On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1...On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.展开更多
Objective To compare the efficacy of toric implantable collamer lens(Toric-ICL)and femtosecond laser-assisted in situ keratomileusis(FS-LASIK)for myopia correction in patients with moderate to high myopia complicated ...Objective To compare the efficacy of toric implantable collamer lens(Toric-ICL)and femtosecond laser-assisted in situ keratomileusis(FS-LASIK)for myopia correction in patients with moderate to high myopia complicated with astigmatism.Methods We retrospectively collected data from 64 patients(aged 18-42 years)with moderate to high myopia complicated with astigmatism(128 eyes)undergoing either Toric-ICL(28 patients/56 eyes)or FS-LASIK(36 patients/72 eyes)at our department between January,2019 and December,2020.The changes of uncorrected distance visual acuity(UCVA),spherical equivalent(SE),mean astigmatism correction index(CI),corneal endothelial cell density(ECD)and intraocular pressure(IOP)following the procedures were compared between the two groups.Results In FS-LASIK group,all the eyes(72/72)achieved an UCVA≥1.0,similar to the rate in Toric-ICL group(55/56 eyes;P=0.2374).The postoperative SE was also comparable between FS-LASIK and Toric-ICL groups[0.43±0.06 D(range:-1.0 to 1.50 D)vs 0.38±0.05 D(range:-0.75 to 1.00 D);P=0.56].The mean astigmatism CI was significantly higher in FS-LASIK group than in Toric-ICL group(0.8561 vs 0.7176;P<0.0001),and 88.89%of the eyes in FS-LASIK group and 69.64%in Toric-ICL group had postoperative astigmatism≤0.50 D.No significant changes were observed in postoperative corneal ECD in FS-LASIK group,whereas ECD decreased significantly after the procedure in Toric-ICL group(P=0.0057).The patients undergoing Toric-ICL exhibited no significant changes of postoperative IOP,but the patients receiving FS-LASIK had significantly reduced IOP after the procedure(P<0.001).Conclusion Although the patients included in Toric-ICL group had higher myopia and astigmatism,Toric-ICL still showed better predictability and efficacy for astigmatic correction in Toric-ICL group.Toric-ICL is an effective and safe equivalent of FS-LASIK for correcting moderate myopia but can be more advantageous for correcting high myopia with astigmatism.展开更多
AIM:To compare the accuracy of manual marking versus an image-guided system for toric implantable collamer lens(TICL)implantation and evaluate the short-term postoperative rotational stability of TICL and corneal surg...AIM:To compare the accuracy of manual marking versus an image-guided system for toric implantable collamer lens(TICL)implantation and evaluate the short-term postoperative rotational stability of TICL and corneal surgically induced astigmatism vector(SIA).METHODS:Retrospective analysis was conducted on eyes with TICL alignment achieved through manual marking(n=75)or VERION image-guided system-assisted marking(n=83).Each group was further classified into horizontal and vertical subgroups based on implant orientation.Additionally,patients were categorized into superior and temporal incision subgroups according to the position of main corneal incision.The misalignment and rotational stability of TICL were analyzed using slit-lamp anterior segment photography.Surgical predictability,efficacy,safety,and corneal SIA were also evaluated.RESULTS:In general,the TICL implantation with manual and digital image-guided systems all achieved robust predictability,efficacy,and safety.The misalignment of TICL was comparable between the manual and VERION groups(0.16°±3.97°vs 0.52°±5.59°,P=0.633),while a significant difference was observed in the absolute misalignment of TICL between the two groups(3.02°±2.55°vs 4.28°±3.61°,P=0.043).There were no significant differences in the distribution of TICL misalignment between the manual and VERION groups or between horizontal and vertical implant orientation groups(P>0.05).Furthermore,different orientations of TICL placement did not show statistically significant differences in rotational stability(P=0.46).Statistically significant differences were found in anterior corneal SIA between the manual and VERION groups(0.46±0.27 vs 0.33±0.21 D,P=0.001),especially for superior incision position(0.60±0.27 vs 0.35±0.23 D,P<0.0001).The anterior SIA exhibited a significant difference between superior and temporal incisions in the manual group(0.60±0.27 vs 0.35±0.20 D,P<0.0001).CONCLUSION:Compared with the conventional manual marking method,this study indicates that the digital image-guided system with VERION is safe and effective in TICL implantation.The digital system offers the advantage of minimizing corneal SIA compared to the manual method.展开更多
To address the challenges associated with multi-sided shells in traditional isogeometric analysis(IGA),this paper introduces a novel isogeometric shell method for trimmed CAD geometries based on toric surfaces and Rei...To address the challenges associated with multi-sided shells in traditional isogeometric analysis(IGA),this paper introduces a novel isogeometric shell method for trimmed CAD geometries based on toric surfaces and Reissner–Mindlin shell theory.By utilizing toric surface patches,both trimmed and untrimmed elements of the CAD surfaces are represented through a unified geometric framework,ensuring continuity and an accurate geometric description.Toric-Bernstein basis functions are employed to accurately interpolate the geometry and displacement of the trimmed shell.For singularities and corner points on the toric surface,the normal vector is defined as the unit directional vector from the center of curvature to the corresponding control point.Several numerical examples of polygonal shells are presented to evaluate the effectiveness and robustness of the proposed method.This approach significantly simplifies the treatment of trimmed shell IGA and provides a promising solution for simulating complex shell structures with intricate boundaries.展开更多
