Some Extensions of PSL(2, p 2) are Uniquely Determined by Their Complex Group Algebras

In Tong-Viet's, 2012 work, the following question arose: Question. Which groups can be uniquely determined by the structure of their complex group algebras?

It is proved here that some simple groups of Lie type are determined by the structure of their complex group algebras. Let p be an odd prime number and S = PSL(2, p ²). In this paper, we prove that, if M is a finite group such that S < M < Aut(S), M = ?₂ × PSL(2, p ²) or M = SL(2, p ²), then M is uniquely determined by its order and some information about its character degrees. Let X ₁(G) be the set of all irreducible complex character degrees of G counting multiplicities. As a consequence of our results, we prove that, if G is a finite group such that X ₁(G) = X ₁(M), then G ? M. This implies that M is uniquely determined by the structure of its complex group algebra.     

Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects

The potential application of SWCNTs as mass nanosensors is examined for a wide range of boundary conditions. The SWCNT is modeled via nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The added nano-objects are considered as rigid solids, which are attached to the SWCNT. The mass weight and rotary inertial effects of such nanoparticles are appropriately incorporated into the nonlocal equations of motion of each model. The discrete governing equation pertinent to each model is obtained using an effective meshless technique. The key factor in design of a mass nanosensor is to determine the amount of frequency shift due to the added nanoparticles. Through an inclusive parametric study, the roles of slenderness ratio of the SWCNT, small-scale parameter, mass weight, number of the attached nanoparticles, and the boundary conditions of the SWCNT on the frequency shift ratio of the first flexural vibration mode of the SWCNT as a mass sensor are also discussed.     

Synthesis of Hexahydrospiro[pyrazolo[3,4‐b]quinoline‐4,1′‐pyrrolo[3,2,1‐ij]quinoline‐2′,5(1H,4′H)‐diones] from 5,6‐dihydro‐4H‐pyrrolo[3,2,1‐ij]quinoline‐1,2‐dione Using Fe3O4@Cu(OH)x as a Nanocatalyst

The tricyclic isatin, 5,6‐dihydro‐4H‐pyrrolo[3,2,1‐ij]quinoline‐1,2‐dione, undergoes three‐component, one‐pot reactions with 1‐aryl‐3‐methylpyrazole‐5‐amines and cyclohexane‐1,3‐diones producing hexacyclic spiro products, hexahydrospiro[pyrazolo[3,4‐b]quinoline‐4,1‐pyrrolo[3,2,1‐ij]quinoline‐2′,5(1H,4′H)‐diones]. Comparable spiro condensation products are also obtained using 4‐hydroxy‐2H‐1‐benzopyran‐2‐one in place of cyclohexane‐1,3‐diones.     

Evaluation of new 99mTc-labeled HYNIC-bombesin analogue for prostate cancer imaging

Journal of Radioanalytical and Nuclear Chemistry - In this study, we introduce a new 99mTc-radiolabeled bombesin derivative for imaging of prostate cancer (PC). We used 6-hydrazinonicotinamide...     

A basic family of iteration functions for polynomial root finding and its characterizations

Let p(x) be a polynomial of degree n?2 with coefficients in a subfield K of the complex numbers. For each natural number m?2, let L_m(x) be the m×m lower triangular matrix whose diagonal entries are p(x) and for each j=1,…,m−1, its jth subdiagonal entries are . For i=1,2, let L_m^i)(x) be the matrix obtained from L_m(x) by deleting its first i rows and its last i columns. L₁⁽¹⁾(x)≡1. Then, the function B_m(x)=x−p(x) defines a fixed-point iteration function having mth order convergence rate for simple roots of p(x). For m=2 and 3, B_m(x) coincides with Newton's and Halley's, respectively. The function B_m(x) is a member of S(m,m+n−2), where for any M?m, S(m,M) is the set of all rational iteration functions g(x) ∈ K(x) such that for all roots θ of p(x), then g(x)=θ+∑_i=m^Mγ_i(x)(θ−x)ⁱ, with γ_i(x) ∈ K(x) and well-defined at any simple root θ. Given g ∈ S(m,M), and a simple root θ of p(x), gⁱ(θ)=0, i=1, …, m−1 and the asymptotic constant of convergence of the corresponding fixed-point iteration is . For B_m(x) we obtain . If all roots of p(x) are simple, B_m(x) is the unique member of S(m,m + n − 2). By making use of the identity , we arrive at two recursive formulas for constructing iteration functions within the S(m,M) family. In particular, the family of B_m(x) can be generated using one of these formulas. Moreover, the other formula gives a simple scheme for constructing a family of iteration functions credited to Euler as well as Schröder, whose mth order member belongs to S(m,mn), m>2. The iteration functions within S(m,M) can be extended to any arbitrary smooth function f, with the uniform replacement of p^(j) with f^(j) in g as well as in γ_m(θ).     

