THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW

We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

ON NUMBER OF LIMIT CYCLES FOR THE QUADRATIC SYSTEMS WITH A WEAK FOCUS AND A STRONG FOCUS

It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).

LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL

In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

Flux Limiter Lattice Boltzmann Scheme Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

We further develop the lattice Boltzmann (LB) model [Physica A 382 (2007) 502] for compressible flows fromtwo aspects.Firstly,we modify the Bhatnagar-Gross-Krook (BGK) collision term in the LB equation,which makes themodel suitable for simulating flows with different Prandtl numbers.Secondly,the flux limiter finite difference (FLFD)scheme is employed to calculate the convection term of the LB equation,which makes the unphysical oscillations atdiscontinuities be effectively suppressed and the numerical dissipations be significantly diminished.The proposed modelis validated by recovering results of some well-known benchmarks,including (i) The thermal Couette Row;(ii) One- andtwo-dimensional Riemann problems.Good agreements are obtained between LB results and the exact ones or previouslyreported solutions.The Rexibility,together with the high accuracy of the new model,endows the proposed modelconsiderable potential for tracking some long-standing problems and for investigating nonlinear nonequilibrium complexsystems.

The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.

结合遗传算法的水库汛限水位动态控制模型研究

针对水库汛限水位动态控制问题,提出一种新的自适应交叉变异遗传算法,解决了水库防洪效益与发电效益之间的矛盾问题,实现了水库水位的调整,缓解了防洪效益与发电效益的冲突。遗传算法使原始汛期水位提升了0.7m,蓄水量提升了2947m^(3),同时增加了发电量233.33×10^(4) kW·h。基于峡山水库实例试验的研究结果表明,结合遗传算法的水库汛限水位动态控制模型,不仅可对水位进行实时性调节,还能提升水库效益,研究结果可应用于各水库防洪系统。

输入基岩地震波数量对土层地震反应影响研究

以成都某地铁站点工程场地为例,采用一维等效线性化方法,将人工合成的不同超越概率下各20条相互独立的地震波作为基岩输入地震动时程,进行了土层地震反应计算,并对计算结果进行了分析研究,得出结论:1)通过对土层地震反应结果的计算分析,给出了PGA、T_(g)和S_(a)(T)值计算结果参数的变异系数和随概率档的变化规律,并验证了上述各参数均值都服从正态分布。2)对于Ⅱ级和地震小区划工作,目前业内较为普遍地采用3条基岩地震波作为土层地震反应计算基岩输入地震动时程的做法和现行地震安评国标的规定,至少采用3条基岩地震波作为输入地震动时程下限数量的规定已不能满足要求,需要增加,建议增加到最少采用15条基岩输入地震波,以保证地震安评工作所提供的场地设计地震动参数更加可靠。

INCOMPRESSIBLE LIMIT OF THE NON-ISENTROPIC MAGNETOHYDRODYNAMIC EQUATIONS IN BOUNDED DOMAINS

The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.

Regular Quasi Cyclic Low Density Parity Check Codes with Girth 8 from Elementary Number Theory

This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.

鄂尔多斯地区气传花粉与过敏性鼻炎特征分析

选取2017~2022年4月1日~9月30日花粉浓度、AR患者就诊量和气象资料进行统计分析,鄂尔多斯市花粉浓度有两次高峰期,分别是4月1日~4月30日和7月20日~9月10日,其中夏秋季花粉影响较重,AR患者集中爆发在8月.2017~2022年花粉年均浓度呈逐年降低趋势,花粉浓度年超标日数由76d降至38d,而AR患者逐年就诊量未见减少.通过花粉、AR患者就诊量与气象因子等影响研究,结果表明:植被覆盖率与花粉浓度呈正相关,植被指数的花粉贡献率为38.3%,相对湿度越大、日照时数越小、风速越小,植被生长越好,花粉浓度也随之增大,气象因子的影响贡献了46.3%的花粉浓度变化,植被和气象条件是导致花粉浓度变化的主要因子.而花粉浓度的爆发与积温、地表积温、日照时数的累积量有关,积温、地表积温、日照时数需分别达到1958℃、2296℃、757h条件.当花粉浓度致敏阈值达到80粒/1000mm^(2),2d后AR患者出现倍增.基于花粉浓度对AR患者的响应关系,构建花粉浓度变化模型预估患者数量,可为当地医疗、环境部分提前预防提供重要依据.

Sequences and Limits

It is widely held that irrational numbers can be represented by infinite digit-sequences. We will show that this is not possible. A digit sequence is only an abbreviated notation for an infinite sequence of rational partial sums. As limits of sequences, irrational numbers are incommensurable with any grid of decimal fractions.

An Algorithm for Generating Random Numbers with Normal Distribution

A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly accurate, with an efficiency that falls between those of the Box-Muller and von Neumann rejection methods.

Limit Theorems for a Storage Process with a Random Release Rule

We consider a discrete time Storage Process Xn with a simple random walk input Sn and a random release rule given by a family {Ux, x ≥ 0} of random variables whose probability laws {Ux, x ≥ 0} form a convolution semigroup of measures, that is, μx × μy = μx + y The process Xn obeys the equation: X0 = 0, U0 = 0, Xn = Sn - USn, n ≥ 1. Under mild assumptions, we prove that the processes and are simple random walks and derive a SLLN and a CLT for each of them.

There Are Infinitely Many Mersnne Composite Numbers with Prime Exponents

By extending both arithmetical operations into finite sets of natural numbers, from the entire set of natural numbers successively deleting some residue classes modulo a prime, we invented a recursive sieve method or algorithm on natural numbers and their sets. The algorithm mechanically yields a sequence of sets, which converges to the set of all primes p such that 2p + 1 divides the Mersenne number Mp. The cardinal sequence corresponding to the sequence of sets is strictly increasing. So that we have captured enough usable structures, without any estimation, the existing theories of those structures allow us to prove an exact result: there are infinitely many Mersenne composite numbers with prime exponents Mp.

