Insight into small eyes: a practical description from phenotypes presentations to the management

This narrative review aimed to have an algorithmic approach to microphthalmos by a systematic search.The definition can be related to a number of special phenotypes.In the more challenging cases of complex microphthalmos,relative anterior microphthalmos,and nanophthalmos,the surgeon can approach these cases more safely if they have a deep understanding of the anatomical variations and ideal formulae for intraocular lens computation and knows how to avoid intra-and post-operative complications.In this article,we review the criteria by which we recognize and describe pre-,intra-,and post-operative considerations,as well as discuss the ideal intraocular lenses for microphthalmos,given the intricate varieties of small eye phenotypes.

Evaluation of the seismic behavior of reinforced concrete structures with flat slab-column gravity frame and shear walls through nonlinear analysis methods

This paper presents an investigation of the seismic behavior of reinforced concrete(RC)structures in which shear walls are the main lateral load-resisting elements and the participation of flat slab floor systems is not considered in the seismic design procedure.In this regard,the behavior of six prototype structures(with different heights and plan layouts)is investigated through nonlinear static and time history analyses,implemented in the OpenSees platform.The results of the analyses are presented in terms of the behavior of the slab-column connections and their mode of failure at different loading stages.Moreover,the global response of the buildings is discussed in terms of some parameters,such as lateral overstrength due to the gravity flat slab-column frames.According to the nonlinear static analyses,in structures in which the slab-column connections were designed only for gravity loads,the slab-column connections exhibited a punching mode of failure even in the early stages of loading.However,the punching failure was eliminated in structures in which a minimum transverse reinforcement recommended in ACI 318(2019)was provided in the slabs at joint regions.Furthermore,despite neglecting the contribution of gravity flat slab-column frames in the lateral load resistance of the structures,a relatively significant overstrength was imposed on the structures by the gravity frames.

Cascaded ELM-Based Joint Frame Synchronization and Channel Estimation over Rician Fading Channel with Hardware Imperfections

Due to the interdependency of frame synchronization(FS)and channel estimation(CE),joint FS and CE(JFSCE)schemes are proposed to enhance their functionalities and therefore boost the overall performance of wireless communication systems.Although traditional JFSCE schemes alleviate the influence between FS and CE,they show deficiencies in dealing with hardware imperfection(HI)and deterministic line-of-sight(LOS)path.To tackle this challenge,we proposed a cascaded ELM-based JFSCE to alleviate the influence of HI in the scenario of the Rician fading channel.Specifically,the conventional JFSCE method is first employed to extract the initial features,and thus forms the non-Neural Network(NN)solutions for FS and CE,respectively.Then,the ELMbased networks,named FS-NET and CE-NET,are cascaded to capture the NN solutions of FS and CE.Simulation and analysis results show that,compared with the conventional JFSCE methods,the proposed cascaded ELM-based JFSCE significantly reduces the error probability of FS and the normalized mean square error(NMSE)of CE,even against the impacts of parameter variations.

Dynamic interactive bitwise meta-holography with ultra-high computational and display frame rates

Interactive holography offers unmatched levels of immersion and user engagement in the field of future display.Despite of the substantial progress has been made in dynamic meta-holography,the realization of real-time,highly smooth interactive holography remains a significant challenge due to the computational and display frame rate limitations.In this study,we introduced a dynamic interactive bitwise meta-holography with ultra-high computational and display frame rates.To our knowledge,this is the first reported practical dynamic interactive metasurface holographic system.We spa-tially divided the metasurface device into multiple distinct channels,each projecting a reconstructed sub-pattern.The switching states of these channels were mapped to bitwise operations on a set of bit values,which avoids complex holo-gram computations,enabling an ultra-high computational frame rate.Our approach achieves a computational frame rate of 800 kHz and a display frame rate of 23 kHz on a low-power Raspberry Pi computational platform.According to this methodology,we demonstrated an interactive dynamic holographic Tetris game system that allows interactive gameplay,color display,and on-the-fly hologram creation.Our technology presents an inspiration for advanced dynamic meta-holography,which is promising for a broad range of applications including advanced human-computer interaction,real-time 3D visualization,and next-generation virtual and augmented reality systems.

