Quantization of Space in the Presence of a Minimal Length

In this article,we apply the Generalized Uncertainty Principle(GUP),which is consistent with quantum gravity theories to an elementary particle in a finite potential well,and study the quantum behavior in this system.The generalized Hamiltonian contains two additional terms,which are proportional to αp~3(the result of the maximum momentum assumption) and α~2p~4(the result of the minimum length assumption),where α ~ 1/M_(PIC) is the GUP parameter.On the basis of the work by Ali et al.,we solve the generalized Schrodinger equation which is extended to include the α~2 correction term,and find that the length L of the finite potential well must be quantized.Then a generalization to the double-square-well potential is discussed.The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of α_0l_(PI) in GUP scenario.     

A Direct Search Frame-Based Adaptive Barzilai-Borwein Method

This paper proposes a direct search frame-based adaptive Barzilai-Borwein method for unconstrained minimization. The method is based on the framework of frame-based algorithms proposed by Coope and Price, but we use the strategy of ABB method and the rotational minimal positive basis to reduce the computation work at each iteration. Under some mild assumptions, the convergence of this approach will be established. Through five hundred and twenty numerical tests using the CUTEr test problem library, we show that the proposed method is promising.     

S~3到CP~4中的等变弱Lagrangian极小浸入

研究3维球面S3到复射影空间CP4中的非常数截面曲率的等变弱Lagrangian极小浸入。     

R-Parity Violation Effects on b1→bχ10in Minimal Supersymmetric Standard Model

We investigate in detail the effects of R-parity lepton number violation on the decay b₁→bχ₁⁰ in the R-parity violating minimal supersymmetric standard model (R_p-MSSM) under the present experimental constraints on R_p parameters. In our numerical calculations we consider two cases of input parameters of the squark and slepton sectors, M_squark<M_slepton and M_squark>M_slepton, for comparison. The results show that the relative R-parity violating correction is not very sensitive to the mass of the lightest neutralino χ₁⁰ and the degenerate R-parity violating coupling parameter λ₂, but strongly depends on M_squark, M_slepton, tan β and the degenerate R-parity violating coupling parameter λ₁. The relative correction is about -4～3% and can exceed -6% in some region of parameter space. Therefore, precise experiment analyses on the decay b₁→bχ₁⁰ may provide a probe of the R-parity violation.     

Singularities of symplectic and Lagrangian mean curvature flows

In this paper, we study the singularities of the mean curvature ?ow from a symplectic surface or from a Lagrangian surface in a K?hler-Einstein surface. We prove that the blow-up ?ow ∑s∞ at a singular point(X₀, T₀) of a symplectic mean curvature ?ow Σ_t or of a Lagrangian mean curvature ?ow Σ_t is a nontrivial minimal surface in ?4, if ∑-∞∞ is connected.     

Finite p-Groups with Few Non-major k-Maximal Subgroups

A subgroup of index p ^k of a finite p-group G is called a k-maximal subgroup of G. Denote by d(G) the number of elements in a minimal generator-system of G and by δ _k (G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G. In this paper, the authors classify the finite p-groups with δ_d(G)(G) ≤ p² and δ_d(G)?1(G) = 0, respectively.     

小球与均质定轴杆的碰撞

从小球与均质定轴杆（质心轴）的碰撞问题出发,讨论了不同类型碰撞所遵循的物理规律,总结了完全非弹性碰撞过程的能量特征．     

欠匹配型磁绝缘感应电压叠加器次级阻抗优化方法

磁绝缘感应电压叠加器(MIVA)次级阻抗对脉冲功率驱动源和负载之间的功率耦合具有重要影响.基于稳态磁绝缘Creedon层流理论和鞘层电子流再俘获(re-trapping)理论,建立了负载欠匹配型MIVA电路分析方法,数值分析获得了MIVA输出参数(输出电压、阴/阳极电流和电功率)随负载欠匹配程度的变化规律.考虑阴极传导电流作为闪光X射线照相二极管的有效电流,建立了以MIVA末端X射线剂量率最大为目标的次级阻抗优化方法.获得了欠匹配型MIVA次级优化阻抗Z_(op)~*的变化规律:随着X射线剂量率对电压依赖程度提高,欠匹配型MIVA次级优化阻抗Z_(op)~*呈指数降低;负载阻抗越大,Z_(op)~*越大.     

Lower bound for quantum integration error on anisotropic Sobolev classes

We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev class R（Wpr（[0, 1]d）） （r R＋d）. Then combining this result with our previous one we determine the optimal bound of n-th minimal query error for anisotropic Hblder- Nikolskii class R（H∞r（[0,1]d）） and Sobolev class R（W∞r（[0,1]d））. The results show that for these two types of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.     

星极小格星半环

借鉴格环和格半环的定义,在星环、星半环的基础上,增加了一个偏序关系＂≤＂,引入了星极小格星环、星极小格星半环、和负星半环等的定义.进一步介绍了它们的一些性质,并得到了与格环和格半环类似的几个重要的命题.其中主要结论之一是得到了在星环R上引入一种偏序关系＂≤＂,使R成为一个星极小格星环,且恰以R的子星半环S为其负星半环的一个充分必要条件.