ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL

This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution)dispersals:{u_(t)=k*u-u+u(1-u-av),x∈R,t∈R,vt=d(k*v-v)+rv(1-v-bu),c∈R,t∈R.(0.1)Here a≠1,b≠1,d,and r are positive constants.By studying the eigenvalue problem of(0.1)linearized at(ϕc(ξ),0),we construct a pair of super-and sub-solutions for(0.1),and then establish the existence of entire solutions originating from(ϕc(ξ),0)as t→−∞,whereϕc denotes the traveling wave solution of the nonlocal Fisher-KPP equation ut=k*u−u+u(1−u).Moreover,we give a detailed description on the long-time behavior of such entire solutions as t→∞.Compared to the known works on the Lotka-Volterra competition system with classical diffusions,this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.

ENTIRE SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS HAVING THE SAME ORDER

In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.

On entire solutions of some Fermat type differential-difference equations

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].

ON ENTIRE SOLUTIONS OF TWO TYPES OF SYSTEMS OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS

In this paper,we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations,and obtain some interesting results.It extends some results concerning complex differential（difference） equations to the systems of differential-difference equations.

lassification and existence of positive entire k-convex radial solutions for generalized nonlinear k-Hessian system

In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z2),x∈R^(N),where G is a nonlinear operator and Sk(λ(D^(2)z))stands for the k-Hessian operator.We first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system ifφ(|x|,z1,z2)=b(|x|)φ(z1,z2)andψ(|x|,z1,z2)=h(|x|)ψ(z1).Moreover,with the help of the monotone iterative method,some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearitiesψ,φare given,which improve and extend many previous works.

Existence and Nonexistence of Entire Positive Solutions for a Class of Singular p-Laplacian Elliptic System

In this paper, we show the existence and nonexistence of entire positive solutions for a class of singular elliptic system We have that entire large positive solutions fail to exist if f and g are sublinear and b and d have fast decay at infinity. However, if f and g satisfy some growth conditions at infinity, and b, d are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded.

Development of a high-speed digital pulse signal acquisition and processing system based on MTCA for liquid scintillator neutron detector on EAST

In this experimental study, involving deuterium–deuterium fusion neutron emission spectroscopy measurement on the experimental advanced superconducting tokamak(EAST), a liquid scintillator detector(BC501 A) was employed. This decision was based on the detector's superior sensitivity, optimal time-response, and its exceptional n–γ discrimination capability. This detector emits fast pulse signals that are as narrow as 100 ns, with high count rates that can peak at several Mcps. However, conventional nuclear circuits faced challenges in performing pulse height analysis, n–γ pulse shape discrimination, and in recording the entire pulse waveform under such high count rate conditions. To address these challenges, a high-speed digital pulse signal acquisition and processing system was designed. The system was developed around a micro-telecommunications computing architecture. Within this structure, a signal acquisition and processing(SAQP) module communicated through PCI Express links, achieving a bandwidth of up to 1.6 GB/s. To accurately capture the detailed shape of the pulses, four channels of analog-to-digital converters were used, each with a 500-MSPS sampling rate and a 14-bit resolution, ensuring an accuracy that surpassed 11 bits. An n–γ discrimination algorithm, based on the two-gate integral method, was also developed. Implemented within field programmable gate arrays, this algorithm provided a real-time n–γ discrimination spectrum for pulse height analysis. The system underwent rigorous testing in a laboratory setting and during an EAST experiment. The results confirmed that the innovative SAQP system can satisfy the demanding requirements of high-parameter experiments, manage count rates of up to 2 Mcps, execute real-time n–γ discrimination algorithms, and record entire pulse waveforms without any data loss.

A Class of Potentials for Hyperbolic Transcendental Entire Maps

We identify a class of transcendental entire maps of finite order, of disjoint-type, satisfying the rapid derivative growth condition. Within this class, we show that there exist hyperbolic transcendental entire maps that generate a large class of potentials which intersect the so-called tame potentials and form a distinct class of potentials. The methods and techniques derived from the thermodynamic formalism are applied to these potentials for transcendental entire maps acting on some subset of the Julia set which is conjugated to the shift map over a code space with a countable alphabet endowed with the euclidean induced metric on the complex plane.

On the growth of transcendental entire solutions of algebraic differential equations

In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail.

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

Promoting Environmental Risk Assessment and Control of Emerging Contaminants in China

1.Introduction In recent years,China has carried out an extensive preventative battle against air,water,and soil pollution,and the nation’s environmental quality-as reflected by conventional pollutant indicators—has significantly improved.At the same time,the issue of emerging contaminants(ECs)is beginning to receive increasing attention.ECs generally refer to newly discovered or noticeable pollutants that pose risks to the ecological environment or human health.Either they have not been included in environmental management,or existing management measures are insufficient to effectively prevent and control their risks.The ECs of greatest concern generally include persistent organic pollutants(POPs),endocrine-disrupting chemicals(EDCs),pharmaceuticals and personal care products(PPCPs),and microplastics.These four categories of ECs are not entirely separate,as they interrelate with each other(Fig.1).Chemical production and product usage are the main sources of ECs.China is the world’s largest producer and consumer of bulk chemicals,and the production value of China’s chemical industry is predicted to reach 50%of the global total by 2030[1].Scientific control of ECs based on their environmental risk assessment is a necessary way to support the prevention and legal governance of ECs.

