A Generalized Hirota Ansatz to Obtain Soliton-Like Solutions for a (3+l)-Dimensional Nonlinear Evolution Equation

Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.

Symbolic Computation and Construction of New Exact Travelling Wave Solutions to (3+1)-Dimensional KP Equation

With the aid of symbolic computation system Maple, many exact solutions for the （3＋1）-dimensional KP equation are constructed by introducing an auxiliary equation and using its new Jacobi elliptic function solutions, where the new solutions are also constructed. When the modulus m → 1 and m →0, these solutions reduce to the corresponding solitary evolution solutions and trigonometric function solutions.

The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution

The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied.First,we design a new disturbance expansion to describe the ion fluid velocity and electric field potential.It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation.Then,based on the piecewise function perturbation,a(3+1)-dimensional generalized modified Korteweg–de Vries Zakharov–Kuznetsov(mKdV-ZK)equation is derived for the first time,which is an extended form of the classical mKdV equation and the ZK equation.The(3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle.Obviously,it is more accurate to depict some complex plasma processes and phenomena.Further,the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed.Finally,using the multi-exponential function method,the non-resonant multiwave solutions are constructed,and the characteristics of ion-acoustic waves are well described.

3维Copula函数在降雨特征多变量频率分析中的应用

鉴于径流数据缺乏且难以长期监测而降雨数据相对完整,通常假定降雨和径流同频率,采用设计降雨进行水文分析计算,但此方法很难真实全面地反映降雨变化特征.为此,提出一种基于3维Copula函数的降雨特征多变量频率分析方法.首先利用降雨强度法将连续的降雨时间序列分割成若干个降雨事件,采用年最大值法取样,统计出表征雨量的特征变量,然后引入3维Copula函数构建降雨特征3变量联合概率模型,并以广州1961~2012年历史降雨数据为例进行分析.结果表明,基于3维Copula函数的多变量分析方法计算简单、可靠性高,可以进行3种不同降雨特征变量的组合分析,得到各种不同量级变量的遭遇概率和条件概率,能够更全面地反映降雨特征并更好地满足水文分析计算需求.

Construction of <i>k</i>-Variate Survival Functions with Emphasis on the Case <i>k</i>= 3

The purpose of this paper is to present a general universal formula for k-variate survival functions for arbitrary k = 2, 3, ..., given all the univariate marginal survival functions. This universal form of k-variate probability distributions was obtained by means of “dependence functions” named “joiners” in the text. These joiners determine all the involved stochastic dependencies between the underlying random variables. However, in order that the presented formula (the form) represents a legitimate survival function, some necessary and sufficient conditions for the joiners had to be found. Basically, finding those conditions is the main task of this paper. This task was successfully performed for the case k = 2 and the main results for the case k = 3 were formulated as Theorem 1 and Theorem 2 in Section 4. Nevertheless, the hypothetical conditions valid for the general k ≥ 4 case were also formulated in Section 3 as the (very convincing) Hypothesis. As for the sufficient conditions for both the k = 3 and k ≥ 4 cases, the full generality was not achieved since two restrictions were imposed. Firstly, we limited ourselves to the, defined in the text, “continuous cases” (when the corresponding joint density exists and is continuous), and secondly we consider positive stochastic dependencies only. Nevertheless, the class of the k-variate distributions which can be constructed is very wide. The presented method of construction by means of joiners can be considered competitive to the copula methodology. As it is suggested in the paper the possibility of building a common theory of both copulae and joiners is quite possible, and the joiners may play the role of tools within the theory of copulae, and vice versa copulae may, for example, be used for finding proper joiners. Another independent feature of the joiners methodology is the possibility of constructing many new stochastic processes including stationary and Markovian.

