VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES

For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Continuity of Hardy-Littlewood Maximal Function

In the paper,we characterize a necessary and sufficient condition which ensures the continuities of the non-centered Hardy-Lit tiewood maximal function Mf and the centered Hardy-Lit tiewood maximal function Mcf on R^n.As two applications,we can easily deduce that Mcf and Mf are continuous if f is continuous,and Mf is continuous if f is of local bounded variation on R.

Upper Bounds for the L_p-norms of the Maximal Functions of Martingales

Let 2≤p【∞ and let (f n) be a martingale. Using exponential bounds of the probabilities of the type P(|f n|】λ‖T(f n)‖ ∞) for some quasi-linear operators acting on martingales, we estimate upper bounds for the L p-norms of the maximal functions of martinglaes. Our result is the extension and improvements of the results obtained previously by HITCZENKO and ZENG .

A MAXIMAL FUNCTION CHARACTERIZATION 0F HARDY SPACES ON SPACES OF HOMOGENEOUS TYPE

A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.

W ^(1,p)(R^n)-BOUNDEDNESS FOR MAXIMAL FUNCTIONS

In this paper, we get W 1,p(Rn)-boundedness for tangential maximal func- tion and nontangential maximal function , which improves J.Kinnunen, P.Lindqvist and Tananka’s results.

SHARP MAXIMAL FUNCTION ESTIMATE AND WEIGHTED INEQUALITIES FOR MAXIMAL MULTILINEAR SINGULAR INTEGRALS

For maximal multilinear Calderon-Zygmund singular integral operators, the sharp maximal function estimate and some weighted norm inequalities are obtained.

Maximally Holomorphic Functions of a Bounded Linear Operator

The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent equivalent operators follow easily from the relation of their maximally holomorphie functions.

TWO GENERALIZATIONS OF HARDY-LITTLEWOOD MAXIMAL OPERATOR

Two generalizations of Hardy-Littlewood maximal operator are considered. Some estimates for them are obtained.

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.

A FOUR-WEIGHT WEAK TYPE MAXIMAL INEQUALITY FOR MARTINGALES

In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,Φ_2 are Young functions, w_i(i = 1,2,3, 4) are weights, f~* =sup n≥0 |f_n| and f_∞=lim n→∞ f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.

WEAK BOUNDS FOR ROUGH SQUARE AND MAXIMAL OPERATORS

With Ω ∈ L (log + L)(S n-1 ) and suitable h ∈ L γ (R 1)(1<γ≤2),the weak type (1,1) of the square function g(f)(x) =k｜ψ k*f｜ 2 12(x) and the maximal operator M ψ(f)(x) = sup k｜ψ k｜*｜f｜(x) where ψ(x)=｜x｜ -n Ω(x)h(｜x｜),ψ k(x)=ψ 2 k (x), are studied in this paper.As a corollary,the weak bounds of M Ω(f) proved by Christ in 1988 are given and the previous weak type results for M ψ(f)(x) are improved.In addition,the weighted weak type (1,1) estimates of the Littlewood Paley function g ψ(f) with power weights is also proved.

Boundedness of Fractional Maximal Operators on Some of Homogeneous Groups

Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an adequate covering Lemma of Calderon-Zygmund type is shown, but also the boundedness of fractional maximal operators M α(0<α≤1) on some of homogeneous groups with respect to a given pair of weight functions (u,v) as above is proved. Moreover, a sufficient and necessary condition for M α∈B(u^qdx, v~~pdx), 0<α<1, 1<p<1α, and 1q=1p-α is also given. Finally, an application of the results is also obtained.

MAXIMAL CHARACTERIZATIONS OF HERZ TYPE HARDY SPACES ON HOMOGENEOUS GROUPS

In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P（G） and HKq^α,P（G）, where 1 〈 q 〈 ∞, Q（1 - 1/q） ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie group.

Composition of Maximal Operators on Space of Homogeneous Type

Let Ф be a Young function and MФ be the maximal operator associated with in the space of homogeneous type. In this paper, the composition of the maximal operators of type MФ is considered, and the result established by Carrozza and Passarelli Di Napoli is generalized to the space of homogeneous type.

