This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary...This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-Liouville fractional integral. Furthermore, a general resultis arrived at for 1-dimensional fractal functions such as with unbounded variation and(or) infinite lengths, which can infer all previous studies such as [2] [3]. This paper’s estimation reveals that the fractional integral does not increase the fractal dimension of f(x), i.e. fractional integration does not increase at least the fractal roughness. And the result has partly answered the fractal calculus conjecture and completely answered this conjecture for all 1-dimensional fractal function (Xiao has not answered). It is significant with a comparison to the past researches that the box dimension connection between a fractal function and its Riemann-Liouville integral has been carried out only for Weierstrass type and Besicovitch type functions, and at most Hlder continuous. Here the proof technique for Riemann-Liouville fractional integral is possibly of methodology to other fractional integrals.展开更多
The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The exact box dimension for such functions many important cases is established. We need to point out that, althoug...The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The exact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.展开更多
We present lower and upper bounds for the box dimension of the graphs of certain nonaffine fractal interpolation functions by generalizing the results that hold for the affine case.
This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 < s < 2, λk> tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ...This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 < s < 2, λk> tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ>1. The results show thatis a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions. For the fractional Riemann-Liouvtlle differential operator Du and the fractional integral operator D-v, the results show that if A is sufficiently large, then a necessary and sufficient condition for box dimensionof Graph(D-v(B)), 0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)), 0 < u < 2 - s, to bes + u is also lim.展开更多
We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integr...We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.展开更多
The paper proposes a new multiple-factor clustering method(NMFCM)with consideration of both box fractal dimension(BFD)and orientation of joints.This method assumes that the BFDs of different clusters were uneven,and c...The paper proposes a new multiple-factor clustering method(NMFCM)with consideration of both box fractal dimension(BFD)and orientation of joints.This method assumes that the BFDs of different clusters were uneven,and clustering was performed by redistributing the joints near the boundaries of clusters on a polar map to maximize an index for estimating the difference of the BFD(DBFD).Three main aspects were studied to develop the NMFCM.First,procedures of the NMFCM and reasonableness of assumptions were illustrated.Second,main factors affecting the NMFCM were investigated by numerical simulations with disk joint models.Finally,two different sections of a rock slope were studied to verify the practicability of the NMFCM.The results demonstrated that:(1)The NMFCM was practical and could effectively alleviate the problem of hard boundary during clustering;(2)The DBFD tended to increase after the improvement of clustering accuracy;(3)The improvement degree of the NMFCM clustering accuracy was mainly influenced by three parameters,namely,the number of clusters,number of redistributed joints,and total number of joints;and(4)The accuracy rate of clustering could be effectively improved by the NMFCM.展开更多
Being as unique nonlinear components of block ciphers,substitution boxes（S-boxes） directly affect the security of the cryptographic systems.It is important and difficult to design cryptographically strong S-boxes th...Being as unique nonlinear components of block ciphers,substitution boxes（S-boxes） directly affect the security of the cryptographic systems.It is important and difficult to design cryptographically strong S-boxes that simultaneously meet with multiple cryptographic criteria such as bijection,non-linearity,strict avalanche criterion（SAC）,bits independence criterion（BIC）,differential probability（DP） and linear probability（LP）.To deal with this problem,a chaotic S-box based on the artificial bee colony algorithm（CSABC） is designed.It uses the S-boxes generated by the six-dimensional compound hyperchaotic map as the initial individuals and employs ABC to improve their performance.In addition,it considers the nonlinearity and differential uniformity as the fitness functions.A series of experiments have been conducted to compare multiple cryptographic criteria of this algorithm with other algorithms.Simulation results show that the new algorithm has cryptographically strong S-box while meeting multiple cryptographic criteria.展开更多
