Generalization of a sharp Hölder's inequality and its application

In this paper, we generalize Hu Ke's sharpness of Hölder's inequality. As application, the obtained result is used to improve the well-known Opial-Olech inequality.     

A new generalized and sharp version of Jordan’s inequality and its applications to the improvement of the Yang Le inequality

A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality. Moreover, a mistake in the proof of sharpening Jordan’s inequality due to Zhu [S.H. Wu, On generalizations and refinements of Jordan type inequality, Octogon Math. Mag. 12(1) (2004) 267–272] is corrected.     

A study of isogeometric analysis for scalar convection–diffusion equations

Isogeometric analysis (IGA), in combination with the streamline upwind Petrov–Galerkin (SUPG) stabilization, is studied for the discretization of steady-state convection–diffusion equations. Numerical results obtained for the Hemker problem are compared with results computed with the SUPG finite element method of the same order. Using an appropriate parameterization for IGA, the computed solutions are much more accurate than those obtained with the finite element method, both in terms of the size of spurious oscillations and of the sharpness of layers.     

Drug binding and order-order and order-disorder transitions in DNA triple helices

The Zimm and Bragg theory for helix-to-coil transitions has been suitably amended and applied to explain the two-step transition in the DNA triplex. The experimental measurements reported elsewhere have been successfully interpre- ted. The order-order and order-disorder transitions associated with the melting of the DNA triple helix, with and without netropsin binding, were characterized by the nucleation parameter, enthalpy change, sharpness of transition, and heat capacity. The destabilization of the triplex and stabilization of the duplex on netropsin binding are reflected in these characteristic parameters.     

基于眼型谐振腔的Fano谐振曲线尖锐度的分析

为了获得较大的尖锐度,提升微环传感器的灵敏度,提出利用眼型谐振腔结构在下路端输出的非对称Fano谐振光谱,眼型谐振腔由一个外环和内环构成,外环与总线波导耦合,内环与外环耦合.利用传输矩阵法对下路端输出光谱进行了数值计算,在不同剩余电场比例系数下,发现非对称Fano谐振峰的尖锐度随电场剩余比例系数的增大而增大;改变外环与总线波导间的场强耦合系数和内环与外环之间的场强耦合系数,其尖锐度的最大值随外环和内环场强耦合系数变化缓慢增大,尖锐度最大值处谐振点传输系数值在不同电场剩余比例系数和内外环场强耦合系数下稳定在-6dB附近.因此利用眼型谐振腔结构下路端的Fano谐振峰,可获得对耦合系数不敏感的尖锐度和谐振点传输系数,降低器件对耦合区加工准确度的要求.     

An analysis of the sharpness of monotonicity results via homotopy for sequential fractional operators

We investigate the connection between the sign of $\left({\Delta }_{1-\mu +a}^{\nu }{\Delta }_a^{\mu }f\right)\left(t\right)$ and the monotone behavior of $t\mapsto f\left(t\right)$. In particular, given a function $f:{\mathbb{N}}_a\to \mathbb{R}$ we consider the homotopy $G_{\nu }:\mathbb{R}\times [0,1]\to \mathbb{R}$ defined by $G_{\nu }\left(f\left(a\right),\eta \right)≔\eta \cdot \frac{1}{2}(1-\nu )\left(\nu \right)f\left(a\right)$, and we analyze the effect of changing $\eta \in [0,1]$ in the condition $\left({\Delta }_{1-\mu +a}^{\nu }{\Delta }_a^{\mu }f\right)\left(t\right)\ge G_{\nu }\left(f\left(a\right),\eta \right)$. We show that as $\eta \to 1^{-}$ there is an increasingly strong connection between the sign of $\left({\Delta }_{1-\mu +a}^{\nu }{\Delta }_a^{\mu }f\right)\left(t\right)$ and the monotone behavior of $f$.     

