一类差分的刻画

函数 Δ:G×G→H是 Cauchy差分 ,即存在函数 f:G→H使 Δ( x,y) =f( x+ y) - f( x) - f( y) ,其中 G和 H是 abelian群并且 H可除 ,推导出使上式成立的充分必要条件是 Δ( x,y) =Δ( y,x)和Δ( x,y) +Δ( x+ y,z) =Δ( x,y+ z) +Δ( y,z)。推广了 Cauchy差分的形式并且利用函数方程组给出了函数 F:G× G→ H具有差分表示 F( x,y) =f ( x+ y) + f ( x- y) - nf ( x) - nf ( y)的几种刻画 ,其中 n是一正整数 ,f是 G到 H的函数。     

费马大定理：Abel猜想的一个证明

1 IntroductionIn 1823 Abel made a conjecture in a particular case of Fermat's last theorem:If n>2and x,y and z are nonzero integers such thatx~n+y~n=z~n(1)then none of x,y or z can be a prime power(see P.Ribenboim[1],p.25).It is clear that we may assume,without loss of generality,that(x,y)=(x,z)=(y,z)=1and 0相似文献   

微分差分方程组边值问题的算法研究

本文给出了如下微分差分方程组边值问题(P_ε):y′(x,ε)=a_1(x)y(x,ε)+b_1(x)z(x,ε)+c_1(x)y(x-1,ε)+d_1(x)z(x-1,ε)+φ_1(x)(0相似文献   

关于丢番图方程ax4+bx2y2+cy4=dz2

针对方程x4±y6=z2与x2 y4=z6求解过程中存在的疑问,证明了丢番图方程3x4-10x2y2 3y4=3z2,(x,y)=1仅有整数解x=0,y2=z2=1和y=0,x2=z2=1.方程x4-14x2y2 y4=z2,(x,y)=1仅有整数解x2=z2=1,y=0和x=0,y2=z2=1.方程x6-y6=2z2,(x,y)=1,z≠0无整数解.方程x6 y6=2z2,(x,y)=1仅有整数解(x2,y2,z2)=(1,1,1).从而更正了文献[1]中的错误.     

拟线性椭圆型方程的差分解法

设Ω为 xy 平面上的一个区域,(?)为其闭包。a(x,y),b(x,y),c(x,y)为(?)上的连续函数,满足ac-b~2>0,a>0,c>0。(1)又设 F(x,y,z,p,q)为五个变元 x,y,z,p,q 的函数,对任何(x,y)∈(?),及任何 z,p,q为一阶连续可微,并满足     

求解条件极值问题的两个充分条件

笔者给出并证明了两个判断条件极值的充分条件.可求解函数z=f(x,y)在附加条件为φ(x,y)=0和函数u=f(x,y,z)在附加条件为φ(x,y,z)=0的条件极值问题.利用Lagrange乘数法求出驻点,再用笔者给出求解条件极值的上述方法即可解决驻点是否为极值点.     

BCI-代数的内在半群结构

设(X, *, 0)为BCI-代数.本文通过在X中引入二元运算“·”x·y=(0*(0*x))*(0*y):(0*y),(x, y∈X),证明了x·y=inf{z∈X|z*x≤y, x, y∈X}及(X,·)为可换幂幺半群.从而揭示了BCI-代数内在的半群结构.     

具有连续变量的脉冲偏差分方程解的振动性

考虑一类具有连续变量的脉冲偏差分方程A(x+τ,y)+A(x,y+τ)-A(x,y)+p(x,y)A(x-rτ,y-lτ)=0,x≥x0,y≥y0-τ,x≠xk;A(xk+τ,y)+A(xk,y+τ)-A(xk,y)=bkA(xk,y),y∈[y0-τ,∞),k∈N(1).其中p(x,y)≥0是[x0,∞)×[y0-τ,∞)上的非负连续函数,τ0,bk是常数,r和l是正整数,0≤x0x1…xk…,且li mxk=∞.获得了此类方程所有解是振动的充分条件.     

关于丢番图方程 x2p+2kyp=z2

设A、B、C是两两互素的正整数,m,n,r是大于1的正整数，对于丢番图方程Ax^m+Byⁿ=Cz^r，(x,y,z)=1，1/m+1/n+1/r＜1，1989年,Tijdeman猜想：该方程仅有有限多组整数解(x,y,z)；1997年，Andrew Bal猜想：如果A=B=C=1,m,n,r均大于2，则该方程没有正整数解.关于上述猜想，本文作者获得了如下结果：设p为奇素数，证明了丢番图方程x^2p+2^ky^p=z²,(x,y)=1，k≥1，y≠0仅有整数解k=3,｜x｜=y=1,｜z｜=3和k=2pl+3,｜x｜=2l,y=1,｜z｜=3·2^pl .从而更正了王云葵关于上述方程所获得的结果.     