The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface tex...The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface texture change of insulating paper,firstly,the thermal aging experiment of insulating paper is carried out,and the insulating paper samples with different aging times are obtained.After then,the images of the aged insulating paper samples are collected and pre-processed.The pre-processing effect is verified by constructing and calculating the gray surface of the sample.Secondly,the texture features of the insulating paper image are extracted by box dimension and multifractal spectrum.Based on that,the extreme learning machine(ELM)is taken as the classification tool with texture features and aging time as the input and output,to train the algorithm and construct the corresponding relationship between the texture feature and the aging time.After then,the insulating paper with unknown aging time is predicted with a trained ELMalgorithm.The numerical test results show that the texture features extracted from the fractal dimension of the micro image can effectively characterize the aging state of insulating paper,the average accuracy can reach 91.6%.It proves that the fractal dimension theory can be utilized for assessing the aging state of insulating paper for onsite applications.展开更多
遥感图像中目标尺度变化大、目标密集分布、相似地物易混淆、背景复杂干扰多以及图像细节不足,现有的旋转目标检测算法通常存在较高的计算负担,并且在精度上仍有提升的空间。针对上述问题,本研究改进当前领先的YOLOv9检测器,开发了一种...遥感图像中目标尺度变化大、目标密集分布、相似地物易混淆、背景复杂干扰多以及图像细节不足,现有的旋转目标检测算法通常存在较高的计算负担,并且在精度上仍有提升的空间。针对上述问题,本研究改进当前领先的YOLOv9检测器,开发了一种高效而准确的遥感图像旋转目标检测器RSO-YOLO(YOLO for Remote Sensing Images with Oriented Bounding Box)。首先,利用一种低照度遥感图像辅助数据增强模块,用于改善弱光、噪点、模糊和对比度不足等问题;其次,设计了一个解耦的角度预测头,使算法拥有对遥感目标方向的感知能力;其次,在模型中引入基于卡尔曼滤波的交并比KFIoU(Kalman Filter Intersection over Union)损失,以解决旋转目标表示引起的角度周期性问题,使用分布焦点损失DFL(Distribution Focal Loss)学习旋转边界框的分布,减少高斯建模方法中近正方形目标的角度不准确问题;再次,创建一种面向旋转目标检测的动态标签分配策略,在分配过程中综合考虑了交并比(IOU)与类别得分(Scores),从而构建更好的能够反映目标特性的样本空间;最后,使用基于海林格距离的概率交并比(ProbIoU)进行非极大值抑制,减少非极大值抑制的计算负担。将本研究提出的遥感图像旋转目标检测器在DIOR-R公开数据集上进行实验验证,与多个典型的旋转目标检测方法进行了比较,结果表明,本研究提出RSO-YOLO方法综合检测精度达到81.1%平均精确率mAP(mean Average Precision),位居第一,且能够保证检测的实时性。此外,使用辅助数据增强模块后可提高1.5%mAP。综上,本研究提出的RSO-YOLO能够同时兼顾旋转目标检测的速度和准确性,对海事与机场监测、城市管理、灾害评估、农林巡检等遥感场景具有工程落地价值与应用潜力,亦为后续面向低照度与复杂背景条件的旋转检测研究提供可复用的模块化方案。。展开更多
文摘This paper discusses further the roughness of Riemann-Liouville fractional integral on an arbitrary fractal continuous functions that follows Rfs. [1]. A novel method is used to reach a similar result for an arbitrary fractal function , where is the Riemann-Liouville fractional integral. Furthermore, a general resultis arrived at for 1-dimensional fractal functions such as with unbounded variation and(or) infinite lengths, which can infer all previous studies such as [2] [3]. This paper’s estimation reveals that the fractional integral does not increase the fractal dimension of f(x), i.e. fractional integration does not increase at least the fractal roughness. And the result has partly answered the fractal calculus conjecture and completely answered this conjecture for all 1-dimensional fractal function (Xiao has not answered). It is significant with a comparison to the past researches that the box dimension connection between a fractal function and its Riemann-Liouville integral has been carried out only for Weierstrass type and Besicovitch type functions, and at most Hlder continuous. Here the proof technique for Riemann-Liouville fractional integral is possibly of methodology to other fractional integrals.
文摘The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The exact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.
文摘We present lower and upper bounds for the box dimension of the graphs of certain nonaffine fractal interpolation functions by generalizing the results that hold for the affine case.
基金Research supported by national Natural Science Foundation of China (10141001)Zhejiang Provincial Natural Science Foundation 9100042 and 1010009.
文摘This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 < s < 2, λk> tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ>1. The results show thatis a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions. For the fractional Riemann-Liouvtlle differential operator Du and the fractional integral operator D-v, the results show that if A is sufficiently large, then a necessary and sufficient condition for box dimensionof Graph(D-v(B)), 0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)), 0 < u < 2 - s, to bes + u is also lim.
文摘We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.
基金funded by the National Natural Science Foundation of China(Grant Nos.41972264 and 52078093)Liaoning Revitalization Talents Program,China(Grant No.XLYC1905015)。
文摘The paper proposes a new multiple-factor clustering method(NMFCM)with consideration of both box fractal dimension(BFD)and orientation of joints.This method assumes that the BFDs of different clusters were uneven,and clustering was performed by redistributing the joints near the boundaries of clusters on a polar map to maximize an index for estimating the difference of the BFD(DBFD).Three main aspects were studied to develop the NMFCM.First,procedures of the NMFCM and reasonableness of assumptions were illustrated.Second,main factors affecting the NMFCM were investigated by numerical simulations with disk joint models.Finally,two different sections of a rock slope were studied to verify the practicability of the NMFCM.The results demonstrated that:(1)The NMFCM was practical and could effectively alleviate the problem of hard boundary during clustering;(2)The DBFD tended to increase after the improvement of clustering accuracy;(3)The improvement degree of the NMFCM clustering accuracy was mainly influenced by three parameters,namely,the number of clusters,number of redistributed joints,and total number of joints;and(4)The accuracy rate of clustering could be effectively improved by the NMFCM.
