Impacts of Aggregation Methods and Trophospecies Number on the Structure and Function of Marine Food Webs

Aggregation of species with similar ecological properties is one of the effective methods to simplify food web researches.However,species aggregation will affect not only the complexity of modeling process but also the accuracy of models’outputs.Selection of aggregation methods and the number of trophospecies are the keys to study the simplification of food web.In this study,three aggregation methods,including taxonomic aggregation(TA),structural equivalence aggregation(SEA),and self-organizing maps(SOM),were analyzed and compared with the linear inverse model–Markov Chain Monte Carlo(LIM-MCMC)model.Impacts of aggregation methods and trophospecies number on food webs were evaluated based on the robustness and unitless of ecological net-work indices.Results showed that aggregation method of SEA performed better than the other two methods in estimating food web structure and function indices.The effects of aggregation methods were driven by the differences in species aggregation principles,which will alter food web structure and function through the redistribution of energy flow.According to the results of mean absolute percentage error(MAPE)which can be applied to evaluate the accuracy of the model,we found that MAPE in food web indices will increase with the reducing trophospecies number,and MAPE in food web function indices were smaller and more stable than those in food web structure indices.Therefore,trade-off between simplifying food webs and reflecting the status of ecosystem should be con-sidered in food web studies.These findings highlight the importance of aggregation methods and trophospecies number in the analy-sis of food web simplification.This study provided a framework to explore the extent to which food web models are affected by dif-ferent species aggregation,and will provide scientific basis for the construction of food webs.

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

The Cumulative Method for Multiplication and Division

This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.

Systematic Method for Constructing Lewis Representations

The systematic method for constructing Lewis representations is a method for representing chemical bonds between atoms in a molecule. It uses symbols to represent the valence electrons of the atoms involved in the bond. Using a number of rules in a defined order, it is often better suited to complicated cases than the Lewis representation of atoms. This method allows us to determine the formal charge and oxidation number of each atom in the edifice more efficiently than other methods.

A New Proof for Congruent Number’s Problem via Pythagorician Divisors

Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2 t+1 ( 2 k Y ) 2 = T 2 , where k∈ℕ;and solutions ( X,Y,Z,T )=( D k , E k , f k , f ′ k )∈ ( 2ℕ+1 ) 4 , are given in pairwise prime numbers.2020-Mathematics Subject Classification 11A05-11A07-11A41-11A51-11D09-11D25-11D41-11D72-11D79-11E25 .

基于Z-number-IBWM-TODIM的应急供应商评估与选择研究

文章针对应急供应商选择过程中评价信息的不完全可靠性及专家背景的多样性问题,提出了一种基于Z-number和IBWM-TODIM方法相结合的评估框架,以此来选择应急供应商。该方法利用Z-number同时描述认知信息的不确定性和可靠性,增强了决策结果的可靠性和合理性;使用解释结构模型ISM确定最优指标和最劣指标,降低BWM方法的主观性,得到了指标权重;通过群体一致性和Z-number中的可靠性信息确定专家权重,使用TODIM方法进行排序,为应急供应商选择提供了更为准确和可靠的决策依据。

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

A METHOD OF SOLVING THE FUZZY FINITE ELEMENT EQUATIONS IN MONOSOURCE FUZZY NUMBERS

For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modem engineering design.

Ranking Method for Complementary Judgment Matrixes with Fuzzy Numbers Based on Hausdorff Metric Distance

A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

Wave Number Method for Three-Dimensional Steady-State Acoustic Problems

Based on the indirect Trefftz approach, a wave number method （WNM） is proposed to deal with three-dimensional steady-state acoustic problems. In the WNM, the dynamic pressure response variable is approximated by a set of wave functions, which exactly satisfy the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions. The unknown coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions. Compared with the boundary element method （BEM）, the WNM have a smaller system matrix, and is applicable to the radiation problems since the wave functions are independent of the domain size. A 3D acoustic cavity is exemplified to show the properties of the method. The results show that the wave number method is more efficient than the BEM, and it is fairly accurate.

Global Stability Analysis of Flow Past Two Side-by-Side Circular Cylinders at Low Reynolds Numbers by a POD-Galerkin Spectral Method

A proper orthogonal decomposition(POD)method is applied to the problem of a two-dimensional flow past two side-by-side circular cylinders.Based on the POD bases,which are constructed by a snapshot method,a low-dimensional model is established for representing two-dimensional incompressible Navier–Stokes equations.Coupled with the low-dimensional model,the Chiba method is used to analyze the global stability of the basic flow.Different bifurcation paths at three major regions are revealed,in good agreement with the available results by other methods.However,the computation amount in the POD method is low,which shows the availability and advantage of the POD method.

