OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION:THE METHOD OF A-HARMONIC APPROXIMATION

In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.

Effects of Tenebrio molitor L.Powder on Growth of Beauveria bassiana

[ Objective] The study aimed to reseamh the effect of Tenebrio molitor powder on the growth of Beauveria bassiana. [ Method ] The larvae of T. molitorwas used as the additive to add in the PDA medium, preparing 7 concentrations including 4, 2, 1,0.5, 0.25, 0.125 and 0.062 5 g/100 ml, the medium without adding any T. molitorlarva was set as control. The indexes such as the growth rate, spore germination rate, mycelium diameter, sporulaUon time, sporulatian quantity and POD activity of B. bassiana were determined. [ Result] Adding T. molitor larva to the PDA medium could increase the growth rate, spore germination rate, sporulation time, sporulatJon quantity and POD actJvity of B. bassiana, while had relatively small effect on spore size and mycelium diameter. The comprehensive evaluation screening showed that the medium with 4 g additive was the best for the growth of B. bassiana, different indexes all had obvious predominance. [ Conclusion] The study provided the basis for using T. molitor to culture B. baasianaa

Effects of meteorological factors on different grades of winter wheat growth in the Huang-Huai-Hai Plain, China

The sown area of winter wheat in the Huang-Huai-Hai（HHH） Plain accounts for over 65% of the total sown area of winter wheat in China. Thus, it is important to monitor the winter wheat growth condition and reveal the main factors that influence its dynamics. This study assessed the winter wheat growth condition based on remote sensing data, and investigated the correlations between different grades of winter wheat growth and major meteorological factors corresponding. First, winter wheat growth condition from sowing until maturity stage during 2011–2012 were assessed based on moderate-resolution imaging spectroradiometer（MODIS） normalized difference vegetation index（NDVI） time-series dataset. Next, correlation analysis and geographical information system（GIS） spatial analysis methods were used to analyze the lag correlations between different grades of winter wheat growth in each phenophase and the meteorological factors that corresponded to the phenophases. The results showed that the winter wheat growth conditions varied over time and space in the study area. Irrespective of the grades of winter wheat growth, the correlation coefficients between the winter wheat growth condition and the cumulative precipitation were higher than zero lag（synchronous precipitation） and one lag（pre-phenophase precipitation） based on the average values of seven phenophases. This showed that the cumulative precipitation during the entire growing season had a greater effect on winter wheat growth than the synchronous precipitation and the pre-phenophase precipitation. The effects of temperature on winter wheat growth varied according to different grades of winter wheat growth based on the average values of seven phenophases. Winter wheat with a better-than-average growth condition had a stronger correlation with synchronous temperature, winter wheat with a normal growth condition had a stronger correlation with the cumulative temperature, and winter wheat with a worse-than-average growth condition had a stronger correlation with the pre-phenophase temperature. This study may facilitate a better understanding of the quantitative correlations between different grades of crop growth and meteorological factors, and the adjustment of field management measures to ensure a high crop yield.

Effects of Si δ-Doping Condition and Growth Interruption on Electrical Properties of InP-Based High Electron Mobility Transistor Structures

The InGaAs/InAIAs/InP high electron mobility transistor （HEM：F） structures with lattice-matched and pseudo- morphic channels are grown by gas source molecular beam epitaxy. Effects of Si ^-doping condition and growth interruption on the electrical properties are investigated by changing the Si-cell temperature, doping time and growth process. It is found that the optimal Si ^-doping concentration （Nd） is about 5.0 x 1012 cm-2 and the use of growth interruption has a dramatic effect on the improvement of electrical properties. The material structure and crystal interface are analyzed by secondary ion mass spectroscopy and high resolution transmission elec- tron microscopy. An InGaAs/InAiAs/InP HEMT device with a gate length of lOOnm is fabricated. The device presents good pinch-off characteristics and the kink-effect of the device is trifling. In addition, the device exhibits fT = 249 GHa and fmax 〉 400 GHz.

A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS

In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.

REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE:1

In this article,we consider interior regularity for weak solutions to nonlinear elliptic systems of divergence type with Dini continuous coefficients under natural growth condition for the case 1〈m〈 2.All estimates in the case of m≥2 is no longer suitable,and we can’t obtain the Caccioppoli’s second inequality by using these techniques developed in the case of m≥2.But the Caccioppoli’s second inequality is the key to use A-harmonic approximation method.Thus,we adopt another technique introduced by Acerbi and Fcsco to overcome the difficulty and we also overcome those difficulties due to Dini condition.And then we apply the A-harmonic approximation method to prove partial regularity of weak solutions.

Extinction of Weak Solutions for Nonlinear Parabolic Equations with Nonstandard Growth Conditions

This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.

Optimal Growth Conditions of Microorganisms Isolated from the Buyeo Royal Tomb No. 1 and Their Effects on Painting Layers

The Buyeo Royal Tomb No. 1 is an ancient tomb built in the late 6th and early 7th century. The four walls of the main room have murals of four guardian deities, and the ceiling has murals of lotus and cloud patterns. This study assessed the optimal growth conditions of two fungal (Fusarium oxysporum, Mortierella sp.) and four bacterial (Bacillus cereus, Cupriavidus campinensis, Streptomyces avidinii, Streptomyces cirratus) strains isolated from the Tomb No. 1, along with their effects on the painting layer. The two fungi showed optimal growth at 20°C - 30°C under both nutrient and non-nutrient conditions. These strains did not decompose or discolor the three pigments (cinnabar, hematite, oyster shell white);however, M. sp. showed slight decomposition of the media (starch paste, sea weed). The four bacterial strains showed the most active growth at 20°C - 25°C under nutrient conditions and did not grow under non-nutrient conditions. These bacteria commonly degraded animal glue and sea weed components. In addition, S. cirratus degraded starch. The genus Streptomyces discolored the pigment medium to brown and black, suggesting a possible risk of discoloration of the murals. The current environment in Tomb No. 1 was sufficient for microorganism growth, and the presence of strains such as soil bacteria and actinomycetes on the mural surface may damage the murals. The findings of this study could be helpful for preserving mural tombs against biological damage caused by microorganisms that are already present or may be present in the tombs in the future. These findings also provide guidelines for comprehensive conservation management.