航线联营下基于转运的飞机航线路径优化

为解决航空运输成本高,运输资源闲置、浪费多的问题,对航线联营下基于转运的飞机航线路径优化问题进行研究。基于货物转运问题,考虑联盟对运营的影响,引入航空联盟选择概率,确定转运前后航段运输的承运及托运问题,并考虑托运运输的衔接问题。由于航空网络中双机场容量限制,运行中全货机飞行时段及空域容量的限制,以总成本最小化为目标,建立了航线联营下基于转运的航线路径优化模型(T-AAAFRP)。设计了改进的遗传算法求解模型。通过实例分析,研究选址和路径优化问题。研究结果表明:设计的算法具有较高的收敛性;转运点数量变化的过程中,双机场城市总被选择作为转运点;需求量、飞机固定成本的变化对优化决策有较大影响;飞机载重量、联盟承运与托运的分摊系数、决策者风险偏好的变化对优化决策有较小影响;总体上转运点数量越多,所承担的总成本越小,使用的飞机数量越少。

基于高分辨率ECOMAC的桥梁结构损伤识别

为了达到精确定位损伤的目的,提出了利用少量传感器信息进行桥梁高分辨率全模态振型识别,获得高分辨率的全桥协调模态置信因子(enhanced coordinate modal assurance criteria,简称ECOMAC)这一动力指纹参数的方法。利用特征正交分解直接分析移动车辆荷载作用下桥梁上的少量传感器所测位移响应,获得主成分矩阵,将主成分矩阵通过低通滤波即可获得高分辨率的模态振型。利用高分辨率模态振型获得高分辨率的协调模态置信因子,并作为损伤指标进行损伤定位。为了验证该方法的有效性,对一梁桥进行数值仿真和实验。数值模拟和实验结果均表明,基于少量传感器下利用高分辨率的协调模态置信因子能够精确识别损伤。

Extensions of the Constructivist Real Number System

The paper reviews the most consequential defects and rectification of traditional mathematics and its foundations. While this work is only the tip of the iceberg, so to speak, it gives us a totally different picture of mathematics from what we have known for a long time. This journey started with two teasers posted in SciMath in 1997: 1) The equation 1 = 0.99… does not make sense. 2) The concept ?does not exist. The first statement sparked a debate that raged over a decade. Both statements generated a series of publications that continues to grow to this day. Among the new findings are: 3) There does not exist nondenumerable set. 4) There does not exist non-measurable set. 5) Cantor’s diagonal method is flawed. 6) The real numbers are discrete and countable. 7) Formal logic does not apply to mathematics. The unfinished debate between logicism, intuitionism-constructivism and formalism is resolved. The resolution is the constructivist foundations of mathematics with a summary of all the rectification undertaken in 2015, 2016 and in this paper. The extensions of the constructivist real number system include the complex vector plane and transcendental functions. Two important results in the 2015 are noted: The solution and resolution of Hilbert’s 23 problems that includes the resolution of Fermat’s last theorem and proof Goldbach’s conjecture.

小样本下基于原型网络的轴向柱塞泵故障诊断模型

在实际工程应用中,有限的故障样本数量及噪声都影响轴向柱塞泵故障诊断的效果,所以,如何提高模型在小样本、噪声条件下轴向柱塞泵故障诊断的性能是一个亟待解决的问题。在样本数量有限、噪声条件下,采用基于深度学习的故障诊断方法会出现过拟合、诊断准确率下降的问题,为此,提出了一种小样本条件下基于原型网络的轴向柱塞泵故障诊断模型(方法)。首先,搭建了轴向柱塞泵故障诊断模型,并等量随机抽取了每个故障的样本以构建多个任务,模型使用一维卷积神经网络作为主干,每个任务中包含当前模型、支持集、查询集;然后,利用模型将样本映射到特征空间,在特征空间中,模型使用支持集的同类样本构建了原型点,并逐个将查询集样本与多个原型点进行了距离度量,实现了轴向柱塞泵不同故障的分类;最后,为了验证基于原型网络的轴向柱塞泵故障诊断模型的有效性,采集了轴向柱塞泵不同元件发生故障时产生的振动信号,并使用上述诊断模型对此进行了故障识别实验;为了验证该诊断模型的优越性,将其与基于卷积神经网络等的模型进行了性能对比。实验结果表明:在样本有限的条件下,采用基于原型网络的轴向柱塞泵故障诊断模型的准确率达到85%以上;同时,在噪声条件下,采用基于原型网络的模型的准确率也能达到85%以上。研究结果表明:基于原型网络的模型的诊断性能优于卷积神经网络模型与传统方法。

顺排布置的水平单层球自然对流换热数值研究

通过将二维Bejan计算模型扩展到三维,研究Gr=103情况下排列数范围为3×3至15×15的水平单层球自然对流换热情况。研究发现:随着排列数增加,卷流作用的增强使得单层球上方区域负压增大,导致通过球体间隙从下方吸入的流体速度升高,进而强化球体和流体之间的换热;由于排列数对上游区域温度边界层影响更大,该区域Nu数受其影响更明显。此外,拟合得到中心球的Nu数和N之间的关联式。基于极限的数学思想,该关联式可以预测不受周围球数增加影响的中心球的Nu数为4.1628,这比Gr数相同情况下的单球的Nu数下降30.2%。该研究既能优化加速器驱动次临界堆系统流态固体靶结构的设计,也能为其他包含大数量多球系统的工业应用提供一定的参考价值。