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
Toric patch is a kind of rational multisided patch,which is associated with a finite integer lattice points set A.A set of weights is defined which depend on a parameter according to regular decomposition of A.When al...Toric patch is a kind of rational multisided patch,which is associated with a finite integer lattice points set A.A set of weights is defined which depend on a parameter according to regular decomposition of A.When all weights of the patch tend to infinity,we obtain the limiting form of toric patch which is called its regular control surface.The diferent weights may induce the diferent regular control surfaces of the same toric patch.It prompts us to consider that how many regular control surfaces of a toric patch.In this paper,we study the regular decompositions of A by using integer programming method firstly,and then provide the relationship between all regular decompositions of A and corresponding state polytope.Moreover,we present that the number of regular control surfaces of a toric patch associated with A is equal to the number of regular decompositions of A.An algorithm to calculate the number of regular control surfaces of toric patch is provided.The algorithm also presents a method to construct all of the regular control surfaces of a toric patch.At last,the application of proposed result in shape deformation is demonstrated by several examples.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
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.
基金Supported by the National Natural Science Foundation of China(12001327,12071057)。
文摘Toric patch is a kind of rational multisided patch,which is associated with a finite integer lattice points set A.A set of weights is defined which depend on a parameter according to regular decomposition of A.When all weights of the patch tend to infinity,we obtain the limiting form of toric patch which is called its regular control surface.The diferent weights may induce the diferent regular control surfaces of the same toric patch.It prompts us to consider that how many regular control surfaces of a toric patch.In this paper,we study the regular decompositions of A by using integer programming method firstly,and then provide the relationship between all regular decompositions of A and corresponding state polytope.Moreover,we present that the number of regular control surfaces of a toric patch associated with A is equal to the number of regular decompositions of A.An algorithm to calculate the number of regular control surfaces of toric patch is provided.The algorithm also presents a method to construct all of the regular control surfaces of a toric patch.At last,the application of proposed result in shape deformation is demonstrated by several examples.
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.
