A NEGATIVE ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS WITH OPEN SET CONDITION

Zhou and Feng posed a conjecture on self-similar set in 2004. In this paper, a self-similar set is constructed which has a best covering but its natural covering is not a best one. Thus, we indeed give a negative answer to the conjecture.

AN ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS

In this paper, we construct a self-similar set which has a best covering but it is not the natural covering, thus negate the conjecture on self-similar sets posed by Z. Zhou in 2004.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

THE RANDOM SHIFT SET AND RANDOM SUB-SELF-SIMILAR SET

First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.

ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS SATISFYING OPEN SET CONDITION

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-similar Cantor set satisfying OSC and give a simple method for computing its exact Hausdorff measure.

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.

The Structure and the Sufficent and Necessary Conditions for Generalized Statistically Self-Similar Sets

We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.

THE DIMENSION FOR RANDOM SUB-SELF-SIMILAR SET

In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

In this paper, authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically self-similar measure.

The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets

In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite （p.c.f.） self-similar sets.

THE EXACT MEASURES OF A CLASS OF SELF-SIMILAR SETS ON THE PLANE

Let S belong to R^2 be the attractor of the iterated function system {f1, f2, f3 } iterating on the unit equilateral triangle So. where fi（x） =λix ＋ bi, i = 1,2, 3, x =（x1, x2）, b1=（0, 0）, b3=（1-λ3 /2,√3/2 （1-λ3）） This paper determines the exact Hausdorff measure, centred covering measure and packing measure of S under some conditions relating to the contraction parameter.

Hlder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

In this paper we establish sharp H/51der estimates of harmonic functions on a class of connected post critically finite （p.c.f.） self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some weU-known examples, such as the Sierpinski gasket, the unit interval, the level 3 Sierpinski gasket, the hexagasket, the 3-dimensional Sierpinski gasket, and the Vicsek set are also considered.

Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points

In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.

A Local Property of Hausdorff Centered Measure of Self-Similar Sets

We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, thenC^s（E∩B（x,r））≤（2r）^sfor all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.

NOTE ON THE PAPER “ AN NEGATIVE ANSWER TO A CONJECTURE ON THE SELF-SIMILAR SETS SATISFYING THE OPEN SET CONDITION”

In this paper, we present a more simple and much shorter proof for the main result in the paper ＂ An negative answer to a conjecture on the self-similar sets satisfy- ing the open set condition＂, which was published in the journal Analysis in Theory and Applications in 2009.

ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION

Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition （OSC）, and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds.

VR环境下SET GO教学法的构建及在耳鼻喉临床教学的应用

SET GO教学法也称为应诊录像教学法,就是在教学过程中,通过观察操作者的视频录像,进行教学的教学法。由于耳、鼻、喉的结构复杂,内部空间狭小,增加了视频录制的难度。在此背景下,吉林药学院附属医院将VR技术融入SET GO教学法中,借助VR技术录制成三维视频,使录制的视频清晰度更高,为SET GO教学法的实施提供了可行性。具体的教学环节分为前期教学、VR模拟操作及录制、VR录像加工、See和Else教学环节、Think教学环节、Goals和Offers教学环节等。通过以上环节的有序实施,提高了耳鼻喉科的临床教学效果。如在视频录制质量评价和SET GO教学效果评价方面,学生各项指标评价的良好率均在90%以上。建议进一步推广和应用。

SETD5介导AKT1磷酸化调控结肠癌细胞的迁移和5-FU敏感性

目的:探讨含SET结构域蛋白5(SETD5)对结肠癌细胞增殖、迁移和对5-氟尿嘧啶(5-FU)药物敏感性的影响及机制。方法:常规培养结肠癌细胞,用Lipofectamine 2000将siSETD5-NC、si-SETD5-1~3质粒转染至HT-29细胞中,将其分为对照组(未处理)、si-SETD5-NC组、si-SETD5组和si-SETD5+SC79组,si-SETD5+SC79组HT-29细胞转染质粒的同时用10µmol/L SC79处理。qPCR法检测NCM460、HT-29和LoVo细胞中SETD5 mRNA表达,流式细胞术、细胞划痕法、WB法和CCK-8法分别检测各组HT-29细胞的凋亡情况、迁移能力、相关蛋白的表达,以及对5-FU的敏感性。结果:SETD5 mRNA在HT-29、LoVo细胞中均呈高表达(均P<0.01)。在HT-29细胞中成功地敲减了SETD5 mRNA(P<0.01)。敲减SETD5 mRNA可明显抑制HT-29细胞的增殖活性(P<0.01)、迁移能力(P<0.01)、相关蛋白(SETD5、p-PI3K、p-AKT1、p-mTOR蛋白)的表达(均P<0.01)、促进细胞凋亡(P<0.01),且提高其对5-FU的敏感性(P<0.01),这些作用均可被AKT激活剂SC79部分阻挡(P<0.05或P<0.01)。结论:SETD5在HT-29、LoVo细胞中高表达,SETD5通过PI3K/AKT1通路促进结肠癌HT-29细胞的增殖、迁移,且降低其对5-FU的敏感性,SETD5是结肠癌临床诊断、治疗的潜在靶点。

基于SET-AHP-TRIZ的坐式康复训练器设计研究

为解决现有坐式康复训练器形式与功能单一、操作使用缺乏智能化等问题,文章构建了基于SET-AHP-TRIZ的设计思路。首先,对产品的现状、用户进行市场调研,采用SET分析法确定目标产品的机会缺口;其次,应用AHP法对需求点进行定量计算,以确定创新过程中需要着重改善的问题;最后,通过应用TRIZ理论分析出现的矛盾问题,并总结其矛盾类型,利用发明原理解决问题,进行坐式康复训练器设计实践,减少了设计过程主观因素的影响,使设计结果更为科学合理,以期提高用户的满意度。

Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.