Analyzing the Form-Finding of a Large-Span Transversely Stiffened Suspended Cable System: A Method Considering Construction Processes

The precise control of the shape of transversely stiffened suspended cable systems is crucial. However, existing form-finding methods primarily rely on iterative calculations that treat loads as fixed known conditions. These methods are inefficient and fail to accurately control shape results. In this study, we propose a form-finding method that analyzes the load response of models under different sag and stress levels, taking into account the construction process. To analyze the system, a structural finite element model was established in ANSYS, and geometric nonlinear analysis was conducted using the Newton-Raphson method. The form-finding analysis results demonstrate that the proposed method achieves precise control of shape, with a maximum shape error ranging from 0.33% to 0.98%. Furthermore, the relationships between loads and tension forces are influenced by the deformed shape of the structures, exhibiting significant geometric nonlinear characteristics. Meanwhile, the load response analysis reveals that the stress level of the self-equilibrium state in the transversely stiffened suspended cable system is primarily governed by strength criteria, while shape is predominantly controlled by stiffness criteria. Importantly, by simulating the initial tensioning process as an initial condition, this method solves for a counterweight that satisfies the requirements and achieves a self-equilibrium state with the desired shape. The shape of the self-equilibrium state is precisely controlled by simulating the construction process. Overall, this work presents a new method for analyzing the form-finding process of large-span transversely stiffened suspended cable system, considering the construction process which was often overlooked in previous studies.

Morphological disruption and visual tuning alterations in the primary visual cortex in glaucoma(DBA/2J)mice

Glaucoma is a leading cause of irreve rsible blindness wo rldwide,and previous studies have shown that,in addition to affecting the eyes,it also causes abnormalities in the brain.However,it is not yet clear how the primary visual cortex(V1)is altered in glaucoma.This study used DBA/2J mice as a model for spontaneous secondary glaucoma.The aim of the study was to compare the electrophysiological and histomorphological chara cteristics of neurons in the V1between 9-month-old DBA/2J mice and age-matched C57BL/6J mice.We conducted single-unit recordings in the V1 of light-anesthetized mice to measure the visually induced responses,including single-unit spiking and gamma band oscillations.The morphology of layerⅡ/Ⅲneurons was determined by neuronal nuclear antigen staining and Nissl staining of brain tissue sections.Eighty-seven neurons from eight DBA/2J mice and eighty-one neurons from eight C57BL/6J mice were examined.Compared with the C57BL/6J group,V1 neurons in the DBA/2J group exhibited weaker visual tuning and impaired spatial summation.Moreove r,fewer neuro ns were observed in the V1 of DBA/2J mice compared with C57BL/6J mice.These findings suggest that DBA/2J mice have fewer neurons in the VI compared with C57BL/6J mice,and that these neurons have impaired visual tuning.Our findings provide a better understanding of the pathological changes that occur in V1 neuron function and morphology in the DBA/2J mouse model.This study might offer some innovative perspectives regarding the treatment of glaucoma.

Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

Exercise-induced adaptation of neurons in the vertebrate locomotor system

Vertebrate neurons are highly dynamic cells that undergo several alterations in their functioning and physiologies in adaptation to various external stimuli.In particular,how these neurons respond to physical exercise has long been an area of active research.Studies of the vertebrate locomotor system’s adaptability suggest multiple mechanisms are involved in the regulation of neuronal activity and properties during exercise.In this brief review,we highlight recent results and insights from the field with a focus on the following mechanisms:(a)alterations in neuronal excitability during acute exercise;(b)alterations in neuronal excitability after chronic exercise;(c)exercise-induced changes in neuronal membrane properties via modulation of ion channel activity;(d)exercise-enhanced dendritic plasticity;and(e)exercise-induced alterations in neuronal gene expression and protein synthesis.Our hope is to update the community with a cellular and molecular understanding of the recent mechanisms underlying the adaptability of the vertebrate locomotor system in response to both acute and chronic physical exercise.

