The response of roots and the rhizosphere environment to integrative cultivation practices in paddy rice

Integrative cultivation practices(ICPs)are essential for enhancing cereal yield and resource use efficiency.However,the effects of ICP on the rhizosphere environment and roots of paddy rice are still poorly understood.In this study,four rice varieties were produced in the field.Each variety was treated with six different cultivation techniques,including zero nitrogen application(0 N),local farmers’practice(LFP),nitrogen reduction(NR),and three progressive ICP techniques comprised of enhanced fertilizer N practice and increased plant density(ICP1),a treatment similar to ICP1 but with alternate wetting and moderate drying instead of continuous flooding(ICP2),and the same practices as ICP2 with the application of organic fertilizer(ICP3).The ICPs had greater grain production and nitrogen use efficiency than the other three methods.Root length,dry weight,root diameter,activity of root oxidation,root bleeding rate,zeatin and zeatin riboside compositions,and total organic acids in root exudates were elevated with the introduction of the successive cultivation practices.ICPs enhanced nitrate nitrogen,the activities of urease and invertase,and the diversity of microbes(bacteria)in rhizosphere and non-rhizosphere soil,while reducing the ammonium nitrogen content.The nutrient contents(ammonium nitrogen,total nitrogen,total potassium,total phosphorus,nitrate,and available phosphorus)and urease activity in rhizosphere soil were reduced in all treatments in comparison with the non-rhizosphere soil,but the invertase activity and bacterial diversity were greater.The main root morphology and physiology,and the ammonium nitrogen contents in rhizosphere soil at the primary stages were closely correlated with grain yield and internal nitrogen use efficiency.These findings suggest that the coordinated enhancement of the root system and the environment of the rhizosphere under integrative cultivation approaches may lead to higher rice production.

ON PARAMETRIC MARCINKIEWICZ INTEGRALS RELATED TO BLOCK SPACES

In this paper,the L2-boundedness of a class of parametric Marcinkiewicz integral μρ Ω,h with kernel function Ω in B 0,0 q(S n-1) for some q>1,and the radial function h(x)∈l∞(Ls)(R +) for 1<s≤∞ are given.The Lp(Rn)(2≤p<∞) boundedness of μ *,ρ Ω,h,λ and μ ρ Ω,h,S with Ω in B 0,0 q(S n-1) and h(|x|)∈l∞(Ls)(R +) in application are obtained.Here μ *,ρ Ω,h,λ and μ ρ Ω,h,S are parametric Marcinkiewicz integrals corresponding to the Littlewood-Paley g* λ function and the Lusin area function S,respectively.

Path integral solutions for n-dimensional stochastic differential equations underα-stable Lévy excitation

In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

LÉVY AREA ANALYSIS AND PARAMETER ESTIMATION FOR FOU PROCESSES VIA NON-GEOMETRIC ROUGH PATH THEORY

This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering.

Endpoint Estimates for Commutators of Fractional Integrals Associated to Operators with Heat Kernel Bounds

Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.

Hypersingular parameterized Marcinkiewicz integrals with variable kernels on Sobolev and Hardy-Sobolev spaces

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.

Orliczφ-弦对数Minkowski不等式

本文通过引进新的混合弦测度和Orlicz混合弦测度概念,并且利用新近建立的Orlicz弦Minkowski不等式,建立了Orlicz空间上的混合弦积分的φ-弦对数Minkowski不等式.我们的结果φ-弦对数Minkowski不等式,在两种特殊情况下分别产生了弦对数Minkowski不等式和L_(p)-弦对数Minkowski不等式.

Multilinear singular and fractional integrals on weighted Hardy spaces

In this paper the boundedness properties of multilinear singular and fractional integrals on the weighted Hardy spaces are studied.

