Relationship between cation–π and anion–π interactions: individual binding energies in the π–Mz+–π–X−–π system

The mutual influence of cation–π and anion–π interactions in the π–M^z+–π–X^?–π system (M^z+ = Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, Ca²⁺ and X^? = F^?, Cl^?) has been studied by quantum mechanical calculations. Both geometric parameters and energy data reveal that cation–π and anion–π interactions enhance each other in the π–M^z+–π–X^?–π system. Individual binding energies (E_ion···π) have been estimated in the quintuplet system using a simple new method from electron charge densities calculated at the bond critical points (BCPs) of the ion···π interaction by the atoms in molecules (AIM) method at the M062X/6-31+G(d) level of theory. With respect to the obtained individual binding energies, the strength of an ion···π interaction depends on the cooperative effects of other components.     

Height of Prime and Weakly Prime Submodules

We will introduce and study new definitions for the height of prime submodules and weakly prime submodules. Also new module versions of catenary are discussed.     

Stabilizing the pull-in instability of an electro-statically actuated micro-beam using piezoelectric actuation

In the present article an investigation is presented into the stability of an electro-statically deflected clamped–clamped micro-beam sandwiched by two piezoelectric layers undergoing a parametric excitation applying an AC voltage to these layers. Applying an electrostatic actuation not only deflects the micro-beam but also decreases the bending stiffness of the structure, which can lead the structure to an unstable position by undergoing a saddle node bifurcation. Utilizing an appropriate AC actuation voltage to the piezoelectric layers produces a time varying axial force, which can play the role of a stabilizer exciting the system parameter. The governing equation of the motion is a nonlinear electro-mechanically coupled type PDE, which is derived using variational principle and discretized, applying Eigen-function expansion method. The resultant is a Mathieu type equation in its damped form. Using Floquet theory for single degree of freedom system the stable and unstable regions of the problem are investigated. The effects of viscous damping and electrostatic actuation on the stable regions of the problem are also studied.     

New generation of dialkylsilylenes with stabilities comparable to diaminosilylenes: a theoretical study

A new family of dialkylsilylenes is introduced which enjoys the stabilizing effect of α-cyclopropyl substituents. The singlet and triplet states of acyclic and saturated/unsaturated cyclic dicyclopropylsilylenes are fully optimized using MP2/6-31G(d) and B3LYP/6-31+G(d) levels. Their higher ΔE(S-T) values compared to the corresponding analogues which possess isopropyl groups instead of cyclopropyl represents the stabilizing interaction of the occupied Walsh orbital of the cyclopropyls with the vacant p-orbital of the silylene center. Appropriate isodesmic reactions clearly show that the stabilizing effect of this interaction on the singlet state is much more considerable than the corresponding triplet state. Cyclopropyls can serve as good sites for bulky substitution and, hence, provide steric protection for silylene.     

Sur un problème de capitulation du corps ℚ\sqrt {p_1 p_2 } , i dont le 2-groupe de classes est élémentaire

Let p ₁ ≡ p ₂ ≡ 1 (mod 8) be primes such that \(\left( {\tfrac{{p_1 }} {{p_2 }}} \right) = - 1\) and \(\left( {\tfrac{2} {{a + b}}} \right) = - 1\) , where p ₁ p ₂ = a ²+b ². Let \(i = \sqrt { - 1} \) , d = p ₁ p ₂, \(\Bbbk = \mathbb{Q}(\sqrt {d,} i),\Bbbk _2^{(1)} \) be the Hilbert 2-class field and \(\Bbbk ^{(*)} = \mathbb{Q}(\sqrt {p_1 } ,\sqrt {p_2 } ,i)\) be the genus field of \(\Bbbk \) . The 2-part \(C_{\Bbbk ,2} \) of the class group of \(\Bbbk \) is of type (2, 2, 2), so \(\Bbbk _2^{(1)} \) contains seven unramified quadratic extensions \(\mathbb{K}_j /\Bbbk \) and seven unramified biquadratic extensions \(\mathbb{L}_j /\Bbbk \) . Our goal is to determine the fourteen extensions, the group \(C_{\Bbbk ,2} \) and to study the capitulation problem of the 2-classes of \(\Bbbk \) .     

