(2+1)维Bogoyavlenskii-Schiff方程的精确解

应用简单方程法求得(2+1)维Bogoyavlenskii-Schiff方程的精确解,这种方法对于研究非线性发展方程具有非常广泛的应用意义.     

(2+1)维破裂孤立子方程组的精确解

本文针对(2+1)维破裂孤立子方程组,采用指数函数法,借助于数学工具Maple软件得到了该方程的两个新的孤立波解。     

一个3x+1推广函数在实轴上的不动点与生成的分形图象

为了理解和分析3x+1推广函数生成分形的结构和性质,以及为了绘制用3x+1函数可以构造的分形艺术图形,讨论了3x+1一个推广函数T(x)在实轴上不动点的分布情况,并证明了T(x)有两个整数不动点-1,0;在除(-1,0)外的每相邻两整数的区间中恰有一个不动点;不动点中有两个(-1.1539和0)是吸引的,其余都是排斥的.在此基础上,绘制了T(x)在两个吸引不动点附近的具有艺术效果的拟三维分形图象和f(x)=T(x)-x的牛顿迭代函数在T(x)一些不动点附近的具有艺术效果的分形图象.     

云计算下基于特殊差分方程的(m+1,t+1)门限秘密共享方案

针对非可信云计算服务提供商窃取用户隐私数据的问题,以齐次常系数线性差分方程为工具,将秘密共享技术应用到云计算环境中,提出一种新的(m+1,t+1)门限秘密共享方案。通过对用户隐私数据的解密密钥进行管理,利用齐次常系数线性差分方程为用户与云服务提供商分别分配特殊秘密份额与普通秘密份额,在没有用户参与的情况下,云服务提供商不能恢复用户隐私数据。分析结果表明,该方案能较好地保障用户隐私数据的存储安全,并且通过优化秘密份额减少了存储开销。     

(2+1)维KD方程的解及分岔行为

通过行波变换,将非线性偏微分方程化为常微分方程,利用辅助常微分方程的解来构造偏微分方程的精确解,获得了(2+1)维Konopelchenko-Dubrovsky方程的孤波解和周期解.然后直接研究变换以后的常微分方程,揭示该方程控制的动力系统的鞍结分岔行为,画出了系统的分岔图.     

3x+1推广函数构造广义M集及其艺术分形图像

提出了3x＋1的又一推广函数F（z）,指出其能引出复杂的分形结构．分析了函数F（z）的基本数学特征,探讨了该映射在C平面上广义M集的图像特征,并绘制了其广义M集的部分美妙的分形图像．利用调色板技术和轨迹井技术结合的方法,绘制F（z）广义M集的艺术分形图像,同时在Carlson（Carlson Paul W．Two artistic orbit trap rending methods for Newton M—set fractals[J]．Computers＆Graphics,1999,23（6）：925—931）的基础上提出了环状M集轨迹井,取得了良好的艺术效果,给人一种美的享受．     

军用飞机维修保障费用的GM(1,1)预测

针对传统费用估算方法样本需求量大,实现繁琐的缺点,本文引入灰色理论,建立了某型机维修保障费用灰色GM(1,1)预测模型,并进行了精度检验,结果表明所建立的模型准确、有效。最后利用建立的模型对该型机一个飞行中队未来几年的维修保障费用进行了预测。     

环Fp+uFp+vFp上的(1+u+v)-循环码

常循环码是一类重要的线性码,由于其纠错性能易于分析,因而广泛应用于实践中,同时,利用有限环上常循环码还可以直接构造最优线性码。定义了有限非链环[Fp+uFp+vFp]上[(1+u+v)]-循环码的相关概念,讨论了其生成多项式;引入了一种新的Gray映射[?],证明了该环上[(1+u+v)]-循环码在此Gray映射[?]下的[p]元象是一个长为[2pn]的2-准循环码,并由此构造出了两个最优二元准循环码。     

LOTUS1-2-3及其编译器软件在数据采集中的应用(四)——1-2-3编译器从3(1/2)位ADC采集数据

31/2位双积分型模数转换器常用于数字显示仪表以测量缓变或静态信号。在典型的MC14433 31/2位ADC上附加三态输出缓冲器后,从外部接在PC机并行口上,然后由1-2-3的用户定义功能UDF将它转换输出的BCD码转换成二进制数读进1-2-3工作表。这为数字显示的测量仪表共享PC机及Lotus 1-2-3等软件的资源提供了一条捷径。     

mBBM方程的精确类孤子解

利用一种函数变换将mBBM方程约化为非线性常微分方程（NLODE）,并由此NLODE出发获得mBBM方程的若干精确类孤子解。由此可见,用这种方法还可以求解一大类非线性发展方程。     

New exact solutions of the (n+1)-dimensional sine-Gordon equation using double elliptic equation method

In this paper, the (n+1)-dimensional sine-Gordon equation is studied using double elliptic equation method. With the aid of Maple, more exact solutions expressed by Jacobi elliptic functions are obtained. When the modulus m of Jacobi elliptic function is driven to the limit 1 and 0, some exact solutions expressed by hyperbolic function solutions and trigonometric functions can also be obtained, respectively.     