Effectiveness of intravitreal ranibizumab for diabetic macular edema in vitrectomized versus non-vitrectomized eyes:a Meta-analysis

AIM:To evaluate the effectiveness and safety of intravitreal ranibizumab(IVR)for diabetic macular edema(DME)in vitrectomized versus non-vitrectomized eyes.METHODS:The PubMed,EMBASE,Web of Science,Cochrane,EBSCO were comprehensively searched for studies comparing vitrectomized and non-vitrectomized eyes with DME.Clinical outcomes of best-corrected visual acuity(BCVA),central macular thickness(CMT),the mean number of intravitreal injection and adverse events were extracted and analyzed.RESULTS:Six studies involving 641 eyes were included.Final visual gain significantly improved and CMT significantly reduced in vitrectomized eyes at 6mo and 12mo visits(P<0.05).Although the mean reduction in CMT among non-vitrectomized eyes was significantly greater than in vitrectomized eyes at the 6mo[mean difference(MD)=53.57,95%confidence interval(CI):28.03 to 78.72,P<0.0001]and 12mo(MD=49.65,95%CI:19.58 to 79.72,P=0.01),no significant difference was detected in improvement in BCVA at either 6mo(MD=0.05,95%CI:-0.02 to 0.13,P=0.14)or 12mo(MD=0.03,95%CI:-0.04 to 0.09,P=0.43).Injection number of ranibizumab in non-vitrectomized eyes was significantly less than that in vitrectomized eyes during 6-month period(MD=0.60,95%CI:0.16 to 1.04,P=0.008),while there was no statistically significant difference between the two groups during 12mo of follow-up.CONCLUSION:Evidence from current study suggests that IVR was useful for both vitrectomized group and nonvitrectomized group with DME.Although less reduction in macular thickness is found in vitrectomized group,visual improvement between two groups is similar.

Dry eye disease in systemic lupus erythematosus: a cross sectional study

AIM:To explore ocular surface manifestations of dry eye disease(DED)and its influencing factors in systemic lupus erythematosus(SLE)patients.METHODS:Ophthalmological examinations were conducted in SLE patients(n=43)and controls(n=41),including Ocular Surface Disease Index(OSDI),objective scatter index(OSI),tear meniscus height(TMH),lipid layer thickness(LLT),non-invasive Keratograph tear breakup time(NIKBUT),corneal fluorescein score(CFS),Schirmer I test.DED was diagnosed according to the Tear Film and Ocular Surface Society Dry Eye Workshop II Criteria.SLE patients were further divided into DED group and non-DED group,the disease activity,clinical manifestations and laboratory investigations were compared between the two groups.The disease activity was evaluated by Systemic Lupus Erythematosus Disease Activity Index 2000(SLEDAI-2K).Receiver operative characteristic(ROC)curve and multiplefactor binary logistic regression were performed.RESULTS:SLE patients showed higher OSDI[9.1(2.8-15.9)vs 6.3(2.2-7.5),P=0.035],higher OSI[1.67(1.09-2.60)vs 0.96(0.87-1.60),P=0.001],higher CFS[1(0-2)vs 0(0-1),P=0.001],lower LLT[65(42-100)vs 100(79.5-100),P=0.010],and lower NIKBUT[8.03(4.02-9.73)vs 9.67(5.26-12.71),P=0.030]than controls.The 32.6%of SLE patients had DED,which was higher than 12.2%of healthy controls.DED group showed higher SLEDAI-2K score[9.7±6.1 vs 5.4±3.4,P=0.025],higher anti-cardiolipin antibody(ACL)[8.7(3.5-13.2)vs 3.6(2.0-6.9),P=0.035],and higher proportion of patients with cutaneous eruption[42.9%vs 6.9%,P=0.015]than non-DED group.According to multiple-factor binary logistic regression analysis,the SLEDAI-2K score(OR=1.194,P=0.041)and cutaneous eruption(OR=7.094,P=0.045)could be consider as risk factors for DED in SLE patients.The ROC curve of the combined factors including age,disease duration,SLEDAI-2K score,ACL,and cutaneous eruption was analyzed,with a sensitivity of 0.786,a specificity of 0.793,and an area under curve of 0.820.CONCLUSION:Ocular surface affection is frequent in SLE patients,and patients with high disease activity and cutaneous eruption show increased risk of DED.

