时间尺度上二阶拟线性阻尼动力方程的振动性分析

研究二阶拟线性时滞阻尼动力方程[a(t)|x^Δ(t)|^λ-1x^Δ(t)]^Δ+b(t)|x^Δ(t)|^λ-1x^Δ(t)+p(t)|x(δ(t))|^λ-1x(δ(t))=0的振动性，其中t ₀∈T，而T为任意时间尺度，考虑方程是非正则情形，即$\int^{∞}_{t_0}$[a^-1(s)e_-b/a(s,t₀)]^1/λ Δs < ∞。 通过引入广义Riccati变换，借助时间尺度上的有关理论，并结合不等式技巧，建立了该方程振动的一些新的充分条件，推广、改进并丰富了现有文献中的结果。     

Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

Effect of atmospheric parameters on fine particulate concentration in suburban Shanghai

A study was conducted on the effect of atmospheric parameters,including temperature,wind speed,and relative humidity,on fine particulate mass concentrations measured in Jiading District of Shanghai,China, during the period from January 2009 to January 2010.A sensitivity analysis was applied to investigate the interaction between atmospheric parameters and particulate mass concentration.The experiment revealed that the concentration of particulates increased with particle size from 0.1 to 1.0μm,and decreased with the increase of particle size from 1.0 to 2.5μm.The effects of atmospheric parameters on fine mass concentrations were significantly particle size-dependent.The PM_1.0-2.5 may come from the size increase of smaller particulates after moisture absorption.And the variation of concentrations of PM_0.1-1.0 was mainly attributed to the accumulation of PM_0.1.The ventilation index and dilution index were calculated on the basis of data collected in December 2009.A correlation analysis indicated that there was a significant relation between these two indexes and the particulate concentration by examining the three particle size ranges,0.0-0.1,0.1-1.0,and 1.0-2.5μm.The Spearman correlation coefficients that related the ventilation index to the concentration for the three particle size ranges were -0.45,-0.56 and -0.47, respectively,while the coefficients that related the dilution index to the concentration were -0.36,-0.42 and -0.45,respectively.     

变限积分的求导方法

结合实例归纳总结不同类型变限积分的求导方法．     

An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets

Incomplete data in soft sets lead to uncertainty and inaccuracy in representing and handling information. This paper introduces notions of complete distance between two objects and relative dominance degree between two parameters. Based on both the notions, an object-parameter method is proposed to predict unknown data in incomplete fuzzy soft sets. The proposal makes full use of known data, including the information from the relationship between known values of all objects on a certain parameter and the information from the relationship between known values of an object on all parameters. The effectiveness of the proposal is verified by many examples under the compared investigation of classical predicted methods.     

Measurement of microchannel fluidic resistance with a standard voltage meter

A simplified method for measuring the fluidic resistance (R_fluidic) of microfluidic channels is presented, in which the electrical resistance (R_elec) of a channel filled with a conductivity standard solution can be measured and directly correlated to R_fluidic using a simple equation. Although a slight correction factor could be applied in this system to improve accuracy, results showed that a standard voltage meter could be used without calibration to determine R_fluidic to within 12% error. Results accurate to within 2% were obtained when a geometric correction factor was applied using these particular channels. When compared to standard flow rate measurements, such as meniscus tracking in outlet tubing, this approach provided a more straightforward alternative and resulted in lower measurement error. The method was validated using 9 different fluidic resistance values (from ∼40 to 600 kPa s mm⁻³) and over 30 separately fabricated microfluidic devices. Furthermore, since the method is analogous to resistance measurements with a voltage meter in electrical circuits, dynamic R_fluidic measurements were possible in more complex microfluidic designs. Microchannel R_elec was shown to dynamically mimic pressure waveforms applied to a membrane in a variable microfluidic resistor. The variable resistor was then used to dynamically control aqueous-in-oil droplet sizes and spacing, providing a unique and convenient control system for droplet-generating devices. This conductivity-based method for fluidic resistance measurement is thus a useful tool for static or real-time characterization of microfluidic systems.     

Graphical Models for Ordinal Data

This article considers a graphical model for ordinal variables, where it is assumed that the data are generated by discretizing the marginal distributions of a latent multivariate Gaussian distribution. The relationships between these ordinal variables are then described by the underlying Gaussian graphical model and can be inferred by estimating the corresponding concentration matrix. Direct estimation of the model is computationally expensive, but an approximate EM-like algorithm is developed to provide an accurate estimate of the parameters at a fraction of the computational cost. Numerical evidence based on simulation studies shows the strong performance of the algorithm, which is also illustrated on datasets on movie ratings and an educational survey.     

Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass

Wave interaction with bodies is an important practical application for smoothed particle hydrodynamics (SPH) which in principle applies to steep and breaking waves without special treatment. However, few detailed tests have been undertaken even with small amplitude waves. In order to reduce computer time a variable particle mass distribution is tested here with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. We consider two well‐defined test cases, in two dimensions, of waves generated by a heaving semi‐immersed cylinder and progressive waves interacting with a fixed cylinder. But first, still water with hydrostatic pressure is tested. The open‐source code SPHysics ( http://www.sphysics.org )^{§Update made here after initial online publication.} is used with a Riemann solver in an Arbitrary Lagrangian–Eulerian formulation. For the heaving cylinder, SPH results for far field wave amplitude and cylinder force show good agreement with the data of Yu and Ursell (J. Fluid Mech. 1961; 11 :529–551). For wave loading on a half‐submerged cylinder the agreement with the experimental data of Dixon et al. (J. Waterway Port Coastal Ocean Div. 1979; 105 :421–438) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. The sensitivity of results to the value of the slope limiter used in the MUSCL‐based Riemann solver is demonstrated. The variable mass distribution leads to a computer run speedup of nearly 200% in these cases. Copyright © 2011 John Wiley & Sons, Ltd.     

Closed-form solutions of general second order linear recurrences and applications

Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect.     

A comparison of different approaches to integrate flamelet tables with presumed-shape PDF in flamelet models for turbulent flames

Flamelet models for turbulent combustion modelling make use of presumed-shape probability density functions (PDFs) for integrating laminar flamelet solutions to obtain an integrated flamelet table that can readily be used for turbulent flame calculations. The existence of non-unique approaches for such an integration has rarely been investigated before. For the first time, this work studies systematically the non-uniqueness of the flamelet table integration approaches. A flamelet model called the flamelet/progress variable model is used in the study, although the issue exists generally in many other flamelet models. Two classes of table integration approaches are investigated, one preserving the laminar flamelet structures during integration and the other not. Three different table integration approaches are examined and compared in detail to provide a thorough understanding of the different approaches. A partially stirred reactor is used as a test case for examining the different approaches. A method based on the transported PDF method is also employed to provide a reference for the assessment of the different flamelet table integration approaches. It is found in general that the flamelet preserving integration approach yields a more reasonable joint PDF of the mixture fraction and the progress variable, and the prediction results are closer to the referenced transported PDF results.