Strip method to construct a two-dimensional quasilattice witheight-fold symmetry

Based on the substitution rule and symmetry, we propose a method to generate an octagonal quasilattice consisting ofsquare and rhombus tiles. Local configurations and Ammann lines are used to guide the growth of the tiles in a quasiperiodicorder. The structure obtained is a perfect eight-fold symmetric quasilattice, which is confirmed by the radial distributionfunction and the diffraction pattern.

Simultaneous guidance of electromagnetic and elastic waves via glide symmetry phoxonic crystal waveguides

A phoxonic crystal waveguide with the glide symmetry is designed,in which both electromagnetic and elastic waves can propagate along the glide plane at the same time.Due to the glide symmetry,the bands of the phoxonic crystal super-cell degenerate in pairs at the boundary of the Brillouin zone.This is the so-called band-sticking effect and it causes the appearance of gapless guided-modes.By adjusting the magnitude of the glide dislocation the edge bandgaps,the bandgap of the guided-modes at the boundary of the Brillouin zone,can be further adjusted.The photonic and phononic guided-modes can then possess only one mode for a certain frequency with relatively low group velocities,achieving single-mode guided-bands with relatively flat dispersion relationship.In addition,there exists acousto-optic interaction in the cavity constructed by the glide plane.The proposed waveguide has potential applications in the design of novel optomechanical devices.

The breaking of spin symmetry in the single-particle resonances in deformed nuclei

The exploration of spin symmetry (SS) in nuclear physics has been instrumental in identifying atomic nucleus structures.In this study,we solve the Dirac equation from the relativistic mean field (RMF) in complex momentum representation.We investigated SS and its breaking in single-particle resonant states within deformed nuclei,with a focus on the illustrative nucleus168Er.This was the initial discovery of a resonant spin doublet in a deformed nucleus,with the expectation of the SS approaching the continuum threshold.With increasing single-particle energy,the splitting of the resonant spin doublets widened significantly.This escalating splitting implies diminishing adherence to the SS,indicating a departure from the expected behavior as the energy levels increase.We also analyzed the width of the resonant states,showing that lower orbital angular momentum resonances possess shorter decay times and that SS is preserved within broad resonant doublets,as opposed to narrow resonant doublets.Comparing the radial density of the upper components for the bound-state and resonant-state doublets,it becomes evident that while SS is well-preserved in the bound states,it deteriorates in the resonant states.The impact of nuclear deformation (β_(2)) on SS was examined,demonstrating that an increase in β_(2) resulted in higher energy and width splitting in the resonant spin doublets,which is attributed to increased component mixing.Furthermore,the sensitivity of spin doublets to various potential parameters such as surface diffuseness (a),radius (R),and depth (Σ0) is discussed,emphasizing the role of these parameters in SS.This study provides valuable insights into the behavior of spin doublets in deformed nuclei and their interplay with the nuclear structure,thereby advancing our understanding of SS in the resonance state.

Unification of Gravitational and Strong Interaction Fields Using Partial Gauge Symmetry

We propose the new field potential by maintaining both the symmetry of the scalar gauge and the conservation law keeping N?ether’s theorem, while disregarding the symmetry of the vector gauge. The new potential forms like the well-type potential where a particle behaves almost freely but is very hard to escape without external energy, which can be interpreted as local confinement and asymptotic freedom. By assuming a 2-dimensional metric tensor in 4-dimensional space-time, we suggest the existence of 3 kinds of particles that resemble QCD with 3 color charges. We also show that the mass term exists but comes to zero and derive the charge and spin values. We can regard the particle with this new potential as a gluon, and the interaction in this well-type potential as a strong interaction for the properties of mass, charge, spin, and its behavior. We suggest the eight-fold way with this new particle, which is similar to the existing method based on SU (3) symmetry. Even though the strong interaction has been analyzed in the standard model and string theory, we build a new consistent model based on the theory of relativity including Riemann geometry, and show the unification of gravitational and strong interactional field.

Two-fold symmetry of the in-plane resistance in kagome superconductor Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with enhanced superconductivity

The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V_(1-x)Ta_(x))_(3)Sb_(5) by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T_(c) ~ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V_(1-x)Ta_(x))_(3)Sb_(5)(x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance(AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V_(1-x)Ta_(x))_(3)Sb_(5). Our findings demonstrate that Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.