Using modified Soil Conservation Service curve number method to simulate the role of forest in flood control in the upper reach of the Tingjiang River in China

To improve flood control efficiency and increase urban resilience to flooding,the impacts of forest type change on flood control in the upper reach of the Tingjiang River(URTR) were evaluated by a modified model based on the Soil Conservation Service curve number(SCS-CN) method. Parameters of the model were selected and determined according to the comprehensive analysis of model evaluation indexes. The first simulation of forest reconstruction scenario,namely a coniferous forest covering 59.35km^2 is replaced by a broad-leaved forest showed no significant impact on the flood reduction in the URTR. The second simulation was added with 61.75km^2 bamboo forest replaced by broad-leaved forest,the reduction of flood peak discharge and flood volume could be improved significantly. Specifically,flood peak discharge of 10-year return period event was reduced to 7-year event,and the reduction rate of small flood was 21%-28%. Moreover,the flood volume was reduced by 9%-14% and 18%-35% for moderate floods and small floods,respectively. The resultssuggest that the bamboo forest reconstruction is an effective control solution for small to moderate flood in the URTR,the effect of forest conversion on flood volume is increasingly reduced as the rainfall amount increases to more extreme magnitude. Using a hydrological model with scenarios analysis is an effective simulation approach in investigating the relationship between forest type change and flood control. This method would provide reliable support for flood control and disaster mitigation in mountainous cities.

Development of New Method for Generating Prime Numbers

The article is devoted to actual problems of prime numbers. A theorem that allows generating a sequence of prime numbers is proposed. An algorithm for generating prime numbers has been developed. A comparison of the proposed theorem, with Wilson’s theorem is also provided.

Travelling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations

We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.

Using an Alternative Method to Estimate the Status of Iodine Nutrition in Pregnant Women

Iodine is an element that is essential for the synthesis of thyroid hormones.Adequate intake of dietary iodine has been recognized as a critical factor for maintaining health.It is a well-known fact that iodine deficiency can impede the production of thyroid hormones in both the mother and fetus,which increases the risk of brain damage in the fetal stage.

Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method

Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications.As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.

Theoretical calculation of tidal Love numbers of the Moon with a new spectral element method

The tidal Love numbers of the Moon are a set of nondimensional parameters that describe the deformation responses of the Moon to the tidal forces of external celestial bodies.They play an important role in the theoretical calculation of the Moon’s tidal deformation and the inversion of its internal structure.In this study,we introduce the basic theory for the theoretical calculation of the tidal Love numbers and propose a new method of solving the tidal Love numbers:the spectral element method.Moreover,we explain the mathematical theory and advantages of this method.On the basis of this new method,using 10 published lunar internal structure reference models,the lunar surface and lunar internal tidal Love numbers were calculated,and the influence of different lunar models on the calculated Love numbers was analyzed.Results of the calculation showed that the difference in the second-degree lunar surface Love numbers among different lunar models was within 8.5%,the influence on the maximum vertical displacement on the lunar surface could reach±8.5 mm,and the influence on the maximum gravity change could reach±6μGal.Regarding the influence on the Love numbers inside the Moon,different lunar models had a greater impact on the Love numbers h_(2) and l_(2) than on k_(2) in the lower lunar mantle and core.

Rapid Determination of Seed Number and Thousand Kernel Weight of Asparagus officinalis L.Using Image Processing Method

Asparagus officinalis L.is favored by its high health function,but its hybrid seeds are expensive.The amount of seed,seed plumpness and germination rate are related to the production costs of breeding enterprises and large growers.Therefore,it is necessary to investigate the seed number and thousand kernel weight of A.officinalis L.This study developed a quick and accurate method to measure the seed number and thousand kernel weight of A.officinalis L.using image processing technology.Seed sample of A.officinalis L.was scanned with 200 dpi resolution,and the seed number was then obtained using Image-ProPlus software.After weighing the seeds,thousand kernel weight was finally calculated.By recording‘macro’,the batch processing of the samples can also be realized.This method is simple and accurate,and can greatly save the time of investigation.