SPECTRAL RADIUSES OF THE GALTON-WATSON BRANCHING PROCESSES

The spectral radiuses of Galton-Watson branching processes which describes the speed of the process escaping from any state are calculated. Under the condition of irreducibility,it is show that this is equal to the spectral radius of Jacobi matrix of its generating function.

校园5G双域专网安全认证方法实践

为顺应时代及产业发展,同时结合校园应用需求和师生教学、实验及生活网络应用场景的不断变化,为满足师生校内校外一体化融合接入需求,建设5G双域专网,与校园网相融合,将5G校园专网灵活便捷的优势和校园身份账号管理融合,在实现校园师生从校内到校外对网络资源无缝体验的同时,保障校内外资源的安全实名管理,积极探索5G融合教育行业解决方案,利用5G+“纺织AIoT”构建校企双元育人模式,深化产教融合,完善课程体系,培养复合型技术技能人才,促进人才链、教育链、产业链、创新链的融合。

e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) Cross Sections and the Λ_(c)^(+) Electromagnetic Form Factors within the Extended Vector Meson Dominance Model

Within the extended vector meson dominance model,we investigate the𝑒e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) reaction and the electromagnetic form factors of the charmed baryon𝛬 Λ_(c)^(+)𝑐.The model parameters are determined by fitting them to the cross sections of the process𝑒e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) and the magnetic form factor|G_(M)|of Λ_(c)^(+) .By considering four charmonium-like states,called𝜓(4500),𝜓(4660),𝜓(4790),and𝜓(4900),we can well describe the current data on the𝑒e^(+)e^(-)→Λ_(c)+Λ_(c)^(- ) reaction from the reaction threshold up to 4.96 GeV.In addition to the total cross sections and|𝐺M|,the ratio|G_(E)/G_(M)|and the effective form factor|Geff|for Λ_(c)^(+) 𝑐are also calculated,and found that these calculations are consistent with the experimental data.Within the fitted model parameters,we have also estimated the charge radius of the charmed Λ_(c)^(+) baryon.

Ground settlement and tunnel response due to twin-curved shield tunnelling in soft ground with small clear distance

Twin curved tunnels are often encountered in shield tunnelling,where significant complexities in densely exploited underground space are observed.In this study,the ground settlement and tunnel deformation due to twin-curved shield tunnelling in soft ground were investigated using numerical simulation and field monitoring.Different curvature radii of twin curved tunnels and subsequent effects of tunnel construction were considered to reveal the tunnelling effect on ground surface settlement and tunnel deformation.The results show that the settlement trough yields one offset towards inside of curved shield tunnelling.The location of settlement trough and maximum settlement were affected by curvature radius but except for the shape and width of settlement trough.Adjacent parallel twin-curved shield tunnelling could increase the offset of existing settlement trough and maximum settlement.Then,an empirical prediction of surface settlement trough due to twin-curved shield tunnelling with same tunnel diameters in soft clay was proposed,which was applicable to curvature radius less than 800 m.Finally,a minimum radius of 600 m of curvature tunnel was proposed in terms of allowable convergence deformation of tunnel.The result could provide guidance on safety evaluation for twin curved shield tunnelling construction.

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

Wind-sand flow simulation and radius optimization of highway embankment under different vertical curve radius

