We present and explore a new shock-capturing particle hydrodynamics approach.Our starting point is a commonly used discretization of smoothed particle hydrodynamics.We enhance this discretization with Roe’s approx-im...We present and explore a new shock-capturing particle hydrodynamics approach.Our starting point is a commonly used discretization of smoothed particle hydrodynamics.We enhance this discretization with Roe’s approx-imate Riemann solver,we identify its dissipative terms,and in these terms,we use slope-limited linear reconstruction.All gradients needed for our method are calculated with linearly reproducing kernels that are constructed to enforce the two lowest-order consistency relations.We scrutinize our reproducing kernel implementation carefully on a“glass-like”particle distribution,and we find that constant and linear functions are recovered to machine precision.We probe our method in a series of challenging 3D benchmark problems ranging from shocks over instabilities to Schulz-Rinne-type vorticity-creating shocks.All of our simulations show excellent agreement with analytic/reference solutions.展开更多
This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω i...This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω is a homogeneous function of degree zero on R^(n)with mean value zero in the unit sphere S^(n-1),Under the assumption that Ω∈L^(∞)(S^(n-1)),the authors establish the L^(q)-estimate and weak(1,1)type estimate as well as the corresponding weighted estimates for po.s with 1<q<∞ and 0<β(q-1)n/q.Moreover,the bounds do not depend on β and the strong(q,q)type and weak(1,1)type estimates for the classical Marcinkiewicz integral po can be recovered from the above estimates of μΩ,β whenβ→0.展开更多
Under natural pollination （NP）, early-fertilized ovaries at the base of ear promote kernel abortion of late-fertilized ovades from the tip in maize （Zea mays L.）. Synchronous pollination （SP） improves maize kern...Under natural pollination （NP）, early-fertilized ovaries at the base of ear promote kernel abortion of late-fertilized ovades from the tip in maize （Zea mays L.）. Synchronous pollination （SP） improves maize kernel set, but the physiological masons behind this response are yet unclear. We e^amined maize kernel growth at the tip of ear subjected to NP or SP with different ~.ant density of 6 plants/rr~ or 9 plants/n~. Synchronous pollination of ears baged before silking was obtained by hand pollination on 3 days after silking （DAS） and samples were taken from natural and hand-pollinated ears on 8, 13, 18, and 23 DAS. At each sampling date, kemel fresh weight, volume and dry weight at the tip of ear were all higher for maize grown under SP than NP, and the contents of soluble sugar, sucrose, starch, nitro- gen and the ratios of soluble sugar to nitrogen （C/N） in kernel at the tip of ear were all higher too for maize grown under SP than NP.展开更多
The filling rate and the starch accumulation in developing maize kernel were analyzed. The changes of enzyme activities associated with sucrose metabolism and starch biosynthesis were investigated. The purpose is to d...The filling rate and the starch accumulation in developing maize kernel were analyzed. The changes of enzyme activities associated with sucrose metabolism and starch biosynthesis were investigated. The purpose is to discuss the enzymatic mechanisms responsible for starch synthesis. Two types of maize cultivars （Zea mays）, high starch maize （Feiyu 3） and normal maize （Yuyu 22）, were grown in a corn field. The factors involved in starch synthesis were performed during the growth period. The kernel filling rate, the sucrose content, the starch accumulating rates and the activities of SS （sucrose synthase）, GBSS （granule-bound starch synthase）, SBE （starch branching enzyme） of Feiyu 3, which has high starch content, were significantly higher than those of Yuyu 22, which has low starch content, after 10 DAP （days after pollination）. Correlation analysis indicated that ADPGPPase （ADP-glucose pyrophosphorylase） and DBE （starch debranching enzyme） were not correlated with the starch accumulating rates and the kernel filling rate, but the SS activity at the middle and late period were highly significantly correlated with the starch accumulating rates and the kernel filling rate. The GBSS activity was highly significantly correlated with the amylose accumulating rate, but not correlated with the kernel filling rate. The SBE activity was highly significantly correlated with the amylopectin accumulating rate and the kernel filling rate. It was not ADPGPPase and DBE, but SS was the rate-limiting factor of starch biosynthesis in developing maize kernels. GBSS had an important effect on amylose accumulation, and SBE had a significant effect on amylopectin accumulation.展开更多
Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded...Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.展开更多
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, fo...The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.展开更多
In this article we obtain weighted norm estimates for multilinear singular integrals with non-smooth kernels and the boundedness of certain multilinear commutators by making use of a sharp maximal function.