Comparisons of different procedures of pre-compaction stress determination on weakly structured soils

Compaction is an important component of soil degradation. In this regard, the pre-compaction stress (σ_pc) concept is considered useful in mechanized agriculture nowadays. When the external forces exceed the internal strength (σ_pc) of soil, soil structure and soil physical quality will deteriorate. This concept was introduced at first for confined consolidation of non-structured, homogenized and saturated subsoils in civil engineering, though it is also suitable for agricultural conditions where the topsoil and subsoil are considered and both are often structured, heterogeneous and unsaturated. The best method for predicting σ_pc is by the plate sinkage test (PST) in the field, but it is expensive and time-consuming. This study was conducted to find an alternative laboratory method besides the confined compaction test (CCT) for predicting σ_pc. The CCT may not be a good method, especially at higher water contents, and for soils with low organic matter content, because of low sharpness of the critical region on the stress–strain curves. The study was performed on five soil types with a range of soil textures and organic matter content from central Iran using three loading types and three pF (i.e. Log [soil matric suction in cm]) values of 2.3, 2.7 and 2.9 with two replicates. Loading types consisted of CCT, the semi-confined compaction test (SCCT) and the kneading compaction test (KCT) at three maximum (or pre-compaction) stresses of 200, 400 and 600 kPa. The experiment was a completely randomized factorial design. The aim was to determine how accurately each loading type test could predict σ_pc of soil pre-compacted by one of the other methods. The applied combinations of CCT–SCCT, SCCT–CCT and KCT–CCT mean that the soil was pre-compacted by the first loading type and evaluated by the second one. The results showed that σ_pc and the sharpness of the σ_pc region were significantly affected by loading types as well as the soil conditions. The sharpest σ_pc region was observed in SCCT and the least sharp in CCT with the overall order being CCT–SCCT > SCCT–CCT > KCT–CCT. The sharpness of the σ_pc region was reduced for the soil samples with higher water content and coarser texture. Regardless of the soil and loading conditions, the prediction by SCCT was consistently more accurate than by CCT. The prediction of σ_pc by SCCT was more precise in comparison with CCT especially at higher stresses and soil water contents. However, the prediction of σ_pc by SCCT was very accurate at pF values of 2.7 and 2.9, and with low σ_pc values, when compared with the actual values of the σ_pc. For the clay soil at a pF value of 2.3, no pre-compaction region (i.e. zero σ_pc) could be determined by CCT at a maximum axial stress of 600 kPa. This was because of the incompressibility of soil water at this near-saturated soil condition at high stress. However, the sharpness of the critical region in SCCT was high enough to predict σ_pc satisfactorily. There was no significant difference between the combinations of SCCT–CCT and KCT–CCT in predicting σ_pc. The SCCT is a compromise method that lies between CCT and PST. SCCT has the advantage of using a limited and definite soil volume that can be modeled as a soil element. Marginal effects of disturbance caused by coring/sampling as well as pre-test sample preparation seem to have minor effects on the stress–strain curve determined by SCCT in comparison with CCT. Moreover, the soil volume needed for this test is the same as for CCT.     

Interpolation between Brezis–Vázquez and Poincaré inequalities on nonnegatively curved spaces: sharpness and rigidities

This paper is devoted to investigate an interpolation inequality between the Brezis–Vázquez and Poincaré inequalities (shortly, BPV inequality) on nonnegatively curved spaces. As a model case, we first prove that the BPV inequality holds on any Minkowski space, by fully characterizing the existence and shape of its extremals. We then prove that if a complete Finsler manifold with nonnegative Ricci curvature supports the BPV inequality, then its flag curvature is identically zero. In particular, we deduce that a Berwald space of nonnegative Ricci curvature supports the BPV inequality if and only if it is isometric to a Minkowski space. Our arguments explore fine properties of Bessel functions, comparison principles, and anisotropic symmetrization on Minkowski spaces. As an application, we characterize the existence of nonzero solutions for a quasilinear PDE involving the Finsler–Laplace operator and a Hardy-type singularity on Minkowski spaces where the sharp BPV inequality plays a crucial role. The results are also new in the Riemannian/Euclidean setting.     

某SUV车门关门声品质建模及优化

本文介绍了汽车关门声品质的客观评价方法和评价参数以及关门声品质影响因素等方面的研究现状。在此基础上,针对某SUV车型车门关门声音的响度和尖锐度偏大的问题,进行了关门声的客观测试和特性分析,结合正交实验设计,建立关门声品质优化模型,针对关门声音振颤的问题,结合CAE分析,确定了车门外板高灵敏度区域,并对该区域进行了吸振处理,措施实施后关门声音的响度、尖锐度以及振颤均达到了更好的水平,且关门声主观评价也有明显提升。