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, bas...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.展开更多
The microRaman scattering of 4H-SiC films, fabricated by low pressure chemical vapor deposition under different growth conditions, is investigated at temperatures ranging from 80 K to 550K. The effects of growth condi...The microRaman scattering of 4H-SiC films, fabricated by low pressure chemical vapor deposition under different growth conditions, is investigated at temperatures ranging from 80 K to 550K. The effects of growth conditions on E2 （TO）, E1 （TO） and A1 （LO） phonon mode frequencies are negligible. The temperature dependences of phonon linewidth and lifetime of E2 （TO） modes are analyzed in terms of an anharmonic damping effect induced by thermal and growth conditions. The results show that the lifetime of E2 （TO） mode increases when the quality of the sample improves. Unlike other phone modes, Raman shift of A1 （longitudinal optical plasma coupling （LOPC）） mode does not decrease monotonously when the temperature increases, but tends to blueshift at low temperatures and to redshift at relatively high temperatures. Theoretical analyses are given for the abnormal phenomena of A1 （LOPC） mode in 4H-SiC.展开更多
In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
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 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.展开更多
This paper deals with reaction-diffusion equations involving nonstandard growth conditions, subject to homogeneous Neumann boundary conditions. The complete clas- sification is established for simultaneous and non-sim...This paper deals with reaction-diffusion equations involving nonstandard growth conditions, subject to homogeneous Neumann boundary conditions. The complete clas- sification is established for simultaneous and non-simultaneous quenching under suitable assumptions on initial data. Moreover, quenching sets and quenching rates are obtained.展开更多
[Objective] The study aimed at selecting the predominant strains being able to degrade kerosene and studying its best growth conditions. [Method] Choosing kerosene as the only carbon source, we selected and separated ...[Objective] The study aimed at selecting the predominant strains being able to degrade kerosene and studying its best growth conditions. [Method] Choosing kerosene as the only carbon source, we selected and separated the predominant strains being able to degrade kerosene from the contaminated soil near petrochemical plants, and then optimized the grow conditions of the bacteria. [Result] The best conditions for the bacteria growth were determined as follows, that is, temperature was 30 ℃, pH=7, salinity was 2.5%, and the rotational speed of the thermostatic shake was 190 r/min. Under the optimal conditions, the degradation rate of kerosene by the bacteria cultured for three days reached 42.6%. [Conclusion] The research could provide scientific references for the restoration of polluted soil by kerosene.展开更多
In the setting of variable exponent,an existence result to a class of parabolic equations with zero order term is proved.The proof of existence relies essentially on selecting some suitable test functions based upon t...In the setting of variable exponent,an existence result to a class of parabolic equations with zero order term is proved.The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously.By virtue of a priori estimates and some limit analyses,the weak limit of the nonlinear principal term is identified via the Young measures method.展开更多
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 ...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）.展开更多
The Buyeo Royal Tomb No. 1 is an ancient tomb built in the late 6<sup>th</sup> and early 7<sup>th</sup> century. The four walls of the main room have murals of four guardian deities, and the ce...The Buyeo Royal Tomb No. 1 is an ancient tomb built in the late 6<sup>th</sup> and early 7<sup>th</sup> 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.展开更多
Let Ω be a bounded domain with smooth boundary Ω in R~n. We consider the following eigenvalue problem for systems of elliptic equations under the natural growth conditions
In this paper we extend the duality(C_(comp)^(∞)(R^(d))^(BMO(R^d))))^(∗)=H^(1)(R^(d))to generalized Campanato spaces with variable growth condition Lp,φ(R^(d))instead of BMO(R^(d)).We also extend the characterizatio...In this paper we extend the duality(C_(comp)^(∞)(R^(d))^(BMO(R^d))))^(∗)=H^(1)(R^(d))to generalized Campanato spaces with variable growth condition Lp,φ(R^(d))instead of BMO(R^(d)).We also extend the characterization of C_(comp)^(∞)(R^(d))BMO(Rd)by Uchiyama(1978)to C_(comp)^(∞)(R^(d))L _(p,φ)(R^(d)).Moreover,using this characterization,we prove the boundedness of singular and fractional integral operators on C_(comp)^(∞)(R_(d))L_(p,φ)(R^(d)).The function space L_(p,φ)(R^(d))treated in this paper covers the case that it is coincide with Lip_(α) on one area,with BMO on another area and with the Morrey space on the other area,for example.展开更多
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 groun...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.展开更多
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...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.展开更多
In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|<sup>m-1</sup>e<sup>b|u|&...In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|<sup>m-1</sup>e<sup>b|u|<sup>γ</sup></sup>at +∞, with γ=N/N-1, m≥1, b】0.展开更多
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...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.展开更多
In this paper, we investigate the interior regularity including the local boundedness and the interior HSlder continuity of weak solutions for parabolic equations of the p（x, t）-Laplacian type. We improve the Moser ...In this paper, we investigate the interior regularity including the local boundedness and the interior HSlder continuity of weak solutions for parabolic equations of the p（x, t）-Laplacian type. We improve the Moser iteration technique and generalize the known results for the elliptic problem to the corresponding parabolic problem.展开更多
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 u...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.展开更多
A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equ...A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equation to the variationalinequalities. We establish the existence and uniqueness of the weak solution of ocrresspending problem under nonstandard growth conditions.展开更多
基金Supported by NSF of China(10531020)the Program of 985 Innovation Engieering on Information in Xiamen University(2004-2007).
