)(DMF)₂·DMF]_n (Cd-BDC-OH), was synthesized based on 2-hydroxyterephthalic acid (BDC-OH) ligand and utilized as a heterogeneous catalyst for Knoevenagel condensation. The structure was fully elucidated by single-crystal X-ray diffraction, Hirshfeld surface analysis, powder X-ray diffraction, field emission-scanning electron microscopy, Fourier transform-infrared spectroscopy and thermogravimetric analysis. The fabricated coordination polymer exhibited high catalytic activity under ambient conditions, and was used without significant drop in product yield in further cycles.     

Liquid–liquid extraction of mercury(II) from aqueous solution using furosemide in benzyl alcohol

Journal of Radioanalytical and Nuclear Chemistry - A simple, efficient and economical liquid–liquid extraction method has been developed for quantitative extraction of mercury(II) from...     

Ziziphora clinopodioides Lam leaves aqueous extract mediated synthesis of zinc nanoparticles and their antibacterial,antifungal, cytotoxicity,antioxidant, and cutaneous wound healing properties under in vitro and in vivo conditions

LamZiziphora clinopodioides Biosynthesis of metal nanoparticles using plant medicine is under exploration is due to wide biomedica applications and research interest in nanotechnology, the recent study was assessing green synthesis of zinc nanoparticle using ), the use of plant material Ziziphoraleaves extract (ZnNPs@ not only makes the process eco‐friendly but also the abundance makes it more economical. Also, in this study, Vis. and– were characterized using different techniques including UVZiziphora were synthesized in aqueous medium using the plant extract as stabilizing and reducing agents. The synthesized ZnNPs@Ziziphora conditions. ZnNPs@in vivo and in vitro under Ziziphorawe investigated the therapeutical properties of ZnNPs@ FT‐IR spectroscopy, . SEM images exhibited a uniform spherical morphology in size of 32.34 Thermal Gravimetric Analysis (TGA)ray diffraction (XRD), scanning electron microscopy (SEM), and Energy Dispersive X‐ray Spectrometry (EDS), and‐X Escherichia coli, and Pseudomonas aeruginosa, Salmonella typhimurium part of this study, these nanoparticles indicated excellent antibacterial properties against Gram‐negative bacteria (in vitronm for the biosynthesized nanoparticles. In the biological , andCandida krusei, Candida albicans, Candida glabrata), antifungal potentials against Bacillus subtilis, andStaphylococcus aureus, Streptococcus pneumoniaO157:H7) and Gram‐positive bacteria ( leaves aqueous extract can be used to yield zinc nanoparticles with a significant amount of antibacterial, antifungal, antioxidant, and cutaneous wound healing properties without any cytotoxicity.Z. clinopodioides ointment ameliorated the cutaneous wounds with increasing the levels of wound contracture, vessel, hydroxyl proline, hexosamine, hexuronic acid, fibrocyte, and fibrocytes/fibroblast rate and decreeing the wound area, total cells, and lymphocyte compared to other groups in rats. The results of UV, FT‐IR, XRD, FE‐SEM, EDS, and TGA confirm that the Ziziphora part of our experiment, ZnNPs@in vivo, non‐cytotoxicity effect against human umbilical vein endothelial cells, and antioxidant activity against DPPH. In the biological Candida guilliermondii     

BF3‐grafted Fe3O4@Sucrose nanoparticles as a highly‐efficient acid catalyst for syntheses of Dihydroquinazolinones (DHQZs) and Bis 3‐Indolyl Methanes (BIMs)

Current paper represents immobilization of sucrose on the Fe₃O₄ core and grafting of boron trifluoride (BF₃) onto the new surface. The catalytic activity of these nanoparticles was tested in syntheses of Dihydroquinazolinones (DHQZs) and Bis (3‐Indolyl) Methanes (BIMs) as two fruitful pharmaceutical structures. Acidic capacity, FT‐IR, XRD, VSM, TGA and SEM–EDX tests are carried out on such novel nanoparticles (NPs). Catalyst has shown more acidic capacity per one gram of NPs than sulfonated homologue which was reported previously.