基于三维copula函数的多水文区丰枯遭遇分析

不同水文区的丰枯遭遇概率分析属于多变量概率分布问题,涉及的水文区越多,变量的维数就越高,问题就越复杂.为找到一种简单通用的多变量(n≥3)水文概率问题的求解方法,以不同水文区丰枯遭遇概率分析为例,引入三维copula函数构建多变量联合概率模型,将其用于分析长江、淮河及黄河流域的径流量的联合概率和条件概率问题。研究结果表明,当变量维数n≥3时,由copula函数可以很容易地构建多变量概率分布模型;对一组水文数据系列,有多个不同copula函数可以选择,可采用拟合优度检验方法择优;copula函数构建的多变量概率模型,可以计算各种条件下的联合概率分布,可以分析各种不同量级水文变量的遭遇概率和条件概率;通过与多维转换为一维方法的比较,三维Frank copula函数具有更优良的拟合优度、无偏性及有效性,且计算更简便。

New lump solutions and several interaction solutions and their dynamics of a generalized(3+1)-dimensional nonlinear differential equation

In this paper,we mainly focus on proving the existence of lump solutions to a generalized(3+1)-dimensional nonlinear differential equation.Hirota’s bilinear method and a quadratic function method are employed to derive the lump solutions localized in the whole plane for a(3+1)-dimensional nonlinear differential equation.Three examples of such a nonlinear equation are presented to investigate the exact expressions of the lump solutions.Moreover,the 3d plots and corresponding density plots of the solutions are given to show the space structures of the lump waves.In addition,the breath-wave solutions and several interaction solutions of the(3+1)-dimensional nonlinear differential equation are obtained and their dynamics are analyzed.

Sonographic evaluation of proximal gastric accommodation in patients with functional dyspepsia

AIM: To assess the value of ultrasonography (US) in evaluation of proximal gastric accommodation disorder in patients with functional dyspepsia (FD). METHODS: Between April 2011 and March 2012, 45 patients with FD and 27 healthy volunteers were enrolled in this study. Two-dimensional ultrasound (2DUS) and 3-dimensional ultrasound (3DUS) were performed sequentially to measure proximal gastric area (PGA), maximal proximal gastric diameter (MPGD), and proximal gastric volume (PGV). These values were measured separately in the two groups every other 5 min for a duration of 25 min after the beginning of ingestion of a test meal. Air pocket grading was done separately for images of 2DUS and blocks of 3DUS obtained at five scanning time points. RESULTS: Both PGA and PGV of patients were significantly smaller than healthy controls (P = 0.000 and 0.002, respectively). Comparing the two parameters between the groups at each time point, the differences were also statistically significant (P = 0.000-0.013), except at 10 min for the PGV (P = 0.077). However, no overall difference was found between the groups in the MPGD measurements (P = 0.114), though it was statistically significant at a 20-minute examination point (P = 0.026). A total of 360 sets or blocks of images were obtained for both 2DUS and 3DUS. For the images analyzed by 2DUS, none were excluded because of gastric gas, and 50 (13.9%) and 310 (86.1%) sets were determined as air pockets grades 1 and 2, respectively. For the images analyzed by 3DUS, 23 (6.4%) blocks were excluded from the measurement due to presence of a large fundus air pocket (grade 3); fifty (13.9%) and 287 (79.7%) blocks were also graded as 1 and 2, respectively. CONCLUSION: Measurement of both PGA and PGV by 2DUS and 3DUS could be useful for assessment of the proximal gastric accommodation.

Assessment of proximal gastric accommodation in patients with functional dyspepsia

Impaired gastric accommodation is one of the most important etiologic factors in the pathophysiology of functional dyspepsia.Ultrasound is a potential alternative method to study changes in gastric volume as a reflection of gastric accommodation.Ultrasound is suitable for patients because it is a non-invasive,easily repeated and non-radioactive procedure,and a previous study has demonstrated the feasibility of 3-dimensional ultrasound in examining functional dyspepsia.The brief article by Fan et al demonstrated that both the proximal gastric area and volume,measured by 2-and 3-dimensional ultrasound respectively,were significantly smaller in patients with functional dyspepsia than in healthy controls.These results are very interesting,but we raise the relevant point that it should have been mandatory to study both changes in gastric volume and their relationship with upper gastrointestinal symptoms in functional dyspepsia.In fact,the relationship between cardinal symptoms and several pathophysiologic mechanisms in functional dyspepsia remains a matter of debate.Moreover,further evaluation of distal gastric volume that has been previously implicated in the origin of functional dyspeptic symptoms is advisable.Therefore,impaired gastric accommodation does not serve as a clear marker of the cardinal symptoms experienced by patients with functional dyspepsia in daily life.