In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is ...In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.展开更多
AIM:To evaluate refractive outcomes and corneal astigmatism changes after Toric implantable collamer lens with a central port(V4c T-ICL)implantation over 1y of follow-up.METHODS:A retrospective study was performed inc...AIM:To evaluate refractive outcomes and corneal astigmatism changes after Toric implantable collamer lens with a central port(V4c T-ICL)implantation over 1y of follow-up.METHODS:A retrospective study was performed including 50 eyes of 50 patients that underwent V4c T-ICL implantation.Uncorrected(UDVA)and corrected(CDVA)distance visual acuities,refraction,refractive and corneal astigmatism changes and corneal coupling correction were evaluated preoperatively,1 and 12mo postoperatively.Vector analysis was used for astigmatism changes.Coefficient of adjustment(CAdj)was calculated for corneal coupling analysis.RESULTS:The mean UDVA achieved was 0.03 logMAR at 1mo and remained unchanged throughout the whole follow-up(P=0.193).At the last visit,84%of the eyes achieved a CDVA of 0.00 logMAR or better.Regarding spherical equivalent refraction(SEQ),96%of eyes were ranges of±1.00 D and 84%of them within±0.50 D.Also,94%of eyes had a remaining refractive cylinder within±1.00 D and 78%of them within±0.50 D.Both,SEQ and refractive cylinder,remain stable over the postoperative follow-up(P=1.000 and P=0.660,respectively).In terms of surgically induced astigmatism(SIA),no statistically significant differences were found over the follow-up(P=0.102)and under correction was found with a correction index lower than the unit at each visit.A keratometric astigmatism induced of 0.59±0.53(vector mean:0.26×73º)D was reached at the last visit.No significant changes in terms of corneal astigmatism orientation were reported over post-surgery visits(P=0.129 and P=0.097 at 1 and 12mo respectively).No clinical significance was found for CAdj on with-the-rule astigmatism.No postoperative complications resulting from the surgery were found.CONCLUSION:Refractive outcomes suggest that the V4c T-ICL implantation for correction of myopic astigmatism was satisfactory in terms of effectiveness,safety,and stability during 1y of follow-up.Corneal astigmatism induced by the incision around 0.5 D is achieved according to the remaining refractive cylinder found at one-year post-surgery.Corneal coupling analysis results in no unexpected spherical change.展开更多
基金supported by the National Natural Science Foundation of China(11931009,12271495,11971450,and 12071449)Anhui Initiative in Quantum Information Technologies(AHY150200)the Project of Stable Support for Youth Team in Basic Research Field,Chinese Academy of Sciences(YSBR-001).
文摘On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.
文摘Objective To compare the efficacy of toric implantable collamer lens(Toric-ICL)and femtosecond laser-assisted in situ keratomileusis(FS-LASIK)for myopia correction in patients with moderate to high myopia complicated with astigmatism.Methods We retrospectively collected data from 64 patients(aged 18-42 years)with moderate to high myopia complicated with astigmatism(128 eyes)undergoing either Toric-ICL(28 patients/56 eyes)or FS-LASIK(36 patients/72 eyes)at our department between January,2019 and December,2020.The changes of uncorrected distance visual acuity(UCVA),spherical equivalent(SE),mean astigmatism correction index(CI),corneal endothelial cell density(ECD)and intraocular pressure(IOP)following the procedures were compared between the two groups.Results In FS-LASIK group,all the eyes(72/72)achieved an UCVA≥1.0,similar to the rate in Toric-ICL group(55/56 eyes;P=0.2374).The postoperative SE was also comparable between FS-LASIK and Toric-ICL groups[0.43±0.06 D(range:-1.0 to 1.50 D)vs 0.38±0.05 D(range:-0.75 to 1.00 D);P=0.56].The mean astigmatism CI was significantly higher in FS-LASIK group than in Toric-ICL group(0.8561 vs 0.7176;P<0.0001),and 88.89%of the eyes in FS-LASIK group and 69.64%in Toric-ICL group had postoperative astigmatism≤0.50 D.No significant changes were observed in postoperative corneal ECD in FS-LASIK group,whereas ECD decreased significantly after the procedure in Toric-ICL group(P=0.0057).The patients undergoing Toric-ICL exhibited no significant changes of postoperative IOP,but the patients receiving FS-LASIK had significantly reduced IOP after the procedure(P<0.001).Conclusion Although the patients included in Toric-ICL group had higher myopia and astigmatism,Toric-ICL still showed better predictability and efficacy for astigmatic correction in Toric-ICL group.Toric-ICL is an effective and safe equivalent of FS-LASIK for correcting moderate myopia but can be more advantageous for correcting high myopia with astigmatism.
