Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed,among which the subgradient extragradient method has obvious advantages.Two different algorithms are given for solving variational inequality problem in this paper.The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition.Two new algorithms adopt inertial technology and non-monotonic step size rule,and their convergence can still be proved when the value of L is not given in advance.Finally,some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.

STRONGLY CONVERGENT INERTIAL FORWARD-BACKWARD-FORWARD ALGORITHM WITHOUT ON-LINE RULE FOR VARIATIONAL INEQUALITIES

This paper studies a strongly convergent inertial forward-backward-forward algorithm for the variational inequality problem in Hilbert spaces.In our convergence analysis,we do not assume the on-line rule of the inertial parameters and the iterates,which have been assumed by several authors whenever a strongly convergent algorithm with an inertial extrapolation step is proposed for a variational inequality problem.Consequently,our proof arguments are different from what is obtainable in the relevant literature.Finally,we give numerical tests to confirm the theoretical analysis and show that our proposed algorithm is superior to related ones in the literature.

Variation and Sexual Dimorphism of Body Size in the Plateau Brown Frog along an Altitudinal Gradient

Variation in body size and sexual size dimorphism（SSD） can have important consequences for animal ecology, behavior, population dynamics and the evolution of life-history traits. Organisms are expected to be larger in colder climate（i.e., Bergmann＇s rule） and SSD varies with body size（i.e., Rensch＇s rule）. However, the underlying mechanisms are still elusive. The plateau brown frog（Rana kukunoris）, a medium-sized anuran species with femalebiased SSD, is endemic to the Qinghai-Tibetan Plateau（QTP）. From 1797 m（Maoxiang＇ping） to 3453 m（Heihe＇qiao） in the eastern margin of the QTP, we surveyed 10 populations of R. kukunoris and collected phalanges and snout vent length（SVL） data for 258 adult individuals（199 males versus 59 females）. Based on these data, we explored how body size and SSD varying along the altitudinal gradient and examined the corresponding effects of temperature. We found body size to be larger at higher altitude for males but not for females, with likely effects from the temperature on the variation in male body size. Sex differences in growth rates may be the main cause of the variation in SSD. Our results suggested that only males follow the Bergmann＇s rule and variation in SSD of R. kukunoris do not support the Rensch＇s rule and its inverse. Therefore, the variations of body size can be different between sexes and the applicability of both Bergmann＇s rule and Rensch＇s rule should depend on species and environment where they live.

The Variation Rule and Anomaly Features of the Available Precipitation in the Growth Period of Crops in the Middle and Southern Part of Ningxia

[ Objective] The aim was to study the available precipitation and its abnormal characteristics during the growth period of crops in the mid- dle and southern part of Ningxia. [ Methed] Through Takahashi＇s evaporation equation, linear trend analysis, Mann -Kendall, Lepage, wavelet analysis, the characteristics of available precipitation and its abnormal characteristics during its growth period in Ningxia were analyzed based on monthly precipitation （March- September）, temperature, and NCAR/NCEP reanalysis data in 9 observation stations from 1961 to 2010. E Result l In recent 50 years, the available precipitation during the growth period of crops in central drought area and south hilly area varied a lot, more in the south and less in the north. The available precipitation in these two areas was reducing and varied a lot in different ages. The available precipitation was less in the middle drought region after 1970s and in the southern hilly region after 1990s and the available precipitation in middle drought area changed significantly. The available precipitation in the two areas appeared in July, August, and September, above 76% of general growth period, while that in March, April and May was 14% lower than that in growth period. No abrupt changes in central drought area and south hilly area. There were the periods of 5 -7 a and 2 -3 a oscillations in the middle drought region, 2 -3 a and 10 -12 a oscillations in the southern hilly region. There were negative anomaly field at 500hPa height in high-precipitation years between the Baikal and the China＇s northwestern, and there were positive anomaly field in low-precipitation years. [ Cenclusion] The study provided reference for the reasonable utilization of available water resources in cen- tral and south Ningxia.

Chebyshev spectral variational integrator and applications

The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.

