广义Fibonacci数列和Lucsa数列的关系式

根据广义的Fibonacci数列{u_n}:u_n+1=Au_n+Bu_n-1和广义Lucas数列{v_n}:v_n+1=Av_n+Bv_n-1的定义, 采用初等方法证明了广义的Fibonacci数列和Lucas数列的几个新的关系式$\sum\limits_{i = 0}^n {{u_i}{v_{n - i}} = \left( {n + 1} \right){u_n}} $、 ${2^{n + 1}}{u_{n + 1}}=\sum\limits_{i = 0}^n {{2^i}{v_i}{A^{n - i}}}$、 $\sum\limits_{i = 0}^n {{{\left( { - B} \right)}^i}{v_{n - 2i}} = 2{u_{n + 1}}} $、 ${3^{n + 1}}{u_{n + 1}} = \sum\limits_{i = 0}^n {{3^i}{v_i}{A^{n - i}}} + \sum\limits_{i = 0}^{n + 1} {{3^{i - 1}}{u_i}{A^{n + 1 - i}}} $、 $\sum\limits_{i = 0}^n {{v_i}{v_{n - i}} = \left( {n + 1} \right){v_n}} + 2{u_{n + 1}} = \left( {n + 2} \right){v_n} + A{u_n}$、 $\left( {{A^2} + 4B} \right)\sum\limits_{i = 0}^n {{u_i}{u_{n - i}}} = \left( {n + 1} \right){v_n} - 2{u_{n + 1}} = n{v_n} - A{u_n} $, 将Fibonacci数列和Lucsa数列关系的结论进行了推广。     

分数阶为2 < α≤3的微分方程两点边值问题解的存在性

利用schauder不动点定理及Green函数的性质得到了分数阶为2<α≤3的微分方程两点边值问题\left\\beginarraylD_0+ ^\alpha u(t)=f\left(t, u(t), ^c D_0+ ^\beta u(t)\right), 0 \leqslant t \leqslant 1 \ u(0)=u(1)=u(0)=0, 2<\alpha \leqslant 3, 0<\beta \leqslant 1\endarray\right., 解的存在性。其中, D₀₊α为Riemann-Liouville分数阶导数, cD₀₊β为caputo's分数阶导数。       

子群的S-半置换性与有限群的p-超可解性

令G为有限群, H是G的子群。称H是G的S-半置换子群, 如果对G的任意Sylow p-子群${G_p}$, 满足($p$, $\left| H \right|$)=1, 都有$H{G_p} = {G_p}H$。本文主要探讨子群的S-半置换性对有限群的$p$-超可解性的影响, 给出了一些关于有限群的$p$-超可解性的判定条件, 并对已知的结果进行了推广。     

满足某些不等式条件的置换的计数

设π是 {1,2 ,… ,n}上的一个置换 ,i,j是两个固定整数 ,本文利用车多项式对满足条件π(k) {k+i,n -k+j(modn) }的置换个数进行计数     

变指数非线性递归数列的极限问题

探讨由递推式F_(n+p)=∑pi=1a_iFb_i(n)n+i-1,n≥1,p≥2,所给出数列{F_n}的敛散性问题。在满足一定条件时,数列{F_n}收敛,且极限值与初始值F_i0,i=1,2,…,p无关。     

关于3x+1问题的一点注记

给出了3x+1问题的三个等价命题,其中构造数列{T(k)(n) 2∑k-1 i=0 xi(n)}+k∞=1,证明它是一个单调递减下有界数列．     

有限非齐次马氏链的一个强大数定律

设{x_n,n≥1}是一有限非齐次马氏链,S_n(k)是序列 x_1,x_2,…,x_n中状态 k 出现的次数,A_n(k,l)是序偶序列(x_1,x_2),(x_2,…,x_3),…,(x_n,x_(n+1))中状态序偶(k,l)出现的次数.本文给出关于 S_n(k)/n 与A_n(k,l)/S_n(k)的强大数定律成立的一个充分条件.     

