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.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

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.

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.

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.

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.

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.

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. .

Occurrence Regularity and Control Research of Apple Early Defoliation Disease in West Sichuan Plateau

[ Objective ] The research aimed to discuss the occurrence regularity of apple early defoliation disease and control effects of fungicides in west Sichuan plateau. [ Method ] Apple early defoliation disease in west Sichuan plateau was systematically investigated during 2009 and 2011, and the control effects of different fungicides during different spraying periods were studied. [ Result] The species of pathogen mainly was Marssonina ma/i （ P. Henn）, accounting for 32.5%, Phyl-losticta Pirina Sa accounted for 29.9%, and Alternaria mali Roberts accounted for 25.7%. The field fluctuation regularity was as follows ： the disease generally be- gan in the mid-May and ended in early and middle October with only one damage peak during the whole year, the fluctuation had positive correlation with rainfall （ R2 =0.891 8 ＊ ＊ ）. Control test showed that 40% flusilazole had the best control effect （86.5%）, which was best to apply after anthesis. [ Conclusion ] The paper provided theoretical basis for the effective control against apple early defoliation disease.

Detection of an increase in EMG regularity during fatiguing contractions

The changes in the evolvement patterns of surface electromyography（EMG）signals during both static and dynamic fatiguing contractions are studied.The main finding is that the EMG signal tends to be more and more regular as muscle fatigues.An increase in the summation of all the regular evolvement patterns denoted by Dreg reflects such a tendency.Compared with traditional measurements,Dreg shows less variability among subjects when characterizing a fatigue process.In addition,the calculation of Dreg in the time domain is free from the restrictions disturbing those of spectral parameters.The detection of an increase in the EMG regularity not only proposes a new and easy way to inspect changes in EMG during the fatigue process,but also provides strong supports to estimate muscle fatigue by means of nonlinear analysis methods such as entropy and complexity measures.The detection method of signal regularity can also be applied to other physiological signals.

Study on the Occurrence and Epidemic Regularity and Region Division of Rice Blast in Nanchong City

With the aim to improve the level of monitoring and warning as well as the comprehensive control of rice blast disease, and to feasibly reduce the disease threat in Nanchong City, the methods of GPS and GIS, systematical monitoring and field survey, rice blast resistance identification, physiologic races of rice blast monitoring, and meteorological data analysis were performed to study the occurrence and epidemic region division, precise demarcation and occurrence and epidemic regularity of rice blast in Nanchong City. This study first completed the epidemic region division and precise demarcation; first clarified the initial affection（beginning period） locations, occurrence characteristics, epidemic trends and characteristics; explicated the existence of four epidemic peak periods of rice blast in the field, where the damage areas of first peak period played a decisive role during the blast epidemic years; in late May, the cumulative occurrence areas and annual occurrence areas presented higher positive correlation with the correlation coefficient of 0.817;and established a prediction model of occurrence areas per year based on the disease field rate at the end of boot stages and the diseased plant rate at dough stages. The results of investigation on the impact factors investigation of blast disease in Nanchong in recent years suggested that the internal causes were the decrease or loss of blast resistance of the rice cultivars, as well as the increase of physiological races with strong resistance to rice blast and the emergence of new virulent physiologic varieties; the external causes were suitable temperature, too much rainy, and sunlight shortage. Between 2010 and 2015, the short-term forecast accuracy for rice blast in Nanchong was up to 100%, and medium-and long-term forecast accuracy was also up to 98% and 95%, respectively, which increased by 5-15% than that before 1997, thereby making the control effect of rice blast in Nanchong increased by 15-30%.

Data-Path Placement Based on Regularity Extraction and Implementation

An algorithm named DPP is addressed.In it,a new model based on the concept of irregularity degree is founded to evaluate the regularity of cells.It generates the structure regularity of cells by exploiting the signal flow of circuit.Then,it converts the bit slice structure to parallel constraints to enable Q place algorithm.The design flow and the main algorithms are introduced.Finally,the satisfied experimental result of the tool compared with the Cadence placement tool SE is discussed.

Effects of Primary and Secondary Trunk Girdling on the Status and Distribution Regularity of Nutrients in Grape

