Some Skew Linear Groups Satisfying Generalized Group Identities

In this article, we consider a type of generalized group identity and extend some earlier results. For example, we show that, if D is a division ring with infinite center, then every subnormal subgroup of GL_n(D) satisfying a generalized group identity over GL_n(D) is central.     

On the limitations of linear beams for the problems of moving mass-beam interaction using a meshfree method

This paper deals with the capabilities of linear and nonlinear beam theories in predicting the dynamic response of an elastically supported thin beam traversed by a moving mass. To this end, the discrete equations of motion are developed based on Lagrange’s equations via reproducing kernel particle method (RKPM). For a particular case of a simply supported beam, Galerkin method is also employed to verify the results obtained by RKPM, and a reasonably good agreement is achieved. Variations of the maximum dynamic deflection and bending moment associated with the linear and nonlinear beam theories are investigated in terms of moving mass weight and velocity for various beam boundary conditions. It is demonstrated that for majority of the moving mass velocities, the differences between the results of linear and nonlinear analyses become remarkable as the moving mass weight increases, particularly for high levels of moving mass velocity. Except for the cantilever beam, the nonlinear beam theory predicts higher possibility of moving mass separation from the base beam compared to the linear one. Furthermore, the accuracy levels of the linear beam theory are determined for thin beams under large deflections and small rotations as a function of moving mass weight and velocity in various boundary conditions.     

Prediction capabilities of classical and shear deformable beam models excited by a moving mass

In this paper, a comprehensive assessment of design parameters for various beam theories subjected to a moving mass is investigated under different boundary conditions. The design parameters are adopted as the maximum dynamic deflection and bending moment of the beam. To this end, discrete equations of motion for classical Euler-Bernoulli, Timoshenko and higher-order beams under a moving mass are derived based on Hamilton's principle. The reproducing kernel particle method (RKPM) and extended Newmark-β method are utilized for spatial and time discretization of the problem, correspondingly. The design parameter spectra in terms of the beam slenderness, mass weight and velocity of the moving mass are introduced for the mentioned beam theories as well as various boundary conditions. The results indicate the existence of a critical beam slenderness mostly as a function of beam boundary condition, in which, for slenderness lower than this so-called critical one, the application of Euler-Bernoulli or even Timoshenko beam theories would underestimate the real dynamic response of the system. Moreover, there would be a roughly linear relation between the weight of the moving mass and the design parameters for a certain value of the moving mass velocity in most cases of boundary conditions.     

On incidence energy of a graph

The Laplacian-energy like invariant LEL(G) and the incidence energy IE(G) of a graph are recently proposed quantities, equal, respectively, to the sum of the square roots of the Laplacian eigenvalues, and the sum of the singular values of the incidence matrix of the graph G. However, IE(G) is closely related with the eigenvalues of the Laplacian and signless Laplacian matrices of G. For bipartite graphs, IE=LEL. We now point out some further relations for IE and LEL: IE can be expressed in terms of eigenvalues of the line graph, whereas LEL in terms of singular values of the incidence matrix of a directed graph. Several lower and upper bounds for IE are obtained, including those that pertain to the line graph of G. In addition, Nordhaus-Gaddum-type results for IE are established.     

Synthesis and characterization of a tetramethyl furanone functionalized diiminedioxime,a potential ligand for Cu radiopharmaceuticals,and its copper(II) and nickel(II) complexes

As part of our on-going effort to develop ⁶⁴Cu-based radiopharmaceuticals for PET (positron emission tomography) imaging of multidrug resistance in cancer, we prepared a tetramethylfuranone-functionalized diiminedioxime ligand, TMFPreH (TMFPreH = 4-[3-(4-hydroxyimino-2,2,5,5-dimethyl-dihydro-furan-3-ylideneamino)-propylimino]-2,2,5,5-tetramethyl-dihydrofuran-3(2H)-one oxime) and its Cu(II) and Ni(II) complexes. When the copper(II) complex was prepared from Cu(ClO₄)₂ in ethanol, it was isolated as a Cu(II)-bridged dimer, but when it was prepared from Cu(OAc)₂ and heated in acetone, an unusual example of an acetone adduct of the ligand is formed by reduction of one of the imine double bonds by the solvent. The Ni(II) complex is square pyramidal with the perchlorate counterion at the apex.     

