Correlation functions of the critical Ashkin-Teller model on a torus

The correlation functions of the critical Ashkin-Teller model on a torus are calculated using a free bosonic field formulation in the continuum limit. The results include in particular correlators of electromagnetic or twist operators. Various applications are discussed.     

On Hyperbolic Once-Punctured-Torus Bundles

For a hyperbolic once-punctured-torus bundle over a circle, a choice of normalization determines a family of arcs in the Riemann sphere. We show that, in each arc in the family, the set of cusps is dense and forms a single orbit of a finitely generated semigroup of Möbius transformations. This was previously known for the case of the complement of the figure-eight knot.     

Magnetohydrodynamic equilibrium interpretation of low-aspect-ratio tokamak plasma

It is very important to calculate the equilibrium magnetic field configuration exactly and to estimate the parameters of the device needed for the equilibrium and stability in the design and operate the low-aspect-ratio tokamak, one of the axis-symmetrical torus devices which is widely used in the research of nuclear fusion using plasma. In the previous researches, there were the theoretical and numerical interpretation methods for the high-aspect-ratio tokamak plasma. But for the low-aspect-ratio tokamak plasma, numerical methods such as the finite element method and iteration method are usually used. In this research, we interpreted and examined the features of magnetohydrodynamic equilibrium of the low-aspect-ratio tokamak plasma in combination with the Green function method and finite element method which has high numerical value accuracy.     

Positive solutions of nonlinear Schrödinger equation with peaks on a Clifford torus

We prove the existence of large energy positive solutions for a stationary nonlinear Schrödinger equation with peaks on a Clifford type torus. Here where with for all Each is a function and is defined by the generalized notion of spherical coordinates. The solutions are obtained by a or a process.     

Construction of complete generalized algebraic groups

With one exception, the holomorph of a finite dimensional abelian connected algebraic group is shown to be a complete generalized algebraic group. This result on algebraic group is an analogy to that on Lie algebra.     

Clifford 环面 Sm(\sqrt{\frac{m}{n}})×Sn-m(\sqrt{\frac{n-m}{n}})的刚性定理

\small\zihao{-5}\begin{quote}{\heiti 摘要:} 设$M$为$n+1$维单位球面$S^{n+1}(1)$中的一个极小闭超曲面，如果 $ n \le S \le n+\frac{2}{3}$, 则有 $S=n$ 且 $M$ 与某一Clifford 环面 $S^m(\sqrt{m/n}) \times S^{n-m}(\sqrt{(n-m)/n})$等距.     

Theta Functions on Noncommutative Tori

Ordinary theta functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta functions as holomorphic elements of projective modules over noncommutative tori (theta vectors). The theory of these new objects is not only more general, but also much simpler than the theory of ordinary theta-functions. It seems that the theory of theta vectors should be closely related to Manin's theory of quantized theta functions, but we don't analyze this relation.     

Weakly infinitely divisible measures on some locally compact Abelian groups

On the torus group, on the group of p-adic integers, and on the p-adic solenoid, we give a construction of an arbitrary weakly infinitely divisible probability measure using a random element with values in a product of (possibly infinitely many) subgroups of ℝ. As a special case of our results, we have a new construction of the Haar measure on the p-adic solenoid.