Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

Infinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation

To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.

Constructing infinite sequence exact solutions of nonlinear evolution equations

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.

A priliminary study on the sequence characteristics and focal mechanism solution of the Jiashi strong earthquake swarm

The sequence characteristics and focal mechanism solution of the Jiashi, Xinjiang strong earthquake swarm are analyzed and studied in this paper. The result shows that before the M S=6.6 earthquake, value h of sequence frequency attenuation coefficient was less than 1, then value h was more than 1. Before occurrence of M S6.0 earthquakes the energy is released either in a continuously strengthened way or a sharply strengthened way, and before M S5.0 earthquakes the sequence frequency shows calm. The study on the focal mechanism solution of the strong earthquake swarm shows that the source faults are mainly in a right lateral, strike slip way and the faults have characteristics of tensor shear.

Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids

In this paper, an infinite sequence of conservation laws for a generalized variable-coefficient fifth-order Korteweg-de Vries equation in fluids are constructed based on the Backlund transformation. Hirota bilinear form and symbolic computation are applied to obtain three kinds of solutions. Variable coefficients can affect the conserved density, associated flux, and appearance of the characteristic lines. Effects of the wave number on the soliton structures are also discussed and types of soliton structures, e.g., the double-periodic soliton, parallel soliton and soliton complexes, are presented.

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.

The New Infinite Sequence Solutions of Multiple Sine-Gordon Equations

By the function transformation and the first integral of the ordinary differential equations, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is researched, and the new solutions are obtained. First, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is changed to the problem of solving the solutions of the nonlinear ordinary differential equation. Second, with the help of the B?cklund transformation and the nonlinear superposition formula of solutions of the first kind of elliptic equation and the Riccati equation, the new infinite sequence soliton-like solutions of two kinds of sine-Gordon equations are constructed.

Effect of welding sequence on residual stress and deformation of 6061-T6 aluminium alloy automobile component

Four different welding sequences of double-pulse MIG welding were conducted for 6061-T6 aluminum alloy automobile bumpers by using nonlinear elastoplasticity finite element method based on ABAQUS software.The post-welding residual stress and deformation were definitely different among the four welding sequences.The results showed that the highest temperature in Solution A was approximately 200℃higher than the melting point of base metal.High residual stress was resulted from this large temperature gradient and mainly concentrated on the welding vicinity between beam and crash box.The welding deformation primarily occurred in both of the contraction of two-ends of the beam and the self-contraction of crash box.Compared with other welding sequences,the residual stress in Solution A was the smallest,whereas the welding deformation was the largest.However,the optimal sequence was Solution B because of the effective reduction of residual stress and good assembly requirements.

Spatiotemporal evolution of the 2021 M_(S)6.4 Yangbi earthquake sequence

Based on the seismic phase reports of the Yangbi area from January 1 to June 25,2021,and the waveform data of M≥4 earthquakes,we obtained the relocation results and focal mechanism solutions of the M_(S)6.4 Yangbi earthquake sequence using the HypoDD and CAP methods.Based on our results,our main conclusions are as follows:(1)the M_(S)6.4 Yangbi earthquake sequence is a typical foreshock-mainshock-aftershock sequence.The fore-shocks of the first two stages have the obvious fronts of migration and their migration rate increased gradually.There was no apparent front of migration during the third stage,and the occurrence of the mainshock was related to stress triggering from a M5.3 foreshock.We tentatively speculate that the rupture pattern of the Yangbi earthquake sequence conforms to the cascading-rupture model;and(2)the main fault of the M_(S)6.4 Yangbi earthquake sequence is a NW-trending right-lateral strike-slip fault.As time progressed,a minor conjugate aftershock belt formed at the northwest end of this fault,and a dendritic branching structure emerged in the southern fault segment,showing a complex seismogenic fault structure.We suggested that the fault of the Yangbi earthquake sequence may be a young sub-fault of the Weixi-Weishan fault.

Existence of Ordered Solutions to Quasilinear Schrodinger Equations with General Nonlinear Term

In this paper, the existence of a pair of ordered solutions for the following class of equations in ?(1)?was studied. A bounded (PS) (Palais-Smale) sequence was constructed and the related variational principle was used to prove the existence of the positive solution. The existence of the ordered solutions is finally found.