与半解函数定义等价的几个定理

<正> 定理1.若f(z)是第二类半解析的,则一定存在实函数φ(x,y),使得f(z)=▽φ(x,y),且这样的φ(x,y)有无穷多个,但彼此相差一个常数。反之,若f(z)=▽φ(x,y),则f(z)是第二类半解析的。其中▽φ(x,y)(?),φ(x,y)及其一阶、二阶偏导数连续。     

Cooling rate effects on the structure and transformation behavior of Cu-Zn-Al shape memory alloys

Different fragments of a hot-rolled and homogenized Cu–Zn–Al shape memory alloy（SMA） were subjected to thermal cycling by means of a differential scanning calorimetric（DSC） device. During thermal cycling, heating was performed at the same constant rate of increasing temperature while cooling was carried out at different rates of decreasing temperature. For each cooling rate, the temperature decreased in the same thermal interval. During each cooling stage, an exothermic peak（maximum） was observed on the DSC thermogram. This peak was associated with forward martensitic transformation. The DSC thermograms were analyzed with PROTEUS software： the critical martensitic transformation start（Ms） and finish（Mf） temperatures were determined by means of integral and tangent methods, and the dissipated heat was evaluated by the area between the corresponding maximum plot and a sigmoid baseline. The effects of the increase in cooling rate, assessed from a calorimetric viewpoint, consisted in the augmentation of the exothermic peak and the delay of direct martensitic transformation. The latter had the tendency to move to lower critical transformation temperatures. The martensite plates changed in morphology by becoming more oriented and by an augmenting in surface relief, which corresponded with the increase in cooling rate as observed by scanning electron microscopy（SEM） and atomic force microscopy（AFM）.     

Mechanical,electrical, and thermal expansion properties of carbon nanotube-based silver and silver-palladium alloy composites

The mechanical, electrical, and thermal expansion properties of carbon nanotube（CNT）-based silver and silver–palladium（10：1, w/w） alloy nanocomposites are reported. To tailor the properties of silver, CNTs were incorporated into a silver matrix by a modified molecular level-mixing process. CNTs interact weakly with silver because of their non-reactive nature and lack of mutual solubility. Therefore, palladium was utilized as an alloying element to improve interfacial adhesion. Comparative microstructural characterizations and property evaluations of the nanocomposites were performed. The structural characterizations revealed that decorated type-CNTs were dispersed, embedded, and anchored into the silver matrix. The experimental results indicated that the modification of the silver and silver–palladium nanocomposite with CNT resulted in increases in the hardness and Young＇s modulus along with concomitant decreases in the electrical conductivity and the coefficient of thermal expansion（CTE）. The hardness and Young＇s modulus of the nanocomposites were increased by 30%？40% whereas the CTE was decreased to 50%-60% of the CTE of silver. The significantly improved CTE and the mechanical properties of the CNT-reinforced silver and silver–palladium nanocomposites are correlated with the intriguing properties of CNTs and with good interfacial adhesion between the CNTs and silver as a result of the fabrication process and the contact action of palladium as an alloying element.     

Fuzzy TOPSIS method to primary crusher selection for Golegohar Iron Mine（Iran）

Selection of the crusher required a great deal of design regarding to the mine planning. Selection of suitable primary crusher from all of available primary crushers is a multi-criterion decision making（MCDM） problem. The present work explores the use of technique for order performance by similarity to ideal solution（TOPSIS） with fuzzy set theory to select best primary crusher for Golegohar Iron Mine in Iran. Gyratory, double toggle jaw, single toggle jaw, high speed roll crusher, low speed sizer, impact crusher, hammer mill and feeder breaker crushers have been considered as alternatives. Also, the capacity, feed size, product size, rock compressive strength, abrasion index and application of primary crusher for mobile plants were considered as criteria for solution of this MCDM problem. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution（FPIS） and fuzzy negative ideal solution（FNIS）. Results of our work based on fuzzy TOPSIS method show that the gyratory is the best primary crusher for the studied mine.     

