A Technique for Estimation of Box Dimension about Fractional Integral

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.

A new multiple-factor clustering method considering both box fractal dimension and orientation of joints

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.

A Successive Shift Box-Counting Method for Calculating Fractal Dimensions and Its Application in Identification of Faults

Fractal dimensions of a terrain quantitatively describe the self-organizedstructure of the terrain geometry. However, the local topographic variation cannot be illustrated bythe conventional box-counting method. This paper proposes a successive shift box-counting method,in which the studied object is divided into small sub-objects that are composed of a series of gridsaccording to its characteristic scaling. The terrain fractal dimensions in the grids are calculatedwith the successive shift box-counting method and the scattered points with values of fractaldimensions are obtained. The present research shows that the planar variation of fractal dimensionsis well consistent with fault traces and geological boundaries.

Combining Fractals and Box-Counting Dimension

In this paper, the box-counting dimension is used to derive an explicit formula for the dimension of a fractal constructed using several contractions or by combining fractals. This dimension agrees with the Hausdorff dimension in the particular case when the scales factors considered are all the same. A more general sufficient condition for the box-counting dimension and the Hausdorff dimension to be the same is given. It is also shown that the dimension of the fractal obtained by combining two fractals is the weighted average of the dimensions of the two fractals.

S-box:six-dimensional compound hyperchaotic map and artificial bee colony algorithm

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.

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS: THE EXACT BOX DIMENSION

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.

ON THE BOX DIMENSION FOR A CLASS OF NONAFFINE FRACTAL INTERPOLATION FUNCTIONS

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.

ON A CLASS OF BESICOVITCH FUNCTIONS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION

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.

Box Dimension of Weyl Fractional Integral of Continuous Functions with Bounded Variation

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.

MiR-142-3p Regulates ILC1s by Targeting HMGB1 via the NF-κB Pathway in a Mouse Model of Early Pregnancy Loss

Objective Innate lymphoid cells(ILCs)are a class of newly discovered immunocytes.Group 1 ILCs(ILC1s)are identified in the decidua of humans and mice.High mobility group box 1(HMGB1)is predicted to be one of the target genes of miR-142-3p,which is closely related to pregnancy-related diseases.Furthermore,miR-142-3p and HMGB1 are involved in regulating the NF-κB signaling pathway.This study aimed to examine the regulatory effect of miR-142-3p on ILC1s and the underlying mechanism involving HMGB1 and the NF-κB signaling pathway.Methods Mouse models of normal pregnancy and abortion were constructed,and the alterations of ILC1s,miR-142-3p,ILC1 transcription factor(T-bet),and pro-inflammatory cytokines of ILC1s(TNF-α,IFN-γand IL-2)were detected in mice from different groups.The targeting regulation of HMGB1 by miR-142-3p in ILC1s,and the expression of HMGB1 in normal pregnant mice and abortive mice were investigated.In addition,the regulatory effects of miR-142-3p and HMGB1 on ILC1s were detected in vitro by CCK-8,Annexin-V/PI,ELISA,and RT-PCR,respectively.Furthermore,changes of the NF-κB signaling pathway in ILC1s were examined in the different groups.For the in vivo studies,miR-142-3p-Agomir was injected in the uterus of abortive mice to evaluate the abortion rate and alterations of ILC1s at the maternal-fetal interface,and further detect the expression of HMGB1,pro-inflammatory cytokines,and the NF-κB signaling pathway.Results The number of ILC1s was significantly increased,the level of HMGB1 was significantly upregulated,and that of miR-142-3p was considerably downregulated in the abortive mice as compared with the normal pregnant mice(all P<0.05).In addition,miR-142-3p was found to drastically inhibit the activation of the NF-κB signaling pathway(P<0.05).The number of ILC1s and the levels of pro-inflammatory cytokines were significantly downregulated and the activation of the NF-κB signaling pathway was inhibited in the miR-142-3p Agomir group(all P<0.05).Conclusion miR-142-3p can regulate ILC1s by targeting HMGB1 via the NF-κB signaling pathway,and attenuate the inflammation at the maternal-fetal interface in abortive mice.

DIMENSIONS FOR RANDOM SELF-CONFORMAL SETS

A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper,we prove that the random self-conformal set is regular almost surely. Also we determine the dimensions for a class of random self-conformal sets.

Box-Behnken响应面优化超声联合双酶法提取当归地上部分总黄酮及其抗氧化活性研究

试验以当归废弃物(当归地上部分)为试验材料,在单因素试验基础上,设计Box-Behnken响应面试验,优化超声联合双酶法提取当归地上部分总黄酮的最佳提取工艺,采用DPPH和ABTS自由基法和FRAP法评价当归地上部分总黄酮的抗氧化活性。结果显示,利用超声联合双酶法提取当归地上部分总黄酮的最佳条件为乙醇浓度50%、液料比50∶1、超声时间41 min、双酶(纤维素酶∶果胶酶=2∶1)用量0.68 g/L、酶解时间93 min,此条件下,当归地上部分总黄酮提取率为8.18%。当归地上部分具有较高的抗氧化活性,在浓度为150 mg/L时,对DPPH自由基清除率为90.3%,略低于VC。在浓度为3 000 mg/L时,对ABTS清除率为88.6%,ABTS的IC50为DPPH IC50近30倍,FRAP抗氧化能力为4.64 (mg VC eq/g sample)。试验表明,当归地上部分的总黄酮具有抗氧化活性。

Box-Cox变换的黄金分割法实现

提出可以使用黄金分割法确定 Box- Cox变换中的参数 ,给出了一种计算步骤。提出了通过多搜索几个区间和回归诊断来更大限度地保证所确定出的参数是合用的。并从理论分析和实例检验两方面说明了与一维格点搜索法相比 ,使用黄金分割法确定 Box- Cox变换中的参数计算量较小 ,容易使计算结果达到较高的精确度 ,且易用性也有所提高。

