Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

The electronic properties and electron transport of sawtooth penta-graphene nanoribbon under uniaxial strain: ab-initio study

ABSTRACT

The electronic properties and electron transport of a sawtooth penta-graphene nanoribbon (SSPGNR) under uniaxial strains are theoretically studied by density-functional theory (DFT) in combination with the non-equilibrium Green's function formalism. We investigated the electronic structures and the current–voltage (I–V) characteristics of the SSPGNRs under a sequence of uniaxial strains in range from 10% compression to 10% stretch. In this strained range, carbon atoms still keep a pentagon network, but with the changing bond lengths. The C–C bond lengths change almost linearly with the tolerable strain. The value of the band gap of SSPGNRs can be depicted as a parabola under uniaxial strain. Our calculations show that the current is monotonous increase with compressive strain at the same applied bias voltage. In case of tensile strain, the variable rule of the current is different that it increases at first and decrease later. The fundamental physical properties (band structure, I–V characteristic) of SSPGNRs seem to be more sensitive to compressive strain than the stretch strain. The current intensity of the compressive-SSPGNR is by 2 orders of magnitude compared to that of the tensile-SSPGNR at the same strain in range from 6% to 10%. The results obtained from our calculations are beneficial to practical applications of these strained structures in SSPGNRs-based electromechanical devices.     

明代生命损失型地震的时空分布特征及成因分析

利用史料记录建立了明代生命损失型地震的数据库，构建生命损失型地震等级序列、10 a尺度上生命损失型地震的频次序列和县次序列，再现明代生命损失型地震的时空分布特征，探讨了生命损失型地震发生及导致人口死亡的时空差异原因。结果表明：（1）从明初到明末，生命损失型地震等级强度有逐渐扩大的趋势。（2）明代前期处于生命损失型地震发生较少的稳定时期；明代中后期处于生命损失型地震发生较多的波动时期。明代生命损失型地震发生频次存在明显的周期性变化特征。（3）生命损失型地震在明代大部分区域皆有分布。灾害重心随时间变化发生移动，由西南到中部再到华北、华东。（4）明代地震频繁的原因除地球本身因素外，太阳活动通过影响气候变化，进而间接影响地壳活动。气候寒冷与干旱和地震有较好的对应关系。明代后期生命损失型地震导致死亡人数大量增加，与明代经济发展，人口密度逐渐增长有关；不同地区生命损失型地震导致的死亡人数不同，且死亡人数与地震频发地区是否处于板块之间的活动构造带和人口分布密度有关。     

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

Tire and soil effects on power loss: Measurement and comparison with finite element model results

In the present study, the effect of vertical load, tire inflation pressure and soil moisture content on power loss in tire under controlled soil bin conditions were investigated. Also a finite element model of tire-soil interaction in order to achieve a suitable model for predicting power loss in tire was created. Increasing the vertical load on the tire had a noteworthy impact on increasing the tire contact volume with the soil, reducing the percentage of slip, and increasing the rolling resistance; although, reducing the load on the tire had the opposite effect. At a constant inflation pressure, by increasing the vertical load on the tire, the amount of power loss due to the rolling resistance and the total power loss in the tire increased. Increase in soil moisture content increased the power loss caused by slip. Increasing the inflation pressure at a constant vertical load, also increasing the soil moisture content, led to an increase in the power loss caused by rolling resistance, and increase total power loss. The obtained error for estimating power loss of rolling resistance and total power loss was satisfactory and confirmed the acceptability of the model for power loss estimation.     

Critical Trace Trudinger-Moser Inequalities on a Compact Riemann Surface with Smooth Boundary

In this paper, the author concerns two trace Trudinger-Moser inequalities and obtains the corresponding extremal functions on a compact Riemann surface (Σ, g) with smooth boundary ?Σ. Explicitly, let λ₁(?Σ) = inf u∈W^1,2 (Σ,g),R ?Σ udsg=0,u6≡0 R Σ(|?gu|2 + u2 )dvg R ?Σ u2 dsg and H = n u ∈ W^1,2 (Σ, g) : Z Σ(|?gu|2 + u2 )dvg ? α Z ?Σ u2dsg ≤ 1 and Z ?Σ u dsg = 0o ,where W^1,2 (Σ, g) denotes the usual Sobolev space and ?g stands for the gradient operator.By the method of blow-up analysis, we obtain sup u∈H Z ?Σ e πu2 dsg ( < +∞, 0 ≤ α < λ1(?Σ),= +∞, α ≥ λ1(?Σ).Moreover, the author proves the above supremum is attained by a function uα ∈ H∩C∞(Σ)for any 0 ≤ α < λ1(?Σ). Further, he extends the result to the case of higher order eigenvalues. The results generalize those of [Li, Y. and Liu, P., Moser-Trudinger inequality on the boundary of compact Riemannian surface, Math. Z., 250, 2005, 363–386], [Yang,Y., Moser-Trudinger trace inequalities on a compact Riemannian surface with boundary,Pacific J. Math., 227, 2006, 177–200] and [Yang, Y., Extremal functions for TrudingerMoser inequalities of Adimurthi-Druet type in dimension two, J. Diff. Eq., 258, 2015,3161–3193]     

Transition metal complexes of Schiff base ligand based on 4,6-diacetyl resorcinol

Novel Schiff base ligand based on the condensation of 4,6-diacetyl resorcinol with 2-amino-4-methylthiazole in addition to its metal complexes with Cr (III), Mn (II), Fe (III), Co (II), Ni (II), Cu (II), Zn (II) and Cd (II) ions have been synthesized. The structure, electronic properties, and thermal behaviour of Schiff base and its metal complexes have been studied by elemental analysis, mass, ¹H NMR, IR spectra, thermal analysis, and theoretically by density function theory. The ligand acted as mononegative bidentate (NO) ligand and all complexes showed octahedral geometry except Cu (II) showed tetrahedral geometry as indicated from the spectral and magnetic studies. The Cu (II), Zn (II) and Cd (II) complexes were non electrolytes while the rest of the complexes were electrolytes. The antibacterial plus anticancer activities of the parent Schiff base and its metal complexes were screened. In addition, the molecular docking study was performed to explore the possible ways for binding to Crystal Structure of Human Astrovirus capsid protein (5ibv) receptor.     

Enhanced electronic and nonlinear optical responses of C24N24 cavernous nitride fullerene by decoration with first row transition metals; A computational investigation

The electronic (energy gap and work function) as well as electrical properties (dipole moment, polarizability, and first hyperpolarizabilities) of the first-row transition metals decorated C₂₄N₂₄ cavernous nitride fullerene were explored using DFT calculations. The transition metals are decorated at N4 cavity of C₂₄N₂₄ fullerene. According to our spin polarized computations, the most stable spin state monotonically increases to sextet for Mn@C₂₄N₂₄ and thereafter dropped off gradually to singlet state for Zn@C₂₄N₂₄ system. The findings demonstrate that transition metals can remarkably decrease the HOMO-LUMO energy gap and work function values up to 63% and 21% of bare C₂₄N₂₄, respectively. As can be seen, when the Sc and Ti metals are located above the N4 cavity of fullerene, systems of enhanced static hyperpolarizabilities (β₀) are delivered. These findings might provide an effective strategy to design high performance eletcro-optical materials based on carbon- nitride fullerene.