Schiff碱型羧酸开链冠醚在化学分离中的应用

讨论了N、N’ -二 (邻氧乙酸 )苄叉乙二胺对Fe3 + 、AL3 + 、Th4 + 、La3 + 、Eu3+ 、UO2 2 + 等离子的分离沉淀条件 .结果表明 :它是Fe3 + 、AL3 + 、Th4 + 、La3 + 、Eu3 + 、UO2 2 + 良好的沉淀剂 ,且控制 pH值在 4.0～5 .0之间时 ,可以一次性定量将Th4 + -Eu3+ 、Th4 + -La3+ 分离     

Effect of microstructure on the mechanical,thermal, and electronic property measurement ofceramic coatings

Ceramic materials were investigated as thermal barrier coatings and electrolytes. Electrophoretic deposition（EPD） and physical vapor deposition（PVD） were employed to fabricate samples, and the mechanical properties and microstructure were examined by nanoindentation and microscopy, respectively. Yttria-stabilized zirconia/alumina（YSZ/Al2O3） composite coatings, a candidate for thermal barrier coatings, yield a kinky, rather than smooth, load–displacement curve. Scanning electron microscope（SEM） examination reveals that the kinky curve is because of the porous microstructure and cracks are caused by the compression of the indenter. Li0.34La0.51 Ti O2.94（LLTO） on Si/Sr Ru O3（Si/SRO） substrates, an ionic conductor in nature, demonstrates electronic performance. Although SEM images show a continuous and smooth microstructure, a close examination of the microstructure by transmission electron microscopy（TEM） reveals that the observed spikes indicate electronic performance. Therefore, we can conclude that ceramic coatings could serve multiple purposes but their properties are microstructure-dependent.     

Optimal paths planning in dynamic transportation networks with random link travel times

A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent（STD）. The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers＇ robust optimal path in a sampled STD network with computation complexity of O（n2＋n·m）. The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.     

Microstructure and properties of electronic packaging shell with high silicon carbide aluminum-base composites by semi-solid thixoforming

The electronic packaging shell with high silicon carbide aluminum-base composites was prepared by semi-solid thixoforming technique. The flow characteristic of the Si C particulate was analyzed. The microstructures of different parts of the shell were observed by scanning electron microscopy and optical microscopy, and the thermophysical and mechanical properties of the shell were tested. The results show that there exists the segregation phenomenon between the Si C particulate and the liquid phase during thixoforming, the liquid phase flows from the shell, and the Si C particles accumulate at the bottom of the shell. The volume fraction of Si C decreases gradually from the bottom to the walls. Accordingly, the thermal conductivities of bottom center and walls are 178 and 164 W·m-1·K-1, the coefficients of thermal expansion（CTE） are 8.2×10-6 and 12.6×10-6 K-1, respectively. The flexural strength decreases slightly from 437 to 347 MPa. The microstructures and properties of the shell show gradient distribution.     

Rate decline analysis of multiple fractured horizontal well in shale reservoir with triple continuum

Multiple fractured horizontal well（MFHW） is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical solution for MFHW surrounded by stimulated reservoir volume（SRV） was presented. Pressure and pressure derivative curves were used to identify the characteristics of flow regimes in shale. Blasingame type curves were established to evaluate the effects of sensitive parameters on rate decline curves, which indicates that the whole flow regimes could be divided into transient flow, feeding flow, and pseudo steady state flow. In feeding flow regime, the production of gas well is gradually fed by adsorbed gases in sub matrix, and free gases in matrix. The proportion of different gas sources to well production is determined by such parameters as storability ratios of triple continuum, transmissibility coefficients controlled by dual flow mechanism and fracture conductivity.     

Real time remaining useful life prediction based on nonlinear Wiener based degradation processes with measurement errors

Real time remaining useful life（RUL） prediction based on condition monitoring is an essential part in condition based maintenance（CBM）. In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item＇s individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.     

Developing a mathematical assessment model for blasting patterns management： Sungun copper mine

Blasting is one of the most important operations in the mining projects that has effective role in the whole operation physically and economically. Unsuitable blasting pattern may lead to unwanted events such as poor fragmentation, back break and fly rock. Multi attribute decision making（MADM） can be useful method for selecting the most appropriate blasting pattern among previously performed patterns. In this work, initially, from various already performed patterns, efficient and inefficient patterns are determined using data envelopment analysis（DEA）. In the second step, after weighting impressive attributes using experts＇ opinion, elimination Et choice translating reality（ELECTRE） was used for ranking the efficient patterns and recognizing the most appropriate pattern in the Sungun Copper Mine, Iran. According to the obtained results, blasting pattern with the hole diameter of 15.24 cm, burden of 3 m, spacing of 4 m and stemming of 3.2 m has selected as the best pattern and has selected for future operation.