Weighted and deflated global GMRES algorithms for solving large Sylvester matrix equations

The solution of a large-scale Sylvester matrix equation plays an important role in control and large scientific computations. In this paper, we are interested in the large Sylvester matrix equation with large dimensionA and small dimension B, and a popular approach is to use the global Krylov subspace method. In this paper, we propose three new algorithms for this problem. We first consider the global GMRES algorithm with weighting strategy, which can be viewed as a precondition method. We present three new schemes to update the weighting matrix during iterations. Due to the growth of memory requirements and computational cost, it is necessary to restart the algorithm effectively. The deflation strategy is efficient for the solution of large linear systems and large eigenvalue problems; to the best of our knowledge, little work is done on applying deflation to the (weighted) global GMRES algorithm for large Sylvester matrix equations. We then consider how to combine the weighting strategy with deflated restarting, and propose a weighted global GMRES algorithm with deflation for solving large Sylvester matrix equations. In particular, we are interested in the global GMRES algorithm with deflation, which can be viewed as a special case when the weighted matrix is chosen as the identity. Theoretical analysis is given to show rationality of the new algorithms. Numerical experiments illustrate the numerical behavior of the proposed algorithms.

     

Simulation of Viscoelastic Fluid Flows in Expansion Geometry Using Finite Volume Approach简

The simulation results on viscoelastic fluid flows in sudden expansion geometry with different expansion ratios are presented. Oldroyd-B, linear Phan-Thien-Tanner （L-PTT） and Finitely Extensible Nonlinear Elastic （FENE-P） based constitutive equations were applied in two-dimensional Cartesian coordinates. The governing equations in transient and fully developed regions were solved using open source software called OpenFOAM. The flow patterns, including velocity profiles, shear stresses and first normal stress differences in some horizontal and vertical sections are illustrated. In addition, effects of the fluid type, flow dynamics and expansion ratio on the flow and vortex patterns in transient and fully developed regions are presented and discussed. The presented results show that existences of vortices cause the inverse velocity and negative stresses in expansion regions of the channel which increase with increment of expansion ratio and Weissenberg number （We）. Furthermore, some dead spaces can be observed at channel expansion regions close to the wall which are also increased. The results also show that at low We numbers all fluids show close behavior while at high We numbers the FENE-P fluid behavior shows high divergence from that of the two other fluids.     

Thermal QCD sum rules study of vector charmonium and bottomonium states

We calculate the masses and leptonic decay constants of the heavy vector quarkonia, J/ψ and ϒ mesons at finite temperature. In particular, considering the thermal spectral density as well as additional operators coming up at finite temperature, the thermal QCD sum rules are acquired. Our numerical calculations demonstrate that the masses and decay constants are insensitive to the variation of temperature up to T ≅ 100 MeV, however after this point, they start to fall altering the temperature. At deconfinement temperature, the decay constants attain roughly to 45% of their vacuum values, while the masses are diminished about 12%, and 2.5% for J/ψ and ϒ states, respectively. The obtained results at zero temperature are in good consistency with the existing experimental data as well as predictions of the other nonperturbative models.     

Phase formation and change of magnetic properties in mechanical alloyed Ni0.5Co0.5Fe2O4 by annealing

The effects of milling time and annealing temperature on phase formation, microstructure and magnetic properties of nickel-cobalt ferrite synthesized from oxide precursors by mechanical alloying were studied. The study of milling time effects on phase formation of milled materials showed that if milling continues up to 55 h, single phase nano-sized nickel-cobalt ferrite is obtained. Also, magnetic properties of powders versus milling time and annealing at different temperatures extensively changed, so that annealing at 1200 °C increased the magnetization saturation of the as-milled powder from 15.1 to 53.6 emu/g. X-ray powder diffraction technique (XRD) with Cu-Ka radiation was employed for phase identification. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were also used to determine the morphology and size of the particles. The magnetic properties were measured by a vibration sample magnetometer (VSM).     

In Vitro Effect of 445 nm Blue Laser and 660 nm Low-Level Laser on the Quantity and Quality of Human Gingival Fibroblasts

Low-level laser therapy (LLLT) has several benefits in dentistry, including anti-inflammatory effects and increased proliferation. This study aimed to investigate the effect of 445 nm blue laser and 660 nm low-power laser on the quantity and quality of human gingival fibroblasts in vitro. In this in vitro experimental study, 445 nm and 660 nm lasers were irradiated on the samples six times. After examining the cells on the 7^th and 14^th days, the data were analyzed using ANOVA PASS11 and the post hoc Tukey test. The results showed the positive effect of the 660 nm laser on fibroblast proliferation. The viability on the 7^th day was the highest in the control group, lowest in the 445 nm laser group and highest in the 660 nm laser group on the 14^th day. In the morphological examination, the cells were spherical with narrow appendages in the control group, spindle-shaped with lamellipodia appendages in the 660 nm laser group and spherical with no cytoplasmic appendages in the 445 nm laser group. Evidence of necrosis and granulation phenomenon was observed in the 445 nm laser group. The use of the 660 nm low-power laser, compared with the 445 nm laser, has a positive effect on the quantity and quality of gingival fibroblasts.