Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

Crustal structure in the Anyuan Coal Mine and its adjacent areas of Jiangxi Province by P-wave receiver functions

We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City,Jiangxi Province for nearly two years.The H-κ-c stacking method was employed to obtain the crustal thickness and Poisson's ratio distribution,then the characteristics of crustal structure below the stations were obtained by using the time-domain linear inversion method.The crustal thickness in the Anyuan Coal Mine and its adjacent areas ranges from approximately 32~35 km,with an average thickness of 33 km,which is consistent with the crustal thickness results in South China from previous studies using the receiver function method.The average Poisson's ratio of the crustal bulk composition in the study area varies between 0.22 and 0.25,which is lower than the global value with a 0.27 average,indicating a predominantly intermediate-acidic or felsic crustal composition.There is a weak negative correlation between Poisson's ratio and crustal thickness estimates in the Anyuan Coal Mine and its adjacent areas,suggesting that the absence of mafic-ultramafic materials in the lower crust is associated with the process of crustal delamination.The velocity inversion results indicate that the crustal structure including three velocity discontinuity interfaces,with the first at a depth of approximately 1.5 km,the second at about 10~15 km,and the third being the Moho.The study also indicates that the results obtained by the H-κ-c stacking method are significantly better than those obtained by the H-κmethod,effectively reducing the standard deviation and dispersion of crustal thickness and vP/vSratio.

Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

Continuously variable transmission(CVT)of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency.The key technology of CVT with noncircular gear has been broken through some countries,and is in the stage of deep application research.Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China,the noncircular gear CVT is still in the preliminary exploration and research stage.The linear functional noncircular gear pair,whose transmission ratio is a linear function in the working section,to realize continuously variable transmission was the research object in this paper.According to the required transmission ratio in the working section,the transmission ratio function in the non-working section was constructed by using a polynomial.And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair.In addition,for improving the stability and bearing capacity of gear transmission,the noncircular gear pair transmission with high contact ratio was designed.Furthermore,the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile,from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment.Finally,an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations

Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.

Crustal and uppermost mantle structure of the northeastern Qinghai-Xizang Plateau from joint inversion of surface wave dispersions and receiver functions with P velocity constraints

Lithospheric structure beneath the northeastern Qinghai-Xizang Plateau is of vital significance for studying the geodynamic processes of crustal thickening and expansion of the Qinghai-Xizang Plateau. We conducted a joint inversion of receiver functions and surface wave dispersions with P-wave velocity constraints using data from the Chin Array Ⅱ temporary stations deployed across the Qinghai-Xizang Plateau. Prior to joint inversion, we applied the H-κ-c method(Li JT et al., 2019) to the receiver function data in order to correct for the back-azimuthal variations in the arrival times of Ps phases and crustal multiples caused by crustal anisotropy and dipping interfaces. High-resolution images of vS, crustal thickness, and vP/vSstructures in the Qinghai-Xizang Plateau were simultaneously derived from the joint inversion. The seismic images reveal that crustal thickness decreases outward from the Qinghai-Xizang Plateau. The stable interiors of the Ordos and Alxa blocks exhibited higher velocities and lower crustal vP/vSratios. While, lower velocities and higher vP/vSratios were observed beneath the Qilian Orogen and Songpan-Ganzi terrane(SPGZ), which are geologically active and mechanically weak, especially in the mid-lower crust.Delamination or thermal erosion of the lithosphere triggered by hot asthenospheric flow contributes to the observed uppermost mantle low-velocity zones(LVZs) in the SPGZ. The crustal thickness, vS, and vP/vSratios suggest that whole lithospheric shortening is a plausible mechanism for crustal thickening in the Qinghai-Xizang Plateau, supporting the idea of coupled lithospheric-scale deformation in this region.