Research of Water Quality Analysis,Treatment and Reuse Technology for Rainwater on the North University Campus

The pollution situation of different underlying surface and the change rule of each water quality index were researched,on the basis of rainwater quality monitoring by different approaches in a university campus. The results showed that due to some factors,such as the underlying surface material pollution,road materials,road surface pollution condition and surrounding atmospheric environment quality,the pollution of different underlying surface rainwater would be different. Main pollutants of rainwater runoff in the city campus area were such as COD,SS,NH;-N,TP,etc. Ultimately,along with the increase of accumulated rainfall,the pollutants tended to gradually decrease. The road rain pollution was more serious than roof runoff pollution and the early rain pollution was serious,but the late rain water quality was much better. According to the rainwater conditions,subsequent rainwater recycling technology and processing technology were determined as a way to alleviate the problem of water shortage and water pollution.

Recognizing Expression Variant and Occluded Face Images Based on Nested HMM and Fuzzy Rule Based Approach

The face recognition with expression and occlusion variation becomes the greatest challenge in biometric applications to recognize people. The proposed work concentrates on recognizing occlusion and seven kinds of expression variations such as neutral, surprise, happy, sad, fear, disgust and angry. During enrollment process, principle component analysis (PCA) detects facial regions on the input image. The detected facial region is converted into fuzzy domain data to make decision during recognition process. The Haar wavelet transform extracts features from the detected facial regions. The Nested Hidden markov model is employed to train these features and each feature of face image is considered as states in a Markov chain to perform learning among the features. The maximum likelihood for the input image was estimated by using Baum Welch algorithm and these features were kept on database. During recognition process, the expression and occlusion varied face image is taken as the test image and maximum likelihood for test image is found by following same procedure done in enrollment process. The matching score between maximum likelihood of input image and test image is computed and it is utilized by fuzzy rule based method to decide whether the test image belongs to authorized or unauthorized. The proposed work was tested among several expression varied and occluded face images of JAFFE and AR datasets respectively.

A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI VARIATIONAL INEQUALITIES

The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.

四种沙蜥的形态地理变异:Bergmann和Allen规律的检验

本文通过比较四种沙蜥近缘种:青海沙蜥(Phrynocephalus vlangalii)、荒漠沙蜥(P.przewalskii)、变色沙蜥(P.versicolor)和叶城沙蜥(P.axillaries)形态特征和分析青海沙蜥种群沿海拔梯度的变异来验证Bergmann和Allen规律在爬行动物沙蜥属的适用性。生存在邻近地区不同海拔梯度的四种沙蜥个体大小种间比较显示遵循Bergmann和Allen规律,分布于高海拔的青海沙蜥尾椎骨数显著少于其它三种低海拔沙蜥,这种沿海拔梯度种间形态变异可能主要由遗传因素决定。青海沙蜥随海拔梯度的上升个体变小,四肢变短,形态变异反Bergmann规律,相对尾长随海拔变异遵循Allen规律,但相对四肢长度反Allen规律。这种变异可能更受到不同海拔梯度环境特征,尤其是高海拔缺氧和食物短缺的影响。

橄榄油Rancimat加速氧化过程中生育酚含量的衰减变化规律研究

通过Rancimat油脂氧化稳定性测定仪加速橄榄油样品的氧化,使用高效液相色谱仪监测各种生育酚含量,研究橄榄油氧化过程中α-、β-、γ-生育酚含量的衰减变化规律。结果表明:温度对生育酚含量的衰减速率起到决定性影响,随着温度不断升高,各生育酚含量的衰减速率急剧加快;并且发现β-、γ-生育酚的稳定性受α-生育酚含量的影响,当橄榄油中α-生育酚含量较高时,β-、γ-生育酚含量衰减非常缓慢,说明两者稳定性较好;当橄榄油中α-生育酚含量衰减接近0时,γ-生育酚与β-生育酚含量迅速衰减为0,说明此时两者的稳定性急剧下降。

