The effect of gravity on self-similarity of Worthington jet after water entry of a two-dimensional wedge

The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to analyze the development of flow field.There is a linear scaling regarding the axial velocity of the jet and the scaling coefficient increases with the Froude number.

AVAPS-AE模式的无创通气对AECOPD合并OSA患者PSG参数、ESS评分及舒适度的影响

目的探讨平均容积保证压力支持-自动呼气压(AVAPS-AE)模式的无创通气对慢性阻塞性肺疾病急性加重期(AECOPD)合并阻塞性睡眠呼吸暂停(OSA)患者多道睡眠监测(PSG)参数、Epworth嗜睡量表(ESS)评分及舒适度的影响。方法选取2020年1月至2022年10月自贡市第一人民医院75例AECOPD合并OSA患者,随机分为3组,各25例,均行无创通气治疗,对照A组予以AVAPS模式,对照B组予以S/T模式,观察组予以AVAPS-AE模式。比较3组治疗前、治疗24 h、48 h及72 h血气分析指标[动脉氧分压(PaO_(2))、动脉血酸碱度(pH)、动脉二氧化碳分压(PaCO_(2))]、PSG参数[微觉醒指数(MAI)、呼吸暂停低通气指数(AHI)、最低脉搏氧饱和度(miniSpO_(2))、睡眠效率(TST/TRT)]、颏舌肌肌电值(GGEMG)各变量[清醒期及睡眠NREM期张力性、峰值、时相性GGEMG]、人机对抗发生率、48 h插管率、ESS、Brog、视觉模拟量表(VAS)及健康相关生存质量(HRQL)评分。结果治疗24 h、48 h及72 h PaO_(2)组间比较:观察组>对照A组>对照B组(P<0.05);PaCO_(2)组间比较:观察组<对照A组<对照B组(P<0.05);TST/TRT、miniSpO_(2)组间比较:观察组>对照A组>对照B组(P<0.05);AHI、MAI组间比较:观察组<对照A组<对照B组(P<0.05);清醒期及睡眠NREM期张力性、峰值、时相性GGEMG组间比较:观察组<对照A组<对照B组(P<0.05);3组人机对抗发生率、48 h插管率比较,差异无统计学意义(P>0.05);ESS、Brog、VAS评分组间比较:观察组<对照A组<对照B组(P<0.05);HRQL评分组间比较:观察组>对照A组>对照B组(P<0.05)。结论AVAPS-AE模式的无创通气用于AECOPD合并OSA有利于改善患者睡眠,减少日间嗜睡,缓解呼吸困难,提高呼吸舒适度及生存质量。

Self-similarity of complex networks under centrality-based node removal strategy

Real-world networks exhibit complex topological interactions that pose a significant computational challenge to analyses of such networks.Due to limited resources,there is an urgent need to develop dimensionality reduction techniques that can significantly reduce the structural complexity of initial large-scale networks.In this paper,we propose a subgraph extraction method based on the node centrality measure to reduce the size of the initial network topology.Specifically,nodes with smaller centrality value are removed from the initial network to obtain a subgraph with a smaller size.Our results demonstrate that various real-world networks,including power grids,technology,transportation,biology,social,and language networks,exhibit self-similarity behavior during the reduction process.The present results reveal the selfsimilarity and scale invariance of real-world networks from a different perspective and also provide an effective guide for simplifying the topology of large-scale networks.

On the Self-Similarity in Biological Processes

We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.

The Golden Ratio Theorem: A Framework for Interchangeability and Self-Similarity in Complex Systems

The Golden Ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-similarity, and the mathematical elegance of the Golden Ratio. This research unravels a unique methodological paradigm, emphasizing the omnipresence of the Golden Ratio in shaping system dynamics. The novelty of this study stems from its detailed exposition of self-similarity and interchangeability, transforming them from mere abstract notions into actionable, concrete insights. By highlighting the fractal nature of the Golden Ratio, the implications of these revelations become far-reaching, heralding new avenues for both theoretical advancements and pragmatic applications across a spectrum of scientific disciplines.

Self-similar very singular solution of a p-Laplacian equation with gradient absorption: existence and uniqueness

This paper investigates the self-similar singular solution of the p-Laplacian evolution equation with the nonlinear gradient absorption terms u t=div(u p-2u)-uq for 1<p<2 and q>in Rn× (0, ∞). It has been proved that when 1<q<p-n/(n+1) there exists a unique self-similar very singular solution.

An Intrusion Alarming System Based on Self-Similarity of Network Traffic

Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle that the number of network traffic can affect the degree ofself-similar traffic, the paper investigates the variety of self-similarity resulted fromunconventional network traffic. A network traffic model based on normal behaviors of user isproposed and the Hursl parameter of this model can be calculated. By comparing the Hurst parameterof normal traffic and the self-similar parameter, we ean judge whether the network is normal or notand alarm in time.

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.

ON THE HITTING PROBABILITY AND POLARITY FOR A CLASS OF SELF-SIMILAR MARKOV PROCESSES

The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.