基于Copula函数的区域洪水频率分析

【目的】洪水频率分析为水利工程的规划、设计和运行提供了理论依据。传统的单变量频率分析方法已被广泛的研究和应用,但区域水文站点之间往往相互关联,单站点的独立洪水频率分析并不能满足实际工作的需求。因此,有必要考虑区域洪水变量间的相关关系,建立联合分布,采用多变量联合概率分析方法以提高洪水频率分析的可靠性。同时,由于区域洪水特性差异显著,需要探究Copula函数在不同区域洪水频率分析中的适用性。【方法】基于盘龙江区域的小河(中和)站、松华坝站、昆明站三个水文站以及长江上游区域的寸滩站、清溪场站、宜昌站三个水文站的洪水资料,建立站点年最大洪峰流量的边缘分布函数,用Kolmogorov-Smirnov法检验其拟合优度,分析站点洪水变量间的相关程度,进而利用嵌套Copula法和Copula函数表达式法构建区域三站点年最大洪峰流量的联合分布,采用分位数图法、均方根误差法和AIC信息准则法在选用的T-Copula、GH Copula、Frank Copula、以及Clayton Copula四类函数模型中进行拟合优度评价,通过优选的函数模型分析计算条件概率。【结果】结果显示:盘龙江和长江上游区域站点的年最大洪峰流量序列均可用P-Ⅲ型分布作为其边缘分布,且站点变量间的相关性良好,可运用Copula函数描述其相关关系,以此建立联合分布。其中,在盘龙江区域站点变量间,T-Copula函数拟合效果最优;在长江上游区域站点变量间,Frank Copula函数拟合效果最优。由优选的Copula函数模型预测下游站点的洪水遭遇量级,预测值与实测值的接近程度均达到85%以上。【结论】在区域站点洪水样本序列可求解其边缘分布,且变量间相关性显著的情况下,Copula函数能够较好描述变量间的相关关系。对于洪水特性差异较大的盘龙江和长江上游两个区域可优选出不同类型的Copula函数建立联合分布进行洪水频率分析,且计算结果能够准确的预测区域站点的洪水遭遇量级。研究成果可为区域联合防洪提供科学参考。

Hyperelliptic Function Solutions of Three Genus for KP Equation Using Direct Method

In this paper, we will use a simple and direct method to obtain some particular solutions of （2＋1）- dimensional and （3＋ 1）-dimensional KP equation expressed in terms of the Kleinian hyperelliptic functions for a given curve y^2 = f（x） whose genus is three. We observe that this method generalizes the auxiliary method, and can obtain the hyperelliptic functions solutions.

On the Quasi-Periodic Wave Solutions and Asymptotic Analysis to a(3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.

多变量干旱事件识别与频率计算方法

干旱持续时间久、影响范围大,时空连续性是干旱的基本特征,以往研究大多考虑单变量或双变量。通过给定阈值识别干旱斑块和判断两相邻时间干旱的连续性,提出了时空连续的干旱事件三维识别方法,用干旱历时、干旱面积、干旱烈度、干旱强度和干旱中心位置5个特征变量对一场干旱事件进行度量;提出了基于Copula函数的干旱历时-面积-烈度三变量频率分析方法。以中国西南地区为例,采用SPI(Standard Precipitation Index)干旱指标识别了近52年发生历时等于或大于3个月的干旱事件,一共78场,其中2009年8月至2010年6月最严重干旱事件的重现期为94年一遇。通过比较概率分布函数和Copula函数,表明在干旱频率分析时需要考虑干旱历时、面积、烈度3个特征变量。

