Iwasawa μ-invariants of elliptic curves and their symmetric powers

In an earlier paper we considered the effects that finite submodules can have on μ-invariants of Selmer groups. In this paper we examine some of the consequences of that theory to elliptic curves and their symmetric powers. One main result is the construction of an isogeny class of elliptic curves, all of which have positive μ-invariants. A second result is a connection between the behaviors of μ-invariants associated with the symmetric powers of an elliptic curve over , and the behavior of the μ-invariant of that elliptic curve over different extensions of .     

ON THE NONLOCAL SYMMETRIES OF THE μ-CAMASSA–HOLM EQUATION

The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm and the Hunter–Saxton equations. This equation admits quadratic pseudo-potentials which allow us to compute some first-order nonlocal symmetries. The found symmetries preserve the mean of solutions. Finally, we discuss also the associated μCH equation.     

非合作n人投标报价服从N(μ,σ~2)分布时局中人投标报价策略的研究

推导了矩阵对策模型 ,对非合作 n人投标报价的分布进行 x2 检验。当非合作 n人投标报价服从N (μ,σ2 )分布时 ,根据参数区间公式 ,估计非合作 n人有效报价平均数的范围 ,局中人 最佳报价可根据矩阵对策模型来确定。该方法确定的报价与最佳标底的误差能控制在较小的范围内 ,适用于招标中合成标底的评标办法 ,对确定报价具有一定的实用价值。     

基于模糊值Choquet积分定义集函数的S性与PGP性

针对模糊测度空间上已建立的模糊值Choquet积分,将这种积分整体看成可测空间上取值于模糊数的集函数,当模糊测度满足一般S性和PGP性时,研究了这种模糊值集函数所保持的遗传性质.     

草酸根桥联手性双核铜的合成、表征、结构与磁性

分别以(8R,10R)-(-)-[4,5]-pineno-2,2′-bipyridine或(8S,10S)-(+)-[4,5]-pineno-2,2′-bipyridine(LRR和LSS)为手性配体合成双核铜络合物[Cu2(μ-ox)(LRR)2(H2O)2(ClO4)2](1)、[Cu2(μ-ox)(LRR)2(CH3COCH3)2(ClO4)2](1a)、[Cu2(μ-ox)(LSS)2(H2O)2(ClO4)2](2)和[Cu2(μ-ox)-(LRR)(LSS)(CH3COCH3)2(ClO4)2](3)(ox2-=草酸根),并探讨了其反应机理.由元素分析、电导率、紫外可见谱(UV-vis)、圆二色(CD)谱和晶体结构分析推测:该系列络合物具有草酸根桥联的双核结构,两个铜(II)离子与草酸根几乎成共平面;1a和3的晶体结构分析表明,每个Cu(II)的配位构型为拉长畸变八面体,双核分子中轴向的两个溶剂分子和两个高氯酸根互为反式配位.对映体络合物1和2的溶液CD光谱大致呈镜像对称,在可见区的极弱CD吸收峰可能源于LRR和LSS蒎烯基上的手性中心对Cu(II)d-d生色团的手性微扰产生的邻位效应.采用最小二乘法和Bleaney-Bowers方程对络合物1的变温磁化率测试数据进行拟合,求得交换积分J=-338.41(4)cm-1,表明铜(II)离子间有较强的反铁磁自旋交换作用.     

Comparative study of new shell-type,sub-2 μm fully porous and monolith stationary phases,focusing on mass-transfer resistance

Today sub-2 μm packed columns are very popular to conduct fast chromatographic separations. The mass-transfer resistance depends on the particle size but some practical limits exist not to reach the theoretically expected plate height and mass-transfer resistance. Another approach applies particles with shortened diffusion path to enhance the efficiency of separations. In this study a systematical evaluation of the possibilities of the separations obtained with 5 cm long narrow bore columns packed with new 2.6 μm shell particles (1.9 μm nonporous core surrounded by a 0.35 μm porous shell, Kinetex™, Core-Shell), packed with other shell-type particles (Ascentis Express™, Fused-Core), totally porous sub-2 μm particles and a 5 cm long narrow bore monolith column is presented. The different commercially available columns were compared by using van Deemter, Knox and kinetic plots. Theoretical Poppe plots were constructed for each column to compare their kinetic performance. Data are presented on polar neutral real-life analytes. Comparison of a low molecular weight compounds (MW = 270–430) and a high molecular weight one (MW ∼ 900) was conducted. This study proves that the Kinetex column packed with 2.6 μm shell particles is worthy of rivaling to sub-2 μm columns and other commercially available shell-type packings (Ascentis Express or Halo), both for small and large molecule separation. The Kinetex column offers a very flat C term. Utilizing this feature, high flow rates can be applied to accomplish very fast separations without significant loss in efficiency.     

~ 1.2 μm near-infrared emission and gain anticipation in Ho doped heavy-metal gallate glasses

Ho³⁺-doped low-phonon-energy heavy-metal gallate glasses (LKBPBG) have been prepared and efficient 1.199 μm emission originating from the ⁵I₆ → ⁵I₈ radiative transition has been observed under 900 nm excitation. The spontaneous emission probability and the maximum stimulated emission cross-section were derived to be 294.31 s^− 1 and 3.46 × 10^− 21 cm², respectively. The ratio of quantum yields between ~ 1.2 and ~ 2.0 μm emissions was identified to be 16%, demonstrating that the ⁵I₆ → ⁵I₈ transition is favorable for optical amplification. The maximum gain coefficient of 1.84 dB/cm at 1.199 μm wavelength was anticipated in the ideal status. These results indicate that the Ho³⁺-doped LKBPBG glasses have a promising potential for the development of ~ 1.2 μm signal amplifier devices.     

Well-posedness,wave breaking and peakons for a modified μ-Camassa–Holm equation

Considered herein is a modified periodic Camassa–Holm equation with cubic nonlinearity which is called the modified μ-Camassa–Holm equation. The proposed equation is shown to be formally integrable with the Lax pair and bi-Hamiltonian structure. Local well-posedness of the initial-value problem to the modified μ-Camassa–Holm equation in the Besov space is established. Existence of peaked traveling-wave solutions and formation of singularities of solutions for the equation are then investigated. It is shown that the equation admits a single peaked soliton and multi-peakon solutions with a similar character of the μ-Camassa–Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and several wave-breaking mechanisms for solutions with certain initial profiles are described in detail.     

N(2,2,0)代数的(∈,∈Vq_(λ,μ))-模糊关联理想若干性质

对N(2,2,0)代数(∈,∈∨q_((λ,μ)))-模糊关联理想若干性质进行了详细的研究.首先,运用点态化的方法证明了(∈,∈∨q_((λ,μ)))-模糊关联理想的同态像与同态原像的基本性质;其次,研究了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积;最后,讨论了(∈,∈∨q_((λ,μ)))-模糊关联理想的直积的投影子集.     

具有非倍测度的参数型Marcinkiewicz积分交换子在Hardy空间的有界性

主要证明了由参数型Marcinkiewicz积分M~p和Lipschitz函数b生成的交换子M_b~p的有界性.在M的核满足一定的条件下,证明了M_b~p不仅从Lebesgue空间L~(n/(n-β))(μ)到Hardy空间H~1(μ)有界,而且从Lebesgue空间L~(n/β)(μ)到RBMO(μ)有界.