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.

Some Results about the Sample Path Properties of Markov Processes with Independent Self-Similar Components

This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.

Measurement of Characteristic Self-Similarity and Self-Diversity for Complex Mechanical Systems

Based on similarity science and complex system theory,a new concept of characteristic self-diversity and corre- sponding relations between self-similarity and self-diversity for complex mechanical systems are presented in this paper.Methods of system self-similarity and self-diversity measure between main system and sub-system are studied.Numerical calculations show that the characteristic self-similarity and self-diversity measure method is validity.A new theory and method of self-similarity and self- diversity measure for complexity mechanical system is presented.

A MODEL OF RANDOM PARTICLES CONSTRUCTED BY THE PRINCIPLE OF SELF-SIMILARITY AND ITS APPLICATION

A model of random particles constructed by the operation of self-similarity in fractalgeometry is presented.The correlation function of the number density has been obtained andcan be used conveniently in theoretical study and computer simulation for wave interaction withrandom media.As an example,this model has been applied to calculate analytically the rangedependence of volume scattering in radar echoes.The result agrees with that of Rastogi andScheucher’s simulation.

Self-similar spatiotemporal solitary waves in Bessel-Hermite optical lattices

An exact self-similar solution to a （3＋l）-dimensional nonlinear Schrodinger equation with gain in the BesselHermite lattice is obtained analytically. The stability of the analytical solution is confirmed by using numerical simulation. It is shown that the light bullet has a stable ellipsoid or vortex profile and a linear spatiotemporal chirp.

MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

Self-similarity of spanwise rotational motions’population trends in decelerating open-channel flow

Decelerating open-channel flow is a type of flow that gradually moves forward with decreasing velocity and increasing water depth.Although all flow parameters change along the streamwise direction,previous studies have revealed that these parameters’vertical distributions at different sections can be universally described with a single profile when being nondimensionalised by appropriate scales.This study focuses on the population trends of spanwise rotational motions at various sections along the main flow direction by particle imaging velocimetry(PIV)measurement.The wall-normal population distributions of density,radius,swirling strength,and convection velocity of the prograde and retrograde motions show similar trends in uniform open-channel flows.The dimensionless representation is invariant along the main flow direction.This study’s results indicate the self-similar characteristic of population trends of spanwise rotational motions prevails in decelerating open-channel flow.

Self-similarity Based Editing of 3D Surface Textures Using Height and Albedo Maps

This paper presents an inexpensive method for self-similarity based editing of real-world 3D surface textures by using height and albedo maps. Unlike self-similarity based 2D texture editing approaches which only make changes to pixel color or inten- sity values, this technique also allows surface geometry and reflectance of the captured 3D surface textures to be edited and relit us- ing illumination conditions and viewing angles that differ from those of the original. A single editing operation at a given location affects all similar areas and produces changes on all images of the sample rendered under different conditions. Since surface height and albedo maps can be used to describe seabed topography and geologic features, which play important roles in many oceanic proc- esses, the proposed method can be effectively employed in applications regarding visualization and simulation of oceanic phenom- ena.

SELF-SIMILAR CRACK EXPANSION METHOD FOR THE STRESS INTENSITY FACTOR ANALYSIS

The Self-Similar Crack Expansion (SSCE) method is proposed to evaluate stress intensity factors at crack tips, whereby stress intensity factors of a crack can be determined by the crack opening displacement over the crack, not just by the local displacement around the crack tip. The crack expansion rate is estimated by taking advantage of the crack self-similarity. Therefore, the accuracy of the calculation is improved. The singular integrals on crack tip elements are also analyzed and are precisely evaluated in terms of a special integral analysis. Combination of these two techniques greatly increases the accuracy in estimating the stress distribution around the crack tip. A variety of two-dimensional cracks, such as subsurface cracks, edge cracks, and their interactions are calculated in terms of the self-similar expansion rate. Solutions are satisfied with errors less than 0.5% as compared with the analytical solutions. Based on the calculations of the crack interactions, a theory for crack interactions is proposed such that for a group of aligned cracks the summation of the square of SIFs at the right tips of cracks is always equal to that at the left tips of cracks. This theory was proved by the mehtod of Self-Similar Crack Expansion in this paper.

ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS

We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of orderβ∈(1/2,3/4]is normal according to the values ofβ.We apply our results to two self-similar Gaussian processes:the subfractional Brownian motion and the bifractional Brownian motion.

On use of the alpha stable self-similar stochastic process to model aggregated VBR video traffic

The alpha stable self-similar stochastic process has been proved an effective model for high variable data traffic. A deep insight into some special issues and considerations on use of the process to model aggregated VBR video traffic is made. Different methods to estimate stability parameter a and self-similar parameter H are compared. Processes to generate the linear fractional stable noise （LFSN） and the alpha stable random variables are provided. Model construction and the quantitative comparisons with fractional Brown motion （FBM） and real traffic are also examined. Open problems and future directions are also given with thoughtful discussions.