Apparent Stress Changes of the 2010 Luanxian Earthquake Sequence

On March 6,2010,an earthquake of M L4. 5 took place in Luanxian,Hebei Province,with plenty of foreshocks and aftershocks. From December 2009 to March 2010,a series of M L≥ 2. 5 earthquakes were recorded by the digital seismic network of the capital region,which were selected to calculate the apparent stress in this region. The results show that,firstly,a high value anomaly of apparent stress appeared before the M L4. 5 and peak value appeared on the main shock, which then decreased after the ML4. 5 earthquake. The apparent stress of the main shock is much greater than that of most aftershocks,the sequence type is considered as a main shock-aftershock. Secondly,the size of apparent stress perfectly reflects the state of the stress field in the hypocenter region,and we can discuss seismic sequence properties through the changing process of apparent stress,in combination with the traditional methods to identify a sequence more accurately. Finally,in the case of magnitude less than or equal to M L3. 3,correlation between magnitude and apparent stress is positive.

Application of a Genetic Algorithm to Computer-aided Bending Sequence Planning

Optimal design of the bending sequence is a key link in sheet metal free bending sequence planning, and it has an important influence on simplifying operation and guaranteeing bending precision. Bending sequence must meet the requirements for not only no collision interference of the work piece and the mold, but also working efficiency and working precision, so bending point choice, molds select, turnover and turn round of sheet metal must be considered in each bending step. In this paper, a genetic algorithm is used to design bending sequence. The interference identification is used to determine coding, exchange and mutation of the genetic algorithm. The genetic algorithm is developed to calculate the current optimal feasible solution of the bending sequence, and then the influence of initial population and evolution generations of this method on the result is analyzed by example verifications. The results prove that a global optimal solution can be obtained while the bending point number was less than 10, and optimal bending sequence which is similar to the global optimal solution can be calculated while the bending point number was more than 10. The results converge gradually to the global optimal solution with the increase of the initial population and evolution generations. As to 18 points bending work-piece, with the initial population size 150 and the evolution generations 100, we can obtain the satisfying solution.

分数阶Riccati方程的Bäcklund变换及其应用

基于整数阶辅助方程法的相关结论,给出了分数阶Riccati方程的包含广义双曲函数解和广义三角函数解的Mittag-Leffler函数新解、Bäcklund变换和解的非线性叠加公式.在此基础上,借助符号计算系统Mathematica,构造了分数阶KdV-mKdV方程、分数阶(3+1)维Zakharov-Kuznetsov方程和分数阶Boussinesq方程的无穷序列新解.

一测多评法测定法制半夏曲中11种成分含量及其GRA、EW-TOPSIS质量评价

目的采用一测多评(QAMS)法同时测定法制半夏曲中肌苷、鸟苷、腺苷等11种成分含量,并建立其灰色关联度分析(GRA)联合熵权逼近理想解排序分析法(EW-TOPSIS)综合质量评价方法。方法采用Shimadzu C 18色谱柱;乙腈-0.5%醋酸为流动相,梯度洗脱,流速1.0 mL·min-1;检测波长254和290 nm。以对甲氧基肉桂酸乙酯为内参比物质,计算其他10个成分的相对校正因子(RCF),测定各成分含量。采用GRA联合EW-TOPSIS模型对法制半夏曲进行综合质量评价。结果法制半夏曲中11种成分在一定浓度范围内线性关系良好,相关系数均>0.999;平均加样回收率96.94%~100.12%(RSD<2.0%,n=9);QAMS与外标法(ESM)实测值无明显差异。GRA模型相对关联度0.2903~0.6187,EW-TOPSIS模型相对接近度0.2114~0.6343;GRA和EW-TOPSIS模型综合评价结果基本一致。结论QAMS法便捷、准确,可用于法制半夏曲多指标成分定量控制,GRA联合EW-TOPSIS模型可用于法制半夏曲综合质量评价。

数列极限的求解方法探析

数列极限的求解是极限学习的基础,针对应用数列极限的定义、数列极限运算技巧及Stolz定理等对数列极限的求解进行探析,发现二个数列极限求解的命题能够解决求解数列极限中的很多问题。列举了几种求解数列极限的方法,为求解数列极限的学习提供参考。