Resilience-incorporated seismic risk assessment of precast concrete frames with“dry”connections

A resilience-incorporated risk assessment framework is proposed and demonstrated in this study to manifest the advantageous seismic resilience of precast concrete frame(PCF)structures with“dry”connections in terms of their low damage and rapid recovery.The framework integrates various uncertainties in the seismic hazard,fragility,capacity,demand,loss functions,and post-earthquake recovery.In this study,the PCF structures are distinguished from ordinary reinforced concrete frame(RCF)structures by characterizing multiple limit states for the PCF based on its unique damage mechanisms.Accordingly,probabilistic story-wise pushover analyses are performed to yield story-wise capacities for the predefined limit states.In the seismic resilience analysis,a step-wise recovery model is proposed to idealize the functionality recovery process,with separate considerations of the repair and non-repair events.The recovery model leverages the economic loss and downtime to delineate the stochastic post-earthquake recovery curves for the resilience loss estimation.As such,contingencies in the probabilistic post-earthquake repairs are incorporated and the empirical judgments on the recovery parameters are largely circumvented.The proposed framework is demonstrated through a comparative study between two“dry”connected PCFs and one RCF designed as alternative structural systems for a prototype building.The results from the risk quantification indicate that the PCFs show reduced loss hazards and lower expected losses relative to the RCF.Particularly,the PCF equipped with energy dissipation devices at the“dry”connections largely reduces the expected economic loss,downtime,and resilience loss by 29%,56%,and 60%,respectively,compared to the RCF.

Experimental and numerical study regarding H-steel all-bolted connection steel frame with composite wall boards

H-steel all-bolted connection steel frame structures with heat preservation and decoration composite wall boards were investigated and the seismic performances of three scaled specimens were studied.The failure modes,hysteresis curves,bearing capacity,ductility,energy dissipation capacity,stiffness degradation and strain distribution were discussed.The calculation method of structural theoretical internal force was presented.The results showed that the overall structural seismic performance was better,and the structural ductility met the demands of elastic-plastic inter-story drift angle for seismic design.The H-steel weak-axis connection structure obtained better energy dissipation capacity,and its bearing capacity and stiffness were slightly different from the strong-axis connection.The heat preservation and decoration performance of composite wallboard and the all-bolted connection of the steel frame realized prefabrication during the whole construction period.The plastic hinge of the steel beam can be moved outwards because of the L-angles,which effectively avoids stress concentration in joint areas and expands the plastic hinge range.The errors between the theoretical structural capacity calculated by the plastic analysis method and the test results were within 2.44%.In addition,structural failure mechanisms and bearing capacities were verified by the finite element(FE)analysis,and the effects of the main parameters on the structures were investigated.The FE verification results were the same as in the test.The research results provide theoretical support and technical guidance for the application of thermal insulation and decorative composite wall panels in H-shaped steel all-bolted steel frames.

Dual‑Atom Nanozyme Eye Drops Attenuate Inflammation and Break the Vicious Cycle in Dry Eye Disease

Dry eye disease(DED)is a major ocular pathology worldwide,causing serious ocular discomfort and even visual impairment.The incidence of DED is gradually increasing with the highfrequency use of electronic products.Although inflammation is core cause of the DED vicious cycle,reactive oxygen species(ROS)play a pivotal role in the vicious cycle by regulating inflammation from upstream.Therefore,current therapies merely targeting inflammation show the failure of DED treatment.Here,a novel dual-atom nanozymes(DAN)-based eye drops are developed.The antioxidative DAN is successfully prepared by embedding Fe and Mn bimetallic single-atoms in N-doped carbon material and modifying it with a hydrophilic polymer.The in vitro and in vivo results demonstrate the DAN is endowed with superior biological activity in scavenging excessive ROS,inhibiting NLRP3 inflammasome activation,decreasing proinflammatory cytokines expression,and suppressing cell apoptosis.Consequently,the DAN effectively alleviate ocular inflammation,promote corneal epithelial repair,recover goblet cell density and tear secretion,thus breaking the DED vicious cycle.Our findings open an avenue to make the DAN as an intervention form to DED and ROSmediated inflammatory diseases.