Equivalence between Linear Tangle and Maximal Single Ideal

The concept of linear tangle was introduced as an obstruction to mixed searching number. The concept of (maximal) single ideal has been introduced as an obstruction to linear-width. Moreover, it was already known that mixed search number is equivalent to linear-width. Hence, by combining those results, we obtain a proof of the equivalence between linear tangle and maximal single ideal. This short report gives an alternative proof of the equivalence.

Boundedness of the Maximal Operator on Lip_α(R^n) (0<α<1)

It provides the boundary proof of the maximal operator on Lipschitz space. i.e.,if f ∈Lip α(R n) (0<α<1) and inf x∈R nM(f)(x) <∞, then almost every x∈R n has M(f)(x) <∞ and exists a constant C independent of f and x ,such that ‖M(f)‖ ∧ α ≤C‖f‖ ∧ α .

不同温湿度大红袍花椒对流辐射干燥试验研究

为对比大红袍花椒热风干燥、热风-红外与热风-微波联合干燥的特性和品质,揭示对流辐射联合干燥大红袍花椒的干燥过程,指导大红袍花椒生产实践。通过薄层干燥试验,研究三种干燥方式在不同温度(50℃、60℃、70℃)和相对湿度(10%、30%、50%)条件下的干燥曲线和有效水分扩散系数,结合Weibull函数的尺度参数α、形状参数β及估算有效水分扩散系数进行干燥动力学分析,采用扫描电子显微镜(SEM)观察干制花椒油苞结构,提取挥发油进行气相色谱质谱(GC-MS)分析。结果表明:热风干燥时间最长,升温降湿有利于提高热风干燥速率、缩短干燥时间,但对热风-红外和热风-微波干燥影响较小;Weibull函数能很好地模拟三种干燥方式,α随干燥条件变化明显,β>1,水分迁移是由物料表面和内部共同控制,估算水分扩散系数变化范围分别为1.303×10^(-7)~2.815×10^(-7)m^(2)/min、7.646×10^(-7)~9.628×10^(-7)m^(2)/min、2.200×10^(-6)~2.778×10^(-6)m^(2)/min,且与温湿度变化相关;热风干燥和热风-红外干燥能较好地保留花椒油苞,热风-微波干燥花椒油苞更为饱满;热风-微波干燥后花椒挥发油提取量最高(7.5%),烯烃类物质相对含量最大,热风干燥花椒提取挥发油含量最低,但挥发油中化合物种类最多。热风-红外联合干燥在缩短干燥时间和保持品质方面是较好的选择。

融合注意力机制和二次特征提取的ResNet小样本农作物病虫害识别

针对传统机器学习方法对于小样本和多类别的农作物叶片病虫害识别效果和时间不理想的问题,本文利用改进的ResNet模型来实现农作物病害识别.通过加入dropout层、激活函数、最大池化层和注意力机制来提高模型的鲁棒性、特征捕捉能力、实现了用较低的模型参数量来提高病虫害识别的准确率.首先对从公共数据集Plant Village获取的图像进行预处理和增强,将ReLU激活函数替换为PReLU,解决ReLU函数在小于0部分神经元坏死的问题;然后在全局平均池化层之前加入dropout层,设置合理的阈值,有效避免过拟合现象的发生,增强模型的鲁棒性;此外,在dropout与全局平均池化层之间加入最大池化层,不仅能扩大神经元的感受野,还能帮助模型获取局部病虫害的最显著特征,减小图片背景的噪声影响,实现二次特征提取;最后嵌入CBAM注意力机制,使模型自动学习输入特征图中最重要的通道信息,并对其进行通道与空间之间加权,从而更好地捕捉图像中的语义信息.实验结果表明,改进后的模型对测试集识别准确度达99.15%,模型参数量仅为9.13M,与Xception、InceptionV3、原ResNet等模型相比,准确率分别超过了1.01,0.68,0.59个百分点,降低了模型参数量,为农作物病虫害识别提供了一种先进的深度学习方法.