Symmetry quantification and segmentation in STEM imaging through Zernike moments

We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy(STEM)images,aimed at improving structural analysis of materials at the atomic scale.This technique is effective against common imaging noises and is potentially suited for low-dose imaging and identifying quantum defects.We showcase its utility in the unsupervised segmentation of polytypes in a twisted bilayer TaS_(2),enabling accurate differentiation of structural phases and monitoring transitions caused by electron beam effects.This approach enhances the analysis of structural variations in crystalline materials,marking a notable advancement in the characterization of structures in materials science.

THE RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR PROBLEMS INVOLVING WEIGHTED FRACTIONAL LAPLACIANS

This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.

Symmetry of upper eyelid after unilateral blepharoptosis repair with minimally invasive conjoint fascial sheath suspension technique

AIM:To investigate the symmetry of upper eyelid in patients with unilateral mild and moderate blepharoptosis who underwent unilateral minimally invasive combined fascia sheath(CFS)suspension.METHODS:A retrospective study of patients who underwent unilateral minimally invasive CFS suspension surgery between January 2018 and December 2021.Inclusion criteria included unilateral mild and moderate ptosis,good levator muscle function(>9 mm)and follow-up of at least 6mo.Pre-and post-operative symmetry was graded subjectively for marginal reflex distance 1(MRD1),tarsal platform show(TPS)and eyebrow fat span(BFS).A t-test was used to evaluate MRD1,TPS and BFS asymmetry by calculating delta values.The Bézier curve tool of the Image J software was used to extract the upper eyelid contours,where the symmetry was measured by the percentage of overlapping curvatures(POC).RESULTS:Totally 105 patients(105 eyelids)were included(mild group,n=84;moderate group,n=21).Postoperatively,all patients increased MRD1 and decreased TPS in the ptotic eye while maintaining unchanged BFS.The asymmetric delta value for MRD1 was measured to be 1.48±0.86 preoperatively,and it decreased to 0.58±0.67 postoperatively in all cases(P=0.0004).In patients with mild ptosis,the asymmetry value of TPS fell significantly from 1.15±0.62 to 0.68±0.38(P=0.0187).The symmetry of the upper eyelid contour increased in all subgroups of patients,with a POC of 59.39%±13.45%preoperatively and POC of 78.29%±13.80%postoperatively.CONCLUSION:Minimally invasive CFS suspension is proved to be an effective means of improving the symmetry of unilateral ptosis in terms of MRD1(all subgroups),POC(all subgroups)and TPS(only mild group),whereas BFS is unaffected.

Angle-resolved photoemission study of NbGeSb with non-symmorphic symmetry

We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By utilizing high-energy photons,we identify the bulk Fermi surface and bulk nodal line along the direction X–R,while the Fermi surface of the surface state is observed by using low-energy photons.We observe the splitting of surface bands away from the high-symmetry point X.The density functional theory calculations on bulk and 1 to 5-layer slab models,as well as spin textures of NbGeSb,verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface.These splitted surface bands cross with each other,forming two-dimensional Weyl-like crossings that are protected by mirror symmetry.Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.

Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO2, H2O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)T, between gaseous and liquid states along any isotherm from critical (Tc) to Boyle (TB) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton’s partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (ω = ρrs(T) = RT) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (w = (p/ρ)T = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρBW(T) = 2ρPA(T) = 3ρPB(T) = 3ρRS(T)/2 for T TB. These simple relationships arise, because the higher virial coefficients (bn, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T TB) within the gas phase. The Boyle-work line (p/ρBW)T is related exactly at lower densities as T → TB, and accurately for liquid densities, by ρBW(T) = −(b2/b3)T. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρRS(0) = (2/3)ρBW(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below TB are obtainable from b2(T). A BW-line ground-state crystal density ρBW(0) can be defined by the pair potential minimum. The Ar2 pair potential, ∅ij(rij) determines b2(T) analytically for all T. This report, therefore, advances the salient objective of liquid-state theory: an argon p(ρ,T) Equation-of-state is obtained from ∅ij(rij) for all fluid states, without any adjustable parameters.