Intraocular pressure before and after capsulorhexis using two viscoelastic substances and two surgical approaches in enucleated porcine eyes

AIM:To investigate the influence of ophthalmic viscoelastic devices(OVDs)and different surgical approaches on the intraocular pressure(IOP)before and after creation of the curvilinear circular capsulorhexis(CCC)as a measure for anterior chamber stability during this maneuver.METHODS:Prospective experimental WetLab study carried out on enucleated porcine eyes.IOP was measured before and after CCC with the iCare Rebound tonometer(iCare ic200;iCare Finland Oy,Vantaa,Finland).The OVDs used were a cohesive one[Z-Hyalin,Carl Zeiss Meditec AG,Germany;hyaluronic acid(HA)]and a dispersive[Z-Celcoat,Carl Zeiss Meditec AG,Germany;hydroxy propylmethylcellulosis(HPMC)].The CCC was created using Utrata forceps or 23 g microforceps in different combinations with the OVDs.RESULTS:Using the Utrata forceps the IOP dropped from 63.65±6.44 to 11.25±3.63 mm Hg during the CCC.The use of different OVDs made no difference.Using the 23 g microforceps the IOP dropped from 65.35±8.15 to 36.55±6.09 mm Hg.The difference between IOP drop using either Utrata forceps or 23 g microforceps was highly significant regardless of the OVD used.CONCLUSION:Using the sideport for the creation of the capsulorhexis leads to a lesser drop in IOP during this maneuver compared to the main incision in enucleated porcine eyes.The use of different OVD has no significant influence on IOP drop.

Dry environment on the expression of lacrimal gland S100A9,Anxa1,and Clu in rats via proteomics

●AIM:To investigate the underlying mechanism of dry environment(autumn dryness)affecting the lacrimal glands in rats.●METHODS:Twenty Sprague-Dawley rats were randomly divided into two groups.The rats were fed in specific pathogen free environment as the control group(n=10),and the rats fed in dry environment as the dryness group(n=10).After 24d,lacrimal glands were collected from the rats.The tissues morphology was observed by hematoxylineosin(HE)staining.Tandem mass tags(TMT)quantitative proteomics analysis technology was used to screen the differential expressed proteins of lacrimal glands between the two groups,then bioinformatics analysis was performed.Further,the immunohistochemical(IHC)method was used to verify the target proteins.●RESULTS:In dryness group,the lacrimal glands lobule atrophied,the glandular cavities enlarged,the sparse nuclear distribution and scattered inflammatory infiltration between the acinus were observed.The proteomics exhibited that a total of 195 up-regulated and 236 downregulated differential expressed proteins screened from the lacrimal glands of rats.It was indicated that the biological processes(BP)of differential expressed proteins mainly included cell processes and single BP.The cellular compositions of differential expressed proteins mainly located in cells,organelles.The molecular functions of differential expressed proteins mainly included binding,catalytic activity.Moreover,the Kyoto Encyclopedia of Genes and Genomes(KEGG)pathway analysis showed that the differential expressed proteins mainly involved lysosome,complement and coagulation cascade,and ribosome pathway.The IHC result verified that the up-regulated expression proteins of Protein S100A9(S100A9),Annexin A1(Anxa1),and Clusterin(Clu)in lacrimal glands of rats in dryness group were higher than control group.●CONCLUSION:The up-regulated expression proteins of S100A9,Anxa1,and Clu may be the potential mechanisms of dry eye symptoms caused by dry environment.This study provides clues of dry environments causing eye-related diseases for further studies.

Field Load Test Based SHM System Safety Standard Determination for Rigid Frame Bridge

The deteriorated continuous rigid frame bridge is strengthened by external prestressing. Static loading tests wereconducted before and after the bridge rehabilitation to verify the effectiveness of the rehabilitation process. Thestiffness of the repaired bridge is improved, and the maximum deflection of the load test is reduced from 37.9 to27.6 mm. A bridge health monitoring system is installed after the bridge is reinforced. To achieve an easy assessmentof the bridge’s safety status by directly using transferred data, a real-time safety warning system is createdbased on a five-level safety standard. The threshold for each safety level will be determined by theoretical calculationsand the outcomes of static loading tests. The highest risk threshold will be set at the ultimate limit statevalue. The remaining levels, namely middle risk, low risk, and very low risk, will be determined usingreduction coefficients of 0.95, 0.9, and 0.8, respectively.