Theoretical study of N–H· · ·O hydrogen bonding properties and cooperativity effects in linear acetamide clusters

We investigated geometry, energy, ${\nu_{{\text{N--H}}}}$ harmonic frequencies, ¹⁴N nuclear quadrupole coupling tensors, and ${n_{\rm O}\to \sigma _{{\text{N--H}}}^\ast}$ charge transfer properties of (acetamide) _n clusters, with n = 1 ? 7, by means of second-order Møller-Plesset perturbation theory (MP2) and DFT method. Dependency of dimer stabilization energies and equilibrium geometries on various levels of theory was examined. B3LYP/6-311++G** calculations revealed that for acetamide clusters, the average hydrogen-bonding energy per monomer increases from ?26.85 kJ mol^?1 in dimer to ?35.12 kJ mol^?1 in heptamer; i.e., 31% cooperativity enhancement. The n-dependent trend of ${\nu_{{\text{N--H}}}\,{and}\,^{14}}$ N nuclear quadrupole coupling values were reasonably correlated with cooperative effects in ${r_{{\text{N--H}}}}$ bond distance. It was also found that intermolecular ${n_{\rm O}\to \sigma_{{\text{N--H}}}^\ast}$ charge transfer plays a key role in cooperative changes of geometry, binding energy, ${\nu_{{\text{N--H}}}}$ harmonic frequencies, and ¹⁴N electric field gradient tensors of acetamide clusters. There is a good linear correlation between ¹⁴N quadrupole coupling constants, C _Q (¹⁴N), and the strength of Fock matrix elements (F _ij ). Regarding the ${n_{\rm O}\to \sigma_{{\text{N--H}}}^\ast}$ interaction, the capability of the acetamide clusters for electron localization, at the N–H· · ·O bond critical point, depends on the cluster size and thereby leads to cooperative changes in the N–H· · ·O length and strength, N–H stretching frequencies, and ¹⁴N quadrupole coupling tensors.     

Highly efficient synthesis of 3-pyrrolyl-indolinones and pyrrolyl-indeno[1,2-b]quinoxalines catalyzed by heteropolyacids

Simple and improved conditions have been found for the synthesis of 3-pyrrolyl-indolinones and pyrrolyl-indeno[1,2-b]quinoxalines by coupling of 4-hydroxyproline with isatins and 11H-indeno[1,2-b]quinoxalin-11-ones using Keggin (H₃PW₁₂O₄₀) and Well-Dawson tungsten heteropolyacids (H₆P₂W₁₈O₆₂).     

PCR-based Gene Synthesis,Molecular Cloning,High Level Expression,Purification, and Characterization of Novel Antimicrobial Peptide,Brevinin-2R,in <Emphasis Type="Italic">Escherichia Coli</Emphasis>

Brevinin-2R, a member of a new family of antimicrobial peptides isolated from the skin of Rana ridibunda, displays antimicrobial activity against bacteria and fungi. In this study, we have used an assembly PCR method for the fast and extremely accurate synthesis of the brevinin-2R gene. A total of six primers were assembled in a single step PCR, and the assembly was then amplified by PCR to produce the final gene. The synthetic gene was cloned into the pET32a (+) vector to allow the expression of brevinin-2R as a Trx fusion protein in Escherichia coli. The results indicated that the expression level of the fusion protein could reach up to 25% of the total cell proteins. The expression products could be easily purified by Ni-NTA chromatography and released from the fusion protein by factor Xa protease. The peptide displayed antimicrobial activity similar to that of the purified brevinin that was reported earlier. This method allows the fast synthesis of a gene that optimized the overexpression in the E. coli system and production of sufficiently large amounts of peptide for functional and structural characterizations.     

Development of a Henry’s constant correlation and solubility measurements of n-pentane,i-pentane,cyclopentane, n-hexane,and toluene in water

In this communication, we report new experimental data on n-pentane, i-pentane, cyclopentane, n-hexane, and toluene solubility in water at low temperature (below 298.15 K) and atmospheric pressure conditions. The new experimental data together with those reported in the literature have been used in developing a new equation for Henry’s constants of normal alkanes (methane to decane), BETEX compounds, and acid gases in aqueous phase over a wide range of temperature (typically from 273.15 K to 373.15 K). The new equation is based on a thermodynamic model, which uses the Peng–Robinson equation of state combined with the classical quadratic mixing rules for modelling non-aqueous phases, while the NRTL model is used to calculate the water activity.The predictions of the developed thermodynamic model are compared to the experimental data and the results of a thermodynamic approach, which uses the Valderrama modification of the Patel–Teja equation of state and non-density dependent mixing rules for modelling all fluid phases. Good agreement is observed between the experimental data and the model predictions.