Bounds on Fractional-Based Metric Dimension of Petersen Networks

The problem of investigating the minimum set of landmarks consisting of auto-machines(Robots)in a connected network is studied with the concept of location number ormetric dimension of this network.In this paper,we study the latest type of metric dimension called as local fractional metric dimension(LFMD)and find its upper bounds for generalized Petersen networks GP(n,3),where n≥7.For n≥9.The limiting values of LFMD for GP(n,3)are also obtained as 1(bounded)if n approaches to infinity.

Lipschitz Estimates for Commutators of N-dimensional Fractional Hardy Operators

在这份报纸，这被证明整流器 H ，被n维的部分强壮的操作员 H 产生的 b 和 b ()( Rn )是从 LP ( Rn )的 hounded 到 Lq ( Rn ) 0 << 1 ， 1 < p ， q <并且嘴唇- 1/q =(+) /n 。而且， H 的固定，同质的 Herz 空间(K) 上的 b， pq (Rn ) 被获得。

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM) with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes–Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

Application of the Algorithm of Fractional Dimension to Extraction Image Edge

The idea of fractional dimension was stated in brief firstly.Then,adopting the fractional statistical similar principle, the method of the least square minimum error was applied to evaluate the fractional dimension of per image pixel depending on the fractional property of image.And the image edge is extracted by magnitude of fractional dimension of image pixel.We presented the algorithm of the local fractional dimension,which made the rule of window size and sentencing the fractional dimension of edge.Although this algorithm was waste time,it is better than the classical ones in extraction edge and anti-jamming.

Fractional-dimensional approach for excitons in Ga As films on AlxGa(1-x)As substrates

Binding energies of excitons in Ga As films on Al_xGa_(1-x)As substrates are studied theoretically with the fractionaldimensional approach. In this approach, the real anisotropic "exciton + film" semiconductor system is mapped into an effective fractional-dimensional isotropic space. For different aluminum concentrations and substrate thicknesses, the exciton binding energies are obtained as a function of the film thickness. The numerical results show that, for different aluminum concentrations and substrate thicknesses, the exciton binding energies in Ga As films on Al_xGa_(1-x)As substrates all exhibit their maxima with increasing film thickness. It is also shown that the binding energies of heavy-hole and light-hole excitons both have their maxima with increasing film thickness.

New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation

In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.

Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method

In this article, we investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger equation, an important equation in quantum mechanics. The fractional Schrodinger equation further precisely describes the quantum state of a physical system changes in time. In order to determine the solutions a suitable transformation is considered to transmute the equations into a simpler ordinary differential equation (ODE) namely fractional complex transformation. We then use the modified simple equation (MSE) method to obtain new and further general exact wave solutions. The MSE method is more powerful and can be used in other works to establish completely new solutions for other kind of nonlinear fractional differential equations arising in mathematical physics. The affect of obtaining parameters for its definite values which are examined from the solutions of two dimensional and three dimensional time-fractional Schrodinger equations are discussed and therefore might be useful in different physical applications where the equations arise in this article.

Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter H∈(1/4,1/2)

A two-dimensional (2D) stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion (FBM) is studied with the Hurst parameter H ∈(1/4,1/2) under the Dirichlet boundary condition. The existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids are obtained by the estimate on the spectrum of the spatial differential operator and the identity of the infinite double series in the analytic number theory. The existence of the mild solution and the random attractor of a random dynamical system are then obtained for the stochastic non-Newtonian systems with H ∈(1/2,1) without any additional restriction on the parameter H.

Singular and non-topological soliton solutions for nonlinear fractional differential equations

In this article, the fractional derivatives are described in the modified Riemann–Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations(FDEs) based on a fractional complex transform and apply it to solve nonlinear space–time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.

The Generalized Pythagorean Comma Harmonic Powers of a Fundamental Frequency Are Equivalent the Standing Wave Harmonic Fraction System