Minimizing Carbon Content with Three-in-One Functionalized Nano Conductive Ceramics:Toward More Practical and Safer S Cathodes of Li-S Cells

Using porous carbon hosts in cathodes of Li-S cells can disperse S actives and offset their poor electrical conductivity.However,such reservoirs would in turn absorb excess electrolyte solvents to S-unfilled regions,causing the electrolyte overconsumption,specific energy decline,and even safety hazards for battery devices.To build better cathodes,we propose to substitute carbons by In-doped SnO_(2)(ITO)nano ceramics that own three-in-one functionalities:1)using conductive ITO enables minimizing the total carbon content to an extremely low mass ratio(~3%)in cathodes,elevating the electrode tap density and averting the electrolyte overuse;2)polar ITO nanoclusters can serve as robust anchors toward Li polysulfide(LiPS)by electrostatic adsorption or chemical bond interactions;3)they offer catalysis centers for liquid–solid phase conversions of S-based actives.Also,such ceramics are intrinsically nonflammable,preventing S cathodes away from thermal runaway or explosion.These merits entail our configured cathodes with high tap density(1.54 g cm^(−3)),less electrolyte usage,good security for flame retardance,and decent Li-storage behaviors.With lean and LiNO_(3)-free electrolyte,packed full cells exhibit excellent redox kinetics,suppressed LiPS shuttling,and excellent cyclability.This may trigger great research enthusiasm in rational design of low-carbon and safer S cathodes.

The Determination Method of Product Engineering Features Based on Linguistic Variables

To overcome the problem of imprecise and unclear information in the development of quality functions,a method for determining the priority of engineering features based on mixed linguistic variables is proposed.First,the evaluation member uses the determined linguistic variable to give the correlation strength evaluation matrix of customer requirements and engineering features.Secondly,the relative importance of the evaluation member and customer requirements are aggregated.Finally,the priority of engineering features is obtained by calculating the deviation.The feasibility and practicability of this method are proven by taking the design of a new product of a long bag low-pressure pulse dust collector as an example.

Experimental Study on Interference Effect of Three Risers Arranged in Tandem with Variable Spacing Ratios

Taking the three-riser group arranged in tandem as the research subject,an experimental study was carried out on the risers arranged in tandem.The purpose is to explore the sensitivity of the dynamic response of each riser to spacing ratio and reveal the physical mechanism of riser groups under the interference effect.The spacing ratios of the adj acent risers are 4.0,5.0,6.0,and 8.0.At the spacing between the risers of 4.0D,the strong feedback effect increases the cross-flow(CF) displacement amplitude of the upstream riser.The shielding effect is the key factor affecting the interference effect on the midstream and downstream risers.At low reduced velocities,the shielding area initially appears,the displacement amplitude of the midstream and downstream risers varies greatly,the vibration of the two risers is still dominated by the first-order mode,and the transition between adjacent vibration modes is restrained.The multi-frequency superposition phenomenon is very significant at high reduced velocities.The most sensitive interference spacing under the test conditions is obtained.Due to the separation of the incoming flow and the double shielding effect of the upstream and midstream risers,the regular vortex-induced vibration in the wake area of the downstream riser is broken,and the vibration in the two directions is weakened.In general,the interference effect is more significant for the CF vibration of the three-riser groups than the in-line(IL) vibration.

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.

SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES

In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.

Second to fourth digit ratio： a predictor of adult lung function

Sex and sex hormones play a major role in lung physiology. It has been proposed that the ratio of the second to fourth digits （digit ratio） is correlated with fetal sex hormones. We therefore hypothesized that digit ratio might help predict lung function. We investigated the relationship between digit ratio and pulmonary function test （PFT） findings. A total of 245 South Korean patients （162 male, 83 female） aged from 34 to 90 years who were hospitalized for urological surgery were prospectively enrolled. Before administering the PFTs, the lengths of the second and fourth digits of the right hand were measured by a single investigator using a digital Vernier caliper. In males （n = 162）, univariate and multivariate analysis using linear regression models showed that digit ratio was a significant predictive factor of forced vital capacity （FVC） and forced expiratory volume in I second （FEV1） （FVC： r = 0.156, P = 0.047; FEVI： r = 0.160, P = 0.042）. In male ever-smokers （n = 69）, lung functions （FVC and FEV1） were correlated with smoking exposure rather than digit ratio. In female never-smokers （n = 83）, lung functions （FEV1 and FEVI/FVC ratio） were positively correlated with digit ratio on univariate analysis （FEVI： r = 0.242, P = 0.027; FEVI/FVC ratio： r = 0.245, P = 0.026）. Patients with lower digit ratios tend to have decreased lung function. These results suggest that digit ratio is a predictor of airway function.

