SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

Investigation on Damage Regularity of Mikania micrantha

[Objectives]The paper was to understand the occurrence and damage regularity of the invasive plant Mikania micrantha in Huadu District of Guangzhou.[Methods]The damage status of M.micranthFa in different forest lands and its annual growth dynamics were investigated by field investigation.[Results]With the change of canopy density from low to high,the occurrence degree of M.micrantha changed from high to low.The occurrence degree of M.micrantha in different forest land types was:abandoned orchard>wasteland>roadside greenbelt>waterside>forest edge>normally managed orchard.[Conclusions]M.micrantha enters the rapid growth period from March to May in spring,with the growth rate gradually slowing down after June.The result provides a theoretical basis and practical guidance for the prevention and control of M.micrantha.

The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles

This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.

THEORETICAL RESULTS ON THE EXISTENCE,REGULARITY AND ASYMPTOTIC STABILITY OF ENHANCED PULLBACK ATTRACTORS:APPLICATIONS TO 3D PRIMITIVE EQUATIONS

Several new concepts of enhanced pullback attractors for nonautonomous dynamical systems are introduced here by uniformly enhancing the compactness and attraction of the usual pullback attractors over an infinite forward time-interval under strong and weak topologies.Then we provide some theoretical results for the existence,regularity and asymptotic stability of these enhanced pullback attractors under general theoretical frameworks which can be applied to a large class of PDEs.The existence of these enhanced attractors is harder to obtain than the backward case[33],since it is difficult to uniformly control the long-time pullback behavior of the systems over the forward time-interval.As applications of our theoretical results,we consider the famous 3D primitive equations modelling the large-scale ocean and atmosphere dynamics,and prove the existence,regularity and asymptotic stability of the enhanced pullback attractors in V×V and H^(2)×H^(2) for the time-dependent forces which satisfy some weak conditions.

GLOBAL REGULARITY OF 2D INCOMPRESSIBLE MAGNETO-MICROPOLAR FLUID EQUATIONS WITH PARTIAL VISCOSITY

This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global regularity of the 2D incompressible magnetomicropolar fluid system for 21 anisotropic partial viscosity cases. He proved the global existence of a classical solution for some cases and established the conditional global regularity for some other cases. In this paper, we also investigate the global regularity of 12 cases in [22]and some other new partial viscosity cases. The global regularity is established by providing new regular conditions. Our work improves some results in [22] in this sense of weaker regular criteria.

Ground fissure development regularity and formation mechanism of shallow buried coal seam mining with Karst landform in Jiaozi coal mine: a case study

A comprehensive study was undertaken at Jiaozi coal mine to investigate the development regularity of ground fissures in shallow buried coal seam mining with Karst landform,shedding light on the development type,geographical distribution,dynamic development process,and failure mechanism of these ground fissures by employing field monitoring,numerical simulation,and theoretical analysis.The findings demonstrate that ground fissure development has an obvious feature of subregion,and its geographical distribution is significantly affected by topography.Tensile type,open type,and stepped type are three different categories of ground fissure.Ground fissures emerge dynamically as the panel advances,and they typically develop with a distance of less than periodic weighting step distance in advance of panel advancing position.Ground fissures present the dynamic development feature,temporary fissure has the ability of self-healing.The dynamic development process of ground fissure with closed-distance coal seam repeated mining is expounded,and the development scale is a dynamic development stage of“closure→expansion→stabilized”on the basis of the original development scale.From the perspective of topsoil deformation,the computation model considering two points movement vectors towards two directions of the gob and the ground surface is established,the development criterion considering the critical deformation value of topsoil is obtained.The mechanical model of hinged structure of inclined body is proposed to clarify the ground fissure development,and the interaction between slope activity and ground fissure development is expounded.These research results fulfill the gap of ground fissures about development regularity and formation mechanism,and can contribute to ground fissure prevention and treatment with Karst landform.

THE REGULARITY AND UNIQUENESS OF A GLOBAL SOLUTION TO THE ISENTROPIC NAVIER-STOKES EQUATION WITH ROUGH INITIAL DATA

A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.