Purpose: The Pythagorean Comma refers to an ancient Greek musical, mathematical tuning method that defines an integer ratio of exponential coupling constant harmonic law of two frequencies and a virtual frequency. A Comma represents a physical harmonic system that is readily observable and can be mathematically simulated. The virtual harmonic is essential and indirectly measurable. The Pythagorean Comma relates to two discrete frequencies but can be generalized to any including infinite harmonics of a fundamental frequency, vF. These power laws encode the physical and mathematical properties of their coupling constant ratio, natural resonance, the maximal resonance of the powers of the frequencies, wave interference, and the beat. The hypothesis is that the Pythagorean power fractions of a fundamental frequency, vF are structured by the same harmonic fraction system seen with standing waves. Methods: The Pythagorean Comma refers to the ratio of (3/2)12 and 27 that is nearly equal to 1. A Comma is related to the physical setting of the maximum resonance of the powers of two frequencies. The powers and the virtual frequency are derived simulating the physical environment utilizing the Buckingham Π theorem, array analysis, and dimensional analysis. The powers and the virtual frequency can be generalized to any two frequencies. The maximum resonance occurs when their dimensionless ratio closest to 1 and the virtual harmonic closest to 1 Hz. The Pythagorean possible power arrays for a vF system or any two different frequencies are evaluated. Results: The generalized Pythagorean harmonic power law for any two different frequencies coupling constant are derived with a form of an infinite number of powers defining a constant power ratio and a single virtual harmonic frequency. This power system has periodic and fractal properties. The Pythagorean power law also encodes the ratio of logs of the frequencies. These must equal or nearly equal the power ratio. When all of the harmonics are powers of a vF the Pythagorean powers are defined by a consecutive integer series structured in the identical form as standard harmonic fractions. The ratio of the powers is rational, and all of the virtual harmonics are 1 Hz. Conclusion: The Pythagorean Comma power law method can be generalized. This is a new isomorphic wave perspective that encompasses all harmonic systems, but with an infinite number of possible powers. It is important since there is new information: powers, power ratio, and a virtual frequency. The Pythagorean relationships are different, yet an isomorphic perspective where the powers demonstrate harmonic patterns. The coupling constants of a vF Pythagorean power law system are related to the vFs raised to the harmonic fraction series which accounts for the parallel organization to the standing wave system. This new perspective accurately defines an alternate valid physical harmonic system.

The Theory and Application of Upwind Finite Difference Fractional Steps Procedure for Seawater Intrusion

Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.

FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

Characteristic finite difference fractional step schemes are put forward. The electric Potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.

基于分数阶Tikhonov正则化的激光吸收光谱燃烧场二维重建光路优化研究

为探究基于激光吸收光谱技术的燃烧场二维测量光路布置方式,实现有限投影下更精确的燃烧场二维重建,根据分数阶微积分理论,提出一种基于分数阶Tikhonov正则化的光路优化方法.将经典的整数阶Tikhonov正则化推广到分数阶模式,建立了基于分数阶Tikhonov正则化的光路设计目标函数.利用遗传算法分析(0,1)范围内不同阶数的计算结果,得到最佳光路布置方式.采用近红外波段7185.6 cm^(-1)的H_(2)O特征吸收谱线结合20条测试光路对10×10离散化网格区域进行计算,对比分析五种光路布置方式对多种分布模型的重建结果,结果表明,基于分数阶Tikhonov正则化的光路布置方式具有最佳重建效果.研究结果对有限投影条件下激光吸收光谱二维测量光路的优化设计理论研究具有重要意义,可以促进激光吸收光谱技术在复杂发动机燃烧场二维重建及燃烧效率提升方面的应用.

Characteristic fractional step finite difference method for nonlinear section coupled system

For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some techniques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis.Optimal order estimates in l2 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.

基于余幂-激活离散超混沌加密的多参数加权分数傅里叶变换安全通信方法

为提高物理层安全传输性能,该文提出一种新的基于2维余幂-激活(2D-CPA)离散超混沌加密的多参数加权分数傅里叶变换(MP-WFRFT)安全通信方法。首先,将激活函数和余弦函数作为非线性因子引入1维立方(cubic)混沌映射,构造2维混沌映射。非线性因子可对原始cubic混沌映射的迭代过程进行扰动,从而获得更加饱满的相轨。利用分岔图、相图、Lyapunov指数谱等对提出的2维混沌映射动力学特性进行了验证。结果表明,构造的2维混沌序列随机性良好,可进入超混沌状态。然后,利用余幂-激活离散超混沌序列分别构建幅度变换矩阵、相位旋转矩阵和MP-WFRFT参数池,完成对星座幅相加密,以及MP-WFRFT动态变换加密过程,进一步消除数据统计特征,同时提升MP-WFRFT变换的抗参数扫描性能。数值仿真结果表明,加密数据的星座图呈类高斯分布,且传输系统对密钥的敏感性良好。

THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION

A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced(chemical) oil production in porous media.Some techniques,such as the calculus of variations,energy analysis method,commutativity of the products of difference operators,decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived.This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields,and the simulation results are quite interesting and satisfactory.