分形曲线Box-counting维数的一种逼近算法

讨论Ｌ２范数意义下线性分形插值函数（ＬＦＩＦ）对给定函数图象的最佳逼近问题。利用［４］的结果得出了求最佳逼近点的方法，利用最佳产、给出了求给定函数国象Ｂｏｘ－ｃｏｕｎｔｉｎｇ维数近似值的方法。

Y-box结合蛋白-1与肿瘤发生

Y-box结合蛋白(Y-box binding protein,YB)是一类广泛存在于多种生物中的蛋白质家族,是一类高度保守的顺式作用调控元件,也是一种广泛表达的转录因子,发挥重要的生物学功能。Y-box结合蛋白-1(Y-box binding protein-1,YB-1)是Y-box结合蛋白家族成员之一,参与基因的转录调节、翻译调控、维持mRNA的稳定性、mRNA选择性剪接、RNA的配对、DNA的修复、细胞增殖和再生等生物学功能。大量研究表明YB-1的异常表达与许多肿瘤,如:前列腺癌、乳腺癌、肺癌、宫颈癌、淋巴瘤、卵巢癌的发生发展具有相关性。对YB-1的研究为肿瘤的治疗提供了新的方向,并可能成为肿瘤诊治的一种新的标志物。

Box-Behnken设计毛细管液相色谱法拆分α-氨基酸对映体的研究

将L-脯氨酸通过3-缩水甘油丙基三甲氧基硅烷键合到球型多孔硅胶基质上,制备了手性配体交换色谱固定相。采用高压匀浆法将制备的填料填充到毛细管柱中,在自组装的毛细管液相色谱仪上对3种α-氨基酸对映体进行了拆分。利用Box-Behnken设计对影响因素(流动相中乙腈的体积分数、中心离子Cu2+的浓度、流速)进行优化,以最大保留时间和分离度为响应值,借助二次多元回归方程,建立了相应的数学模型。响应曲面图表明:DL-天冬酰胺在5%乙腈、5 mmol/L Cu2+、流速0.139μL/min,苏氨酸在10%乙腈、5mmol/L Cu2+、流速0.167μL/min,丝氨酸在5%乙腈、7 mmol/L Cu2+、流速0.167μL/min的条件下均能得到基线分离。表明通过所制备的手性固定相,采用配体交换色谱模式可获得拆分DL-氨基酸的理想效果。

Box-Behnken法冷鲜滩羊肉蛋白质的高光谱模型优化

高光谱成像技术是一种将成像与光谱相结合的新型无损检测技术,属于间接分析方法;光谱模型的建立非常关键,需综合考察各建模因素间的交互作用。应用Box-Behnken法设计响应面试验优化冷鲜滩羊肉蛋白质含量的可见/近红外高光谱定量检测模型。使用可见/近红外高光谱成像系统采集冷鲜滩羊肉样本的高光谱图像,分析肉样反射光谱特性。采用二维相关光谱技术(2DCOS),以冷鲜滩羊肉中蛋白质含量为“外界扰动”,研究扰动条件下光谱信号的动态变化,解析二维相关光谱谱图特征,寻找与微扰相关的敏感变量。分别采用多元散射校正(multiplicative scatter correction,MSC)和标准正态变量变换(standard normalized variate,SNV)提取有用信号,优化所选特征波段光谱质量。为实现数据快速降维,减少大量光谱数据处理负担,采用变量组合集群分析法(variable combination population analysis,VCPA)和应用竞争性自适应加权算法(competitiv e adaptive reweighted sampling,CARS)对2DCOS范围内特征波段进行二次优选。根据D esign-Expert软件中Box-Behnken法设计响应面试验,以特征优选、光谱预处理及多元校正方法为考察因素,各因素中3种不同方法为水平,建立冷鲜滩羊肉蛋白质含量分析的优化检测体系。结果表明,波长473,679,734和814 nm处存在较强的自相关峰,473~814 nm范围内的特征波段为冷鲜滩羊肉蛋白质检测的敏感区域;MSC和SNV能够消除肉样自身散射作用的干扰,CARS和VCPA对特征波段进行二次优选,分别优选出了16和9个特征波长;各因素对蛋白质可见/近红外光谱模型预测性能的影响顺序为特征优选方法>预处理方法>多元校正方法,优选出2DCOS-SNV-LSSVM模型具有较高的运行速率和预测能力,其R_(c)=0.8588,RMSEC=0.0058;R_(p)=0.8604,RMSEP=0.0057。研究表明,Bo x-Behnken法在可见/近红外高光谱(400~1000 nm)建模参数优化选择中的应用,可以有效地实现滩羊肉品质智能监控与质量安全快速无损分析,为分析对象光谱模型的优化及提高预测结果的准确性提供理论参考。

Box-Behnken响应面设计法优化排脓散水提工艺

目的优选排脓散最佳水提工艺。方法采用Box-Behnken响应面设计法,以水提液中3个指标性成分(柚皮苷、新橙皮苷、芍药苷)的含量和出膏率的综合评价作为考察指标,考察料液比、浸泡时间、提取时间3个因素对提取工艺的影响。结果排脓散水提的最佳工艺条件为15倍水,浸泡67min,提取74min。结论 Box-Behnken实验设计法优化排脓散的水提工艺方法可行,预测性较好。

Upper Bound Estimation of Fractal Dimensions of Fractional Integral of Continuous Functions

Fractional integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville fractional integral is v, fractal dimension of Riemann-Liouville fractional integral of any continuous functions on a closed interval is no more than 2 - v.