基于小波变换的分数阶微分算法在肝脏肿瘤CT图像纹理增强中的应用

图像纹理增强过程中容易丢失平滑区域纹理细节，而分数阶微分增强虽然能够非线性保留平滑区域纹理细节，但对频率分辨率敏感。针对这个问题，提出一种基于小波变换的分数阶微分纹理增强算法，应用于平扫计算机断层扫描（CT）图像的肝脏肿瘤区域的纹理增强。首先，通过小波变换将图像感兴趣区分解成多个子带分量；其次，基于分数阶微分定义构造一个带补偿参数的分数阶微分掩膜；最后，使用该掩膜与每个高频子带分量进行卷积并利用小波逆变换重组图像感兴趣区。实验结果表明，该方法在使用较大分数阶次显著增强肿瘤区域的高频轮廓信息的同时，有效地保留了低频平滑的纹理细节：增强后的肝细胞癌区域与原区域相比，信息熵平均增加36.56%，平均梯度平均增加321.56%，平均绝对差值平均为9.287；增强后的肝血管瘤区域与原区域相比，信息熵平均增加48.77%，平均梯度平均增加511.26%，平均绝对差值平均为14.097。     

Phase portraits of Abel quadratic differential systems of second kind with symmetries

We provide normal forms and the global phase portraits on the Poincaré disk of the Abel quadratic differential equations of the second kind having a symmetry with respect to an axis or to the origin. Moreover, we also provide the bifurcation diagrams for these global phase portraits.     

A novel differential evolution mapping technique for generic combinatorial optimization problems

Differential evolution is primarily designed and used to solve continuous optimization problems. Therefore, it has not been widely considered as applicable for real-world problems that are characterized by permutation-based combinatorial domains. Many algorithms for solving discrete problems using differential evolution have been proposed, some of which have achieved promising results. However, to enhance their performance, they require improvements in many aspects, such as their convergence speeds, computational times and capabilities to solve large discrete problems. In this paper, we present a new mapping method that may be used with differential evolution to solve combinatorial optimization problems. This paper focuses specifically on the mapping component and its effect on the performance of differential evolution. Our method maps continuous variables to discrete ones, while at the same time, it directs the discrete solutions produced towards optimality, by using the best solution in each generation as a guide. To judge its performance, its solutions for instances of well-known discrete problems, namely: 0/1 knapsack, traveling salesman and traveling thief problems, are compared with those obtained by 8 other state-of-the-art mapping techniques. To do this, all mapping techniques are used with the same differential evolution settings. The results demonstrated that our technique significantly outperforms the other mapping methods in terms of the average error from the best-known solution for the traveling salesman problems, and achieves promising results for both the 0/1 knapsack and the traveling thief problems.     

A Reliable Stochastic Numerical Analysis for Typhoid Fever Incorporating With Protection Against Infection

In this paper, a reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection has been considered. We have compared the solutions of stochastic and deterministic typhoid fever model. It has been shown that the stochastic typhoid fever model is more realistic as compared to the deterministic typhoid fever model. The effect of threshold number T* hold in stochastic typhoid fever model. The proposed framework of the stochastic non-standard finite difference scheme (SNSFD) preserves all dynamical properties like positivity, bounded-ness and dynamical consistency defined by Mickens, R. E. The stochastic numerical simulation of the model showed that increase in protection leads to low disease prevalence in a population.     

Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

Deposition of UF5 on the surface of steel material having oxide coating in contact with gaseous UF6

When UF6 is handled in leak tight system, the amount of uranium compound formed on the surface of containers, valves, and others in UF6 handling facilities is not so significant for a short term that special attention has not been given to this problem. The present work was done to throw some more light on this problem based on the recent experiment. We discuss the possibility that the intermolecular transfer of a fluorine atom from UF6 to UF5 may participate in the formation of uranium compound. The discussion includes also the unique features contained in the experimental result, the reaction processes assumed in this problem, and the derivation of a rate equation for expressing the deposition of uranium compound. Furthermore, we propose a new method for determining nonlinear parameters included in a governing differential equation having two variables for expressing the deposition of uranium compound from experimental raw data.     

一类Hilfer型分数阶微分方程解的存在和唯一性

用Banach不动点定理和上下解方法研究了α(1<α <2)阶数和β(0≤β ≤1)类型Hilfer分数阶微分方程的解,给出了方程解的存在和唯一性,并通过例证验证了本文所得结果的有效性.     

基于DoG检测图像特征点的快速二进制描述子

针对SIFT描述子实时性差和传统二进制描述子对尺度、旋转和视角变化鲁棒性差的问题,本文通过优化采样模式和添加灰度差分不变量比较测试进行改进,提出了一种鲁棒性更高的二进制描述子。首先,设计了一种尺度关联、编号标记的采样模式;然后,旋转采样模式中各采样点到特定位置,确保描述子尺度、旋转不变性;接着,分析了采样点点对模式对描述子的影响,选择使用机器学习训练后的128对采样点对;最后,选择灰度值比较测试及梯度绝对值和比较测试构建二进制描述子。实验中采用DoG检测图像关键点,结果表明:本文提出的描述子在描述子构建和描述子匹配上比SIFT描述子分别快84%和67%;在有视角变化的图像匹配上,准确率比传统的二进制描述子高3%~5%,召回率平均要高30%以上。本文提出的特征点描述方法适用于时间要求高的图像匹配领域。