Effect of the traditional Chinese medicine fumigation combined with the meibomian gland squeezer for treatment of dry eye associated with meibomian gland dysfunction

Background:To observe the effect of traditional Chinese medicine fumigation combined with the meibomian gland squeezer for the treatment of dry eye associated with meibomian gland dysfunction(MGD).Methods:This is a randomized,controlled,non-masked,single-center study.Seventy-four cases(74 eyes)of dry eye associated with MGD were randomly divided into two groups.Thirty-seven patients were chosen as the treatment group was treated by the traditional Chinese medicine fumigation 3 times a week combined with the meibomian gland squeezer once a week for one month.The other 37 cases were sorted as the control group and only treated with the meibomian gland squeezer once a week for one month.Both groups received the primary treatment for 1 month,including Tobradex eye ointment once a day and 0.1%sodium hyaluronate eye drops 4-6 times daily.Patients were evaluated at baseline and 2-week and 1-month visits for the ocular symptom scores,international ocular surface disease index(OSDI),fluorescein tear break-up time(TBUT),corneal fluorescein staining test(CFS),Schirmer I test,meibum quality and meibum expressibility.Results:Sixty-seven patients were followed in the study,and the mean age was 57(±12.6)years.Thirty-three patients(11 males)in the treatment group and 34 patients(8 males)in the control group were followed in the study,and the mean age of the two groups was 45.36±15.02 years and 43.68±13.43 years,respectively.Before treatment,there was no significant difference between the two groups in gender,age,ocular symptom scores,OSDI,TBUT,CFS,Schirmer I test,meibum quality,and meibum expressibility(P>0.05).Compared with baseline,the 2 groups had different degrees of improvement in the ocular symptom scores,OSDI,TBUT,CFS,meibum quality,and meibum expressibility at the 2-week and 1-month visits(P<0.05),and the treatment group showed a more significant improvement in the ocular symptom scores,OSDI,TBUT,CFS,meibum quality and meibum expressibility compared with the control group(P<0.05).In addition,no serious adverse events were observed in each group.Conclusions:The traditional Chinese medicine fumigation combined with the meibomian gland squeezer may be safe,effective,and helpful for the treatment of dry eye associated with MGD.

Frame Length Dependency for Fundamental Frequency Extraction in Noisy Speech

The fundamental frequency plays a significant part in understanding and perceiving the pitch of a sound. The pitch is a fundamental attribute employed in numerous speech-related works. For fundamental frequency extraction, several algorithms have been developed which one to use relies on the signal’s characteristics and the surrounding noise. Thus, the algorithm’s noise resistance becomes more critical than ever for precise fundamental frequency estimation. Nonetheless, numerous state-of-the-art algorithms face struggles in achieving satisfying outcomes when confronted with speech recordings that are noisy with low signal-to-noise ratio (SNR) values. Also, most of the recent techniques utilize different frame lengths for pitch extraction. From this point of view, This research considers different frame lengths on male and female speech signals for fundamental frequency extraction. Also, analyze the frame length dependency on the speech signal analytically to understand which frame length is more suitable and effective for male and female speech signals specifically. For the validation of our idea, we have utilized the conventional autocorrelation function (ACF), and state-of-the-art method BaNa. This study puts out a potent idea that will work better for speech processing applications in noisy speech. From experimental results, the proposed idea represents which frame length is more appropriate for male and female speech signals in noisy environments.

Effect of bivalirudin on myocardial microcirculation and adverse events after interventional therapy in older patients with acute coronary syndrome

BACKGROUND Bivalirudin,a direct thrombin inhibitor,is used in anticoagulation therapies as a substitute for heparin,especially during cardiovascular procedures such as percutaneous coronary intervention.AIM To explore the effect of bivalirudin on myocardial microcirculation following an intervention and its influence on adverse cardiac events in elderly patients with acute coronary syndrome(ACS).METHODS In total,165 patients diagnosed with acute myocardial at our hospital between June 2020 and June 2022 were enrolled in this study.From June 2020 to June 2022,elderly patients with ACS with complete data were selected and treated with interventional therapy.The study cohort was randomly divided into a study group(n=80,administered bivalirudin)and a control group(n=85,administered unfractionated heparin).Over a 6-mo follow-up period,differences in emergency processing times,including coronary intervention,cardiac function indicators,occurrence of cardiovascular events,and recurrence rates,were analyzed.RESULTS Significant differences were observed between the study cohorts,with the observation group showing shorter emergency process times across all stages:Emergency classification;diagnostic testing;implementation of coronary intervention;and conclusion of emergency treatment(P<0.05).Furthermore,the left ventricular ejection fraction in the observation group was significantly higher(P<0.05),and the creatine kinase-MB and New York Heart Association scores were CONCLUSION In elderly patients receiving interventional therapy for ACS,bivalirudin administration led to increased activated clotting time achievement rates,enhanced myocardial reperfusion,and reduced incidence of bleeding complications and adverse cardiac events.