文摘AIM:To compare the accuracy of manual marking versus an image-guided system for toric implantable collamer lens(TICL)implantation and evaluate the short-term postoperative rotational stability of TICL and corneal surgically induced astigmatism vector(SIA).METHODS:Retrospective analysis was conducted on eyes with TICL alignment achieved through manual marking(n=75)or VERION image-guided system-assisted marking(n=83).Each group was further classified into horizontal and vertical subgroups based on implant orientation.Additionally,patients were categorized into superior and temporal incision subgroups according to the position of main corneal incision.The misalignment and rotational stability of TICL were analyzed using slit-lamp anterior segment photography.Surgical predictability,efficacy,safety,and corneal SIA were also evaluated.RESULTS:In general,the TICL implantation with manual and digital image-guided systems all achieved robust predictability,efficacy,and safety.The misalignment of TICL was comparable between the manual and VERION groups(0.16°±3.97°vs 0.52°±5.59°,P=0.633),while a significant difference was observed in the absolute misalignment of TICL between the two groups(3.02°±2.55°vs 4.28°±3.61°,P=0.043).There were no significant differences in the distribution of TICL misalignment between the manual and VERION groups or between horizontal and vertical implant orientation groups(P>0.05).Furthermore,different orientations of TICL placement did not show statistically significant differences in rotational stability(P=0.46).Statistically significant differences were found in anterior corneal SIA between the manual and VERION groups(0.46±0.27 vs 0.33±0.21 D,P=0.001),especially for superior incision position(0.60±0.27 vs 0.35±0.23 D,P<0.0001).The anterior SIA exhibited a significant difference between superior and temporal incisions in the manual group(0.60±0.27 vs 0.35±0.20 D,P<0.0001).CONCLUSION:Compared with the conventional manual marking method,this study indicates that the digital image-guided system with VERION is safe and effective in TICL implantation.The digital system offers the advantage of minimizing corneal SIA compared to the manual method.
基金the National Key Research and Development Projects(Grant Nos.2021YFB3300601,2021YFB3300603,2021YFB3300604)the Fundamental Research Funds for the Central Universities(No.DUT22QN241)is acknowledged.
文摘To address the challenges associated with multi-sided shells in traditional isogeometric analysis(IGA),this paper introduces a novel isogeometric shell method for trimmed CAD geometries based on toric surfaces and Reissner–Mindlin shell theory.By utilizing toric surface patches,both trimmed and untrimmed elements of the CAD surfaces are represented through a unified geometric framework,ensuring continuity and an accurate geometric description.Toric-Bernstein basis functions are employed to accurately interpolate the geometry and displacement of the trimmed shell.For singularities and corner points on the toric surface,the normal vector is defined as the unit directional vector from the center of curvature to the corresponding control point.Several numerical examples of polygonal shells are presented to evaluate the effectiveness and robustness of the proposed method.This approach significantly simplifies the treatment of trimmed shell IGA and provides a promising solution for simulating complex shell structures with intricate boundaries.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.12201314).
文摘In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.
文摘AIM:To evaluate refractive outcomes and corneal astigmatism changes after Toric implantable collamer lens with a central port(V4c T-ICL)implantation over 1y of follow-up.METHODS:A retrospective study was performed including 50 eyes of 50 patients that underwent V4c T-ICL implantation.Uncorrected(UDVA)and corrected(CDVA)distance visual acuities,refraction,refractive and corneal astigmatism changes and corneal coupling correction were evaluated preoperatively,1 and 12mo postoperatively.Vector analysis was used for astigmatism changes.Coefficient of adjustment(CAdj)was calculated for corneal coupling analysis.RESULTS:The mean UDVA achieved was 0.03 logMAR at 1mo and remained unchanged throughout the whole follow-up(P=0.193).At the last visit,84%of the eyes achieved a CDVA of 0.00 logMAR or better.Regarding spherical equivalent refraction(SEQ),96%of eyes were ranges of±1.00 D and 84%of them within±0.50 D.Also,94%of eyes had a remaining refractive cylinder within±1.00 D and 78%of them within±0.50 D.Both,SEQ and refractive cylinder,remain stable over the postoperative follow-up(P=1.000 and P=0.660,respectively).In terms of surgically induced astigmatism(SIA),no statistically significant differences were found over the follow-up(P=0.102)and under correction was found with a correction index lower than the unit at each visit.A keratometric astigmatism induced of 0.59±0.53(vector mean:0.26×73º)D was reached at the last visit.No significant changes in terms of corneal astigmatism orientation were reported over post-surgery visits(P=0.129 and P=0.097 at 1 and 12mo respectively).No clinical significance was found for CAdj on with-the-rule astigmatism.No postoperative complications resulting from the surgery were found.CONCLUSION:Refractive outcomes suggest that the V4c T-ICL implantation for correction of myopic astigmatism was satisfactory in terms of effectiveness,safety,and stability during 1y of follow-up.Corneal astigmatism induced by the incision around 0.5 D is achieved according to the remaining refractive cylinder found at one-year post-surgery.Corneal coupling analysis results in no unexpected spherical change.