C^(1,α)-PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS

We prove C1.α-partial regularity of weak solutions of nonlinear elliptic systems under the main assumption that Aia and Bi satisfy the controllable growth condition or the natural growth condition.

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

In this article, we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients. The authors use a new method introduced by Duzaar and Grotowski, to prove partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation and directly establish the optimal HSlder exponent for the derivative of a weak solution on its regular set.

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT OF NONLINEARITY

The authors of this article study the existence and uniqueness of weak so- lutions of the initial-boundary value problem for ut = div（（｜u｜^δ ＋ d0）｜↓△｜^p（x,t）-2↓△u） ＋ f（x, t） （0 〈 δ 〈 2）. They apply the method of parabolic regularization and Galerkin＇s method to prove the existence of solutions to the mentioned problem and then prove the uniqueness of the weak solution by arguing by contradiction. The authors prove that the solution approaches 0 in L^2 （Ω） norm as t →∞.

POSITIVE PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS

The nonlinear differential equationx′(t)=-δ(t)x(t)+f(t,x(t))(*)is considered,where δ(t) is a periodic function of periodic T,f(t,x) is continuous and periodic in t.It is showed that (*) has at least two positive T-periodic solutions under certain growth conditions imposed on f.Applications will be presented to illustrate the main results.

PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.

THE HOLDER CONTINUITY OF GENERALIZED SOLUTIONS OF A CLASS QUASILINEAR PARABOLIC EQUATIONS

Let A and B satisfy the structural conditions (2), the local Holder continuity interior to Q = G X (0, T) is proved for the generalized solutions of quasilinear parabolic equations as follows: u(t) - divA(x, t, u, del u) + B(x, t, U, del u) = 0.

Effective shape-controlled growth of monolayer MoS2 flakes by powder-based chemical vapor deposition

In the recent years, transition-metal dichalcogenides such as MoS2 have attracted considerable attention owing to their unique structure and electronic properties. Chemical vapor deposition （CVD） is a popular method for producing MoS2 flakes with different shapes. Here, we report an effective method for achieving a broad range of shape evolution in CVD-grown monolayer MoS2 flakes. By controlling the S and MoO3 temperatures, the shape of the monolayer MoS2 flakes was varied from hexagonal to triangular via intermediate shapes such as truncated and multi-apex triangles. The shape evolution of the MoS2 flakes can be explained by introducing the term “nominal Mo：S ratio”, which refers to the amount of loaded MoO3 and evaporated S powders. By using the nominal Mo：S ratio, we predicted the potential reaction atmosphere and effectively controlled the actual proportion of MoO3-x with respect to S in the growth region, along with the growth temperature. From the systematic investigation of the behavior of the shape evolution, we developed a shape-evolution diagram, which can be used as a practical guide for producing CVD-grown MoS2 flakes with desired shapes

Integrated sensor system for monitoring rice growth conditions based on unmanned ground vehicle system

Ground-based platform systems provide a good tool for monitoring and managing crop conditions in precision agriculture applications and have been widely used for monitoring crop conditions.To develop an unmanned ground vehicle system(UGVS)based multi-sensors and test the feasibility of this system for monitoring rice conditions,an UGVS was developed to collect real-time rice condition information including NDVI values,reflectance measurements and crop canopy temperature in this study.Major components of the integrated system are GreenSeeker R100 system,hyper-spectroradiometer and infrared temperature sensor.The leaf area index(LAI)was measured by the CGMD302 Spectrometer.The Independent Samples T-Test method and the one way ANOVA method were used to determine the best spectral indices and analyze the relationship between the vegetation indices and rice LAI.It was found that the two best spectral indices for estimating LAI were NDVI(860 nm and 750 nm)with the correlation coefficient(R^(2))at 0.745 and RVI(853 nm and 751 nm)with the R^(2)at 0.724.The results show the UGVS can support multi-source information acquisition and is useful for crop management and precision agriculture applications.

Multidimensional BSDEs with Weak Monotonicity and General Growth Generators

This paper aims at solving a multidimensional backward stochastic differential equation （BSDE） whose generator g satisfies a weak monotonicity condition and a general growth condition in y. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonieity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition in y and the monotonieity condition with the general growth condition in y, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results.

The Method of A-Harmonic Approximation and Boundary Regularity for Nonlinear Elliptic Systems under the Natural Growth Condition

We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.

The method of p-harmonic approximation and optimal interior partial regularity for energy minimizing p-harmonic maps under the controllable growth condition

In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic approximation method together with the technique used to get the decay estimation on some Degenerate elliptic equations and the obstacle problem by Tan and Yan. In particular, we directly get the optimal regularity.

Regularity of Solutions of Certain Parabolic System with Nonstandard Growth Condition

By the use of Moser iteration and Campanato space estimate,the L~∞ and C~α regularity gradient of solutions of nonlinear parabolic system (u^2)/(t)-▽(g|▽u|▽u^2)=0 with nonstandard growth conditions are obtained under the natural structure constraints.