Symmetry主动脉吻合器在心脏不停跳冠状动脉旁路移植术中的应用

目的 总结非体外循环心脏不停跳冠状动脉旁路移植术 (Off-pumpcoronaryarterybypassgrafting ,OPCAB)中使用Symmetry主动脉吻合器的近期效果。 方法 2 0 0 2年 9月～ 2 0 0 3年 6月 ,2 0 4例冠心病行OPCAB ,其中 16 7例使用大隐静脉移植物 ,应用Symmetry主动脉吻合器 10 0例。 结果 使用吻合器 14 2个 ,吻合失败弃用 2个 ,3个吻合口漏血需手工修补 ,成功率 96 5 % (137 14 2 ) ,近端吻合口 (1 4± 0 5 )个 例 ,远端吻合口 (3 5± 0 8)个 例。近端吻合口血流量 (46 5± 2 2 3)ml min。吻合器安装时间 (4 0± 1 1)min ,吻合口完成时间均在 10s以内 ,手术时间 (3 2± 0 4 )h。手术死亡率 1% (1 10 0 ) ,无围手术期心肌梗塞、脑卒中等并发症 ,出血二次开胸 1例 ,但非吻合口出血。术后引流量 (5 4 1± 2 74 )ml,输血率 36 0 % (36 10 0 )。术后住院 (7 8± 1 6 )天。 结论 Symmetry主动脉吻合器可安全有效地应用于CABG术 ,近期临床效果满意 ,可缩短吻合时间和手术时间 ,避免主动脉钳夹 。

Symmetry主动脉吻合器对大隐静脉移植物的损伤

目的 观察使用Symmetry主动脉吻合器时对大隐静脉移植物内皮有无损伤。 方法 对 10例使用Symmetry主动脉吻合器行冠状动脉旁路移植术患者进行自身对照研究。在主动脉吻合器使用前和使用后 ,切取自体大隐静脉片断 ,进行Ⅷ因子免疫组化染色 ,对照血管内皮损伤情况。结果 血管内皮细胞均匀着色 ,为深褐色颗粒 ,损伤处褐色颗粒排列中断。吻合器组内皮损伤处平均为 2 .5 5处 ,对照组为 2 .0处。

非厄米PT对称多通道光波导体系的调控及动力学

宇称-时间(PARITY-TIME PT)对称光学波导系统中有关PT对称性的调控主要通过周期性变化的复折射率材料来实现.本文中我们给出了一种对于已耦合的双通道波导体系中额外引入周期调制的中性波导操纵PT对称性的构型,通过高频近似将系统转换为重整化参数后的等效未调制系统后,发现可以通过额外引入单频周期调制的光波导去调控体系的PT对称性,并且讨论了周期调制的非厄米三通道波导体系的能谱特性.最后通过解析和数值的方法给出了光在非厄米三通道光学波导中的动力学演化.

Symmetry吻合装置应用于非体外循环冠状动脉旁路移植

目的:报告临床应用桥血管-主动脉吻合装置,在非体外循环冠状动脉旁路移植手术的初步经验,探讨其可行性与安全性。方法:2003年10月-12月,23例在非体外循环下冠状动脉旁路移植(OPCAB)手术中应用Symmetry桥血管-主动脉吻合装置实现主动脉无钳夹技术。4例患者伴有严重的升主动脉钙化性粥样硬化。应用吻合装置完成近端吻合口共计59个,平均2.6个/例。术前应用升主动脉薄层CT平扫评价其粥样硬化及钙化程度,术中采用升主动脉超声检查结合手指扪查升主动脉的方法,避开钙化斑块,进行近端吻合口的定位。再血管化的顺序为:(1)左乳内动脉与左前降支远端吻合;(2)应用主动脉无钳夹技术,以吻合装置完成所有静脉桥血管与主动脉近端吻合;(3)顺次完成所有静脉桥血管与冠状动脉远端吻合。术后以抗血小板药物治疗6个月。术后患者均接受门诊或电话随访。结果:全组应用吻合装置完成近端吻合口59个均获得成功,术中未发现吻合口漏血需手工缝合修补情况。全组无手术死亡病例。围术期未发生心肌梗死。无脑血管意外、二次开胸止血、心功能衰竭等严重围术期并发症。术后1年随访,发现23例患者中有2例心绞痛症状复发,其中1例复查冠状动脉造影证实所有桥血管均通畅。另1例患者未能复查冠状动脉造影,于术后18个月死亡。结论:Symmetry桥血管-主动脉吻合装置可以安全地应用于OPCAB手术。特别是为实现冠脉手术的主动脉无钳夹技术,以解决升主动脉钙化问题,提供了一种可选择的方法。但其对于静脉桥血管远期通畅率的影响值得关注,并有待进一步大组病例临床研究的证实。