中国1961-2010年气象干旱的时空规律——基于SPEI和Intensity analysis方法的研究

利用中国752个气象站降水、气温资料,选择标准化降水蒸散发指数SPEI为干旱指标,采用Intensity analysis方法,从时间间隔、干旱等级变化和转换三个层面分析了1961-2010年中国气象干旱变化规律。结果表明:1961-2010年中国气象干旱的变化速率趋于上升,总变化面积由60%上升至80%以上,1980-1990年代、1990年代至21世纪初两个时间段的年平均变化相对于整个时间段较快。1960-1980年代干旱变化较为平缓,1960-1970年代干旱等级的转换主要以中等以下的干旱等级之间的转换为主导;1970-1980年代以无干旱与轻微、中等和严重干旱等级之间的相互转换为主导。1980年代至21世纪初干旱有加重的趋势,1980-1990年代以无干旱向极端干旱的转换为主导;1990年代至21世纪初中等以下的干旱向严重和极端干旱的转变成为了主导,而严重干旱则以向极端干旱转换为主导,极端干旱以向中等干旱转换为主导。

青海省察尔汗盐湖区卤水中十二烷基吗啉的分布特征及变化规律

青海省察尔汗盐湖区钾肥生产目前主要使用的反浮选药剂是十二烷基吗啉(DMP),但目前对于察尔汗盐湖区卤水中DMP的浓度及分布特征尚不清楚。采集了察尔汗盐湖区33个采样点的卤水样(其中部分为淡水样),采用甲基橙分光光度法对水样中DMP浓度进行定量检测,分析湖区DMP浓度及分布特征。研究结果表明:(1)察尔汗盐湖区DMP浓度的空间分布呈现整体较低、部分地区出现高值的特征。(2)在湖区所采的不同类型水样中,DMP浓度呈现生产线卤水>盐田卤水>盐湖卤水>淡水≈采卤渠卤水的分布特征,质量浓度介于0.06~18.90 mg/L,平均值为2.16 mg/L。(3)卤水中DMP浓度受pH、电导率、Na^(+)、K^(+)、Mg^(2+)变化影响。

旱地沙蜥三个地理种群形态变异与两性异形——Bergmann法则、Allen法则和Rensch法则的检验

环境对动物体型和暴露附器大小的影响已有大量研究,但对两性异形的影响研究尚不多见,本文研究了旱地沙蜥Phrynocephalus helioscopus 3个地理种群形态的两性异形和地理变异,综合了Bergmann法则、Allen法则和Rensch法则分析其体型、四肢和尾部大小的变化规律。结果表明,伊宁和塔城种群的雌、雄亚成体体型差异无统计学意义(P>0.05),北屯市雄性体型显著大于雌性(P<0.05);伊宁和北屯种群的雌性成体体型均显著大于雄性(P<0.05),但塔城地区两性体型差异无统计学意义(P>0.05)。协方差分析结果表明,亚成体两性间只有塔城地区的雄性前肢长显著大于雌性(P<0.05);3个地区雄性成体均具有较大的后肢和尾部(P<0.01),伊宁市雌性具有较长的前肢(P<0.05),塔城和北屯市两性前肢长差异均无统计学意义(P>0.05),3个地区旱地沙蜥的体型呈反Bergmann法则的现象;四肢和尾部的大小遵循Allen法则;体型、前肢长、后肢长和尾长不遵循Rensch法则。旱地沙蜥3个地理种群受弥散性的自然选择压力比定向性的繁殖力选择和性选择的作用更强。

Banach空间中的一类非线性混合似变分不等式

应用辅助似变分不等式技巧,解决自反Banach空间中一类非线性混合似变分不等式解的存在性,通过迭代法则计算其近似解,并证明该迭代序列的收敛性.

乳腺癌复发恐惧变化规律及预测因子研究进展

综述乳腺癌复发恐惧的纵向变化规律和有关预测因子研究进展,指出低、中水平复发恐惧随时间逐渐下降,但具有个人差异性,高水平复发恐惧有相对独特的变化轨迹。年轻、低经济收入、情绪不乐观、低社会支持、更多的身体症状、家族史等是高水平复发恐惧的预测因子。目前国内仍缺少与乳腺癌复发恐惧的纵向及干预研究,未来可以加大在此方面的研究力度,争取对高危人群做到早识别、早干预。