Acute effects of static stretching on peak and end-range hamstring-to-quadriceps functional ratios

AIM: To evaluate if static stretching influences peak and end-range functional hamstring-to-quadriceps(H/Q) strength ratios in elite women athletes. METHODS: Eleven healthy female athletes in an elite competitive level participated to the study. All the participants fulfilled the static stretching or non-stretching(control) intervention protocol in a randomized design on different days. Two static unassisted stretching exercises, one in standing and one in sitting position, were used to stretch both the hamstring and quadriceps muscles during these protocols. The total time for the static stretching was 6 ± 1 min. The isokinetic peak torque measurements for the hamstring and quadriceps muscles in eccentric and concentric modes and the calculations for the functional H/Q strength ratios at angular velocities of 60°/s and 180°/s were made before(pre) and after(post) the control or stretching intervention. The strength measurements and functional strength ratio calculations were based during the entire- and end-range of knee extension.RESULTS: The pre-test scores for quadriceps and hamstring peak torque and end range values were not significantly different between the groups(P > 0.05). Subsequently, although the control group did notexhibit significant changes in quadriceps and hamstring muscle strength(P > 0.05), static stretching decreased eccentric and concentric quadriceps muscle strength at both the 60°/s and 180°/s test speeds(P < 0.01). Similarly, static stretching also decreased eccentric and concentric hamstring muscle strength at both the 60°/s and 180°/s test speeds(P < 0.01). On the other hand, when the functional H/Q strength ratios were taken into consideration, the pre-intervention values were not significant different between the groups both during the entire and end range of knee extension(P > 0.05). Furthermore, the functional H/Q strength ratios exhibited no significant alterations during the entire and end ranges of knee extension both in the static stretching or the control intervention(P > 0.05). CONCLUSION: According to our results, static stretching routine does not influence functional H/Q ratio. Athletes can confidently perform static stretching during their warm-up routines.

A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation

This paper is an extension and generalization of the study carried out by [1] on the estimation of the population ratio (R) of the population means of two variables (y and x) under Simple Random Sampling (SRS) scheme, using a variable transformation of the auxiliary variable, x. All the six estimators proposed by [1] are easily identified as special cases of the proposed class of estimators. Asymptotic properties of the proposed class of estimators are derived theoretically and subsequently verified using empirical illustrations. Some of the proposed estimators are found to have relatively large gains in efficiency over the customary ratio estimator, ?for the given data set.

Dynamical Behavior of Discrete Ratio-Dependent Predator-Prey System

In this paper, we propose a discrete ratio-dependent predator-prey system. The stability of the fixed points of this model is studied. At the same time, it is shown that the discrete model undergoes fold bifurcation and flip bifurcation by using bifurcation theory and the method of approximation by a flow. Numerical simulations are presented not only to demonstrate the consistence with our theoretical analyses, but also to exhibit the complex dynamical behaviors, such as the cascade of period-doubling bifurcation in period-2 and the chaotic sets. The Maximum Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. These results show that the direct discrete method has more rich dynamic behaviors than the discrete model obtained by Euler method.