冠状动脉搭桥术中Symmetry主动脉近端吻合器的实验研究

目的利用Symmetry主动脉近端吻合器进行静脉移植物与升主动脉吻合的动物实验,评价其吻合时间、吻合口血流量和通畅率,为临床应用提供科学依据。方法以犬作为实验对象,取自体股静脉作为移植血管,在非体外循环心脏不停跳下完成主动脉至冠状动脉的冠状动脉旁路手术(OPCABG)。以Symmetry主动脉近端吻合器完成的近端吻合口作为实验组(N=10),以5～0Prolene缝线手工缝合的近端吻合口作为对照组(N=10)。测量、比较两组的吻合时间;术中应用多谱勒血流量仪测量吻合口的血流量;静脉内注射新福林提高血压,观察不同压力下吻合口的渗漏。结果实验组吻合时间为98.30士9.63s,对照组为200.50士7.54s,P<O.01。实验组吻合口的血流量平均为12.07士0.60ml/min,对照组为11.96士0.80ml/min,P>0.05。实验组所能承受的最大血压平均为180士7.0mmHg,明显高于对照组160士8.0mmHg,P<O.01。结论Symmetry主动脉近端吻合器是一种简易、有效、快速和可靠的冠状动脉近端吻合装置。可避免钳夹主动脉,减少神经系统并发症,并在微创冠状动脉搭桥术中有较高的应用价值。

The Noether's Theory of Constrained Birkhoffian System

By using the synmeby and the qusi-symmetry of the infinitesimal transformation of the transformation group G1 and by imposing restrictions of constraints on the transformation, the Noether's theory of constrained Birkhoffian system has been established. The theory includes the generalized Noether's theorem obtaining the first integrals from the known symmetry and quasi-symmetry and its inverse obtaining the corresponding symmetry and quasi-symmetry from the known first integrals for the systerm.

振动疗法联合悬吊训练前交叉韧带重建后患者运动及膝关节功能的变化

背景:物理疗法对前交叉韧带重建术后恢复至关重要。近年来,许多医师都在优化前交叉韧带重建术后的物理康复方案,但仍然缺乏高效的前交叉韧带重建术后康复训练疗法。目的:探讨振动疗法联合悬吊训练对前交叉韧带重建患者术后运动及膝关节功能的影响。方法:纳入在上海体育大学附属体育医院就诊的80例首次行单侧前交叉韧带重建患者,按照随机数字表法将患者随机分为振动疗法组和振动疗法+悬吊训练组,每组40例。振动疗法组患者在前交叉韧带重建术后第13周开始进行振动疗法训练(每次10 min,1次/d,每周6次),振动疗法+悬吊训练组患者在前交叉韧带重建术后第13周开始进行振动疗法(每次10 min,1次/d,每周6次)联合悬吊训练(每周2次),共训练8周。训练前及训练8后,采用膝关节Lysholm评分评价膝关节功能,采用等速肌力评估训练系统评估屈膝对称性指数,采用平衡测试系统评估双侧多轴平均轨迹误差差值。结果与结论:(1)与训练前比较,两组患者训练8周后的膝关节Lysholm评分、屈膝与伸膝对称性指数均升高(P<0.05),双侧多轴平均轨迹误差差值降低(P<0.05);与振动疗法组比较,振动疗法+悬吊训练组患者膝关节Lysholm评分、屈膝与伸膝对称性指数均升高(P<0.05),双侧多轴平均轨迹误差差值降低(P<0.05);(2)结果表明,与单独进行振动疗法相比,振动疗法联合悬吊训练可显著改善前交叉韧带重建患者的膝关节功能,增加肌肉力量和对称性,提高平衡稳定性。

Symmetry主动脉吻合器在OPCAB术中的应用

目的:总结非体外循环心脏不停跳冠状动脉旁路移植术(Off-pump coronary artery bypass grafting,OP-CAB)中使用 Symmetry 主动脉吻合器的近期效果。方法:2002年9月-2004年9月,585例冠心病患者行 OPCAB,其中497例使用大隐静永移植物,应用 Symmetry 主动脉吻合器25例。结果:使用吻合器35个,近端吻合口(1.4±0.2)个/例,成功率97.14%(34/35),吻合失败弃用1个,1个吻合口漏血需手工修补。吻合器安装时间(4.3±1.5)分钟,吻合口完成时间均在10S 以内,手术时间(3.2±0.4)小时。手术死亡率4%(1/25),无围手术期心肌梗死、脑卒中并发症,出血二次开胸1例,但非吻合口出血。术后总引流量(592±224)ml,输血率44%(11/25)。术后住院(9.8±1.6)天。结论:Symmertry 主动脉吻合器可安全有效地应用于 OPCAB 术,近期临床效果满意。可缩短吻合时间和手术时间,避免主动脉钳夹,降低中风并发症。