In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the w...In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.展开更多
The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) i...The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.展开更多
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P...In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.展开更多
This work focuses on drop breakage for liquid-liquid system with an adoption of numerical simulation by using computational fluid dynamics and population balance model (PBM) coupled with two-fluid model (TFM). Two dif...This work focuses on drop breakage for liquid-liquid system with an adoption of numerical simulation by using computational fluid dynamics and population balance model (PBM) coupled with two-fluid model (TFM). Two different breakage kernels based on identical breakage mechanism but different descriptions of breaking time are take n into account in this work. Eight cases corresp on ding to distinct configurations of agitator are carried out to validate numerical predictions, namely agitators with different porosity and hole diameters, respectively implemented in Cases 1 to 5 and Cases 6 to 8. The results are compared with experimental data for testing the applicability of both kernels. Simulations are implemented, in this work, with an approach of class method for the solution of population balance model by the special-purpose computational fluid dynamics solver Fluent 16.1 based on finite volume method, and the grids used for meshing the solution domain are accomplished in a commercial software Gambit 2.4.6. The effects of configurations of agitator corresponding to different parameters mentioned above on final Sauter mean diameter are equally concentrated in this work. Analysis of both kernels and comparisons with experimental results reveal that, the second kernel has more decent agreement with experiments, and the results of investigations on effects of agitator configurations show that the in fluences of these parameters on Sauter mean diameter are marginal, but appropriate porosity and hole diameter are actually able to decrease Sauter mean diameter. These outcomes allow us to draw general conclusions and help investigate performances of liquid-liquid system.展开更多
In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish th...In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.展开更多
FHB is one of the most destructive diseases of wheat. Resistance testing depends strongly on inoculation methods, and on measured traits. Therefore a four-year (2009-2012) study was performed using spray inoculation +...FHB is one of the most destructive diseases of wheat. Resistance testing depends strongly on inoculation methods, and on measured traits. Therefore a four-year (2009-2012) study was performed using spray inoculation + polyethylene (PE) bag cover, spray inoculation + mist irrigation, and spawn method supported by mist irrigation on 40 genotypes, 20 from Hungary and 20 from IFA Tulln, Austria. Each year four isolates were used in artificial inoculations except the spawn method where stalk debris served the inoculum. Visual Fusarium head blight (FHB) scores, Fusarium damaged kernels (FDK) and deoxynivalenol (DON) contamination were checked. 7680 FHB and FDK, as well as 3840 DON analyses served as the background for the statistical evaluation. The most reliable method used was the spray + polyethylene (PE) bag;the other two were significantly poorer being valid for all traits. The FHB scores were the least reliable, whereas the FDK was much more consequent and the DON gave the best results. The FDK gave much better predictions for DON contamination than FHB. The cultivars responses correlated well at different epidemic severities. The presence of the kernel resistance was confirmed and a new trait as extra kernel susceptibility was described. Presence of DON resistance was confirmed again, and extra DON susceptibility was described as a new trait. DON performance varied on the most sensitive cultivar between 0.32 and 143 mg/kg (mean 17.52 mg/kg) and on the most resistant genotype between 0.00 and 18.19 mg/kg (mean 1.87 mg/kg). Correlations between stability and resistance level are r = 0.85 for FHB, 0.78 for FDK, and 0.88 for DON, all at a significance level of p = 0.001. The very close correlation between FDK and DON contamination (r = 0.81, p = 0.001) proves that control of DON contamination needs appropriate resistance. In the breeding program evaluation of FDK is the most important, and then DON will be decided. Variety registration must be updated;otherwise no improvement on the field will occur.展开更多