The Simultaneous Fractional Dimension of Graph Families

For a connected graph G with vertex set V,let RG{x,y}={z∈V:dG(x,z)≠dG(y,z)}for any distinct x,y∈V,where dG(u,w)denotes the length of a shortest uw-path in G.For a real-valued function g defined on V,let g(V)=∑s∈V g(s).Let C={G_(1),G_(2),...,G_(k)}be a family of connected graphs having a common vertex set V,where k≥2 and|V|≥3.A real-valued function h:V→[0,1]is a simultaneous resolving function of C if h(RG{x,y})≥1 for any distinct vertices x,y∈V and for every graph G∈C.The simultaneous fractional dimension,Sdf(C),of C is min{h(V):h is a simultaneous resolving function of C}.In this paper,we initiate the study of the simultaneous fractional dimension of a graph family.We obtain max1≤i≤k{dimf(Gi)}≤Sd_(f)(C)≤min{∑k i=1 dimf(Gi),|V|/2},where both bounds are sharp.We characterize C satisfying Sdf(C)=1,examine C satisfying Sdf(C)=|V|/2,and determine Sdf(C)when C is a family of vertex-transitive graphs.We also obtain some results on the simultaneous fractional dimension of a graph and its complement.

分数阶热弹理论下一维六方准晶杆的动态响应

基于分数阶热弹理论,对两端固定的有限长一维六方准晶杆受到移动热源作用时产生的动态响应进行研究。得到了该问题的控制方程,并利用拉普拉斯变换及其数值反演进行求解。对温度、位移、应力关于时间、热源速度、分数阶参数的扰动情况分别进行图像绘制。结果表明:时间与热源速度一定时,位移、温度、应力都会随着分数阶参数的增加而增加,但分数阶参数对位移产生的影响更小。

基于多维度变异学习与收散归优的鲸鱼优化算法

针对鲸鱼优化算法(WOA)在解决高维、多峰、最优值非原点等问题时存在的收敛精度低、易被局部最优捕获等缺陷,提出了一种基于多维度变异学习与收散归优的鲸鱼优化算法(MLDOWOA)。首先,引入自适应权值以及优势个体干扰动态调整个体螺旋包围的方向,提高了算法的全局搜索能力和收敛精度;然后提出多维度变异学习机制对种群变异方向进行自适应规划,进一步扩大了算法的搜索范围;最后引入收散归优机制协调了搜索步长,帮助种群突破了中后期搜索停滞的局限。通过8个高维基准函数和4个固定维基准函数对MLDOWOA算法进行测试,结果表明同基本算法WOA、SSA以及改进的ACWOA、AWOA、MSIWOA、ADWOA相比,该算法在收敛精度和应对高维函数的能力上具有显著的优越性。将该算法应用于FOPID控制器的参数整定,并将实验结果同近年来该工程问题的研究成果进行对比分析,证明了该算法在FOPID参数整定问题中具有卓越的性能。

心电图QRS波时程比值联合实时三维超声心动图在心力衰竭患者中的应用价值

目的 探讨心电图QRS波时程比值(TEF)联合实时三维超声心动图在心力衰竭患者中的应用价值。方法 选择2020年8月至2021年8月鹤壁市人民医院收治并确诊为心力衰竭的200例患者作为病例组,另选择同期进行健康体检的100例健康受试者作为对照组。所有入组患者均接受彩色多普勒超声心动图仪及心电图检查。彩色多普勒超声心动图仪检测患者左心室射血分数(LVEF)、左心室舒张末期容积(LVEDV)、左心室收缩末期容积(LVESV)、左心室16节段达到最小收缩末期容积时间的标准差标准化值(Tmsv16-SD%)与最大时间差标准化值(Tmsv16-Dif%)、心电图检测左心室QRS波时限(QRSd);Person相关性分析左心室常规功能相关指标与心功能分级相关性。结果 病例组Ⅱ级、Ⅲ级和Ⅳ级患者LVEF水平明显低于对照组,而LVEDV、LVESV、Tmsv16-SD%和Tmsv16-Dif%水平明显高于对照组,且心功能级别越高上述指标变化越明显,差异有统计学意义(P <0.05)。患者LVEF随心功能不全加重明显降低,左心室QRS波时程随心功能不全加重明显增大,且随着心功能不全病情进展,LVEF与TEF逐渐降低,LVEF与NYHA心功能分级呈负相关,差异有统计学意义(r=-0.715,P <0.001),LVEDV、LVESV、TMSV16-SD%、Tmsv16-DIF%与NYHA分级呈正相关,差异有统计学意义(r=0.725、0.793、0.879、0.873,P <0.001)。结论 TEF联合三维超声心动图对心力衰竭患者心脏功能受损诊断具有较高价值,为提前制订患者救治方案、改善患者预后提供有价值医学证据。