On a graph of ideals

We associate a graph Γ₊(R) to a ring R whose vertices are nonzero proper right ideals of R and two vertices I and J are adjacent if I+J=R. Then we try to translate properties of this graph into algebraic properties of R and vice versa. For example, we characterize rings R for which Γ₊(R) respectively is connected, complete, planar, complemented or a forest. Also we find the dominating number of Γ₊(R).     

Accurate free vibration analysis of thick laminated circular plates with attached rigid core

This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin's first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis.     

Exohedral chemical functionalization of C48B6N6 with NH3: Binding energies and electronic structures of C48B6N6–(NH3)n=1−6

Theoretical study of exohedral chemical functionalization of C₄₈B₆N₆ with NH₃ molecules has been investigated using DFT. It was found that NH₃ molecule can be chemically adsorbed on boron sites of C₄₈B₆N₆, with a charge transfer from NH₃ to C₄₈B₆N₆. Adsorption energy and the quantity of electron charge transfer from latest adsorbed ammonia to C₄₈B₆N₆ decreased with increasing in the adsorbed NH₃ molecules. Despite the strong adsorption energies, electronic properties of C₄₈B₆N₆ is preserved after modification(s) with NH₃ molecule(s) and chemical modification of C₄₈B₆N₆ with NH₃ molecules can be viewed as some kind of safe modification.     

DFT-NEGF study of transport properties and NDR behavior in fused furan and thiophene dimmers

The nonequilibrium Green's function approach in combination with density-functional theory is used to perform quantum mechanical calculations of the electron transport properties of furan and thiophene dimmers. Both the molecular systems have two S-linker and translated into the Gold junction with (1 1 1) surfaces. The studied molecular junctions at zero bias voltage are HOMO-based junctions and currents through these systems are driven by hole transport. The current–voltage characteristics of the both studied molecular junctions illustrate that negative differential resistance (NDR) feature is observed over the bias voltage of 2.0 V. Higher conductivity of fused furan dimmer and NDR character have been explained by the monitoring of the transmission resonance peak across the bias window against varying bias voltages.     

Interval estimation of $$$$ in ranked set sampling

This article deals with constructing a confidence interval for the reliability parameter using ranked set sampling. Some asymptotic and resampling-based intervals are suggested, and compared with their simple random sampling counterparts using Monte Carlo simulations. Finally, the methods are applied on a real data set in the context of agriculture.     

Stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces

The aim of this paper is to investigate Hyers–Ulam–Rassias stability of preserving lattice functional equation in various spaces. First, we prove stability of generalized preserving lattice functional equation in Banach lattices. Next, we show stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces.     

A novel Mn PVC membrane electrode based on a recently synthesized Schiff base

A new PVC membrane electrode for manganese(II) ion based on a recently synthesized Schiff base of 5-[(4-nitrophenylazo)-N-hexylamine]salicylaldimine is reported. The electrode exhibits a Nernstian response for Mn²⁺ ions over a wide concentration range (4.0 × 10⁻⁷ to 1.8 × 10⁻² mol L⁻¹) with a slope of 30.1 (±1.0). The limit of detection is 1.0 × 10⁻⁷ mol L⁻¹. The electrode has a fast response time (∼10 s), a satisfactory reproducibility and relatively long life time. The proposed sensor revealed good selectivities over a wide variety of other cations include hard and soft metals. This electrode could be used in a pH range of 4.5-7.5. It was used as an indicator electrode in potentiometric titration of manganese(II) ions with EDTA solution.     

Effect of nanoplatelet dispersion on mechanical behavior of polymer nanocomposites

By manipulating processing conditions, three levels of exfoliation of synthetic α-zirconium phosphate (α-ZrP) nanoplatelets in epoxy matrices have been achieved. Transmission electron microscopy and wide angle X-ray diffraction were utilized to confirm the three different levels of exfoliation of nanoplatelets in epoxy/α-ZrP nanocomposites. As expected, it was found that modulus and strength of the nanocomposite are affected by how well the nanoplatelets disperse. It was also found that the operative fracture mechanisms depend strongly on the state of the nanoplatelets dispersion. The crack deflection mechanism, which leads to a tortuous path crack growth, was only observed for poorly dispersed nanocomposites. Delamination of intercalated nanoplatelets and crack deflection were observed in a moderately dispersed system. In the case of fully exfoliated system, the crack only propagated in a straight fashion, which indicates that the fully exfoliated individual nanoplatelet can not affect the propagation of crack at all. The implication of the present findings for structural applications of polymer nanocomposites is discussed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1459–1469, 2007     

One-pot synthesis of functionalized hydantoin derivatives via a four-component reaction between an amine, an arylsulfonyl isocyanate and an alkyl propiolate or dialkyl acetylenedicarboxylate in the presence of triphenylphosphine

An effective route to functionalized hydantoin derivatives is described, involving the reaction of a urea derivative resulting from the addition of a primary amine to an arylsulfonyl isocyanate, and an alkyl propiolate or dialkyl acetylenedicarboxylate in the presence of triphenylphosphine. The reactive 1:1 intermediate obtained from the addition of triphenylphosphine to the alkyl propiolate or dialkyl acetylenedicarboxylate was trapped by NH-acids such as the urea derivative to produce functionalized hydantoin derivatives.     

Magnetic resonance T1ρ imaging of osteoarthritis: a rabbit ACL transection model

Objective

The objective of this study was to develop quantitative T_1ρ-weighted magnetic resonance imaging methodology for the detection and characterization of cartilage degeneration in a rabbit anterior cruciate ligament (ACL) transection model.

Methods

The right knee ACLs of 18 adult female New Zealand white rabbits were transected. The left knee joint served as a sham control. The rabbits were euthanized at 3 (Group 1), 6 (Group 2) and 12 (Group 3) weeks postoperatively. High-resolution 3D fat-saturated spoiled gradient echo images and T_1ρ-weighted images were obtained in both the sagittal and axial planes at 3 T using a quadrature wrist coil. Following MR analysis, histological slides from the lateral femoral condyle cartilage were graded using the Mankin grading system.

Results

For all three groups, the average overall T_1ρ values were significantly higher in the ACL-transected knee compared to control knee, and the percentage differences in T_1ρ values between ACL-transected and control increased with the duration of time after transection. The average Mankin score for ACL-transected knees was higher than that for control for each time point, but this difference was statistically significant only for all groups combined.

Conclusions

This study demonstrates the feasibility of using T_1ρ-weighted imaging as a useful tool in the detection and quantification of cartilage damage in all knee compartments in an ACL-transected rabbit model of cartilage degeneration.