图与其补图Q谱半径之和的上界

设G为n阶简单图,利用边数m,最小、最大顶点度δ和Δ以及色数k给出了G与其补图-G的Q谱半径之和的上界,当G不含孤立点时有:2(n-1)≤ρ(Q(G))+ρ(Q(-G))≤2(Δ-δ+n-1)和ρ(Q(G))+ρQ(-G))≤2n-3+2-12(n-1)n,其中t=min{k,-k}。当-G含l个孤立点时有:ρ(Q(G))+ρ(Q(-G))≤2n-3+2-1k(n-1)2+l,同时给出了图G与其补图-G的拉普拉斯谱半径之和的一个上界。     

高等数学中2个问题的注记

针对文 [1]中讨论的当b =7、13、12时 ,数列 {an} =bk- bk+an-2 的极限A分别为2、3、4时的结论 ;证明了 :当bk =k2 +k+1(k为自然数 )时 ,数列 {an}的极限为k。同时还给出了著名的Cauchy中值定理与Taylor中值定理的一个统一的推广定理。     

Some New Results on Terai''''s Conjecture

0rnOnvCroNtetZ,N,Qhethesetsofintegers,positiveinte-gersandrati0nalnurnhersrespecti1,el},andletP=jpIpisan0ddprime}andPN=1p"]pisanoddprime,neNl.Clearl},PCPN'lnl993,Terai[l]presentedthef0l-lotving:C0njeC~.Ifa'+b'=c'ttitha,b,cCN,gcd(a,6,c)=landae1'en,tLhenthedi0phantineequati0n.'+b"=c",x,m,nCN(l)hash1eonl\solution(x)m,n)=(a,2,2).InLl],Teraipro1,edthatifb,cePsuchthat(i)b'+1=2c,(ii)d=lorevenif6=l(m0d4),tvheredistheorderofapriInedivisorof[c]intheidealclassgroup0fQ(m),thentheconjectureh0lds…     

基于DPoS扩展的量子加密区块链

区块链技术的安全性依赖基于数学计算单向困难性的加密算法,其在量子计算机的指数级加速下暴露出脆弱性.虽然已有一系列抗量子攻击区块链被提出,但它们往往建设成本高昂,不利于普及推广.对此,提出了基于委托权益证明(Delegated Proof of Stake,DPoS)扩展的量子加密区块链,相比于Kiktenko等的原始量...     

K-bitonic sort

Ak-bitonic sort which generalizes the bitonic sort is proposed. The theorem of the bitonic sort, which merges two monotonic sequences into one order sequence, is extended into the theorem ofk-bitonic sort. Thek-bitonic sort merges (K (=2k or 2k−1) monotonic sequences into one order sequence in steps, where is an integer andk≥1. Thek-bitonic sort is the Batcher's bitonic sort whenk=1. Project supported by the National 863 Foundation of China (863-306-05-01-1) and the National Natural Science Foundation of China (Grant No. 69673037).     

Thermodynamic properties of aqueous aluminate ion, AI(OH) 4? (aq)

The heat effect of the reactions between metallic aluminum and NaOH(aq) solution of various concentrations were calorimetrically determined. Combining with the thermodynamic properties of related substances led to the thermodynamic properties of Al(OH) ₄ ⁻ (aq) as following: Project supported by the National Doctorate Program Fund of China Synopsis of the first author Chen Qiyuan, professor, born in 1948, major research field is metallurgical physicochemistry (metallurgical thermodynamics and kinetics)     

一个具有Robin自由边界的双曲肿瘤生长模型解的定性分析

研究了一个具有Robin自由边界的双曲肿瘤生长数学模型,该模型包含了一个描述营养物浓度变化的椭圆型方程,一个描述肿瘤半径的常微分方程和描述肿瘤细胞生长的两个双曲型偏微分方程.本文通过特征线方法结合Banach不动点定理证明了该模型整体解的存在性和唯一性.最后证明当KR=0时,有(limt→∞)R(t)=∞.     