上海市不同历时暴雨组合概率研究

基于上海市徐家汇站1960—2011年的日降雨资料,分析上海市年最大1d和3d降水量年际变化和年代际变化特性;择优选择GH Copula函数构建了年最大1 d与3 d降水量的联合分布模型,并推算它们的同现重现期和组合风险概率。结果表明:年最大1 d和3 d降水随时间呈增加趋势,自20世纪70年代开始其均值随年代增加;年最大1 d和3 d设计暴雨同频遭遇风险率在75%~85%之间,且同现风险率随年最大1 d设计暴雨值增大而增加。在设计上海市防洪排涝标准时若考虑最大1 d和3 d降水量的遭遇组合,有利于提升防洪排涝能力,保障防洪安全。

基于不同分布曲线的常州市暴雨组合概率

基于常州雨量站1951—2015年的年最大1 d、3 d降水量资料,利用Copula联结函数构建联合分布函数,推算相应的同现重现期和组合风险率,并以此为基础,评价常州市2015年"6·26"暴雨可能的重现期和风险率。结果表明:某一设计标准下的年最大1 d、3 d降水遭遇时的同现重现期大于年最大1 d或3 d降水单变量对应的重现期;同一设计频率的暴雨遭遇的风险率较高,且随着重现期增大而减小;"6·26"暴雨的同现重现期为218 a,同现风险率为17.4%,此次暴雨具有特殊性和罕见性,常州市未来的防洪形势将更为严峻。

Preoperative liver functional volumetry performed by 3D-99mTc-GSA scintigraphy/vascular fusion imaging using SYNAPSE VINCENT: a preliminary study

Aim:The present study was designed to evaluate the feasibility of preoperative liver functional volumetry performed by 3D-technetium-99m-diethylenetriaminepentaacetic acid-galactosyl-human serum albumin(99mTc-GSA)scintigraphy/vascular fusion imaging using SYNAPSE VINCENT and to examine the discrepancy between conventional and functional volumetry.Methods:The study group comprised 15 patients who underwent preoperative 3-dimensional(3D)-99mTc-GSA scintigraphy/vascular fusion imaging using SYNAPSE VINCENT software before hepatectomy between July 2014 and August 2015.The diagnosis was hepatocellular carcinoma(n=4),metastatic liver tumor(n=10),or intrahepatic cholangiocarcinoma(n=1).Right hepatectomy was performed in 2 patients,left hepatectomy in 3 patients,right posterior sectionectomy in 3 patients,segmentectomy in 2 patients,and partial hepatectomy in 4 patients.99mTc-GSA scintigraphy and computed tomography(CT)were performed to construct 3D-99mTc-GSA scintigraphy/vascular fused images.The conventional volume ratio of the planned resection region without tumor(%CT),and the functional volume ratio of the planned resection region without tumor(%GSA)were calculated.The discrepancy ratio was calculated as follows:discrepancy ratio=100-%GSA/%CT×100(%).Results:The%GSA(17.9±16.7%)was significantly lower than the%CT(21.5±17.6%)(P<0.036).In all except 2 patients,the%GSA was lower than the%CT.The discrepancy ratio ranged from-4%to 75%(median,20.7%).Conclusion:3D-99mTc-GSA scintigraphy/vascular fused images constructed using SYNAPSE VINCENT were useful for noninvasively performing functional liver volumetry in patients scheduled to undergo various patterns of hepatectomy.In planned resection regions without tumor,the functional volume ratio was about 20%lower than the conventional volume ratio.

基于三维Copula函数的永宁江流域洪潮遭遇分析

沿海平原洪涝灾害严重,致灾因子众多,需依据多变量水文频率分析成果进行防洪排涝规划设计。为解决沿海地区多变量遭遇问题,以永宁江流域为研究对象,采用三维非对称Gumbel-Hougaard Copula和Clayton Copula函数构建了暴雨、洪峰及潮位的三维联合分布模型,通过计算联合风险率、同现风险率、条件风险率及其重现期分析不同洪潮遭遇组合的风险,并提出了不同支流暴雨条件下的干流洪峰及潮位最可能组合方案。结果表明:三维Gumbel-Hougaard Copula函数计算的联合分布与经验分布拟合程度较高,能够明确计算出不同暴雨条件下的最可能洪峰和潮位组合,评估遭遇组合的风险,可为永宁江流域防洪排涝规划设计提供决策参考。