In this paper, we obtain a formula for submanifolds in Sn+p by calculating the Laplacian of the Moebius second fundamental form. Using this formula, we obtain some pinching theorems about the minimal eigenvalue of the...In this paper, we obtain a formula for submanifolds in Sn+p by calculating the Laplacian of the Moebius second fundamental form. Using this formula, we obtain some pinching theorems about the minimal eigenvalue of the Blaschke tensor.展开更多
The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n＋p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form φ and the Blaschke tensor A. In t...The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n＋p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form φ and the Blaschke tensor A. In this paper, we obtain the upper bound of the Moebius scalar curvature of submanifolds with parallel Moebius form in S^n＋p.展开更多
A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic...A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (g<sub>e</sub> = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.展开更多
BACKGROUND Moebius syndrome(MBS)is a nonprogressive and rare congenital neuromuscular disorder involving the facial nerve and abductor nerve;it mainly manifests as facial paralysis and eye strabismus paralytic symptom...BACKGROUND Moebius syndrome(MBS)is a nonprogressive and rare congenital neuromuscular disorder involving the facial nerve and abductor nerve;it mainly manifests as facial paralysis and eye strabismus paralytic symptoms.Tissues in the oral cavity are also compromised,characterized by microstomia,micrognathia,tongue malformation,cleft lip,high arched palate or cleft palate,bifid uvula,and dental malocclusion.Therefore,dentistry plays a fundamental and crucial role in caring for these individuals.However,there is limited available data on MBS treatment,particularly regarding dental management.CASE SUMMARY This case report presents dental treatment of a 21-year-old man with MBS and discusses crucial interactions among oral complications of MBS.In this case,the patient was clinically characterized by congenital neuromuscular disorder,occlusal disorders,and tooth and gum problems.It is noteworthy that the patient presented early eruption of deciduous teeth 2 mo after birth,which has not been reported in other MBS cases and suggests a potentially new clinical manifestation of this syndrome.It is important to note that MBS cannot be cured,and oral manifestations of this syndrome can be managed by a multidisciplinary health care team that helps the patient maintain oral hygiene and dental health.After a series of oral treatments,no obvious poor oral hygiene,swollen gums,or abnormal imaging results were observed after 2 years of follow-up.CONCLUSION This case addressed the oral clinical manifestations of MBS and difficulties experienced during dental management,and suggested early tooth eruption as a potentially new clinical manifestation of this syndrome.Knowledge of the loopmediated association among oral complications of this syndrome is essential to perfecting treatments.展开更多
文摘In this paper, we obtain a formula for submanifolds in Sn+p by calculating the Laplacian of the Moebius second fundamental form. Using this formula, we obtain some pinching theorems about the minimal eigenvalue of the Blaschke tensor.
基金Supported by the NSF of China(10671087)Supported by the NSF of Jiangxi Province(2008GZS0024)
文摘The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n＋p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form φ and the Blaschke tensor A. In this paper, we obtain the upper bound of the Moebius scalar curvature of submanifolds with parallel Moebius form in S^n＋p.
文摘A symmetrical quartic polynomial, named golden one, can be connected to coefficients of the icosahedron equation as well as to the gyromagnetic correction of the electron and to number 137. This number is not a mystic one, but is connected with the inverse of Sommerfeld’s fine-structure constant and this way again connected with the electron. From number-theoretical realities, including the reciprocity relation of the golden ratio as effective pre-calculator of nature’s creativeness, a proposed closeness to the icosahedron may point towards the structure of the electron, thought off as a single-strand compacted helically self-confined charged elemantary particle of less spherical but assumed blunted icosahedral shape generated from a high energy double-helix photon. We constructed a chiral Moebius “ball” from a 13 times 180˚twisted double helix strand, where the turning points of 12 generated slings were arranged towards the vertices of a regular icosahedron, belonging to the non-centrosymmetric rotation group I532. Mathematically put, we convert the helical motion of an energy quantum into a stationary motion on a Moebius stripe structure. The radius of the ball is about the Compton radius. This chiral closed circuit Moebius ball motion profile can be tentatively thought off as the dominant quantum vortex structure of the electron, and the model may be named CEWMB (Charged Electromagnetic Wave Moebius Ball). Also the gyromagnetic factor of the electron (g<sub>e</sub> = 2.002319) can be traced back to this special structure. However, nature’s energy infinity principle would suggest a superposition with additional less dominant (secondary) structures, governed also by the golden mean. A suggestion about the possible structure of delocalized hole carriers in the superconducting state is given.
文摘BACKGROUND Moebius syndrome(MBS)is a nonprogressive and rare congenital neuromuscular disorder involving the facial nerve and abductor nerve;it mainly manifests as facial paralysis and eye strabismus paralytic symptoms.Tissues in the oral cavity are also compromised,characterized by microstomia,micrognathia,tongue malformation,cleft lip,high arched palate or cleft palate,bifid uvula,and dental malocclusion.Therefore,dentistry plays a fundamental and crucial role in caring for these individuals.However,there is limited available data on MBS treatment,particularly regarding dental management.CASE SUMMARY This case report presents dental treatment of a 21-year-old man with MBS and discusses crucial interactions among oral complications of MBS.In this case,the patient was clinically characterized by congenital neuromuscular disorder,occlusal disorders,and tooth and gum problems.It is noteworthy that the patient presented early eruption of deciduous teeth 2 mo after birth,which has not been reported in other MBS cases and suggests a potentially new clinical manifestation of this syndrome.It is important to note that MBS cannot be cured,and oral manifestations of this syndrome can be managed by a multidisciplinary health care team that helps the patient maintain oral hygiene and dental health.After a series of oral treatments,no obvious poor oral hygiene,swollen gums,or abnormal imaging results were observed after 2 years of follow-up.CONCLUSION This case addressed the oral clinical manifestations of MBS and difficulties experienced during dental management,and suggested early tooth eruption as a potentially new clinical manifestation of this syndrome.Knowledge of the loopmediated association among oral complications of this syndrome is essential to perfecting treatments.
