关于椭圆曲线E_D:y~2=x~3-D~2x的BSD猜想

本文证明了形如ｙ~２＝ｘ~３－ｐ-１~２…ｐ-ｎ~２ｘ的一类椭圆曲线的Ⅲ群２-分支在一定条件下同构于 Ｚ／２Ｚ × Ｚ／２Ｚ,其阶为 ４,与Ｌ函数部分的相应结果和 Ｒｕｂｉｎ Ｋ．关于有复乘的椭圆曲线的重要结果一起,我们知道ＢＳＤ猜想对本文定理中的椭圆曲线成立．     

哈密顿系统的低维环面的保存性

本文给出了关于哈密顿系统低维环面的一个推广的KAM定理,它适用于同时存在法向频率和双曲法向分量的情况.其证明基于尤建功的一个定理的光滑性表述及法向双曲不变流形理论的应用.文中还给出了另外两种情况下的推广.     

A combined analytical singularity subtraction method and compact implicit differencing scheme for aerodynamic mixing

In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical. With this restriction, it may be concluded that an important family of methods for mathematical/computational development are reduced or approximate models. In this study, a combined perturbation/numerical modeling methodology is developed. The numerical portion of the model uses a compact finite difference scheme, while analytical solutions are used to resolve singular behavior that is inherent to this flow. Solutions are presented to illustrate the efficiency of this methodology.     

Boat-like Au nanoparticles embedded mesoporous γ-Al2O3 films: an efficient SERS substrate

A new water-dispersible nanostructure based on magnetite (Fe₃O₄) and usnic acid (UA) was prepared in a well-shaped spherical form by a precipitation method. Nanoparticles were well individualized and homogeneous in size. The presence of Fe₃O₄@UA was confirmed by transmission electron microscopy, Fourier transform-infrared spectroscopy, and X-ray diffraction. The UA was entrapped in the magnetic nanoparticles during preparation and the amount of entrapped UA was estimated by thermogravimetric analysis. Fabricated nanostructures were tested on planktonic cells growth (minimal inhibitory concentration assay) and biofilm development on Gram-positive Staphylococcus aureus (S. aureus), Enterococcus faecalis (E. faecalis) and Gram-negative Escherichia coli (E. coli), Pseudomonas aeruginosa (P. aeruginosa) reference strains. Concerning the influence of Fe₃O₄@UA on the planktonic bacterial cells, the functionalized magnetic nanoparticles exhibited a significantly improved antimicrobial activity against E. faecalis and E. coli, as compared with the Fe₃O₄ control. The UA incorporated into the magnetic nanoparticles exhibited a very significant inhibitory effect on the biofilm formed by the S. aureus and E. faecalis, on a wide range of concentrations, while in case of the Gram-negative microbial strains, the UA-loaded nanoparticles inhibited the E. coli biofilm development, only at high concentrations, while for P. aeruginosa biofilms, no inhibitory effect was observed. The obtained results demonstrate that the new water-dispersible Fe₃O₄@UA nanosystem, combining the advantages of the intrinsic antimicrobial features of the UA with the higher surface to volume ratio provided by the magnetic nanocarrier dispersible in water, exhibits efficient antimicrobial activity against planktonic and adherent cells, especially on Gram-positive strains.     

Sur les plus grands facteurs premiers d'un entier

Let and, for each integern such that (n)k, denote byP _k (n) itsk ^th largest prime factor. Further, given a set of primesQ of positive density <1 satisfying a certain regularity condition, defineP(n, Q), as the largest prime divisor ofn belonging toQ, assuming thatP(n,Q)=+ if no such prime factor exists. We provide estimates of , fork2, and of . We also study the median value of the functionP(n,Q) and that of the functionP _k (n) for eachk1.     

Different Faces of the Shearlet Group

Recently, shearlet groups have received much attention in connection with shearlet transforms applied for orientation sensitive image analysis and restoration. The square integrable representations of the shearlet groups provide not only the basis for the shearlet transforms but also for a very natural definition of scales of smoothness spaces, called shearlet coorbit spaces. The aim of this paper is twofold: first we discover isomorphisms between shearlet groups and other well-known groups, namely extended Heisenberg groups and subgroups of the symplectic group. Interestingly, the connected shearlet group with positive dilations has an isomorphic copy in the symplectic group, while this is not true for the full shearlet group with all nonzero dilations. Indeed we prove the general result that there exist, up to adjoint action of the symplectic group, only one embedding of the extended Heisenberg algebra into the Lie algebra of the symplectic group. Having understood the various group isomorphisms it is natural to ask for the relations between coorbit spaces of isomorphic groups with equivalent representations. These connections are examined in the second part of the paper. We describe how isomorphic groups with equivalent representations lead to isomorphic coorbit spaces. In particular we apply this result to square integrable representations of the connected shearlet groups and metaplectic representations of subgroups of the symplectic group. This implies the definition of metaplectic coorbit spaces. Besides the usual full and connected shearlet groups we also deal with Toeplitz shearlet groups.     

Intriguing sets in partial quadrangles

The point‐line geometry known as a partial quadrangle (introduced by Cameron in 1975) has the property that for every point/line non‐incident pair (P, ?), there is at most one line through P concurrent with ?. So in particular, the well‐studied objects known as generalized quadrangles are each partial quadrangles. An intriguing set of a generalized quadrangle is a set of points which induces an equitable partition of size two of the underlying strongly regular graph. We extend the theory of intriguing sets of generalized quadrangles by Bamberg, Law and Penttila to partial quadrangles, which gives insight into the structure of hemisystems and other intriguing sets of generalized quadrangles. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:217‐245, 2011     

伴随奇点分支的退化异宿轨道的保存和横截性

本文应用指数三分性和不变流形的局部几何表示方法,给出异宿流形上的轨道当两个奇点经历超;临界分支和摄动时保存和横截的条件．     

Magnetically induced chessboard pattern in the conductance of a Kondo quantum dot

We quantitatively describe the main features of the magnetically induced conductance modulation of a Kondo quantum dot-or chessboard pattern-in terms of a constant-interaction double quantum dot model. We show that the analogy with a double dot holds down to remarkably low magnetic fields. The analysis is extended by full 3D spin density functional calculations. Introducing an effective Kondo coupling parameter, the chessboard pattern is self-consistently computed as a function of magnetic field and electron number, which enables us to explain our experimental data quantitatively.     

The effect of Cu substitution on the A1g mode of La0.7Sr0.3MnO3 manganites

We report on the first Raman data of Cu substituted La_1−ySr_yMn_1−xCu_xO₃ (0≤x≤0.10 and 0.17≤y≤0.3, accordingly in order to have the same Mn⁴⁺/[Mn⁴⁺+Mn³⁺] ratio), collected in the frequency range 100-900 cm⁻¹ and at room temperature, with parallel (e_i∥e_s) and crossed (e_i⊥e_s) polarizations of the incident (e_i) and scattered (e_s) light. Spectra were fitted with a Drude-Lorentz model, and peaks at 190-220 and 430 cm⁻¹, together with two broad structures centered at near 500 and 670 cm⁻¹, have been found. We also have observed that the A_1g mode is substantially shifted with increasing Cu substitution. The A_1g phonon shift is a linear function of the tolerance factor t and the rhombohedral angle α_r, thus following the structural changes of the MnO₆ octahedra in the system.