In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can...In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can be used involving other variables also,such as ρ and μ.In this study,these different ensemble representations(E,?,F,and R) are briefly reviewed.Particular attention is then given to the corresponding second-order(functional) derivatives,and their analogieswith the second-order derivatives of thermodynamic state functions U,F,H,and G,which are related to each other via Legendre transformations,just as the DFT functionals(Nalewajski and Parr,1982).Starting from an analysis of the convexity/concavity of the DFT functionals,for which explicit proofs are discussed for some cases,the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives.The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals.Thus,the DFT functionals are scrutinized based on the convexity/concavity of their two variables,to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional.Considering two ensemble representations,F and ?,F is eliminated as it has two dependent(extensive)variables,N and ρ.For ?,on the other hand,which is concave for both of its intensive variables(μ and υ),an inequality is derived from its three second-order(functional) derivatives:the global softness,the local softness,and the softness kernel.Combined with the negative value of the diagonal element of the linear response function,this inequality is shown to be compatible with the Berkowitz-Parr relationship,which relates the functional derivatives of ρ with υ,at constant N and μ.This was recently at stake upon quantifying Kohn's Nearsightedness of Electronic Matter.The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted.Potential research paths for this study are briefly addressed;the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships,as derived in this paper,for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.展开更多
The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to...The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recur- sively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.展开更多
Let D = （ V, A ） be a digraph with minimum indegree at least one and girth at least k, where k ≥ 2 is an integer. In this paper, the following results were proved. A digraph D has a （ k, l ）-kernel if and only ff...Let D = （ V, A ） be a digraph with minimum indegree at least one and girth at least k, where k ≥ 2 is an integer. In this paper, the following results were proved. A digraph D has a （ k, l ）-kernel if and only ff its line digraph L （ D ） does, and the number of （ k, l ）-kernels in D is equal to the number of （ k, l ） -kernels in L （ D ）, where 1 ≤1 〈 k. As a consequence, previous results about k- kernels in the line digraphs were gained.展开更多
Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
基金supported by the Swedish Research Council(VR)under grant number 2020-05044by the research environment grant"Gravitational Radiation and Electromagnetic Astrophysical Transients"(GREAT)funded by the Swedish Research Council(VR)under Dnr 2016-06012+2 种基金by the Knut and Alice Wallenberg Foundation under grant Dnr.KAW 2019.0112by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)under Germany's Excellence Strategy-EXC 2121"Quantum Universe"-390833306by the European Research Council(ERC)Advanced Grant INSPIRATION under the European Union's Horizon 2020 Research and Innovation Programme(Grant agreement No.101053985).
文摘We present and explore a new shock-capturing particle hydrodynamics approach.Our starting point is a commonly used discretization of smoothed particle hydrodynamics.We enhance this discretization with Roe’s approx-imate Riemann solver,we identify its dissipative terms,and in these terms,we use slope-limited linear reconstruction.All gradients needed for our method are calculated with linearly reproducing kernels that are constructed to enforce the two lowest-order consistency relations.We scrutinize our reproducing kernel implementation carefully on a“glass-like”particle distribution,and we find that constant and linear functions are recovered to machine precision.We probe our method in a series of challenging 3D benchmark problems ranging from shocks over instabilities to Schulz-Rinne-type vorticity-creating shocks.All of our simulations show excellent agreement with analytic/reference solutions.
文摘This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω is a homogeneous function of degree zero on R^(n)with mean value zero in the unit sphere S^(n-1),Under the assumption that Ω∈L^(∞)(S^(n-1)),the authors establish the L^(q)-estimate and weak(1,1)type estimate as well as the corresponding weighted estimates for po.s with 1<q<∞ and 0<β(q-1)n/q.Moreover,the bounds do not depend on β and the strong(q,q)type and weak(1,1)type estimates for the classical Marcinkiewicz integral po can be recovered from the above estimates of μΩ,β whenβ→0.
基金Supported by National Natural Science Foundation of China(31271645)Agricultural Science and Technology Project of Shanxi Province(20140311007-4)~~
文摘Under natural pollination （NP）, early-fertilized ovaries at the base of ear promote kernel abortion of late-fertilized ovades from the tip in maize （Zea mays L.）. Synchronous pollination （SP） improves maize kernel set, but the physiological masons behind this response are yet unclear. We e^amined maize kernel growth at the tip of ear subjected to NP or SP with different ~.ant density of 6 plants/rr~ or 9 plants/n~. Synchronous pollination of ears baged before silking was obtained by hand pollination on 3 days after silking （DAS） and samples were taken from natural and hand-pollinated ears on 8, 13, 18, and 23 DAS. At each sampling date, kemel fresh weight, volume and dry weight at the tip of ear were all higher for maize grown under SP than NP, and the contents of soluble sugar, sucrose, starch, nitro- gen and the ratios of soluble sugar to nitrogen （C/N） in kernel at the tip of ear were all higher too for maize grown under SP than NP.
基金grants from the National Natural Science Foundation of China （30471025） Agricultural Science and Technology Span Project （2003, 19） the High Level Person Start-Up Fund of Qingdao Agricultural University, China （630629）.