Wideband low-scattering metasurface with an in-band reconfigurable transparent window

Active metasurfaces with dynamically reconfigurable functionalities are highly demanded in various practical applications.Here,we propose a wideband low-scattering metasurface that can realize an in-band reconfigurable transparent window by altering the operation states of the PIN diodes loaded on the structures.The metasurface is composed of a band-pass frequency selective surface(FSS)sandwiched between two polarization conversion metasurfaces(PCMs).PIN diodes are integrated into the FSS to switch the transparent window,while a checkerboard configuration is applied in PCMs for the diffusive-reflective function.A sample with 20×20 elements is designed,fabricated,and experimentally verified.Both simulated and measured results show that the in-band functions can be dynamically switched between beam-splitting scattering and high transmission by controlling the biasing states of the diodes,while low backscattering can be attained outside the passband.Furthermore,the resonant structures of FSS also play the role of feeding lines,thus significantly eliminating extra interference compared with conventional feeding networks.We envision that the proposed metasurface may provide new possibilities for the development of an intelligent stealth platform and its antenna applications.

Community Structures of Phytoplankton with Emphasis on Toxic Cyanobacteria in an Ohio Inland Lake during Bloom Season

The community structures of phytoplankton are important factors and indicators of lake water quality. Harmful algal blooms severely impact water supply, recreational activities and wildlife habitat. This study aimed to examine the phytoplankton composition and variations using microscopy, and identify harmful Cyanobacteria in weekly samples taken from four sites at Harsha Lake in southwest Ohio. Over the course of the summer in 2015, the phytoplankton of Harsha Lake consisted mainly of 13 taxa belonging to Bacillariophyta, Chlorophyta, Cryptophyta, Cyanobacteria, Dinophyta and Euglenophyta. Their significant successions started with Bacillariophyta and/or Chlorophyta, then bloomed with Cyanobacteria and ended with Chlorophyta and/or Dinophyta. Cyanobacteria members: Microcystis, Planktothrix, Dolichospermum, Aphanizomenon, Cylindrospermopsis, and Oscillatoria from the Cyanophyceae were identified to be dominant genera. These organisms varied spatially and temporally in similar patterns along with the variations of nutrients and formed the summer bloom with the total biomasses ranging from 0.01 to 114.89 mg L-1 with mean of 22.88 mg L-1. M. aeruginosa and P. rubescens were revealed as the microcystin producers, while A. circinalis and Aphanizomenon sp. were identified as a saxitoxin producer through cloning and sequencing PCR products of mcyA, mcyE and sxtA genes. The biomasses of phytoplankton, Cyanobacteria and Microcystis were positively correlated to nutrients, especially to total nitrogen. The total ELISA measurement for microcystin positively correlated with Cyanobacteria (R2 = 0.66, P Microcystis (R2 = 0.64, P 2 = 0.59, P < 0.0001). The basic information on the occurrence and biomasses of Cyanobacteria and total phytoplankton, and the analysis for toxic species, which were the first report for the inland water in Ohio, USA, will document the succession patterns of phytoplankton and toxin production over a season and provide data to predict risk occurrence to both human and ecological factors.

Efficient polysulfide blocker from conductive niobium nitride@graphene for Li-S batteries

Lithium sulfur batteries are one of the most promising alternative electrochemical systems,but their practical applications are largely hindered by the serious shuttling problems and sluggish redox kinetics.Here,the conductive and polar niobium nitride(NbN)is in-situ introduced onto graphene with ultrasmall size and high dispersion,and their composite is used to construct an efficient lithium polysulfide blocking layer.The graphene helps to construct highly conductive pathways,and niobium nitride serves as the sulfiphilic sites to chemically adsorb the migrating lithium polysulfides and catalyze their redox conversion.Hence,the cells with the Nb N/G interlayers exhibit a long cycle life with a lower capacity decay of 0.096%/cycle at 1 C for 300 cycles and high rate capability of 937 m Ah g^-1 at 2 C.Further coupling with a sulfur/carbon nanofiber electrode,the cell with an ultra-high sulfur loading of 10.8 mg cm^-2 delivers an areal capacity of 12.5 m Ah cm^-2 at 0.1 C.