Spatial Variability of Soil Carbon to Nitrogen Ratio and Its Driving Factors in Ili River Valley,Xinjiang,Northwest China

Soil carbon to nitrogen(C/N) ratio is one of the most important variables reflecting soil quality and ecological function,and an indicator for assessing carbon and nitrogen nutrition balance of soils.Its variation reflects the carbon and nitrogen cycling of soils.In order to explore the spatial variability of soil C/N ratio and its controlling factors of the Ili River valley in Xinjiang Uygur Autonomous Region,Northwest China,the traditional statistical methods,including correlation analysis,geostatistic alanalys and multiple regression analysis were used.The statistical results showed that the soil C/N ratio varied from 7.00 to 23.11,with a mean value of 10.92,and the coefficient of variation was 31.3%.Correlation analysis showed that longitude,altitude,precipitation,soil water,organic carbon,and total nitrogen were positively correlated with the soil C/N ratio(P < 0.01),whereas negative correlations were found between the soil C/N ratio and latitude,temperature,soil bulk density and soil p H.Ordinary Cokriging interpolation showed that r and ME were 0.73 and 0.57,respectively,indicating that the prediction accuracy was high.The spatial autocorrelation of the soil C/N ratio was 6.4 km,and the nugget effect of the soil C/N ratio was 10% with a patchy distribution,in which the area with high value(12.00–20.41) accounted for 22.6% of the total area.Land uses changed the soil C/N ratio with the order of cultivated land > grass land > forest land > garden.Multiple regression analysis showed that geographical and climatic factors,and soil physical and chemical properties could independently explain 26.8%and 55.4% of the spatial features of soil C/N ratio,while human activities could independently explain 5.4% of the spatial features only.The spatial distribution of soil C/N ratio in the study has important reference value for managing soil carbon and nitrogen,and for improving ecological function to similar regions.

The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term

By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.

Time-dependent effects of castration on the bladder function and histological changes in the bladder and blood vessels

We examined the effect of androgens on bladder blood flow （BBF）, bladder function and histological changes in castrated male rats. Male Wistar rats were classified into unoperated group （control group）, groups castrated at the age of 8weeks （group 8wPC） and groups castrated at the age of 4weeks （group 4wPC）. Each rat was used at the age of 20weeks. BBF was measured using fluorescent microspheres. Bladder cystometry was performed without anesthesia or restraint; the bladder was first irrigated with saline and then with 0.25% acetic acid （AA） solution. Maximum voiding pressure and voiding interval were measured. The bladder and lilac artery were histologically examined for differences in smooth muscle and quantity of collagen fiber to analyze the effect of castration on the smooth muscle content. No differences were noted in BBF following castration. The voiding intervals for all groups were shortened （P 〈 0.001） following AA irrigation. No significant difference was noted in the maximum voiding pressure. Histological changes were observed in bladder and lilac artery. Smooth muscle/collagen ratio at the bladder was lower in groups 8wPC and 4wPC compared to the control group （P 〈 0.01）, while that at the lilac artery was decreased in group 4wPC compared to the control group （P〈 0.001）. In conclusion, our findings indicate that castration does not alter BBF, but leads to histological changes in the bladder as well as its associated blood vessels.

COMPLETE MONOTONICITY FOR A NEW RATIO OF FINITELY MANY GAMMA FUNCTIONS

In this paper,by deriving an inequality involving the generating function of the Bernoulli numbers,the author introduces a new ratio of finitely many gamma functions,finds complete monotonicity of the second logarithmic derivative of the ratio,and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.

Distributions of Ratios: From Random Variables to Random Matrices

The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.

Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator＇s Wave Functions

<正> We reveal that the two-variable Hermite function h_(m,n),which is the generalized Bargmann representationof the two-mode Fock state,involves quantum entanglement of harmonic oscillator's wave functions.The Schmidtdecomposition of h_(m,n),is derived.It also turns out that h_(m,n)can be generated by windowed Fourier transform of thesingle-variable Hermite functions.As an application,the wave function of the two-variable Hermite polynomial stateS(γ)H_(m,n)(μa_1~+,μa_2~+)|00>,which is the minimum uncertainty state for sum squeezing,in<η|representation is calculated.