Objective] The study aimed to investigate the effects of primary and sec-ondary trunk girdling on the status and distribution regularity of nutrients in grape. [Method] Using grape cultivar ‘Rose Honey’ as the experimental material, the ef-fects of primary and secondary trunk girdling on carbon and nitrogen nutrition, min-eral nutrition and nutrient distribution regularity in leaves and branches above the girdling wound and roots below the girdling wound were analyzed. [Result] Girdling could significantly increase non-structural carbohydrate content （such as soluble sugar and starch） in branches above the girdling wound, reduce soluble protein and total nitrogen contents, and significantly improve C/N ratio. Specifical y, the highest C/N ratio in primary girdling group and secondary girdling group was 9.04 and 5.35, respectively, but C/N ratio in control group was only 4.89 in the same period. Girdling not only significantly decreased the content of non-structural carbohydrates （such as soluble sugar and starch） in roots, but also significantly declined soluble protein and total nitrogen content, which also reduced C/N ratio in various degrees. Specifical y, the lowest C/N ratio in primary girdling group and secondary girdling group was 1.16 and 3.06, respectively, while that in control group was 3.15 in the same period. ln addition, primary girdling exerted much greater effects on carbon and nitrogen nutrition than secondary girdling. Moreover, girdling significantly de-creased the contents of phosphorus, potassium, ferrum and copper in grape leaves, branches and roots. Specifical y, primary girdling exerted greater effects on ferrum and copper contents in leaves and branches. The contents of ferrum and copper in the first batch of samples exhibited significant differences between primary girdling group and control group： ferrum content in leaves was 75.05 μg/g DW in primary girdling group and that in control group was 85.29 μg/g DW; ferrum content in branches was 76.45 ？g/g DW in primary girdling group and copper content was 7.82 μg/g DW, while ferrum and copper contents in control group were 95.96 and 10.74 μg/g DW, respectively. [Conclusion] This study provided the basis for accu-rately regulating tree nutrition and ensuring safe and effective use of girdling tech-nique in ‘Rose Honey’ production.

PARTIAL REGULARITY FOR MINIMIZERS OF HIGHER ORDER QUASICONVEX FUNCTIONALS

We consider the following quasiconvex functional I(u)=∫ Gf(x,δu,D mu) d x where u is a vector valued function in W m,p (G),m>1 and p>2. The partial C m,a —regularity is proved for minimizers of I(u) under weaker conditions.

Factors affecting headway regularity on bus routes

The common phenomenon of uneven headway in bus service is explored based on the automatic vehicle location （AVL） data of Route 2 in Yichun City of Jiangxi province from 6：00 to 9：00 in the morning. The headway regularity of two stages 6： 00--7：00 and 7： 00--9：00 is comparatively analyzed, and it is found that both the traffic conditions and the passenger demand affect headway regularity. A bus arrival model, which assumes that the dwell time of a bus is linear in headway, is built to probe the effect of scheduled headway, and the model is simulated by Matlab. The simulation results reveal that the departure intervals and fluctuations affect headway regularity. Longer intervals and less fluctuation mean higher regularity of headway. And, the fluctuation has a more obvious influence on headway regularity than the interval. Controlling the fluctuations of scheduled headway can effectively raise the regularity of headway and improve the level of public transport service.

Effective regularity in modulation on gastric motility induced by different acupoint stimulation

AIM： To investigate whether manual acupuncture at representative acupoints in different parts of the body can modulate responses of gastric motility in rats and regular effects in different acupoint stimulation. METHODS： The gastric motor activity of rats was recorded by the intrapyloric balloon. The changes of gastric motility induced by the stimulation were compared with the background activity in intragastric pressure and/or waves of gastric contraction recorded before any stimulation. Morphological study was also conducted by observing the Evans dye extravasation in the skin after mustard oil injection into the intragastric mucous membrane to certify cutaneous innervations of blue dots related to gastric segmental innervations. RESULTS： In all six rats that received mustard oil injections into intragastric mucosa, small blue dots appeared in the skin over the whole abdomen, but mainly in peri-midline upper- and middle- abdomen and middle-back, a few in thigh and groin. It may speculate that cutaneous innervations of blue dots have the same distribution as gastric segmental innervations. Acustimulation in acupoints of head-neck, four limbs, upper chest-dorsum and Iower-dorsum induced markedly augmentation of gastric motility （acupoints on headneck such as St-2： n = 16, 105.19 ± 1.36 vs 112.25 ± 2.02 and St-3： n = 14, 101.5 ± 1.75 vs 109.36 ± 1.8; acupoints on limbs such as Sp-6： n = 19, 100.74 ± 1.54 vs 110.26 ± 3.88; St-32： n = 17, 103.59 ± 1.64 vs 108.24 ± 2.41; St-36： n = 16, 104.81 ± 1.72 vs 110.81 ± 2.74 and U-11： n = 17, 106.47 ± 2.61 vs 114.77 ± 3.77, P 〈 0.05-0.001）. Vigorous inhibitory regulations of gastric motility induced by acu-stimulation applied in acupoints on whole abdomen and middle-dorsum were significantly different as compared with the controls before acu-stimulation （abdomen acupoints such as Cv-12： n = 11, 109.36 ± 2.09 vs 101 ± 2.21; Cv-6： n = 18, 104.39 ± 1.42 vs 91.83 ± 3.22 and St-21： n = 12, 107 ± 2.97 vs 98.58 ± 2.81; acupoints on middledorsum such as BI-17： n = 19, 100.63 ± 1.4 vs 92.21 ± 2.07 and BI-21： n = 19, 103.84 ± 1.48 vs 97.58 ± 2.16, P 〈 0.05-0.001）. CONCLUSION： Regular regulatory effects of facilitation and inhibition on gastric motility appear to be somatotopically organized in the acupoints of whole body, and the effective regularity of site-special acupoints on gastric motility is involved in segmental innervations between stomach and acupoints.