A Two-Party Password-Authenticated Key Exchange Protocol with Verifier

To tackle with the security lack in the password-authenticated key exchange protocol, this paper proposes a two-party password-authenticated key exchange protocol based on a verifier. In the proposed protocol, a user stores his password in plaintext, and the server stores a verifier for the user’s password, using DL difficult problem and DH difficult problem, through the session between user and server to establish a session key. The security discussion result shows that the proposed protocol provides forward secrecy, and can effectively defend against server compromising fake attacks, dictionary attacks and middleman attacks. Protocol efficiency comparisons reveal our protocol is more reasonable.

Targeted mechanical forces enhance the effects of tumor immunotherapy by regulating immune cells in the tumor microenvironment

Mechanical forces in the tumor microenvironment(TME)are associated with tumor growth,proliferation,and drug resistance.Strong mechanical forces in tumors alter the metabolism and behavior of cancer cells,thus promoting tumor progression and metastasis.Mechanical signals are transformed into biochemical signals,which activate tumorigenic signaling pathways through mechanical transduction.Cancer immunotherapy has recently made exciting progress,ushering in a new era of“chemo-free”treatments.However,immunotherapy has not achieved satisfactory results in a variety of tumors,because of the complex tumor microenvironment.Herein,we discuss the effects of mechanical forces on the tumor immune microenvironment and highlight emerging therapeutic strategies for targeting mechanical forces in immunotherapy.

国外需求促进了中国出口企业创新吗?

本文运用详细的海关数据构建了中国出口企业面临的国外需求指标,并进一步按目的国类型与贸易方式细分,研究了国外需求与中国出口企业创新之间的关系。结果表明:总体上,来自发达国家的需求显著抑制了中国出口企业的创新。异质性分析表明,国外需求与出口企业创新的关系在不同要素密集度以及不同所有制企业中表现各有不同。在发达国家的需求中,加工贸易是抑制中国出口企业创新的重要原因。在一般贸易方式下,来自发达国家与发展中国家的“需求引致创新”效应依然有效,体现为,发达国家的需求对中国出口企业创新的影响偏向于过程创新,而发展中国家的需求对中国出口企业创新的影响偏向于产品创新。本文为中国当前的双循环发展战略调整提供了有价值的参考依据。

陕西省小蚕人工饲料共育技术现状、问题与对策

总结陕西省近年来人工饲料小蚕共育的推广现状及成功经验,分析了蚕农人工饲料养蚕认识不到位、小蚕共育温湿度控制不标准、人工饲料适应性蚕品种少、发生小蚕等问题及其原因,提出了加快品种选育、建立饲料配送中心、加强技术培训、给以资金扶持等对策和建议。

Influence of Cavitation on Unsteady Vortical Flows in a Side Channel Pump

Previous investigation on side channel pump mainly concentrates on parameter optimization and internal unsteady vortical flows.However,cavitation is prone to occur in a side channel pump,which is a challenging issue in promoting performance.In the present study,the cavitating flow is investigated numerically by the turbulence model of SAS combined with the Zwart cavitation model.The vapors inside the side channel pump firstly occur in the impeller passage near the inlet and then spread gradually to the downstream passages with the decrease of NPSHa.Moreover,a strong adverse pressure gradient is presented at the end of the cavity closure region,which leads to cavity shedding from the wall.The small scaled vortices in each passage reduce significantly and gather into larger vortices due to the cavitation.Comparing the three terms of vorticity transport equation with the vapor volume fraction and vorticity distributions,it is found that the stretching term is dominant and responsible for the vorticity production and evolution in cavitating flows.In addition,the magnitudes of the stretching term decrease once the cavitation occurs,while the values of dilatation are high in the cavity region and increase with the decreasing NPSHa.Even though the magnitude of the baroclinic torque term is smaller than vortex stretching and dilatation terms,it is important for the vorticity production along the cavity surface and near the cavity closure region.The pressure fluctuations in the impeller and side channel tend to be stronger due to the cavitation.The primary frequency of monitor points in the impeller is 24.94 Hz and in the side channel is 598.05 Hz.They are quite corresponding to the shaft frequency of 25 Hz(fshaft=1/n=25 Hz)and the blade frequency of 600 Hz(fblade=Z/n=600 Hz)respectively.This study complements the investigation on cavitation in the side channel pump,which could provide the theoretical foundation for further optimization of performance.