Qualitative analysis of aromatic compounds via 1D TOCSY techniques

The aromatic compounds,including o-xylene,m-xylene,p-xylene,and ethylbenzene,primarily originate from the catalytic reforming of crude oil,and have a wide variety of applications.However,because of similar physical and chemical properties,these compounds are difficult to be identified by gas chromatography(GC)without standard samples.With the development of modern nuclear magnetic resonance(NMR)techniques,NMR has emerged as a powerful and efficient tool for the rapid analysis of complex and crude mixtures without purification.In this study,the parameters of one-dimensional(1D)total correlation spectroscopy(TOCSY)NMR techniques,including 1D selective gradient TOCSY and 1D chemicalshift-selective filtration(CSSF)with TOCSY,were optimized to obtain comprehensive molecular structure information.The results indicate that the overlapped signals in NMR spectra of nonpolar aromatic compounds(including o-xylene,m-xylene,p-xylene and ethylbenzene),polar aromatic compounds(benzyl alcohol,benzaldehyde,benzoic acid),and aromatic compounds with additional conjugated bonds(styrene)can be resolved in 1D TOCSY.More importantly,full molecular structures can be clearly distinguished by setting appropriate mixing time in 1D TOCSY.This approach simplifies the NMR spectra,provides structural information of entire molecules,and can be applied for the analysis of other structural isomers.

On the Julia Sets of Permutable Transcendental Entire Functions

Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is any transcendental entire function with h′(z)=0 having infinitely many solutions, p(z) is a polynomial with deg p ≥2 and a(≠0) ∈ C .

The Green Wall of Aksu

An afforestation project transforms a desert prefecture in Xinjiang into an oasis.Yusupjan Alim would win any reality show like Survivor hands down.The 36-year-old forest ranger started his career planting trees in the bleak and blazing Gobi Desert in 2004 in circumstances entirely different from today’s.At that time,there were no mobile phones,no GPS or transportation.The team would go deep into the desert on a truck,carrying naan,the flatbread of Xinjiang that would keep for days.It was their staple,if not only,food.

THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS

We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.

THE GROWTH ORDER OF SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS

Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equations.

UNIQUENESS OF ENTIRE FUNCTIONS SHARING ONE VALUE

We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].

Is it necessary to use the entire root as a donor when transferring contralateral C7 nerve to repair median nerve？

If a partial contralateral C7 nerve is transferred to a recipient injured nerve, results are not satisfactory. However, if an entire contralateral C7 nerve is used to repair two nerves, both recipient nerves show good recovery. These findings seem contradictory, as the above two methods use the same donor nerve, only the cutting method of the contralateral C7 nerve is different. To verify whether this can actually result in different repair effects, we divided rats with right total brachial plexus injury into three groups. In the entire root group, the entire contralateral C7 root was transected and transferred to the median nerve of the affected limb. In the posterior division group, only the posterior division of the contralateral C7 root was transected and transferred to the median nerve. In the entire root ＋ posterior division group, the entire contralateral C7 root was transected but only the posterior division was transferred to the median nerve. After neurectomy,the median nerve was repaired on the affected side in the three groups. At 8, 12, and 16 weeks postoperatively, electrophysiological examination showed that maximum amplitude, latency, muscle tetanic contraction force, and muscle fiber cross-sectional area of the flexor digitorum superficialis muscle were significantly better in the entire root and entire root ＋ posterior division groups than in the posterior division group. No significant difference was found between the entire root and entire root ＋ posterior division groups. Counts of myelinated axons in the median nerve were greater in the entire root group than in the entire root ＋ posterior division group, which were greater than the posterior division group. We conclude that for the same recipient nerve, harvesting of the entire contralateral C7 root achieved significantly better recovery than partial harvesting, even if only part of the entire root was used for transfer. This result indicates that the entire root should be used as a donor when transferring contralateral C7 nerve.

Entire Catchment and Buffer Zone Approaches to Modeling Linkage Between River Water Quality and Land Cover——A Case Study of Yamaguchi Prefecture,Japan

This study investigated the linkages between river water quality and land use in river catchments in Yama- guchi Prefecture, the western Japan, in order to examine the effect of land use changes of both entire catchment and buffer zone on river water quality. Dissolved Oxygen (DO), pH, Biological Oxygen Demand (BOD), Suspended Solids (SS), Escherichia coli, Total Nitrogen (TN) and Total Phosphorus (TP) were considered as river water quality indica- tors. Satellite images were applied to generating the land use map. Multiple regression model was applied to linking the changes in the river water quality with the land uses in both entire catchment area and buffer zone. The results in- dicate that the integrative application of land use data from the entire catchment and the buffer zone could give rise to more robust model to predict the concentrations of Suspended Solids (r2=0.88) and Total Nitrogen (r2=0.90), rather than models which separately considered land use data in catchment and buffer zone.