Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.

A fractional differential constitutive model for dynamic stress intensity factors of an anti-plane crack in viscoelastic materials

Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

Reconstruction of Sub-Decadal Winter Half-Year Temperature during 1651-2010 for the North China Plain Using Records of Frost Date

We extracted 374 pieces of records of frost date from historical documents. Using these records, we reconstructed winter half-year (October to next April) temperature series, with a resolution of 5-year, for the North China Plain during 1651-2010. The results show that the temperature changes in the North China Plain were divided into four phases. With the reference period of 1951-1980, two cold phases, 1651-1700 and 1781-1900, have cold anomaly of 0.83°C and 0.60°C respectively. However, between the two cold phases, 1701-1780 was a relative warm phase with the cold anomaly of 0.36°C referring to the mean of 1951-1980. After the 1900, the climate came into a warm phase. The mean temperature of 1901-2010 was 0.11°C higher than the mean of 1951-1980. During 1651-2010, the 1996-2000 is the warmest 5-year with the warm anomaly of 1.25°C than that of the reference period of 1951-1980.

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

A Diagnostic Analysis of Winter Atmospheric Circulation during the 1982-1983 ENSO Event

In this paper, the winter atmospheric circulation, the convection along the equator and their variations of 1982 and 1983 are investigated. It is suggested that there was a well organized three dimensional structure of anomalies of the atmospheric circulations during 1982 winter which may be related to the variations of the convection in the equatorial region.

Diagnostic performance of dynamic contrast-enhanced magnetic resonance imaging parameters and serum tumor markers in rectal carcinoma prognosis

BACKGROUND Rectal carcinoma(RC),one of the most common malignancies globally,presents an increasing incidence and mortality year by year,especially among young people,which seriously affects the prognosis and quality of life of patients.At present,dynamic contrast-enhanced magnetic resonance imaging(DCE-MRI)parameters and serum carbohydrate antigen 19-9(CA19-9)and CA125 Levels have been used in clinical practice to evaluate the T stage and differentiation of RC.However,the accuracy of these evaluation modalities still needs further research.This study explores the application and value of these methods in evaluating the T stage and differentiation degree of RC.AIM To analyze the diagnostic performance of DCE-MRI parameters combined with serum tumor markers(TMs)in assessing pathological processes and prognosis of RC patients.METHODS A retrospective analysis was performed on 104 RC patients treated at Yantai Yuhuangding Hospital from May 2018 to January 2022.Patients were categorized into stages T1,T2,T3,and T4,depending on their T stage and differentiation degree.In addition,they were assigned to low(L group)and moderate-high differentiation(M+H group)groups based on their differentiation degree.The levels of DCE-MRI parameters and serum CA19-9 and CA125 in different groups of patients were compared.In addition,the value of DCE-MRI parameters[volume transfer constant(Ktrans),rate constant(Kep),and extravascular extracellular volume fraction(Ve)in assessing the differentiation and T staging of RC patients was discussed.Furthermore,the usefulness of DCE-MRI parameters combined with serum CA19-9 and CA125 Levels in the evaluation of RC differentiation and T staging was analyzed.RESULTS Ktrans,Ve,CA19-9 and CA125 were higher in the high-stage group and L group than in the low-stage group and M+H Group,respectively(P<0.05).The areas under the curve(AUCs)of the Ktran and Ve parameters were 0.638 and 0.694 in the diagnosis of high and low stages,respectively,and 0.672 and 0.725 in diagnosing moderate-high and low differentiation,respectively.The AUC of DCE-MRI parameters(Ktrans+Ve)in the diagnosis of high and low stages was 0.742,and the AUC in diagnosing moderate-high and low differentiation was 0.769.The AUCs of CA19-9 and CA-125 were 0.773 and 0.802 in the diagnosis of high and low stages,respectively,and 0.834 and 0.796 in diagnosing moderate-high and low differentiation,respectively.Then,we combined DCE-MRI(Ktrans+Ve)parameters with CA19-9 and CA-125 and found that the AUC of DCE-MRI parameters plus serum TMs was 0.836 in the diagnosis of high and low stages and 0.946 in the diagnosis of moderate-high and low differentiation.According to the Delong test,the AUC of DCE-MRI parameters plus serum TMs increased significantly compared with serum TMs alone in the diagnosis of T stage and differentiation degree(P<0.001).CONCLUSION The levels of the DCE-MRI parameters Ktrans and Ve and the serum TMs CA19-9 and CA125 all increase with increasing T stage and decreasing differentiation degree of RC and can be used as indices to evaluate the differentiation degree of RC in clinical practice.Moreover,the combined evaluation of the above indices has a better effect and more obvious clinical value,providing important guiding importance for clinical condition judgment and treatment selection.