It is of great practical value to explore the correlation between the vertical curve radius of desert highway and the increase of sand accumulation in local lines,and to select the appropriate vertical curve radius for reducing the risk of sand accumulation.In this study,three-dimensional models of desert highway embankments with different vertical curve radii were constructed,and Fluent software was used to simulate the wind-sand flow field and sand accumulation distribution of vertical curve embankments.The results show that:(1)Along the direction of the road,the concave and the convex vertical curve embankments have the effect of collecting and diverging the wind-sand flow,respectively.When the radius of the concave vertical curve is 3000 m,5000 m,8000 m,10000 m and 20000 m,the wind velocity in the middle of the vertical curve is 31.76%,22.58%,10.78%,10.53%and 10.44%,higher than that at both ends.When the radius of the convex vertical curve is 6500 m,8000 m,10000 m,20000 m and 30000 m,the wind velocity at both ends of the vertical curve is 14.06%,9.99%,6.14%,3.22%and 2.41%,higher than that in the middle.The diversion effect also decreases with the increase of the radius.(2)The conductivity of the concave and convex vertical curve embankments with different radii is greater than 1,which is the sediment transport roadbed.The conductivity increases with the increase of radius and gradually tends to be stable.When the radius of the concave and convex vertical curves reaches 8000 m and 20000 m respectively,the phenomenon of sand accumulation is no longer serious.Under the same radius condition,the concave vertical curve embankment is more prone to sand accumulation than the convex one.(3)Considering the strength of the collection and diversion of the vertical curve embankment with different radii,and the sand accumulation of the vertical curve embankment in the desert section of Wuma Expressway,the radius of the concave vertical curve is not less than 8000 m,and the radius of the convex vertical curve is not less than 20000 m,which can effectively reduce the sand accumulation of the vertical curve embankment.In the desert highway area,the research results of this paper can provide reference for the design of vertical curve to ensure the safe operation of desert highway.

Discharge evolution law of debris flow based on a sharp bend physical modeling test

For the basins with debris flow development,its channel terrain exhibits a tortuous shape,which significantly restricts the movement of debris flows and leads to severe erosion effects on the concave bank.Therefore,this study aims to analyze the shear force of debris flows within the bend channel.We established the relationship between the shear force and bend curvature through laboratory experiments.Under the long-term erosion by debris flows,the curvature radius of bends gradually increases,however,when this increasing trend reaches an equilibrium state with the intensity of debris flow discharge,there will be no significant change in curvature radius.In general,the activity pattern and discharges of debris flows would remain relatively stable.Hence,we can infer the magnitude of debris flow discharges from the terrain parameters of the bend channel.

A new method of calculating crown projection area and its comparative accuracy with conventional calculations for asymmetric tree crowns

This paper introduces a new method of calculating crown projection area(CPA),the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and integration.This novel method and other four existing methods of calculating CPA were compared using detailed crown radius measurements from 30 tall trees of Eucalyptus pilularis variable in crown size,shape,and asymmetry.The four existing methods included the polygonal approach and three ways of calculating CPA as the area of a circle using the arithmetic,geometric and quadratic mean radius.Comparisons were made across a sequence of eight non-consecutive numbers(from 2 to 16)of measured crown radii for each tree over the range of crown asymmetry of the 30 trees through generalized linear models and multiple comparisons of means.The sequence covered the range of the number of crown radii measured for calculating the CPA of a tree in the literature.A crown asymmetry index within the unit interval was calculated for each tree to serve as a normative measure.With a slight overestimation of 2.2%on average and an overall mean error size of 7.9%across the numbers of crown radii that were compared,our new method was the least biased and most accurate.Calculating CPA as a circle using the quadratic mean crown radius was the second best,which had an average overestimation of 4.5%and overall mean error size of 8.8%.These two methods remained by and large unbiased as crown asymmetry increased,while the other three methods showed larger bias of underestimation.For the conventional method of using the arithmetic mean crown radius to calculate CPA as a circle,bias correction factors were developed as a function of crown asymmetry index to delineate the increasing magnitude of bias associated with greater degrees of crown asymmetry.This study reveals and demonstrates such relationships between the accuracy of CPA calculations and crown asymmetry and will help increase awareness among researchers and practitioners on the existence of bias in their CPA calculations and for the need to use an unbiased method in the future.Our new method is recommended for calculating CPA where at least four crown radius measurements per tree are available because that is the minimum number required for its use.

Nuclear charge radius predictions by kernel ridge regression with odd-even effects

The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.