文摘The filling rate and the starch accumulation in developing maize kernel were analyzed. The changes of enzyme activities associated with sucrose metabolism and starch biosynthesis were investigated. The purpose is to discuss the enzymatic mechanisms responsible for starch synthesis. Two types of maize cultivars （Zea mays）, high starch maize （Feiyu 3） and normal maize （Yuyu 22）, were grown in a corn field. The factors involved in starch synthesis were performed during the growth period. The kernel filling rate, the sucrose content, the starch accumulating rates and the activities of SS （sucrose synthase）, GBSS （granule-bound starch synthase）, SBE （starch branching enzyme） of Feiyu 3, which has high starch content, were significantly higher than those of Yuyu 22, which has low starch content, after 10 DAP （days after pollination）. Correlation analysis indicated that ADPGPPase （ADP-glucose pyrophosphorylase） and DBE （starch debranching enzyme） were not correlated with the starch accumulating rates and the kernel filling rate, but the SS activity at the middle and late period were highly significantly correlated with the starch accumulating rates and the kernel filling rate. The GBSS activity was highly significantly correlated with the amylose accumulating rate, but not correlated with the kernel filling rate. The SBE activity was highly significantly correlated with the amylopectin accumulating rate and the kernel filling rate. It was not ADPGPPase and DBE, but SS was the rate-limiting factor of starch biosynthesis in developing maize kernels. GBSS had an important effect on amylose accumulation, and SBE had a significant effect on amylopectin accumulation.
文摘Let T be a singular integral operator bounded on Lp(Rn) for some p, 1 < p < ∞. The authors give a sufficient condition on the kernel of T so that when b ∈BMO, the commutator [b,T](f) = T(bf) - bT(f) is bounded on the space Lp for all p, 1 < p < ∞. The condition of this paper is weaker than the usual pointwise Hormander condition.
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
文摘The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.
文摘In this article we obtain weighted norm estimates for multilinear singular integrals with non-smooth kernels and the boundedness of certain multilinear commutators by making use of a sharp maximal function.
基金supported in part by National Natural Foundation of China (Grant No. 11161042 and No. 11071250)
文摘In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^＊ on the weighted amalgam spaces （Lω^q,L^p）^α（R^n）as 1〈q≤α〈p≤∞.
基金Supported by the973Project( G1 9990 75 1 0 5 ) and the National Natural Science Foundation of China( 1 0 2 71 0 1 6)
文摘The fractional integral operators with variable kernels are discussed.It is proved that if the kernel satisfies the Dini-condition,then the fractional integral operators with variable kernels are bounded from Hp(Rn) into Lq(Rn) when 0<p≤1 and 1/q=1/p-α/n.The results in this paper improve the results obtained by Ding,Chen and Fan in 2002.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
基金Supported by the NSFC（10771144 11071171） Supported by the Beijing Natural Science Foundation（1082005） Supported by the Excellent Doctoral Thesis Prize of Beijing（2008）
文摘We obtain the Bergman kernel for a new type of Hartogs domain.The corresponding LU Qi-Keng's problem is considered.
文摘In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.
基金Supported by the National Natural Science Foundation of China(21776180,21306116)
文摘This work focuses on drop breakage for liquid-liquid system with an adoption of numerical simulation by using computational fluid dynamics and population balance model (PBM) coupled with two-fluid model (TFM). Two different breakage kernels based on identical breakage mechanism but different descriptions of breaking time are take n into account in this work. Eight cases corresp on ding to distinct configurations of agitator are carried out to validate numerical predictions, namely agitators with different porosity and hole diameters, respectively implemented in Cases 1 to 5 and Cases 6 to 8. The results are compared with experimental data for testing the applicability of both kernels. Simulations are implemented, in this work, with an approach of class method for the solution of population balance model by the special-purpose computational fluid dynamics solver Fluent 16.1 based on finite volume method, and the grids used for meshing the solution domain are accomplished in a commercial software Gambit 2.4.6. The effects of configurations of agitator corresponding to different parameters mentioned above on final Sauter mean diameter are equally concentrated in this work. Analysis of both kernels and comparisons with experimental results reveal that, the second kernel has more decent agreement with experiments, and the results of investigations on effects of agitator configurations show that the in fluences of these parameters on Sauter mean diameter are marginal, but appropriate porosity and hole diameter are actually able to decrease Sauter mean diameter. These outcomes allow us to draw general conclusions and help investigate performances of liquid-liquid system.