Breather waves and rational solutions in the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

We consider the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation, which can be used to describe the incompressible fluid. We derive the Hirota bilinear form of the equation via the Bell polynomial. By using Hirota’s direct method, we obtain the $N$-soliton wave solutions of the equation. Based on the resulting Hirota’s bilinear equation, we directly derive the breather wave solutions and rational solutions of the equation. Moreover, we employ the long wave limit method to derive the first-order and second-order rational solutions. In order to better understand the dynamical behaviors of the equation, we provide some graphical analyses to discuss the properties for the dynamic behaviors of these solutions.     

Lax pair,Darboux transformation and Nth-order rogue wave solutions for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

A new (2+1)-dimensional Heisenberg ferromagnetic spin chain equation is investigated, which can be used to describe magnetic soliton excitations in two dimensional space fields and a time field. The Lax pair of the equation is first constructed. Based on the Lax pair, initial seed solution and Darboux transformation, the analytic first-, second- and third-order rogue wave solutions are obtained, and a general expression of the $N$th-order ($N>3$) rogue wave solutions is presented. The impacts of the system parameters on the rogue waves are demonstrated through numerical visualization method.     

Rational solutions and their interaction solutions of the (2+1)-dimensional modified dispersive water wave equation

A bilinear form for the modified dispersive water wave (mDWW) equation is presented by the truncated Painlevé series, which does not lead to lump solutions. In order to get lump solutions, a pair of quartic–linear forms for the mDWW equation is constructed by selecting a suitable seed solution of the mDWW equation in the truncated Painlevé series. Rational solutions are then computed by searching for positive quadratic function solutions. A regular nonsingular rational solution can describe a lump in this model. By combining quadratic functions with exponential functions, some novel interaction solutions are founded, including interaction solutions between a lump and a one-kink soliton, a bi-lump and a one-stripe soliton, and a bi-lump and a two-stripe soliton. Concrete lumps and their interaction solutions are illustrated by 3d-plots and contour plots.     

改进GM（1,1）模型及其在色谱保留值研究中的应用

针对常规ＧＭ（１，１）模型的两点不足，提出用迭代回归法加以改进，并用于多环芳烃容量因子随流动相组成变化关系的建模，获得了精度更高的拟合和预测结果。     

一个3x+1近似推广函数的不动点与分形图像

为研究以3x+1推广函数T(x)为代表的复指数函数的分形性质,构造了一个3x+1近似推广函数B(x).通过对B(x)的复解析分析,得出了B(x)在实轴和复平面上不动点的性质与求解方法,证明了0点为唯一的吸引不动点;说明了B(x)在复平面上迭代的对称性,求出了函数迭代在整数点处的敛散区域.最后通过绘制函数的分形图像对求得的B(x)分形性质加以验证,同时提出了B(x)收敛域和发散域逐层嵌套的猜想.     

Enhanced PL and VUV absorption of BaZr(BO3)2:Eu3+ by Al3+ incorporation

Abstract— The photoluminescence (PL) and vacuum‐ultraviolet excitation (VUV) properties of BaZr(BO₃)₂ doped with the Eu³⁺ activator ion were studied as a new red phosphor for PDP applications. The excitation spectrum shows strong absorption in the VUV region with an absorption band edge at 200 nm. The charge‐transfer excitation band of Eu³⁺ was enhanced by co‐doping with an Al³⁺ ion into the BaZr(BO₃)₂ lattices. The PL spectrum shows the strongest emission at 615 nm, corresponding to the electric dipole ⁵D₀ → ⁷F₂ transition of Eu³⁺ in BaZr(BO₃)₂, which results in good red‐color purity.     

Exact wave solutions for a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation

In this work, we investigate a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation. Based on the simplified Hirota bilinear method, we first construct its soliton solutions. Meanwhile, we correct the formula of N-soliton solution for this equation. On the basis of these solitons we further calculate its lump solutions, periodic waves. Meanwhile, rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method. Some figures are given to display the behavior of these solutions.