Adaptive Resource Allocation Algorithm for 5G Vehicular Cloud Communication

The current resource allocation in 5G vehicular networks for mobile cloud communication faces several challenges,such as low user utilization,unbalanced resource allocation,and extended adaptive allocation time.We propose an adaptive allocation algorithm for mobile cloud communication resources in 5G vehicular networks to address these issues.This study analyzes the components of the 5G vehicular network architecture to determine the performance of different components.It is ascertained that the communication modes in 5G vehicular networks for mobile cloud communication include in-band and out-of-band modes.Furthermore,this study analyzes the single-hop and multi-hop modes in mobile cloud communication and calculates the resource transmission rate and bandwidth in different communication modes.The study also determines the scenario of one-way and two-way vehicle lane cloud communication network connectivity,calculates the probability of vehicle network connectivity under different mobile cloud communication radii,and determines the amount of cloud communication resources required by vehicles in different lane scenarios.Based on the communication status of users in 5G vehicular networks,this study calculates the bandwidth and transmission rate of the allocated channels using Shannon’s formula.It determines the adaptive allocation of cloud communication resources,introduces an objective function to obtain the optimal solution after allocation,and completes the adaptive allocation process.The experimental results demonstrate that,with the application of the proposed method,the maximum utilization of user communication resources reaches approximately 99%.The balance coefficient curve approaches 1,and the allocation time remains under 2 s.This indicates that the proposed method has higher adaptive allocation efficiency.

Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Hemiarthroplasty for irreparable distal radius fractures in the elderly:A comprehensive review

BACKGROUND Elderly patients maintaining functional independence can now be candidates for primary wrist hemiarthroplasty to manage acute irreparable distal radius fractures(DRFs).However,further investigation with long-term follow-up is required to validate these initial findings.AIM To review the literature on the outcomes of distal radius hemiarthroplasty with available implants to assess its viability as a treatment option.METHODS A comprehensive review of the literature was conducted using electronic databases,including PubMed,Medline,and Scopus.The search terms employed were"distal radius fracture","hemiarthroplasty","wrist arthroplasty",and related terminology.The search was restricted to articles published in English from 1980 until June 2023.Inclusion criteria encompassed cases or case series of DRF treated with hemiarthroplasty,providing clinical or radiographic outcomes,and published in peer-reviewed journals.RESULTS A total of 2508 articles from PubMed and 883 from Scopus were identified initially.Following screening and removal of duplicates,13 articles met the inclusion criteria.These articles,predominantly clinical retrospective studies,provided insights into hemiarthroplasty outcomes,including functional improvements and complications.Hemiarthroplasty was a treatment option for complex DRF,particularly those cases with severe comminution,intraarticular involvement,or severe osteoporosis.Functional outcomes demonstrated improvements in pain relief,wrist mobility,and grip strength,with variability across studies.Complications included implant loosening,infection,nerve injury,and stiffness,with varying incidence rates influenced by surgical techniques and implant choice.Long-term outcomes were inadequately documented,warranting further research.CONCLUSION Hemiarthroplasty is a promising treatment for irreparable DRF in the elderly.Long-term outcomes and complications require further study.

Characterization and Application of S-Band Polarimetric Radar and X-Band Phased Array Radar for a Tornadic Storm Event on June 16,2022

The X-band phased array radar offers faster scanning speed and higher spatial resolution compared to the S-band radar,making it capable of enhancing tornado monitoring and early warning capabilities.This study analyzed the characteristics and nowcasting signals of a tornado case that occurred on June 16,2022 in the Guangzhou region.Our findings indicate that the violent contraction of rotation radius and the dramatic increase in rotation speed were important signal characteristics associated with tornado formation.The X-band phased array radar,with its high temporal and spatial resolution,provided an opportunity to capture early warning signals from polarimetric characteristics.The X-band phased array radar demonstrated noteworthy ability to identify apparent tornado vortex signature(TVS)features in a 10-minute lead time,surpassing the capabilities of the CINRAD/SA radar.Additionally,due to its higher scanning frequency,the Xband phased-array radar was capable of consistently identifying TVS with shorter intervals,enabling a more precise tracking of the tornado's path.The application of professional radars,in this case,provides valuable insights for the monitoring of evolutions of severe local storms and even tornadoes and the issuance of early warning signals.