Efficacy of Online Learning and Influence on Skin and Eyes Among College Students

To evaluate the efficacy of online learning and explore the impact of long-term use of electronic products on facial skin as well as eyes.A cross-sectional survey was conducted to 180 sophomores in Xi′an Jiaotong University by cluster random sampling from September to October 2021.The questionnaire covering study condition,skin lesion and Ocular Surface Disease Index.χ_(2) test was used to compare the facial skin condition among different groups,and spearman correlation test was used to test the correlation of rank data.During online education,students′learning pressure is reduced,their autonomy is improved,and the learning efficiency is reduced.There were differences in the incidence of facial itching and papules among different groups.Duration of use of electronic products was positively correlated with the facial itching,with an r value of 0.231(P<0.05);the proportion of pigmentation in non-blue light protection groups(12.8%)was higher than that in blue light protection groups(1.7%),the difference was statistically significant(χ_(2)=8.384,P<0.05).The prevalence of dry eye among college students is 66.7%,and the proportion of moderate to severe dry eye is 34.5%.The study autonomy has been improved during online teaching.Long-term use of electronic products and no blue light protection have an impact on facial skin.Students should enhance the knowledge of skin-care and eye-care and develop better habits.

The Research on the Paths of Popular Science Education about Myopia Prevention and Control among College Students in the Context of Shifting the Focus Forward

Currently, the number of myopic people in China has reached as high as 600 million, and it shows a trend of “early onset, high incidence, and a high degree of severity”. The issue of myopia among children and adolescents has attracted widespread attention from all sectors of society. Comprehensive myopia prevention and control efforts have been launched nationwide. Popular science education, vision screening, and improving visual environments are effective measures for preventing myopia. However, among the target audience for comprehensive myopia prevention and control, the preschool children group has been neglected, and the work of myopia prevention and control for this group has been significantly weakened and marginalized. Due to insufficient awareness of prevention and control, the hyperopia reserve in the preschool children group is being continuously depleted, leading to the early onset of myopia. In light of this situation, the focus of myopia prevention and control needs to shift forward, and it is worth exploring and pondering how college students with a background in optometry can develop entertaining and engaging popular science education materials and methods.

Video Frame Prediction by Joint Optimization of Direct Frame Synthesis and Optical-Flow Estimation

Video prediction is the problem of generating future frames by exploiting the spatiotemporal correlation from the past frame sequence.It is one of the crucial issues in computer vision and has many real-world applications,mainly focused on predicting future scenarios to avoid undesirable outcomes.However,modeling future image content and object is challenging due to the dynamic evolution and complexity of the scene,such as occlusions,camera movements,delay and illumination.Direct frame synthesis or optical-flow estimation are common approaches used by researchers.However,researchers mainly focused on video prediction using one of the approaches.Both methods have limitations,such as direct frame synthesis,usually face blurry prediction due to complex pixel distributions in the scene,and optical-flow estimation,usually produce artifacts due to large object displacements or obstructions in the clip.In this paper,we constructed a deep neural network Frame Prediction Network(FPNet-OF)with multiplebranch inputs(optical flow and original frame)to predict the future video frame by adaptively fusing the future object-motion with the future frame generator.The key idea is to jointly optimize direct RGB frame synthesis and dense optical flow estimation to generate a superior video prediction network.Using various real-world datasets,we experimentally verify that our proposed framework can produce high-level video frame compared to other state-ofthe-art framework.

Characteristics and C-E Translation Methods of the Four-Character Frame in the Subtitles of the Documentary Daming Palace

This paper studies the four-character frame in the subtitle of the documentary Daming Palace, aiming to provide a reference for the translation of the documentary four-character case as well as better spread Chinese culture. By analyzing, researching and summarizing the subtitle of Daming Palace and reading a lot of literature, the author has found that in Daming Palace the four-character frame is characterized by the use of the absolute four-character frames and the recurrence of some four-character frames, and that C-E translation methods of the four-character frame are mainly literal translation, free translation, provincial translation and concise translation.

High-Order Method with Moving Frames to Compute the Covariant Derivatives of Vectors on General 2D Curved Surfaces

The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.