不同前茬作物和施肥水平下麦田土壤不同形态无机磷含量及其对冬小麦磷累积量的贡献

为研究不同前茬作物下土壤无机磷形态的差异及对后茬作物冬小麦磷累积的影响,开展了二因素田间试验,测定了3种前茬作物(玉米、大豆、花生)和2个磷肥施肥水平(P_(2)O_(5)150 kg/hm^(2),常规施肥(+F);P_(2)O_(5)0 kg/hm^(2),限肥(-F))处理下播种前和收获后耕层(0~15 cm)土壤全磷、速效磷以及不同形态无机磷的质量分数,同时测定冬小麦植株磷累积量,运用通径分析法,分析了土壤中不同形态无机磷对冬小麦植株磷积累量的贡献.结果表明:与常规施肥相比,限肥显著降低土壤全磷、速效磷和不同形态无机磷的含量.在常规施肥水平下,玉米前茬处理的土壤速效磷质量分数最高且显著高于其他前茬处理,为18.61 mg/kg,总无机磷、Fe-P和Ca_(10)-P的质量分数也最高,分别为592.55 mg/kg、41.97 mg/kg和338.77 mg/kg;大豆前茬处理的土壤全磷质量分数最高且显著高于其他前茬处理,为972.80 mg/kg,Al-P和O-P的含量也在大豆前茬处理的质量分数最高,分别为43.44 mg/kg和64.37 mg/kg;花生前茬处理的土壤Ca_(2)-P和Ca_(8)-P的质量分数最高,分别为27.53 mg/kg和94.14 mg/kg,但与玉米前茬和大豆前茬的处理结果差异不显著.在限肥水平下,玉米前茬处理土壤的全磷、速效磷和O-P的质量分数最高且显著高于其他前茬处理,分别为770.47 mg/kg、13.50 mg/kg、58.99 mg/kg;大豆前茬处理土壤Ca_(10)-P的质量分数最高且显著高于其他前茬处理,为320.62 mg/kg,总无机磷、Al-P和Fe-P的质量分数与其他前茬处理差异不显著,分别为541.96 mg/kg、34.50 mg/kg和36.42 mg/kg;花生前茬处理土壤Ca_(2)-P和Ca_(8)-P的质量分数最高但与花生前茬处理的差异不显著,分别为23.04 mg/kg和78.78 mg/kg.2个磷肥水平下冬小麦植株磷累积量均在花生前茬处理下最高,分别为33.11 kg/hm^(2)和25.14 kg/hm^(2).在常规施肥水平下,花生前茬处理与玉米、大豆前茬处理的差异不显著,而在限肥水平下显著高于玉米、大豆前茬处理.经通径分析,土壤无机磷不同形态对冬小麦植株磷累积量的直接影响(直接通径系数)由大到小为Ca_(2)-P、Al-P、Fe-P、Ca_(8)-P、O-P、Ca_(10)-P.结合通径系数和相关系数表明,Ca_(2)-P是小麦磷累积的直接来源,其次是Al-P,而Fe-P和Ca_(8)-P是小麦的缓效磷源,O-P和Ca_(10)-P是小麦比较难以利用的磷源.在2种施肥水平下,前茬作物极显著影响全磷、速效磷、和无机磷的含量,进而影响冬小麦的植株磷累积量.

2’,3’-双脱氢-2’,3’-双脱氧腺苷的合成

以腺苷为原料，利用Corey-Winter烯化反应分4步合成了2’，3’-双脱氧-2’，3’-双脱氧腺苷，总收率51％。用1HNMR和13CNMR表征了中间体及目标产物。

GC-MS与GC-FTIR联合测定C9烃馏分组成

混合碳九组成复杂,估计为环状烯烃、芳烃、多环烃、烷烃等,目前该产品主要用于生产石油树脂.随着我国乙烯生产能力的不断扩大,其产量也在不断增加,为充分利用碳九资源,研究开拓其新的应用领域非常必要.……

Distribution,fractionation,and contamination assessment of heavy metals in offshore surface sediments from western Xiamen Bay,China

