A result on the sum of element orders of a finite group

Let G be a finite group and $$\psi (G)=\sum _{g\in {G}}{o(g)}$$. There are some results about the relation between $$\psi (G)$$ and the structure of G. For instance, it is proved that if G is a group of order n and $$\psi (G)>\dfrac{211}{1617}\psi (C_n)$$, then G is solvable. Herzog et al. in (J Algebra 511:215–226, 2018) put forward the following conjecture: Conjecture. If G is a non-solvable group of order n, then $$\begin{aligned} {\psi (G)}\,{\le }\,{{\dfrac{211}{1617}}{\psi (C_n)}}, \end{aligned}$$with equality if and only if $$G \cong A_5$$. In particular, this inequality holds for all non-Abelian simple groups. In this paper, we prove a modified version of Herzog’s Conjecture.     

Improving Thompson's Conjecture for Suzuki Groups

Let G be a finite group and cs(G) be the set of conjugacy class sizes of G. In 1987, J. G. Thompson conjectured that, if G is a finite group with Z(G) = 1 and M is a nonabelian simple group satisfying that cs(G) = cs(M), then G ? M. This conjecture has been proved for Suzuki groups in [5 Guiyun, C. (1996). On Thompson's conjecture. J. Algebra 185(1):184–193.[Crossref], [Web of Science ®] , [Google Scholar]]. In this article, we improve this result by proving that, if G is a finite group such that cs(G) = cs(Sz(q)), for q = 2^2m+1, then G ? Sz(q) × A, where A is abelian. We avoid using classification of finite simple groups in our proofs.     

An Upper Bound for the Total Restrained Domination Number of Graphs

Let G be a graph with vertex set V. A set ${D \subseteq V}$ is a total restrained dominating set of G if every vertex in V has a neighbor in D and every vertex in ${V \setminus D}$ has a neighbor in ${V \setminus D}$ . The minimum cardinality of a total restrained dominating set of G is called the total restrained domination number of G, and is denoted by γ _tr (G). In this paper, we prove that if G is a connected graph of order n ≥ 4 and minimum degree at least two, then ${\gamma_{tr}(G) \leq n-\sqrt[3]{n \over 4}}$ .     

Solid-phase Extraction and High Performance Liquid Chromatographic Determination of Folic Acid in Fortified Foodstuffs: a Recommended Process Utilizing a New Strong Anion Exchange Sorbent

Journal of Analytical Chemistry - A highly efficient solid-phase extraction (SPE) column filled with a silica-based strong anion exchange sorbent was reported in the current study. The fabricated...     

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Pd-PEPPSI type complexes are widely used as precatalyst in a variety of organic reactions, including the Negishi, Kumada and Suzuki-Miyaura cross-coupling reactions. The aim of this research is to determine potential proposed reaction pathways 1, 2, or 2′ (See Schemes 1 and S1–S4 ) for Pd-PEPPSI precatalyst activation in the presence of ethylene glycol as a solvent also in the gas phase at Cam-B3LYP-D3 method nominated among eight DFT methods examined. There is also investigation into the impact of promoter bases (NaOEt, NaOⁱPr, NaO^tBu) on precatalyst activation of Pd-PEPPSI. Eventually, the most favorable proposed reaction pathway and promoter base for reducing Pd(II) to Pd(0) are predicted computationally. Notably, our findings are consistent with the organ Pd-PEPPSI type complexes that offer increased catalytic activity and provide basic information in the presence of solvents designing the monoligated Pd(0)-solvent.     

Enhanced Heterotrophic Denitrification: Effect of Dairy Industry Sludge Acclimatization and Operating Conditions

Heterotrophic denitrification of drinking water was enhanced by selection of an anoxic sludge taken from a dairy industry among the sludges taken from various industries, and the effect of carbon sources was examined. Acclimatization to high nitrate concentration was then carried out in a five-stage process. Considering removals of both nitrate and nitrite, the sludge taken from anoxic unit of Tehran Pegah dairy industry was shown to be the superior microbial culture, with ethanol as carbon source as compared to acetate. To enhance the rate of denitrification, acclimatization to nitrate (at 100, 200, 400, 800, and 1,600 mg N-NO₃/L) was carried out in sequencing batch reactors over a 3-month period under anoxic condition, and comparisons were made between the performances of acclimated and non-acclimated sludges at each stage. It was found that acclimatization up to the fourth stage enhanced the specific denitrification rate to a high value of 29.6 mg N-NO₃/h/g mixed liquor suspended solids (MLSS), with no significant nitrite accumulation. Additionally, the effect of initial pH (6, 6.5, 7, and 7.5) and carbon-to-nitrogen (C/N) ratio (1, 1.5, 2, and 3) on the performance of this final acclimated sludge was assessed, where initial pH of 7 and C/N ratio of 1.5 resulted in the best performances considering both nitrate and nitrite removal.     