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61176085,11474365 and 61377055the Department of Education of Guangdong Province under Grant No gjhz1103the Open-Project Program of the State Key laboratory of Opto-Electronic Material and Technologies of Sun Yatsen University
文摘The microRaman scattering of 4H-SiC films, fabricated by low pressure chemical vapor deposition under different growth conditions, is investigated at temperatures ranging from 80 K to 550K. The effects of growth conditions on E2 （TO）, E1 （TO） and A1 （LO） phonon mode frequencies are negligible. The temperature dependences of phonon linewidth and lifetime of E2 （TO） modes are analyzed in terms of an anharmonic damping effect induced by thermal and growth conditions. The results show that the lifetime of E2 （TO） mode increases when the quality of the sample improves. Unlike other phone modes, Raman shift of A1 （longitudinal optical plasma coupling （LOPC）） mode does not decrease monotonously when the temperature increases, but tends to blueshift at low temperatures and to redshift at relatively high temperatures. Theoretical analyses are given for the abnormal phenomena of A1 （LOPC） mode in 4H-SiC.
文摘In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
基金Supported by National Natural Science Foundation of China (10976026)the Education Department of Fujian Province (JK2009045)
文摘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.
文摘This paper deals with reaction-diffusion equations involving nonstandard growth conditions, subject to homogeneous Neumann boundary conditions. The complete clas- sification is established for simultaneous and non-simultaneous quenching under suitable assumptions on initial data. Moreover, quenching sets and quenching rates are obtained.
基金Supported by National Key Technology R&D Program of China (2010BAD03B01)
文摘[Objective] The study aimed at selecting the predominant strains being able to degrade kerosene and studying its best growth conditions. [Method] Choosing kerosene as the only carbon source, we selected and separated the predominant strains being able to degrade kerosene from the contaminated soil near petrochemical plants, and then optimized the grow conditions of the bacteria. [Result] The best conditions for the bacteria growth were determined as follows, that is, temperature was 30 ℃, pH=7, salinity was 2.5%, and the rotational speed of the thermostatic shake was 190 r/min. Under the optimal conditions, the degradation rate of kerosene by the bacteria cultured for three days reached 42.6%. [Conclusion] The research could provide scientific references for the restoration of polluted soil by kerosene.
文摘In this paper the author proves that the Phragmen Lindelof principle holds for solutions of elliptic equation (1) with nonstandard growth conditions.
基金Supported by the National Natural Science Foundation of China(Grant No.11901131)the University-Level Research Fund Project in Guizhou University of Finance and Economics(Grant No.2022KYYB01)。
文摘In the setting of variable exponent,an existence result to a class of parabolic equations with zero order term is proved.The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously.By virtue of a priori estimates and some limit analyses,the weak limit of the nonlinear principal term is identified via the Young measures method.
基金Partially supported by the NSF(11271154)of China the 985 program of Jilin University
文摘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）.
文摘The Buyeo Royal Tomb No. 1 is an ancient tomb built in the late 6<sup>th</sup> and early 7<sup>th</sup> 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.
文摘Let Ω be a bounded domain with smooth boundary Ω in R~n. We consider the following eigenvalue problem for systems of elliptic equations under the natural growth conditions
基金This work is supported by the Youth Foundation, NSFC.
文摘In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem with natural growth conditions.
基金Supported by Grant-in-Aid for Scientific Research(C)(Grant No.21K03304)Japan Society for the Promotion of Sciencethe Research Institute for Mathematical Sciences,an International Joint Usage/Research Center located in Kyoto University。
文摘In this paper we extend the duality(C_(comp)^(∞)(R^(d))^(BMO(R^d))))^(∗)=H^(1)(R^(d))to generalized Campanato spaces with variable growth condition Lp,φ(R^(d))instead of BMO(R^(d)).We also extend the characterization of C_(comp)^(∞)(R^(d))BMO(Rd)by Uchiyama(1978)to C_(comp)^(∞)(R^(d))L _(p,φ)(R^(d)).Moreover,using this characterization,we prove the boundedness of singular and fractional integral operators on C_(comp)^(∞)(R_(d))L_(p,φ)(R^(d)).The function space L_(p,φ)(R^(d))treated in this paper covers the case that it is coincide with Lip_(α) on one area,with BMO on another area and with the Morrey space on the other area,for example.
文摘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.
基金Supported by NSF(No. 10531020) of Chinathe Program of 985 Innovation Engineering on Information in Xiamen University (2004-2007) and NCETXMU
文摘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.
基金Supported by the Youth FoundationNatural Science Foundation, People's Republic of China.
文摘In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|<sup>m-1</sup>e<sup>b|u|<sup>γ</sup></sup>at +∞, with γ=N/N-1, m≥1, b】0.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10531020)the Program of 985 Innovation Engineering on Information in Xiamen University (2004-2007).
文摘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.
文摘In this paper, we investigate the interior regularity including the local boundedness and the interior HSlder continuity of weak solutions for parabolic equations of the p（x, t）-Laplacian type. We improve the Moser iteration technique and generalize the known results for the elliptic problem to the corresponding parabolic problem.
基金This work was supported by NNSF of China under Grant 39570223 and Grant 19675005
文摘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.
文摘A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equation to the variationalinequalities. We establish the existence and uniqueness of the weak solution of ocrresspending problem under nonstandard growth conditions.