关于不定方程x^(3)-1=114y^(2)

不定方程是数论中不可或缺的一个分支,它有着悠久的历史与丰富的内容,其理论和方法在各学科和实际生活中都有广泛的应用。运用同余式、递归序列、平方剩余以及Pell方程的解的性质等初等方法对不定方程x^(2)-1=114y^(2)的整数解进行了讨论。首先利用因式分解将原不定方程分解为8种情形,其次运用转化、取模等技巧对8种情形分别分析,最终得出不定方程x^(2)-1=114y^(2)仅有整数解(x,y)=(1,0)。

丢番图方程x^(3)+1=603y^(2)的整数解

设D含有6k+1型的素因子,其中k是正整数,关于丢番图方程x^(3)+1=Dy^(2)(D>0)的求解一直是数论中未彻底解决的问题之一.利用同余式、递归序列、因式分解法以及Pell方程解的性质及初等数论方法,并结合分类讨论的数学思想,研究了丢番图方程x^(3)+1=603y^(2)在不同情形下的整数解问题,得到了当D=603时,该丢番图方程有且仅有平凡整数解(x,y)=(-1,0),此结论对这一类方程的研究具有一定的借鉴作用.

浮选-消解顺序对土壤中微塑料提取效率的影响

通过向实验土样中定量添加不同类型的微塑料,比较了两种浮选液(氯化锌ZnCl_(2)和氯化钠NaCl)、浮选-消解顺序对微塑料提取效率的影响.结果表明,NaCl浮选液对PVC类高密度(ρ>1.30 g/cm^(3))微塑料不能发挥浮选作用,而ZnCl_(2)浮选液对各种密度的微塑料都能起到较好的浮选效果;不论供试土壤还是实际土壤的应用中,ZnCl_(2)浮选液与先浮选后消解的组合展现出了较高的提取效率.本研究结论为土壤中微塑料的分离提取方法提供了科学依据.

2021年5月21日云南漾濞M_(S)6.4地震序列双差重定位及其构造意义

文中基于2021年5月1日—2022年6月18日中国地震台网中心收集的2021年5月21日云南漾濞M_(S)6.4地震序列的相关数据,利用双差定位法进行了重新定位,得到了2681个精定位地震事件。结果表明,漾濞地震序列的扩展方向为NW-SE向,长约32km,但并非简单的单侧扩展,而是呈西北窄、东南宽的雁列状分布结构特征,且发震优势深度为5~10km。前震有明显的空间迁移特征,且主震南、北两侧的地震活动差异性明显。这些地震在EW向、SN向、垂直向的平均定位误差约为0.47km、0.50km和0.62km,平均均方根走时残差约为0.22s。采用gCAP全波形反演方法获得该地震序列主断裂上M_(S)≥4.0主要地震事件的震源机制解,结果显示出明显的右旋走滑分量。利用基于小地震反演断层面参数的方法,通过拟合获得了发震断层面的参数,发现主断层面走向在126°~137°之间变化,且由北至南走向逐渐增大,倾向SW,倾角为79°~87°,由北至南倾角逐渐变小。结合该区域的构造应力场及前人的近震层析成像结果推测,漾濞地震的发震构造为漾濞县城西南山地区域中NW-SE走向的高倾角走滑断裂系,该断裂系由一条走滑主断层和多条次级斜交小断层组成,且该地区的地震活动可能受区域应力与深部流体作用共同影响。

具有周期系数的Kirchhoff-型差分方程同宿解的存在性

运用临界点理论研究一类具有周期系数的Kirchhoff-型差分方程同宿解问题。首先,构造了差分方程所对应的能量泛函。在文中的假设条件下,保证了能量泛函具有山路几何结构,从而得到了一个Palais-Smale序列。然后,利用一个可变号的全局性条件证明了该Palais-Smale序列的有界性。进一步,借助于l^(2)空间的紧支撑子集的性质和系数的周期性得到了该差分方程的一个非平凡同宿解。最后,给出两个例子说明了主要结论的正确性。