Green synthesis and chemical characterization of Thymus vulgaris leaf aqueous extract conjugated gold nanoparticles for the treatment of acute myeloid leukemia in comparison to doxorubicin in a leukemic mouse model

Recently, metallic nanoparticles have been used for the treatment of several disorders, such as cancer. Indeed, finding the chemotherapeutic drug of nanoparticles is in researching the priority of both developed and developing countries. The present study confirms the ability of aqueous extract of Thymus vulgaris grown under in vitro condition for the biosynthesis of gold nanoparticles (AuNPs). Also, in this study, we indicated the antioxidant, cytotoxicity, and anti-acute myeloid leukemia properties of AuNPs compared to doxorubicin in a leukemic mouse model. The synthesized AuNPs were characterized using different techniques including X-ray diffraction (XRD), energy Dispersive X-ray Spectrometry (EDS), fourier-transform infrared spectroscopy (FT-IR) spectroscopy, ultraviolet–visible spectroscopy (UV–Vis.), transmission electron microscopy (TEM), and scanning electron microscopy (SEM). In vivo design, induction of acute myeloid leukemia was done by 7,12-Dimethylbenz[a]anthracene (DMBA) in 75 mice. Then, the animals were randomly divided into six subgroups, including control, untreated, doxorubicin, AuNPs, T. vulgaris, and HAuCl₄. By quantitative real-time PCR, sphingosine-1-phosphate receptor-1 and sphingosine-1-phosphate receptor-5 mRNA expression in lymphocytes were significantly (P ≤ 0.01) raised by treating the leukemic mice with the AuNPs and doxorubicin. Also, AuNPs similar to doxorubicin, significantly (P ≤ 0.01) enhanced the anti-inflammatory cytokines (IL4, IL5, IL10, IL13, and IFNα) and the platelet, lymphocyte, and red blood cell (RBC) parameters and reduced the pro-inflammatory cytokines (IL1, IL6, IL12, IL18, IFNY, and TNFα), and the total white blood cell (WBC), blast, monocyte, neutrophil, eosinophil, and basophil counts as compared to the untreated mice. In vitro design, 2,2-diphenyl-1-picrylhydrazyl (DPPH) test revealed similar antioxidant potentials for doxorubicin and AuNPs. Furthermore, AuNPs similar to doxorubicin had low cell viability dose-dependently against 32D-FLT3-ITD, Human HL-60/vcr, and Murine C1498 cell lines without any cytotoxicity on HUVEC cell line. Above results confirm the excellent antioxidant, cytotoxicity, and anti-acute myeloid leukemia effects of AuNPs compared to doxorubicin. After confirming these results in clinical trial studies, AuNPs can be used as a chemotherapeutic drug for the treatment of acute myeloid leukemia in human.     

Zeolite nanoparticles (H-ZSM5) as a highly efficient,green, and reusable heterogeneous catalyst for selective oxidation of sulfides to sulfoxides under mild conditions

H-ZSM5 is applied as an efficient, highly reusable, and heterogeneous catalyst for the oxidation of sulfides to sulfoxides using 30% H₂O₂ under solvent-free conditions at room temperature. A variety of aromatic and aliphatic sulfides with different functional groups were successfully oxidized with good to excellent yields in short reaction times. The catalyst can be easily recovered by simple filtration and recycled for several consecutive runs without any significant loss of its catalytic activity.     

Kiwifruit Actinidin: A Proper New Collagenase for Isolation of Cells from Different Tissues

Actinidin is a cysteine protease abundant in Kiwifruit. This enzyme is known as a meat-tenderizing protease. In this project, actinidin was purified from kiwifruit by salt precipitation and ion exchange chromatography. Collagenolytic effect of the purified enzyme was tested in four different buffer systems. Thereafter, the enzyme was used for isolation and culture of cells from three different tissues: endothelial cells from human umbilical vein, hepatocytes from rat liver, and thymic epithelial cells from rat thymus. Our results revealed that actinidin can hydrolyze collagen types I and II at neutral and alkaline buffers. Furthermore, actinidin compared with type II or IV collagenase isolated intact human umbilical vein endothelial cells, hepatocytes, and thymic epithelial cells with viability more than 90%. These results address a novel and valuable collagenase, which can be used efficiently for hydrolysis of collagen and isolation of different cell populations from various solid tissues.