Extracting angle-domain common-image gathers in VTI media using ansiotropic-Helmholtz P/S wave-mode decomposition

Common-image gathers are extensively used in amplitude versus angle(AVA)and migration velocity analysis(MVA).The current state of methods for anisotropic angle gathers extraction use slant-stack,local Fourier transform or low-rank approximation,which requires much computation.Based on an anisotropic-Helmholtz P/S wave-mode decomposition method,we propose a novel and efficient approach to produce angle-domain common-image gathers(ADCIGs)in the elastic reverse time migration(ERTM)of VTI media.To start with,we derive an anisotropic-Helmholtz decomposition operator from the Christoffel equation in VTI media,and use this operator to derive the decomposed formulations for anisotropic P/S waves.Second,we employ the first-order Taylor expansion to calculate the normalized term of decomposed formulations and obtain the anisotropic-Helmholtz decomposition method,which generates the separated P/S wavefields with correct amplitudes and phases.Third,we develop a novel way that uses the anisotropic-Helmholtz decomposition operator to define the polari-zation angles for anisotropic P/S waves and substitute these angles to decomposing formulations.The polarization angles are then calculated directly from the separated vector P-and S-wavefields and converted to the phase angles.The ADCIGs are thusly produced by applying the phase angles to VTI ERTM.In addition,we develop a concise approximate expression of residual moveout(RMO)for PP-reflections of flat reflectors in VTI media,which avoids the complex transformations between the group angles and the phase angles.The approximate RMO curves show a good agreement with the exact solution and can be used as a tool to assess the migration velocity errors.As demonstrated by two selected examples,our ADCIGs not only produce the correct kinematic responses with regards to different velocity pertubatation,but also generate the reliable amplitude responses versus different angle.The final stacking images of ADCIGs data exhibit the identical imaging effect as that of VTI ERTM.

Advanced biosensing technologies for monitoring of agriculture pests and diseases:A review

The threat posed to crop production by pests and diseases is one of the key factors that could reduce global food security.Early detection is of critical importance to make accurate predictions,optimize control strategies and prevent crop losses.Recent technological advancements highlight the opportunity to revolutionize monitoring of pests and diseases.Biosensing methodologies offer potential solutions for real-time and automated monitoring,which allow advancements in early and accurate detection and thus support sustainable crop protection.Herein,advanced biosensing technologies for pests and diseases monitoring,including image-based technologies,electronic noses,and wearable sensing methods are presented.Besides,challenges and future perspectives for widespread adoption of these technologies are discussed.Moreover,we believe it is necessary to integrate technologies through interdisciplinary cooperation for further exploration,which may provide unlimited possibilities for innovations and applications of agriculture monitoring.

Correlation analysis of longitudinal cracks and vertical deformation within asphalt pavement of cold regions

The asphalt pavement longitudinal crack is a common distress in cold regions,resulting from uneven deformation of the subgrade.Analysis of the correlation law between uneven deformation and crack distress is of positive significance for understanding the mechanism of crack initiation,and putting forward treatment measures.In view of the complexity of longitudinal crack inducement and road surface deformation,the grey relational method was used to analyze this relationship.Through long-term monitoring of the vertical deformation data of typical road sections,the vertical deformation law of the pavement surface and its deformation characteristics under the action of temperature field are analyzed.Parameters such as vertical relative deformation,vertical relative deformation rate and vertical differential deformation VDSr were constructed to describe vertical deformation characteristics.Typical distribution characteristics of longitudinal fractures and their length and distribution characteristics are also described.The grey correlation analysis theory was utilized to analyze the relationship between deformation characteristics of sections,cross sections and monitoring points and longitudinal crack characteristics(length and location).The analysis reveals a linear positive correlation or a high correlation between several indicators.This study can provide a deeper understanding of the occurrence and development mechanism of longitudinal cracks in asphalt pavement of cold areas,and give references for the research of road engineering structure,materials and distress prevention.