基金supported by the National Natural Science Foundation of China(6060309260975042)
文摘Being as unique nonlinear components of block ciphers,substitution boxes（S-boxes） directly affect the security of the cryptographic systems.It is important and difficult to design cryptographically strong S-boxes that simultaneously meet with multiple cryptographic criteria such as bijection,non-linearity,strict avalanche criterion（SAC）,bits independence criterion（BIC）,differential probability（DP） and linear probability（LP）.To deal with this problem,a chaotic S-box based on the artificial bee colony algorithm（CSABC） is designed.It uses the S-boxes generated by the six-dimensional compound hyperchaotic map as the initial individuals and employs ABC to improve their performance.In addition,it considers the nonlinearity and differential uniformity as the fitness functions.A series of experiments have been conducted to compare multiple cryptographic criteria of this algorithm with other algorithms.Simulation results show that the new algorithm has cryptographically strong S-box while meeting multiple cryptographic criteria.
基金This work was supported by the Tianyou Youth Talent Lift Program of Lanzhou Jiaotong University,the Youth Science Foundation of Lanzhou Jiaotong University(No.2019029)the University Innovation Fund Project of Gansu Provincial Department of Education(No.2020A-036)the Young Doctor Foundation of JYT.GANSU.GOV.CN(No.2021QB-060).
文摘The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface texture change of insulating paper,firstly,the thermal aging experiment of insulating paper is carried out,and the insulating paper samples with different aging times are obtained.After then,the images of the aged insulating paper samples are collected and pre-processed.The pre-processing effect is verified by constructing and calculating the gray surface of the sample.Secondly,the texture features of the insulating paper image are extracted by box dimension and multifractal spectrum.Based on that,the extreme learning machine(ELM)is taken as the classification tool with texture features and aging time as the input and output,to train the algorithm and construct the corresponding relationship between the texture feature and the aging time.After then,the insulating paper with unknown aging time is predicted with a trained ELMalgorithm.The numerical test results show that the texture features extracted from the fractal dimension of the micro image can effectively characterize the aging state of insulating paper,the average accuracy can reach 91.6%.It proves that the fractal dimension theory can be utilized for assessing the aging state of insulating paper for onsite applications.
文摘遥感图像中目标尺度变化大、目标密集分布、相似地物易混淆、背景复杂干扰多以及图像细节不足,现有的旋转目标检测算法通常存在较高的计算负担,并且在精度上仍有提升的空间。针对上述问题,本研究改进当前领先的YOLOv9检测器,开发了一种高效而准确的遥感图像旋转目标检测器RSO-YOLO(YOLO for Remote Sensing Images with Oriented Bounding Box)。首先,利用一种低照度遥感图像辅助数据增强模块,用于改善弱光、噪点、模糊和对比度不足等问题;其次,设计了一个解耦的角度预测头,使算法拥有对遥感目标方向的感知能力;其次,在模型中引入基于卡尔曼滤波的交并比KFIoU(Kalman Filter Intersection over Union)损失,以解决旋转目标表示引起的角度周期性问题,使用分布焦点损失DFL(Distribution Focal Loss)学习旋转边界框的分布,减少高斯建模方法中近正方形目标的角度不准确问题;再次,创建一种面向旋转目标检测的动态标签分配策略,在分配过程中综合考虑了交并比(IOU)与类别得分(Scores),从而构建更好的能够反映目标特性的样本空间;最后,使用基于海林格距离的概率交并比(ProbIoU)进行非极大值抑制,减少非极大值抑制的计算负担。将本研究提出的遥感图像旋转目标检测器在DIOR-R公开数据集上进行实验验证,与多个典型的旋转目标检测方法进行了比较,结果表明,本研究提出RSO-YOLO方法综合检测精度达到81.1%平均精确率mAP(mean Average Precision),位居第一,且能够保证检测的实时性。此外,使用辅助数据增强模块后可提高1.5%mAP。综上,本研究提出的RSO-YOLO能够同时兼顾旋转目标检测的速度和准确性,对海事与机场监测、城市管理、灾害评估、农林巡检等遥感场景具有工程落地价值与应用潜力,亦为后续面向低照度与复杂背景条件的旋转检测研究提供可复用的模块化方案。。