Surface sediment samples were collected at 21 offshore sites in western Xiamen Bay, Southeast China. Total concentrations of Li, V, Cr, Co, Ni, Cu, Zn, St, Mn, Pb, Ba, Fe, and Ti were determined by inductively coupled plasma-optical emission spectrometry; Hg was determined by atomic fluorescence spectrometry. A modified BCR sequential extraction procedure was used to extract fractions of the above elements. Concentrations of Pb, Cr, and Hg at most sites met the primary standard criteria of Marine Sediment Quality except site S12 for Pb and S7 for Cr, while concentrations of Zn at 17 sites and Cu at seven sites exceeded the criteria. The mean concentration of Hg was three times higher than the background, with a possible source being the Jiulong River. Fe, Ti, Ba, Co, V, and Li dominated the residual phase, mainly from terrestrial input. Ni, Cr, Pb, and Hg in the non-residual phase varied largely between sites. Sr, Mn, Cu, and Zn were mainly in the non- residual fraction. Most sites showed considerable ecological risk; exceptions were site S7 （very high） and sites S10, S11, and S14 （moderate）. Cu showed moderate-to-high pollution and Pb exhibited no-to-low pollution, while other metals had a non-pollution status according to their ratios of secondary phase to primary phase （RSP）. Results of two assessment methods showed moderate pollution and a very high ecological risk for Cu, Zn, Ni, and Cr at site S7, which might be due to the local sewage treatment plant.

A diagnostic experiment of the influence of CO_2on winter wheat

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Exact solutions for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit

The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.

BOUNDEDNESS OF HIGHER ORDER COMMUTATORS OF GENERALIZED FRACTIONAL INTEGRAL OPERATORS ON HARDY SPACES

Let Tμ,b,m be the higher order commutator generated by a generalized fractional integral operator Tμ and a BMO function b. In this paper, we will study the boundedness of Tμ,b,m on classical Hardy spaces and Herz-type Hardy spaces.

Origins of intraseasonal rainfall variations over the southern South China Sea in boreal winter

This study investigates the origins of intraseasonal rainfall variations over the southern South China Sea（SCS） region in boreal winter.It is found that intraseasonal rainfall variations over the southern SCS have different origins on the 10-20-day and 30-60-day time scales.On the 10-20-day time scale,large rainfall anomalies over the southern SCS are preceded by strong northerly wind anomalies associated with the East Asian winter monsoon（EAWM）,by about two days.On the 30-60-day time scale,the strong EAWM-related northerly wind anomalies almost appear simultaneously with large rainfall anomalies over the southern SCS.In addition,obvious large rainfall anomalies occur over the southeastern tropical Indian Ocean about one week before the peak southern SCS rainfall anomalies.It indicates that the convection and related circulation anomalies with origins over the tropical Indian Ocean may play an important role in inducing intraseasonal rainfall variations over the southern SCS on the 30-60-day time scale,but not on the 10-20-day time scale.

Synchronizing Fractional Unified Hyperchaotic System via Impulsive Control

This work investigates synchronization of two fractional unified hyperchaotic systems via impulsive control.The stable theory about impulsive fractional equation is studied based on the stable theory about fractional linear system.Then according to the theorem proposed the sufficient condition on feedback strength and impulsive interval are established to guarantee the synchronization.Numerical simulations show the effectiveness of the theorem.

Computable extensions of generalized fractional kinetic equations in astrophysics

Fractional calculus and special functions have contributed a lot to mathematical physics and its various branches. The great use of mathematical physics in distinguished astrophysical problems has attracted astronomers and physicists to pay more attention to available mathematical tools that can be widely used in solving several problems of astrophysics/physics. In view of the great importance and usefulness of kinetic equations in certain astrophysical problems, the authors derive a generalized fractional kinetic equation involving the Lorenzo-Hartley function, a generalized function for fractional calculus. The fractional kinetic equation discussed here can be used to investigate a wide class of known （and possibly also new） fractional kinetic equations, hitherto scattered in the literature. A compact and easily computable solution is established in terms of the Lorenzo-Hartley function. Special cases, involving the generalized Mittag-Leffler function and the R-function, are considered. The obtained results imply the known results more precisely.

