The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group

The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.

Design Strategy of Underground Space of Urban Rail Transit Complex Based on Integration Concept

With the accelerated development and utilization of urban underground space,the underground space design of complex based on rail transit has attracted much attention.By sorting out the integration concept and constructing the logical framework of integrated design,the integrated design strategy is proposed from the aspects of function,transportation,space and environment on the urban scale,and the evaluation points of integrated design effect are put forward from the aspects of accessibility,coordination,openness and symbolism.

INTS10对HCC细胞周期、凋亡、生长和迁移能力的影响

为了探究整合因子复合物亚基10(integrator complex subunits 10,INTS10)对人肝细胞癌(hepatocellular carcinoma,HCC)细胞周期、凋亡、生长和迁移能力的影响及其潜在的分子作用机制,利用慢病毒感染法获得稳定过表达或敲低INTS10的HCC细胞系,采用qRT-PCR和Western blotting检测INTS10 mRNA和蛋白表达水平,接着采用CCK-8法、克隆形成和BrdU实验检测细胞生长情况,采用Transwell小室实验检测细胞迁移能力,采用流式分析术检测细胞的周期和凋亡.结果显示:过表达INTS10可显著抑制HCC细胞的凋亡、生长和迁移能力,促进G1期细胞数量的增加,而敲低INTS10则呈现相反的表型.通过通路富集分析发现,周期相关通路被显著富集,过表达INTS10后,CDC25A和CDK4的mRNA和蛋白质水平显著减少,而CDKN1A的水平显著增加,敲低INTS10则呈现相反趋势.综上,本研究初步揭示了INTS10在HCC细胞中可能通过影响G1/S期相关蛋白质的表达而发挥抑癌基因的功能,为下一步更为深入的功能和机制研究提供了基础.

3种灵长类动物SAGE1与INTS3相互作用保守性的验证

目的·研究恒河猴(Rhesus)、狨猴(Marmoset)、倭狐猴(Mouse Lemur)这3种代表性灵长类动物的癌-睾丸抗原(cancer-testis antigen,CTA)家族成员之一的肉瘤抗原1(sarcoma antigen 1,SAGE1)的进化,及其与整合体复合物(integrator complex,INT)亚基INTS3之间的相互作用的保守性。方法·首先在HEK293T细胞中利用免疫共沉淀(coimmunoprecipitation,Co-IP)的方法验证3种灵长类动物的SAGE1和INTS3相互作用。随后在互作蛋白截短的片段上分别添加His-SUMO和GST标签,并在大肠埃希菌中进行表达,经过系列纯化步骤得到目标蛋白。通过表面等离子体共振(surface plasmon resonance,SPR)实验测定目标蛋白之间的结合强弱,借助广角激光散射凝胶排阻层析(size exclusion chromatographywithmulti-anglelightscattering,SEC-MALS)技术检测复合物的结合比例,并利用分子对接技术预测SAGE1和INTS3截短体的结合模型。分析人类INTS3和SAGE1互作界面,挑选在灵长类中也相对保守的关键互作氨基酸位点,将其突变后再次使用Co-IP分析INTS3和SAGE1的结合情况。结果·通过Co-IP方法,确定3种灵长类动物中INTS3和SAGE1全长蛋白之间存在相互作用。截短体蛋白经过外源诱导表达和多步纯化,获得高纯度蛋白样品;经过SPR对其进行结合和解离检测分析,得到了它们的解离常数在微摩尔级别;并且SEC-MALS结果显示INTS3与SAGE1的结合比例为2∶1。使用分子对接预测SAGE1和INTS3截短体结合模型,发现该复合物具有典型的“蝴蝶型结构”,由INTS3二聚体组成“蝴蝶身体”,由SAGE1组成“蝴蝶头部”,结合界面中疏水相互作用构成了主要的互作模式。分析突变后的SAGE1与INTS3全长蛋白相互作用,它们之间的结合明显减弱。结论·恒河猴、狨猴、倭狐猴中INTS3与SAGE1存在相互作用,并且相互作用具有高度的保守性。

HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.

Synthesis of Heat Integrated Complex Distillation Systems via Stochastic Optimization Approaches

This paper addresses the application of stochastic optimization approaches to the synthesis of heatintegrated complex distillation system, which is characterized by large-scale combinatorial feature. Conventionaland complex columns, thermally coupled (linked) side strippers and side rectifiers as well as heat integration betweenthe different columns are simultaneously considered. The problem is formulated as an MINLP (mixed-integernonlinear programming) problem. A simulated annealing algorithm is proposed to deal with the MINLP problemand a shortcut method is applied to evaluate all required design parameters as well as the total cost function. Twoillustrating examples are presented.

Compact implicit integration factor methods for some complex-valued nonlinear equations

The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.

New constraints on the P-T path of HT/UHT metapelites from the Highland Complex of Sri Lanka

We report here rare evidence for the early prograde P-Tevolution of garnet-sillimanite-graphite gneiss(khondalite)from the central Highland Complex,Sri Lanka.Four types of garnet porphyroblasts(Grt_1,Grt_2,Grt_3 and Grt_4)are observed in the rock with specific types of inclusion features.Only Grt_3 shows evidence for non-coaxial strain.Combining the information shows a sequence of main inclusion phases,from old to young:oriented quartz inclusions at core,staurolite and prismatic sillimanite at mantle,kyanite and kyanite pseudomorph,and biotite at rim in Grt_1;fibrolitic sillimanite pseudomorphing kyanite±corundum,kyanite,and spinel+sillimanite after garnet+corundum in Grt_2;biotite,sillimanite,quartz±spinel in Grt_3;and ilmenite,rulite,quartz and sillimanite in Grt_4.The pre-melting,original rock composition was calculated through stepwise re-integration of melt into the residual,XRF based composition,allowing the early prograde metamorphic evolution to be deduced from petrographical observations and pseudosections.The earliest recognizable stage occurred in the sillimanite field at around 575℃ at 4.5 kbar.Subsequent collision associated with Gondwana amalgamation led to crustal thickening along a P-T trajectory with an average dP/dT of ~30 bar/℃ in the kyanite field,up to ~660℃ at 6.5 kbar,before crossing the wet-solidus at around 675 ℃ at 7.5 kbar.The highest pressure occurred at P > 10 kbar and T around 780℃ before prograde decompression associated with further heating.At 825℃ and 10.5 kbar,the rock re-entered into the sillimanite field.The temperature peaked at 900℃ at ca.9-9.5 kbar.Subsequent near-isobaric cooling led to the growth of Grt_4 and rutile at T ~880℃.Local pyrophyllite rims around sillimanite suggest a late stage of rehydration at T<400℃,which probably occurred after uplift to upper crustal levels.U-Pb dating of zircons by LAICPMS of the khondalite yielded two concordant ^(206)Pb/^(238)U age groups with mean values of 542±2 Ma(MSWD=0.24,Th/U=0.01-0.03)and 514±3 Ma(MSWD=0.50,Th/U=0.01-0.05)interpreted as peak metamorphism of the khondalite and subsequent melt crystallization during cooling.

Boundary integral equations for dynamic rupture propagation on vertical complex fault system in half-space:Theory

The boundary integral equation method （BIEM） is now widely used in numerical studies on earthquake rupture dynamics, and is proved to be a powerful tool to deal with problems on complex fault system. However, since this method heavily lies on the specific forms of Green＇s function and only the Green＇s function in full-space has a closed analytic expression, it is usually limited to a full-space medium. In this study, as a first step to extend this method to an arbitrary complex fault system in half-space, the boundary integral equations （BIEs） for dynamic strike-slip on vertical complex fault system in half-space are derived based on exact Green＇s function for isotropic and homogeneous half-space. Effect of the geometry of the complex fault system are dealt with carefully. Final BIEs is composed of two parts： contribution from full-space, which has been thoroughly investigated by Aochi and his co-workers by using the Green＇s function for full-space, and that from free surface, which is studied in detail in this study.

ON THE REGULARIZATION METHOD OF THE FIRST KIND OFFREDHOLM INTEGRAL EQUATION WITH A COMPLEX KERNEL AND ITS APPLICATION

The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.

THE CAUCHY INTEGRAL OF MANY COMPLEX VARIABLES PASSIVE OPERATORS AND MULTIDIMENSIONAL DISPERSION RELATIONS

This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance

Integrated Design Approach for Solving Complexity of Design Problem

The engineering problems today become more and more complex particularly in the area of new product development. It requires the multi-disciplinary design method to solve complex problems. This paper presents an integrated design system for solving complexity during multi-disciplinary design. Complexity could be solved if the design problems, given by any individuals who are concerned, are structured. The design system uses the multi-viewpoint concept to allow experts to share their information and knowledge in common views. Knowledge modules are used to store semantics from the experts of different disciplines. Then the system agent acts as an internal designer to help support the individuals to translate any semantics provided from one discipline and then propagate to other related disciplines. With these tools, the integrated design system can structure and solve the complexity of design problems.

Direct Solutions of Some Singular Integral Equations on the Building Domain of Complex Biballs

By means of the method of solid angle coefficients and the permutation formula on the building domain of complex biballs,direct solutions of some singular integral equations with variable coefficients are discussed and the explicit formulas for these solutions are obtained.

PARALLEL INFORMATION-BASED COMPLEXITY OF NUMERICAL INTEGRATION ON SOBOLEV CLASS W_q^s(Ω)

This paper deals with the parallel information-based complexity of numerical integration on Sobolev class. We obtain tight bounds on the complexity, considered as a function of two variables simultaneously:the number of processors, the rquired precision. This result seems to be new even in serial case.

Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

A new approach for flow simulation in complex hydraulic fracture morphology and its application:Fracture connection element method

Efficient flow simulation and optimization methods of hydraulic fracture morphology in unconventional reservoirs are effective ways to enhance oil/gas recovery.Based on the connection element method(CEM)and distribution of stimulated reservoir volume,the complex hydraulic fracture morphology was accurately described using heterogeneous node connection system.Then a new fracture connection element method(FCEM)for fluid flow in stimulated unconventional reservoirs with complex hydraulic fracture morphology was proposed.In the proposed FCEM,the arrangement of dense nodes in the stimulated area and sparse nodes in the unstimulated area ensures the calculation accuracy and efficiency.The key parameter,transmissibility,was also modified according to the strong heterogeneity of stimulated reservoirs.The finite difference and semi-analytical tracking were used to accurately solve the pressure and saturation distribution between nodes.The FCEM is validated by comparing with traditional numerical simulation method,and the results show that the bottom hole pressure simulated by the FCEM is consistent with the results from traditional numerical simulation method,and the matching rate is larger than 95%.The proposed FCEM was also used in the optimization of fracturing parameters by coupling the hydraulic fracture propagation method and intelligent optimization algorithm.The integrated intelligent optimization approach for multi-parameters,such as perforation number,perforation location,and displacement in hydraulic fracturing is proposed.The proposed approach was applied in a shale gas reservoir,and the result shows that the optimized perforation location and morphology distribution are related to the distribution of porosity/permeability.When the perforation location and displacement are optimized with the same fracture number,NPV increases by 70.58%,which greatly improves the economic benefits of unconventional reservoirs.This work provides a new way for flow simulation and optimization of hydraulic fracture morphology of multi-fractured horizontal wells in unconventional reservoirs.

THE INTEGRAL FORMULA ON COMPLEX SUBMANIFOLD AND APPLICATION

First, this paper gives another integral representation an bounded convex domain in complex submanifold. Second, using this integral representation, the author easely gets the strengthen consequence of Elgueta.

地理学的时代特征、二元论与可持续发展

地理学作为一门学科总体上与科学体系的发展亦步亦趋。20世纪自然地理学与人文地理学的分裂曾严重消解了地理学的整体性和统一性,同时专业分化与研究主题的纵深发展造成了学科的空心化。面对21世纪复杂性科学、地球系统科学和新的科学综合体的到来,在全球化和可持续发展的大背景下,我们应该在大学课堂上让自然与人文再度融合,通过学术语言的规范、学科理论的构建、研究范式的转换,将二元论的影响消融于无形,能以一种整体化、系统性的观念来应对人类的未来和地球的可持续性发展这一艰巨而复杂的任务。

思政元素融入复变函数与积分变换课程的教学案例研究

为培养新时代中国社会主义的建设者和接班人,贯彻落实立德树人的根本任务,在复变函数与积分变换的教学过程中自然地融入课程思政元素,建立该课程的课程思政教学案例库是势在必行的。首先,深入挖掘思政元素与数学专业知识的结合点。其次,对线上线下混合教学模式进行课程思政设计。最后,形成适合本课程的课程思政教学案例。通过对课程思政案例的教学实践,教育引导学生成为热爱祖国、富有理想、视野宽广、德才兼备的创新型人才。