基金Supported by the Anhui Polytechnic University Foundation for Recruiting Talent(2011YQQ004)Supported by the Provincial Natural Science Research Project of Anhui Colleges(KJ2011A032)+1 种基金Supported by the Young Teachers Program of Anhui Province(2006jql042)Supported by the Grant for Younth of Anhui Polytechnic University (2010YQ047)
文摘In this paper,the authors introduce the central bounded oscillation space CBMO q (R n),let [b,T,α ] be the commutator generated by fractional integral operators with variable kernels and CBMO function,we establish the boundedness of [b,T,α ] on homogeneous Morrey-Herz spaces.
文摘FHB is one of the most destructive diseases of wheat. Resistance testing depends strongly on inoculation methods, and on measured traits. Therefore a four-year (2009-2012) study was performed using spray inoculation + polyethylene (PE) bag cover, spray inoculation + mist irrigation, and spawn method supported by mist irrigation on 40 genotypes, 20 from Hungary and 20 from IFA Tulln, Austria. Each year four isolates were used in artificial inoculations except the spawn method where stalk debris served the inoculum. Visual Fusarium head blight (FHB) scores, Fusarium damaged kernels (FDK) and deoxynivalenol (DON) contamination were checked. 7680 FHB and FDK, as well as 3840 DON analyses served as the background for the statistical evaluation. The most reliable method used was the spray + polyethylene (PE) bag;the other two were significantly poorer being valid for all traits. The FHB scores were the least reliable, whereas the FDK was much more consequent and the DON gave the best results. The FDK gave much better predictions for DON contamination than FHB. The cultivars responses correlated well at different epidemic severities. The presence of the kernel resistance was confirmed and a new trait as extra kernel susceptibility was described. Presence of DON resistance was confirmed again, and extra DON susceptibility was described as a new trait. DON performance varied on the most sensitive cultivar between 0.32 and 143 mg/kg (mean 17.52 mg/kg) and on the most resistant genotype between 0.00 and 18.19 mg/kg (mean 1.87 mg/kg). Correlations between stability and resistance level are r = 0.85 for FHB, 0.78 for FDK, and 0.88 for DON, all at a significance level of p = 0.001. The very close correlation between FDK and DON contamination (r = 0.81, p = 0.001) proves that control of DON contamination needs appropriate resistance. In the breeding program evaluation of FDK is the most important, and then DON will be decided. Variety registration must be updated;otherwise no improvement on the field will occur.
基金S.F. wishes to thank the Research Foundation Flanders (FWO) and the European Union＇s Horizon 2020 Marie Sklodowska-Curie grant (No. 706415) for financially suppor(ing his post-doctoral research at the ALGC group. ED.P. and P.G. acknowledge (he Research Fo
文摘In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can be used involving other variables also,such as ρ and μ.In this study,these different ensemble representations(E,?,F,and R) are briefly reviewed.Particular attention is then given to the corresponding second-order(functional) derivatives,and their analogieswith the second-order derivatives of thermodynamic state functions U,F,H,and G,which are related to each other via Legendre transformations,just as the DFT functionals(Nalewajski and Parr,1982).Starting from an analysis of the convexity/concavity of the DFT functionals,for which explicit proofs are discussed for some cases,the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives.The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals.Thus,the DFT functionals are scrutinized based on the convexity/concavity of their two variables,to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional.Considering two ensemble representations,F and ?,F is eliminated as it has two dependent(extensive)variables,N and ρ.For ?,on the other hand,which is concave for both of its intensive variables(μ and υ),an inequality is derived from its three second-order(functional) derivatives:the global softness,the local softness,and the softness kernel.Combined with the negative value of the diagonal element of the linear response function,this inequality is shown to be compatible with the Berkowitz-Parr relationship,which relates the functional derivatives of ρ with υ,at constant N and μ.This was recently at stake upon quantifying Kohn's Nearsightedness of Electronic Matter.The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted.Potential research paths for this study are briefly addressed;the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships,as derived in this paper,for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.
文摘The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recur- sively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.
基金Project supported by National Natural Science Foundation ofChina(Grant No .10571117)
文摘Let D = （ V, A ） be a digraph with minimum indegree at least one and girth at least k, where k ≥ 2 is an integer. In this paper, the following results were proved. A digraph D has a （ k, l ）-kernel if and only ff its line digraph L （ D ） does, and the number of （ k, l ）-kernels in D is equal to the number of （ k, l ） -kernels in L （ D ）, where 1 ≤1 〈 k. As a consequence, previous results about k- kernels in the line digraphs were gained.
基金Supported by the National Natural Science Foundation of China(1057115610871173)
文摘Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