Regularity classification and corresponding analysis method requirements of horizontally curved bridges with unequal pier heights

The seismic behavior of horizontally curved bridges,particularly with unequal height piers,is more complicated than that of straight bridges due to their geometric properties.In this study,the seismic responses of several horizontally curved single-column-bent viaducts with various degrees of curvature and different pier heights have been investigated,employing three different analysis approaches:namely,modal pushover analysis,uniform load method,and nonlinear time history analysis.Considering the investigated bridge configurations and utilizing the most common regularity indices,the results indicate that viaducts with 45-degree and 90-degree deck subtended angles can be categorized as regular and moderately irregular,respectively,while the bridges with 180-degree deck subtended angle are found to be highly irregular.Furthermore,the viaducts whose pier heights are asymmetric may be considered as irregular for almost all ranges of the deck subtended angles.The effects of higher transverse and longitudinal modes are discussed and the minimum analysis requirements are identified to assess the seismic response of such bridge configurations for design purposes.Although the Regularity Indices used here are useful tools to distinguish between regular and irregular bridges,further studies are needed to improve their reliability.

THE REGULARITY CRITERIA OF WEAK SOLUTIONS TO 3D AXISYMMETRIC INCOMPRESSIBLE BOUSSINESQ EQUATIONS

In this paper,we obtain new regularity criteria for the weak solutions to the three dimensional axisymmetric incompressible Boussinesq equations.To be more precise,under some conditions on the swirling component of vorticity,we can conclude that the weak solutions are regular.

THE EXISTENCE OF WEAK SOLUTIONS AND PROPAGATION REGULARITY FOR A GENERALIZED KDV SYSTEM

This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).

Lipschitz Regularity of Viscosity Solutions to the Infinity Laplace Equation

In this paper, we study the viscosity solutions of the Neumann problem in a bounded C2 domain Ω, where ΔN∞ is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .

LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS

This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.

Outline of Uranium Resources Characteristics and Metallogenetic Regularity in China

Uranium,as one of twenty-six kinds of important minerals in China,is strategic resource and energy mineral,which has been thoroughly investigated in the project of National Potential Evaluation of Uranium Resource.During the implementation of this project,the authors summarized the metallogenic regularity of uranium resource in China systematically,through the researches of geological characteristics of uranium resource,uranium deposits type（genetic and prediction type）,temporal and spatial distribution,and metallogenic series.Based on the investigation of present situation and progress in uranium exploration,this paper proposes the uranium deposits in China should be divided into 4 classes,9 types,21 subtypes in genetic,and 50 types in prediction;suggests to divide China into 29 uranium metallogenic belts and 20 uranium prospective area,and constructs 20uranium-polymetallic metallogenic series,through summarizing temporal and spatial distribution characteristics and metallogenic regularity of uranium deposits in China.The above research is beneficial to the comprehensive understanding of regional uranium metallogenic regularity,and will direct the uranium exploration in the future.

REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions （u,w, b）, i.e., u ∈ Lq（0, T; LP（R3） for 2/q＋3/P≤ 1with 3〈P≤∞,u∈C（[0,T）;L3（R3））or△u∈Lq（0,T,LP）for 3/2〈P≤∞ satisfying 2/q＋3/P≤ 2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p = ∞, the blow-up criteriacan be extended to more general spaces △u E L1 （0, T; B0∞,∞（R3）.

Distribution Characteristics and Metallogenic Regularity of Graphite Deposits in Qinling Orogen,China

Qinling orogen is one of the five main repository distribution provinces of large scale graphite resources. Graphite occurrence strata are multitudinous including NeoArchaean group to Neopaleozoic. Mineral deposit types are complete consisting of crystal flaky graphite deposit and aphanitic graphite deposit, ore types of the former are main graphite gneiss, graphite schist and graphitized marble, and ore types of the latter are main graphite layer metamorphosised from coal bed and graphitic carbargilite. At present, most graphite deposits with low research degree only implement preliminary investigations of the graphite resource, which has a good prospect. Based on the basic material of dozens of graphite deposits, spots and plays discovered in the Qinling orogen, this paper applied geologic multidisciplinary analysis method to disclose the graphite deposit types of the Qinling orogen, mainly through outdoors geologic survey and specimen examination with analysis of some typical deposits： regional metamorphism crystal graphite deposits and thermo-contact metamorphic aphanitic graphite deposits, with the control of latitudinally trending regional tectonic, graphite deposits of the Qinling orogen distribute sublatitudinally trending three large ore belts： I the Neoarchean-Proterozoic basement crystal graphite enrichment deposits zone along the south margin of North China plate; II the Carboniferous intermountain basin group aphanitic graphite enrichment deposits zone near the Shangdan suture of the West Qinling; III Paleozoic crystal graphite enrichment deposits zone in the Qinling paleomicroplate of the west part of the East Qinling.Conclusions are reached from multiple inquiries： Qinling multi-cycle complex continental collision orogen zone has experienced multiple tectonic framework transformation and polyphase tectonic thermal event from NeoArchean Erathem adjointing multiple graphite tectonic mineralization cycle. In the light of chief control of mineralization and ore types, each of the three large graphite deposits belts of the Qinling orogen has its own genesis： I graphite deposits enriched metallogenetic zone is that regional tectogenetic movement from NeoArchaean caused polyphase metapepsis, which superimposed up and reconstructed NeoArchean Erathem to Proterozoic basement, forming regional metamorphic big flake crystal graphite deposits; I! graphite deposits enriched metallogenetic zone is that polyphase regional tectogenetic movement associated with multiple heating caused by multiphase igneous intrusion, which resulted in original coal layers emerging multiple thermo-contact metamorphisms and formed thermo-contact metamorphic aphanitic graphite deposits. III graphite deposits enriched metallogenetic zone is that Palaeozoic cap- rock experienced polyphase metapepsis, forming regional metamorphic finely flake crystal graphite deposits. Cemprehensive research of metallogenetic mechanism in graphite deposits and its associated profitable deposits of the Qinling orogen is importance for future exploration.