Efficacy of tibial transverse transport combined with platelet-rich plasma versus platelet-rich plasma alone in the treatment of diabetic foot ulcers:A meta-analysis

Background:Diabetic foot ulcers(DBFU)are one of the main complications of diabetes.Platelet-rich plasma(PRP)treatment is a commonly used treatment option.Tibial transverse transport(TTT)also has a therapeutic effect on DBFU.Some studies have found that the TTT combined with PRP(TTT&PRP)has a significant effect on DBFU.Methods:PubMed,Cochrane Library,Web of Science,EMBASE,Chinese Biomedical Literature,CNKI,VIP,and Wanfang databases were used to find literature on the treatment of DBFUs using the TTT and PRP treatment according to the inclusion criteria.The specific inclusion criteria are as follows:(1)research type:clinical controlled trials,including retrospective cohort and randomized controlled studies;(2)diagnosis of DBFUs that does not include a definitively diagnosed traumatic ulcer;(3)original materials of Chinese and English literature published in full text.The exclusion criteria are:(1)the research group was not defined or grouped;(2)nonrandomized controlled trials,non-cohort studies,non-case-control studies,retrospective studies,and case reports;(3)repetitive research and animal experimentation;(4)ulcers caused by other diseases;(5)conservative treatment or no use of invasive treatment methods.Review Manager software(version 5.3)was used to conduct a meta-analysis of the included results.Result:The literature included 6 randomized controlled studies,including 508 patients,254 patients in the PRP treatment group,and 254 patients in the TTT&PRP group.The meta-analysis results showed that in terms of treatment efficacy,the TTT&PRP combined treatment group had a higher efficacy than the PRP group.After treatment,the TTT&PRP group had better treatment effects in psychological function,physiological function,and social function compared to the PRP group.After treatment,the TTT&PRP group showed a significant increase in serum epidermal growth factor(EGF),vascular endothelial growth factor(VEGF),basic fibroblast growth factor(bFGF),and platelet-derived growth factor(PDGF)levels compared to the PRP group.In terms of wound healing after treatment,the TTT&PRP group performed better than the PRP group in terms of postoperative wound reduction rate,bacterial clearance rate,granulation tissue coverage rate,and granulation tissue growth thickness.Conclusion:TTT combined with PRP was more effective than PRP alone in treating DBFUs.

Changing trends in gastric and colorectal cancer among surgical patients over 85 years old:A multicenter retrospective study,2001–2021

BACKGROUND Whether patients over 85 years old with gastrointestinal cancer should undergo surgery remains controversial.We aimed to describe the changing trends of characteristics to provide more information to decision makers,and strive to find appropriate surgical plan.AIM To describe the changing trends of characteristics to provide more information to decision makers,and strive to find appropriate surgical plan.METHODS A total of 218 gastric cancer(GC)patients and 563 colorectal cancer(CRC)patients who underwent surgery between 2001 and 2021 were enrolled in this retrospective analysis.Changes in clinicopathological features,surgical treatments,and survival status were analyzed longitudinally at 5-year intervals.RESULTS Only 14 GC patients underwent laparoscopic surgery where 219 CRC patients had this procedure.Cardia and esophagogastric junction cancer increased in GC patients,and the proportion of sigmoid colon cancer decreased in CRC patients.Pulmonary infection gradually became the most common postoperative complication,its incidence in period 4 reached 48.79%.However,the incidence of anastomotic leakage decreased from 26.79%to 9.38%(P<0.01).Additionally,30-d mortality significantly decreased from 32.14%to 9.01%.Increases were observed in 5-year overall survival(OS)in GC patients from period 1 to period 4(18.18%vs 33.32%,respectively)and CRC patients(0 vs 36.32%,respectively).Disease-free survival(DFS)also increased in GC and CRC patients(7.14%vs 27.74%and 0 to 36.03%,respectively).The average survival time of GC patients following radial lymphadenectomy was higher than in patients that underwent limited lymphadenectomy(26 vs 22 mo,respectively),the same was seen in CRC patients(44 vs 33 mo,respectively).This advantage was particularly evident in patients with TNM I,but not in patients with TNM II/III period cancer.CONCLUSION The safety as well as effectiveness of surgery in ultra-elderly patients is increasing.Radical lymphadenectomy has advantages in patients with TNM I gastrointestinal cancer,but not TNM II/III.