最大跳跃数M(19,10)

如果n及k（n≥k）是两个较大的正整数,那么要计算出最大跳跃数M（n,k）的值非常困难,Brualdi与Jung曾给出了当1≤k≤n≤10时M（n,k）的值,对于k=10,n=19,证明了M（19,10）=33,这证实了Brualdi与Jung的关于最大跳跃数M（2k+1,k+1）的值的猜想在k=9时成立,但是他们的另一个猜想M（n,k）相似文献   

扰动Newton法求解函数互补问题

把R0 -矩阵的概念推广到了非线性互补问题 (NLCP) :y - f(x) =0 ,x y =(x1y1,… ,xnyn) T=0 ,x ,y∈Rn+ 的情形 ,应用扰动Newton法求解当 f :Rn→Rn是连续可微的P0 -函数时的互补问题。在无严格互补解的条件下证明了若 f(x)是一个连续可微的P0 -函数 ,满足李卜西兹条件 ,且存在一个常数c>0和 0 <ε≤ 1对所有x∈Rn+ 有 fi0 (x) - fi0 (0 )≥c‖x‖ε,其中 ,xki0 =maxi∈I{xki}成立 ,则产生的序列 { ωk}大范围收敛到NLCP的解。并证明了若 ( f(x ) ) γ γ是一个P矩阵 ,那么序列 { ωk}Q - 2阶收敛到NLCP的解ω 。     

Numerical simulation of unsteady cavitating flows around a transient pitching hydrofoil

The objective of this paper is to improve the understanding of the influence of multiphase flow on the turbulent closure model,the interplay between vorticity fields and cavity dynamics around a pitching hydrofoil.The effects of pitching rate on the subcavitating and cavitating response of the pitching hydrofoil are also investigated.In particular,we focus on the interactions between cavity inception,growth,and shedding and the vortex flow structures,and their impacts on the hydrofoil performance.The calculations are 2-D and performed by solving the incompressible,multiphase Unsteady Reynolds Averaged Navier Stokes(URANS)equations via the commercial CFD code CFX.The k-SST(Shear Stress Transport)turbulence model is used along with the transport equation-based cavitation models.The density correction function is considered to reduce the eddy viscosity according to the computed local fluid mixture density.The calculation results are validated with experiments conducted by Ducoin et al.(see Computational and experimental investigation of flow over a transient pitching hydrofoil,Eur J Mech/B Fluids,2009,28:728–743 and An experimental analysis of fluid structure interaction of a flexible hydrofoil in various flow regimes including cavitating flow,Eur J Mech B/fluids,2012,36:63–74).Results are shown for a NACA66 hydrofoil subject to slow(quasi static,6°/s,*0.18)and fast(dynamic,63°/s,*1.89)pitching motions from=0°to=15°.Both subcavitaing(=8.0)and cavitating(=3.0)flows are considered.For subcavitating flow(=8.0),low frequency fluctuations have been observed when the leading edge vortex shedding occurs during stall,and delay of stall is observed with increasing pitching velocity.For cavitating flow(=3.0),small leading edge cavities are observed with the slow pitching case,which significantly modified the vortex dynamics at high angles of attack,leading to high frequency fluctuations of the hydrodynamic coefficients and different stall behaviors compared to the subcavitating flow at the same pitching rate.On the other hand,for the fast pitching case at=3.0,large-scale sheet/cloud cavitation is observed,the cavity behavior is unsteady and has a strong impact on the hydrodynamic response,which leads to high amplitude fluctuations of the hydrodynamic coefficients,as well as significant changes in the stall and post-stall behavior.The numerical results also show that the local density modification helps to reduce turbulent eddy viscosity in the cavitating region,which significantly modifies the cavity lengths and shedding frequencies,particularly for the fast pitching case.In general,compared with the experimental visualizations,the numerical results with local density correction have been found to agree well with experimental measurements and observations for both slow and fast transient pitching cases.     

关于Smarandache因子个数为n的最小数问题

n∈N＋,Smarandache因子个数为n的最小数Tn定义为最小的正整数k,使得d（k）=n.即Tn=min{k：k∈N,d（k）=n},其中d（n）为Dirichlet除数函数.利用初等方法以及素数的分布性质研究ln（Tn）在Smarandache简单数列上的均值分布问题,并给出一个较强的渐近公式.