PARTIAL REGULARITY FOR WEAK SOLUTIONS OF STATIONARY NAVIER-STOKES SYSTEMS

This article is concerned with the partial regularity for the weak solutions of stationary Navier-Stokes system under the controllable growth condition.By A-harmonic approximation technique,the optimal regularity is obtained.

REGULARITY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS IN R^N

The purpose of this article is to establish the regularity of the weak solutions for the nonlinear biharmonic equation {△^2u ＋ a（x）u = g（x, u）u∈ H^2（R^N）, where the condition u∈ H^2（R^N） plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.

A Preliminary Review of Metallogenic Regularity of Copper Deposits in China

Copper resources in China are rich, but imported copper products are still required. Researches on metallogenic regularity of major types of copper deposits by geologists have involved in worldwide classification, significant copper belts, representative copper deposits, etc. Studies on metallogenic regularity of copper deposits in China also have made achievements with a long-term work. Combined with latest exploration advances obtained in recent ten years, this review aims to conclude the achievements of researches on copper metallogenic regularity in China. Based on data of 814 copper deposits and other ore （mineralized） occurrences, ten prediction types of copper deposits have been suggested. Porphyry and skarn copper ores are taken as the key targets. Porphyry copper deposits are the most important one which concentrate in Gangdese, Changdu-Sanjiang, Dexing and East Tianshan. The Cenozoic and Mesozoic are the major metallogenic epochs. Four main metallogenic epochs are been studied based on the copper ore geochronological data including Precambrian Era （Archean and Proterozoic）, Paleozoic Era, Mesozoic Era and Cenozoic Era. Based on the study of metallogenic series of ore deposits in China, twenty-seven metallogenic series of copper deposits are proposed. This is suggested to deepen the study of metallogenic regularity of copper ore and provide the theory guide for copper resources prediction in China.

GEVREY REGULARITY FOR SOLUTION OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION

In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.

A Preliminary Review of Metallogenic Regularity of Gold Deposits in China

Gold is one of the most important mineral resources in China with its rich mineral resources. In recent years, significant progress has been made on the process of gold resource exploration. Some large and giant gold deposits were newly found and some important expansions in the main mining regions were also been completed. Studies on metailogenic regularity of gold deposits in China also have made achievements with a long-term work. This review aims to conclude the achievements of research on gold metallogenic regularity in China. Based on the data of about 2000 gold deposits and other ore （mineralized） occurrences, gold deposits in China were classified into five prediction types： gold deposits genetically related to granite-greenstone formation, gold deposits related to sedimentary formation （including the Carlin type and the metamorphosed clastic rock related vein gold deposit）, gold deposits genetically related to volcanic rocks （including the continental and marine types）, gold deposits genetically related to intrusions （including the porphyry type and the inner intrusion and contact zone related gold deposit）, gold deposits of supergenesis （including fracture zone-altered rock gold deposit, placer gold deposit, gossan type gold precise chronology data of gold deposits indicate deposit and soil type gold deposit）. Statistics on that there occurred 5 main periods of gold- mineralization in geological history of China. They were Neoarchean to Paleoproterozoic, Meso- Neoproterozoic, Paleozoic, Mesozoic, and Cenozoic. Gold deposits in China mainly formed in the Mesozoic and the Cenozoic. On the studies of the spatial-temporal distribution characteristics of gold deposits, 53 gold-forming belts were delineated in China. The metallogenic regularity of gold deposits was preliminarily summarized and 71 gold metallogenic series were proposed in China. This suggests that it is necceary to deepen the study on metallogenic regularity of gold deposits and to provide the theory guide for the ore-prospecting for gold resources in China.