Stress analysis of thermally affected rotating nanoshafts with varying material properties

Based on the surface elasticity theory of Gurtin-Murdoch, thermo-elastic fields within rotating nanoshafts with varying material properties subjected to a thermal field are explicitly examined. Accounting for the surface energy effect, the nonclassical boundary conditions are enforced in the cases of fixed-free and free-free conditions. The effects of variation of material properties, temperature of the envi-ronment, angular velocity, and radius of the outer radius on the radial displacement, hoop and radial stresses are investi-gated. In all performed studies, the role of the surface effect on the thermo-elastic field of the nanostructure is methodi-cally discussed.     

Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories

Dynamic analysis of nanotube structures under excitation of a moving nanoparticle is carried out using nonlocal continuum theory of Eringen. To this end, the nanotube structure is modeled by an equivalent continuum structure (ECS) according to the nonlocal Euler-Bernoulli, Timoshenko and higher order beam theories. The nondimensional equations of motion of the nonlocal beams acted upon by a moving nanoparticle are then established. Analytical solutions of the problem are presented for simply supported boundary conditions. The explicit expressions of the critical velocities of the nonlocal beams are derived. Furthermore, the capabilities of various nonlocal beam models in predicting the dynamic deflection of the ECS are examined through various numerical simulations. The role of the scale effect parameter, the slenderness ratio of the ECS and velocity of the moving nanoparticle on the time history of deflection as well as the dynamic amplitude factor of the nonlocal beams are scrutinized in some detail. The results show the importance of using nonlocal shear deformable beam theories, particularly for very stocky nanotube structures acted upon by a moving nanoparticle with low velocity.     

Determination of 4‐Nitrobenzaldehyde in Water Samples by Combination of Switchable Solvent Based Microextraction and Electrochemical Detection on MWCNTs Modified Electrode

A novel approach is presented to determine 4‐nitrobenzaldehyde in water samples. The procedure is based on switchable solvent based liquid‐liquid microextraction (SS‐LLME) and then determination by differential pulse voltammetry at multi‐walled carbon nanotubes modified glassy carbon electrode. Dipropylamine, a solvent with switchable polarity, was used as an extraction solvent that can be miscible/immiscible upon the changes of pH of sample solution. Effects of experimental conditions on SS‐LLME were investigated using a one‐factor‐at‐a‐time methodology. Under optimized conditions, a calibration curve was linear in the concentration range of 1.0 and 350 μg L^?1. Limits of quantification and detection were empirically 1.0 μg L^?1 and 0.3 μg L^?1, respectively. Intraday and Interday RSDs%, calculated in three concentration levels, were in the range of 6.2–7.8 % confirm the proper precision of the method. Finally, the performance of the method was evaluated successfully in real samples including drinking water, tap water and river water.     

Structural increment system for 11-vertex nido-boranes and carboranes

An increment system forming a set of quantitative rules that govern the relative stabilities of 11-vertex nido-boranes and carboranes is presented. Density functional theory computations at the B3LYP/6-311+G//B3LYP/6-31G level with ZPE corrections were carried out for 61 different boron hydride and carborane structures from [B(11)H(14)](-) to C(4)B(7)H(11) to determine their relative stabilities. Disfavored structural features that destabilize a cluster structure relative to a hypothetical ideal situation were identified and weighted by so-called energy penalties. The latter show additive behavior and allow us to reproduce (within 5 kcal mol(-)(1)) the DFT computed relative energies. Energy penalties for four structural features, i.e., adjacent carbon atoms, CC, a hydrogen atom bridging between a carbon and a boron atom, CH-B, an endo-terminal hydrogen atom at an open face carbon atom, CH(2) and an endo-H between two carbon atoms, C(BH(2))C for the 11-vertex nido-cluster are quite similar to those reported for the 6-vertex nido-cluster, thus showing a behavior independent of the cluster size. Hydrogen structural features, however, vary strongly with the cluster size. Two unknown 11-vertex nido-carboranes were identified which are thermodynamically more stable than known positional isomers.     

Stability of a family of multi-time-level difference schemes for the advection equation

Summary For the linear advection equation we consider explicit multi-time-level schemes of highest order which are one step in space direction only. If a stencil involvesk time steps we show that it is stable in theL ₂-sense for Courant numbers in the interval (0, 1/k). Since the order is 2k–1 one can use these schemes for high order discretization of the boundary conditions in hyperbolic initial value problems.Part of this work has been performed in the project Mehrschritt-Differenzenschemata of the Schwerpunktprogramm Finite Approximationen in der Strömungsmechanik which has been supported by the DFG