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.     

Strongly Flat and Condition (P) Covers of Acts Over Monoids

In this article we characterize monoids over which every right S-act has a strongly flat (condition (P)) cover. Similar to the perfect monoids, such monoids are characterized by condition (A) and having strongly flat (condition (P)) cover for each cyclic right S-act. We also give a new characterization for perfect monoids as monoids over which every strongly flat right S-act has a projective cover.     

Bessel-type inequalities in Hilbert C *-modules

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules.     

Isolation of beta-glucan from the cell wall of Saccharomyces cerevisiae

Beta-glucan, one of the major cell wall components of Saccharomyces cerevisiae (S. cerevisiae), has been found to enhance immune functions. At present study, we developed an optimal procedure to extract and purify beta-glucan. At first, yeast cells were grown in sabouraud dextrose agar and then cultured in yeast extract-peptone-glucose (YPG) broth. After incubation, cells were harvested, washed and disrupted by means of sonication method. The obtained cell walls were used to prepare alkali-soluble beta-glucan (glucan-S1). In this regard, 2% sodium hydroxide (NaOH) and 3% acetic acid were used in alkaline-acid extraction, respectively. This preparation contained 2.4% protein. In the next step, DEAE sephacel chromatography was used to remove remaining proteins (glucan-S2). Subsequently this preparation was applied into concanavalin-A sepharose column to remove manann. Finally, beta-glucan free of mannoprotein complexes was prepared (glucan-S3).     

Synthesis and Characterization of a Fluorescent Water-Borne Polyurethane Based on a Novel Naphthalimide Dye

A waterborne-polyurethane (WPU) dye, based on the fluorescent dye 4-diamino propane-N-allyl-1,8- naphthalimide (WPU-DAN), was synthesized by attaching 4-diamino propane-N-allyl-1,8- naphthalimide (DAN) onto both ends of the polyurethane (PU) chains according to a prepolymer?ionomer process. The synthetic process was confirmed by Fourier transform infrared spectroscopy (FTIR) and UV-visible absorption. The glass transition temperature, molecular weight and average particle sizes were measured. The glass transition temperatures of WPU and WPU-DAN were 46.6 and 49.8°C, respectively. In addition, the particle size distributions of WPU-DAN and WPU were 140 and 134 nm, respectively. The thermal behaviour of WPU-DAN showed improvement compared to WPU. The fluorescence intensity of WPU-DAN was enhanced more than DAN due to the naphthalimide groups attached to the chains, and the fluorescence intensity of WPU-DAN and DAN were increased by increasing temperature. Moreover, the fluorescence intensity of WPU-DAN emulsion was stable during 30 days and no loss of fluorescence intensity occurred for these days.     

Optimization of ammonium removal from waste water by natural zeolite using central composite design approach

The aims of the present study are to investigate removal of ammonium ion from wastewater using natural Western Azarbaijan zeolite and to optimize effective parameters by experimental design. In order to remove ammonium ions from aqueous solutions, experiments were carried out using column method as functions of the initial ammonium concentration, flow rate and pH of the solution. The results clearly confirmed that all mentioned parameters have vital affects on removing ammonium ions from wastewater and effluents, so got optimized. Central composite design with response surface methodology was applied for the optimization of main experiment parameters. The significance of the independent variables and their interactions were tested by the analysis of variance ANOVA and f-test statistics. Optimization of the variables for maximum removal efficiency by natural zeolite was performed using the quadratic model. The model predicted maximum removal efficiency under the optimum conditions including initial ammonium concentration of 30?mg?l^?1; flow rate of 1?ml?min^?1 and pH 6, which was very close to the experimental value determined in column experiment. The cation exchange capacity of natural Western Azarbaijan zeolite was found to be 1.79?meq?g^?1. Based on the experimental results, it can be concluded that the natural Western Azarbaijan zeolite has an excellent potential for removing ammonium ions from aqueous solutions and it is suggested as a suitable material for wastewater treatment.     

On r-recognition by prime graph of Bp(3) where p is an odd prime

Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p and p′ are joined by an edge if there is an element in G of order pp′. We denote by k(Γ(G)) the number of isomorphism classes of finite groups H satisfying Γ(G) = Γ(H). Given a natural number r, a finite group G is called r-recognizable by prime graph if k(Γ(G)) =  r. In Shen et al. (Sib. Math. J. 51(2):244–254, 2010), it is proved that if p is an odd prime, then B _p (3) is recognizable by element orders. In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(B _p (3)), where p > 3 is an odd prime, then G @ B_p(3){G\cong B_p(3)} or C _p (3). Also if Γ(G) = Γ(B ₃(3)), then G @ B₃(3), C₃(3), D₄(3){G\cong B_3(3), C_3(3), D_4(3)}, or G/O₂(G) @ Aut(²B₂(8)){G/O_2(G)\cong {\rm Aut}(^2B_2(8))}. As a corollary, the main result of the above paper is obtained.     

Affinity of two novel five-coordinated anticancer Pt(II) complexes to human and bovine serum albumins: a spectroscopic approach

The interactions of two organoplatinum complexes, [Pt(C^N)Cl(dppa)], 1, and [Pt(C^N)Cl(dppm)], 2 (C^N = N(1), C(2')-chelated, deprotonated 2-phenylpyridine, dppa = bis(diphenylphosphino)amine, dppm = bis(diphenylphosphino)methane), as antitumor agents, with bovine serum albumin (BSA) and human serum albumin (HSA) have been studied by fluorescence and UV-vis absorption spectroscopic techniques at pH 7.40. The quenching constants and binding parameters (binding constants and number of binding sites) were determined by fluorescence quenching method. The obtained results revealed that there is a strong binding interaction between the ligands and proteins. The calculated thermodynamic parameters (ΔG, ΔH, and ΔS) confirmed that the binding reaction is mainly entropy-driven, and hydrophobic forces played a major role in the reaction. The displacement experiment shows that these Pt complexes can bind to the subdomain IIA (site I) of albumin. Moreover, synchronous fluorescence spectroscopy studies revealed some changes in the local polarity around the tryptophan residues. Finally, the distance, r, between donor (serum albumin) and acceptor (Pt complexes) was obtained according to F?rster theory of nonradiation energy transfer.     

Synthesis of a new smart temperature responsive glycopolymer via click-polymerisation

A novel temperature responsive water-soluble glycopolymer was synthesised via copper wire-catalysed click-polymerisation. Di-hydroxyl terminated poly(ethylene glycol) was quantitatively alkyne end-capped to yield di-alkyne terminated poly(ethylene glycol) (DAT-PEG). 2,3,4,2′,3′,4′-hexa-O-acetyl-6,6′-diazido-6,6′-dideoxy-α,α-D-trehalose (HADADT) was prepared from the di hydrated α,α-D-Trehalose by tosylation/acetylation followed by azidation. Click-polymerisation reaction between DAT-PEG and HADADT was successfully carried out to produce an alternating glycopolymer with triazole rings as linkers in high yield. All the intermediates as well as the glycopolymer were fully characterised by NMR, MS, IR, SEC, TGA and DSC. The cloud point of the aqueous solution of glycopolymer was investigated by optical microscopy and UV–vis spectroscopy. The LCST was found to be within physiological range of about 39 °C, known as fever temperature.