L2 Syntactic Alignment in the Reading-Writing Integrated Continuation Task: Evidence From Chinese EFL Learners’ Description of Motion Events

This study investigated how the mode in which the reading-writing integrated continuation task was conducted modulates the effects of second language(L2) syntactic alignment, through the English motion event construction with manner verbs. Ninety Chinese students were assigned to either of the two experimental groups or a control group, and they all experienced a pretest, an alignment phase and a posttest. In the alignment phase, the two experimental groups completed a reading-writing integrated continuation task but in different modes. For the multi-turn mode,participants reconstructed a picture story by continuing the episodes extracted from the story with one episode presented and continued at a time;for the single-turn mode, the first half of the same picture story was presented as a chunk, and then participants read and continued it. Results show that L2 learners aligned with the target structure in completing the story, and the alignment effect was retained in the posttest conducted after a delay of two weeks. Moreover, syntactic alignment was modulated by task mode with the multi-turn group exhibiting stronger immediate and longterm alignment effects. We conclude that the continuation task is a fruitful context for L2 structural alignment, and the magnitude of alignment effect hinges on interactive intensity.

An Integrated Genetic,Physical and Transcript Map of Homoeologous Chromosomes 12 and 26 in Upland Cotton(Gossypium hirsutum L.)

While Upland cotton(Gossypium hirsutum L.) represents 95% of the world production,its genetic improvement is hindered by the shortage of effective genomic tools and resources.The

一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算

利用三角函数幂公式、L′Hospital法则、分部积分公式,得到含有三角函数的第一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算公式,其中n≥1且θ≠0.

Occurrence Reasons and Integrated Control of Physiological Chlorosis ofCinnamomum camphora L. in Urban Area of Pingdingshan City

The relevant factors for physiological chlorosis of Cinnamomum camphora L. in Pingdingshan were studied combining with references and production sur- vey. The resuhs showed that the disease was the integrated results of soil environment, planting situation, microenvironment construction and maintenance manage- ment. Therefore, the countermeasures of ＂prevention first, restore tree vigor; integrated control, enhance tree vigor＂ were proposed. Chlorosis of C. camphora had been basically controlled after four years, and the control effect was obvious.

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.

SOME BOUNDED RESULTS OF θ(t)-TYPE SINGULAR INTEGRAL OPERATORS

Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ (t)_type singular integral operators in L p B(R n),(1≤p<+∞) and H 1 B(R n) spaces are discussed.

Unified treatment of the bound states of the Schioberg and the Eckart potentials using Feynman path integral approach

We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term. In order to determine the l-states solutions, we use the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space-time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions. We show that the Eckart potential can be derived from the Schioberg potential. The obtained results are compared to those produced by other methods and are found to be consistent.

L^p integrability of trigonometric series with special varying coefficients

Very recently, Yu, Le and Zhou introduced the so called △B1^＊ and △B2^＊ conditions, which are generalizations of the monotone condition. By applying these two new conditions, the author essentially generalizes the classical results of Chen on the necessary and sufficient conditions of the Lp integrability of trigonometric series. In fact, the present paper gives the first result on the necessary and sufficient conditions of the Lp integrability of trigonometric series, where coefficients may have different signs.

On the Fractional Derivatives with an Exponential Kernel

The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional derivatives are proposed,including the Fourier transform and the Laplace transform.Then,the L2 discretisation for the exponential Caputo derivative with a∈(1,2)is established.The estimation of the truncation error and the properties of the coefficients are discussed.In addition,a numerical example is given to verify the correctness of the derived L2 discrete formula.

BOUNDEDNESS OF MARCINKIEWICZ INTEGRAL ON THE WEIGHTED HERZ-TYPE HARDY SPACES

In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from HKq^a、P（ω1;ω2） into Kq^a、p （ω1; ω2）.

A BMO ESTIMATE FOR THE MULTILINEAR SINGULAR INTEGRAL OPERATOR

The behavior on the space L^∞（R^n） for the multilinear singular integral operator defined by TAf（x）=∫RnΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）△A（y）（x-y））f（y）dy is considered, where 12 is homogeneous of degree zero, integrable on the unit sphere and has vanishing is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishingmoment of order one, A has derivatives of order one in BMO（R^n）. It is proved that if Ω satisfies some minimum size condition and an L1-Dini type regularity condition, then for f ∈ L^∞（R^n）, TAf is either infinite almost everywhere or finite almost everywhere, and in the latter case, TAf ∈ BMO（R^n）.

An Accurate Numerical Integrator for the Solution of Black Scholes Financial Model Equation

In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10–10.