Fractionation characteristics of rare earth elements(REEs) linked with secondary Fe, Mn, and Al minerals in soils

Soil secondary minerals are important scavengers of rare earth elements(REEs) in soils and thus affect geochemical behavior and occurrence of REEs. The fractionation of REEs is a common geochemical phenomenon in soils but has received little attention, especially fractionation induced by secondary minerals. In this study, REEs(La to Lu and Y) associated with soil-abundant secondary minerals Fe-, Al-, and Mn-oxides in 196 soil samples were investigated to explore the fractionation and anomalies of REEs related to the minerals. The results show right-inclined chondrite-normalized REE patterns for La–Lu in soils subjected to total soil digestion and partial soil extraction. Light REEs(LREEs) enrichment features were negatively correlated with a Eu anomaly and positively correlated with a Ce anomaly. The fractionation between LREEs and heavy REEs(HREEs) was attributed to the high adsorption affinity of LREEs to secondary minerals and the preferred activation/leaching of HREEs.The substantial fractions of REEs in soils extracted byoxalate and Dithionite-Citrate-Bicarbonate buffer solutions were labile(10 %–30 %), which were similar to the mass fraction of Fe(10 %–20 %). Furthermore, Eu was found to be more mobile than the other REEs in the soils, whereas Ce was less mobile. These results add to our understanding of the distribution and geochemical behavior of REEs in soils, and also help to deduce the conditions of soil formation from REE fractionation.

绿肥填闲种植和施氮对旱作冬小麦农田土壤氮组分的影响

【目的】研究绿肥填闲种植和施氮对旱作冬小麦农田土壤氮组分的影响,探讨旱地绿肥填闲种植系统提升土壤供氮能力的途径。【方法】冬小麦−夏季绿肥田间定位试验开始于2017年,采用绿肥填闲作物和施氮双因素设计,其中绿肥填闲作物包括苏丹草单播(SG)、长武怀豆单播(SB)、苏丹草与怀豆混播(MIX)和裸地休闲(CK)4个处理,冬小麦施氮量包括0、60、120 kg/hm^(2)3个水平。2023年6月小麦收获后采集0—10、10—20和20—40 cm土壤样品,测定土壤全氮(STN)、颗粒有机氮(PON)、潜在矿化氮(PMN)和微生物量氮(MBN)含量。【结果】与CK处理相比,种植绿肥并未显著影响各土层STN含量,但提高了0—10 cm土层PON含量(增幅为25.8%~54.8%)、0—10和10—20 cm土层PMN含量(增幅分别为9.7%~14.1%和11.2%~13.7%)以及0—10、10—20和20—40 cm土层MBN含量(增幅分别为15.1%~24.1%、18.2%~28.8%和22.3%~32.5%)。不同绿肥处理间比较,SB和MIX处理较SG显著提高了0—10 cm土层PON含量(增幅均为23.1%),SB处理各土层MBN含量均显著高于SG处理(增幅为7.79%~8.93%),而各土层PMN含量在不同绿肥处理间差异均不显著。供试土壤氮组分相对含量大小排序为PON>MBN>PMN,绿肥处理较CK均显著提高了0—10 cm土层PON、PMN、MBN相对含量、10—20 cm土层PMN和MBN相对含量以及20—40 cm土层PON和MBN相对含量。施氮提高了0—20 cm土层氮组分及其相对含量,但对20—40 cm土层没有显著影响。相关性分析结果表明,除STN外,PON、PMN和MBN含量均与系统年均氮输入呈显著正相关关系;STN、PON、PMN、MBN含量间均呈显著正相关,且PON较其它活性组分更能指示土壤供氮能力变化。【结论】夏季绿肥填闲种植和施氮均能显著提高旱地冬小麦单作系统0—20 cm土层氮组分含量及其相对含量,其中长武怀豆与氮肥120 kg/hm^(2)联合施用更有助于提高农田土壤供氮能力。

基于低空无人机遥感的冬小麦覆盖度变化监测

无人机遥感作为卫星遥感的有益补充,具有高时效、高分辨率、低成本、低损耗、低风险及可重复等优点。为了利用无人机遥感系统进行快速机动地监测大面积农作物覆盖度变化,更好地服务和指导农业生产,该文设计了一套以低空无人直升机为平台的多光谱载荷观测系统,并以冬小麦为研究对象,对冬小麦生长过程中的5个主要生育期进行监测,提出一种从时间序列影像的植被指数直方图曲线中获取植被指数阈值的方法,并利用植被指数阈值法提取研究区域内冬小麦覆盖度时序变化曲线,分析了空间尺度对提取植被覆盖度的影响。研究结果表明,利用低空无人机遥感监测冬小麦覆盖度变化的方法可行,分析结果可靠,在大面积农作物覆盖度的测量有很好的应用前景。