安康地区杂交桑引进栽培技术及产品开发示范效果

通过试验示范和推广杂交桑栽培,结合生产实践和安康具体气候特点,总结了杂交桑建园、栽植、管理、收获等技术要点。宽窄行密株栽植,667 m 2栽3000~4000株,无干树型养成,每年剪伐4次,主施有机肥,以芽、叶、枝条为主要采收形式。开展蛋白桑饲料研发、富硒桑叶配合饲料养猪、粉体饲料养鸡和青贮饲料养羊试验,其效果明显;通过对产品理化指标检测及生理性能分析,研究桑叶饲料的功能作用,为富硒桑饲料产业化开发和推广应用提供科学依据。

The Mechanism of Cornus officinalis Total Glycosides and Cornus Polysaccharide on Myocardial Protection in Rats with Acute Myocardial Infarction

Objective: To investigate effects of Cornus officinalis Total Glycosides (COTG) and Cornus Polysaccharide (CP) on myocardial protection and on expression of mitochondria biogenesis related gene of acute myocardial infarction (AMI) rats, Materials and Methods: Ninety-six SD rats of SPF level were randomly divided into 5 groups: sham operation group, model group, preventive treatment group, COTG treatment group, CP treatment group, and there were 12 cases in each one. By legating the left anterior descending branch of coronary artery method, acute myocardial infarction model was established. The rat of sham operation group and model group was intragastric administered with physiological saline;other groups were given with corresponding drugs. The cardiac function, the myocardial infarct area, the expression of mitochondrial biogenesis genes such as PGC-1α, PGC-1β, NRF-1mRNA and GSK-3β mRNA, GSK-3β Protein Expression were analyzed. Results: The results revealed that compared with model group, myocardial infarction size, LVDs, LVDd, LVESV, LVEDP, and -dp/dt decreased;LVSP increased in preventive treatment group, COTG treatment group, and CP treatment group (p < 0.05);LVEDV increased in preventive treatment group (p < 0.05), PGC 1 alpha, and PGC 1 beta;the NRF-1 mRNA expression increased in preventive treatment group, COTG treatment group, and CP treatment group (p < 0.05). Compared with CP and COTG treatment group, PGClpha, beta PGC 1, the NRF-1 mRNA expression increased in preventive treatment group (p < 0.05). Compared with the sham operation group, GSK-3 beta mRNA and protein expression increased in model group, preventive treatment group, COTG treatment group, and CP treatment group (p < 0.05). Compared with model group, GSK-3 beta mRNA expression reduced in preventive treatment group, COTG treatment group, and CP treatment group (p Cornus officinalis total glycosides and Cornus polysaccharides can effectively protect myocardial mitochondria of acute myocardial infarction rats by activating GSK-3β signaling pathways, and reduce the myocardial infarct size, which has great significance for improving cardiac function.

基于试验函数的霍普夫分岔搜索新算法与电压稳定指标分析

本文首先回顾了现有的一般分岔理论领域中搜索霍普夫分岔的主要方法及其局限性,而后试图将成熟的折叠分岔点的搜索办法和指标体系推广到霍普夫分岔的情形,文章基于矩阵张量积和交换积的概念,提出了霍普夫分岔试验函数及其对应的霍普夫分岔指标和算法,文中提出的霍普夫试验函数不但具有普适性,而且基于指标的试验函数给出了当前运行点到霍普夫分岔点的距离,最后通过一个典型的动态测试系统分析,得出了很多有创新价值的结论。