中国新疆博斯腾湖现代碳库效应研究

碳库效应存在影响了14 C测年的准确性,制约了沉积物在湖泊研究中的应用。本文研究位于典型西风环流带的新疆博斯腾湖现代碳库效应,结合同位素地球化学、水化学等方法,探讨了博斯腾湖碳库效应的影响机制。研究结果表明,博斯腾湖最大现代碳库年龄为3535年,最小为现代碳,集中在670~945年。而过去碳库效应集中在1033~2200年。深水区表现为碳库年龄较小且稳定;在入湖口碳库效应最大,富水生植物浅水区碳库效应最小。与过去碳库年龄相比较,现代碳库效应整体表现更为年轻。研究发现,博斯腾湖口受流域外源“死”碳影响,深水区受湖水与大气CO_(2)交换率差异影响,富水生植物浅水区可能受水生植物光合作用影响。此外,核爆效应也对博斯腾湖现代碳库效应产生了影响,可能导致最高约1000年的年代误差。利用深水区放射性碳比活度(pMC)平均值与大气碳比活度差值(~18%),得出深水区沉积物存在约846年现代碳库效应,再经核爆效应校正后得出博斯腾湖存在最高约1800年碳库效应。

煤矿井下地磁定位的日变研究

近年来定位技术发展十分迅速,其中井下定位技术成为研究热点。在井下突发人员逃生、救援定位与导航等应急情况时,地磁定位可在无网络、无电时利用单兵PDA中内置的地磁基准图进行精准定位。首先分析了井下地磁定位的机理,并构建了井下地磁定位框架;再针对井下地磁的扰动现象进行日变测量,并分析了其变化规律。多项实验结果表明,在无干扰条件下,井下地磁变化较小且呈周期性变化。

汉江襄阳城区段水质变化规律及特征分析

为全面掌握汉江襄阳城区段沿程水质变化情况,合理制定相应保护措施,基于2018—2022年汉江襄阳城区段出入境断面及支流水质监测数据,对汉江襄阳城区段水环境质量、变化趋势和相关特征开展综合分析评价。结果表明,2018—2022年汉江襄阳城区段入境与出境断面水质状况总体为优,但出境断面氨氮、总磷、总氮的质量浓度较入境断面均有明显增高,主要支流唐白河、清河及南渠的汇入对出境断面水质影响较大。2018—2021年汉江襄阳城区段出入境断面主要监测指标质量浓度分布表现为丰水期>枯水期,2022年表现为枯水期>丰水期。汉江襄阳城区段水质氮污染贡献明显高于磷污染,仍以氮污染为主,水质中氮主要以游离氨和铵盐以外的形式存在。相关性分析结果表明,入境断面与出境断面中氨氮、总氮与各指标相关性差别较大,总磷、溶解氧与各参数间的相关性基本一致。研究结果可为制定汉江水环境改善及污染防治措施提供科学依据。

大汶河水文要素变异规律研究

以戴村坝水文站以上即大汶河中上游流域为研究对象,基于流域降水及戴村坝站日径流数据,采用多种水文统计方法,研究大汶河水文要素的演变特征,结果表明:大汶河降雨和径流整体呈下降趋势;采用主成分分析法(PCA),从IHA的33个指标中优选出9个指标作为水文变异规律研究的代表性指标,用于大汶河水文改变度的评价,水文整体改变度与IHA指标体系的水文改变度仅相差7.52%;优选指标可全面合理的评价大汶河水文情势变化。

近60年黑龙江省极端降水事件分布特征

文中采用泰森多边形、反距离权重、Mann-Kendall检验和小波分析法分析黑龙江省1960—2021年33个气象站逐日降水数据,系统研究了6个极端降水指数的空间分布特征、时间尺度上的趋势变化、突变性和周期性。结果表明,极端降水指数空间分布变化显著,研究区北部和南部降水量较大、西部地区降水强度较大;在0.05的置信区间内,极端降水事件突变多发生在20世纪60年代和80年代左右,且主周期变化中心为41年前后;人为因素和自然因素极大地影响着极端降水指数的变化,极端降水事件对城市化进程、自然地理因素和大尺度气候因子有一定的指示作用。