强乘积图的最小强半径

A strong product graph is denoted by G_(1)■G_(2),where G_(1) and G_(2) are called its factor graphs.This paper gives the range of the minimum strong radius of the strong product graph.And using the relationship between the cartesian product graph G_(1)■G_(2) and the strong product graph G_(1)■G_(2),another different upper bound of the minimum strong radius of the strong product graph is given.

非正则赋权有向图A_(α)谱半径的上界

Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.

Spatial Distribution Characteristics and Coverage Rate of Commercial Facilities in 15-minute Radius Livelihood Service Circles of Chunshu Street

Building a 15-minute radius livelihood service circle from the needs of residents is a topdown process of optimizing urban layout and promoting high-quality development implemented by the government.In September 2022,Xicheng District of Beijing served as a national pilot of the 15-minute radius livelihood service circle.Based on the data of POI,urban walking network and building outline,this paper studies the coverage of commercial service facilities in the 15-minute radius livelihood service circle of Chunshu Street by using kernel density analysis and urban network analysis tools.The research shows that the commercial facilities are concentrated in Zhuangsheng Square and Dazhalan commercial district.There are large gaps in housekeeping and couriers logistics facilities,which need to be further improved.

Rare Bilateral Radius and Ulna Fractures: A Case Report

Introduction: Forearm fractures involving both the radius and ulna, present distinctive challenges in orthopedic trauma management. This case report explores the complexities of a rare case of bilateral fractures, emphasizing the importance of a comprehensive approach for optimal outcomes. Case Presentation: This report presents the case of a 40-year-old motorcyclist who was involved in a road accident and arrived at the emergency department shortly after the incident. Clinical examination revealed closed fractures in both forearms with mild swelling and severe tenderness. Fortunately, no neurovascular issues or compartment syndrome were detected. The patient was administered intravenous fluids and effective pain relief. Forearm splints were applied and the arms were elevated using pillows. Radiographs showed fractures in the right distal radius and ulna, as well as the left mid-shaft radius and ulna. Under general anesthesia, open reduction and internal fixation were per-formed using plates and screws for all four fractures. Postoperatively, the patient’s arms were immobilized and elevated, with gradual recovery during follow-up appointments over six months, eventually achieving full function without complaints. Conclusion: This article highlights the possibility, although infrequent, of bilateral shaft fractures of the ulna and radius. With thorough clinical assessment and radiological investigation, such fractures can be well-defined. The required definitive treatment, which usually involves open reduction and internal fixation, can be performed.

Anisotropy of Trabecular Bone from Ultra-Distal Radius Digital X-Ray Imaging: Effects on Bone Mineral Density and Age

Background: When applied to trabecular bone X-ray images, the anisotropic properties of trabeculae located at ultra-distal radius were investigated by using the trabecular bone scores (TBS) calculated along directions parallel and perpendicular to the forearm. Methodology: Data from more than two hundred subjects were studied retrospectively. A DXA (GE Lunar Prodigy) scan of the forearm was performed on each subject to measure the bone mineral density (BMD) value at the location of ultra-distal radius, and an X-ray digital image of the same forearm was taken on the same day. The values of trabecular bone score along the direction perpendicular to the forearm, TBSx, and along the direction parallel to the forearm, TBSy, were calculated respectively. The statistics of TBSx and TBSy were calculated, and the anisotropy of the trabecular bone, which was defined as the ratio of TBSy to TBSx and changed with subjects’ BMD and age, was reported and analyzed. Results: The results show that the correlation coefficient between TBSx and TBSy was 0.72 (p BMD and age was reported. The results showed that decreased trabecular bone anisotropy was associated with deceased BMD and increased age in the subject group. Conclusions: This study shows that decreased trabecular bone anisotropy was associated with decreased BMD and increased age.

Gravitation, Density Upper Limit and Quantization of Space

The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity.