We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson's minimal tori. This provides an alternative proof of the resul...We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson's minimal tori. This provides an alternative proof of the result by Perdomo (Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 (2007), 23 34).展开更多
We consider the quantum mechanical SU(2) transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU(2) operators (J±,...We consider the quantum mechanical SU(2) transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU(2) operators (J±, Jz) from the point of view of squeezing we find that (J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation (the eigenvectors of J+ or J-) of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.展开更多
We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra ass...We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra associated with the U(N) Lie algebra. There is no ghost related to the Lorentzian signature in this model. It is invariant under 64 supersymmetry transformations although the supersymmetry algebra does not close. From the model, we derive the BFSS matrix theory and the IIB matrix model in a large N limit by taking appropriate vacua.展开更多
After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
文摘We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson's minimal tori. This provides an alternative proof of the result by Perdomo (Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 (2007), 23 34).
基金supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 11275123)the Key Project of Natural Science Fund of Anhui Province,China(Grant No.KJ2013A261)
文摘We consider the quantum mechanical SU(2) transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU(2) operators (J±, Jz) from the point of view of squeezing we find that (J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation (the eigenvectors of J+ or J-) of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.
文摘We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in [1]. It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra associated with the U(N) Lie algebra. There is no ghost related to the Lorentzian signature in this model. It is invariant under 64 supersymmetry transformations although the supersymmetry algebra does not close. From the model, we derive the BFSS matrix theory and the IIB matrix model in a large N limit by taking appropriate vacua.
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.