Classifying spaces for polarized mixed Hodge structures and for Brieskorn lattices

Classifying spaces and moduli spaces are constructed for two invariants of isolated hypersurface singularities, for the polarized mixed Hodge structure on the middle cohomology of the Milnor fibre, and for the Brieskorn lattice as a subspace of the Gauß–Manin connection. The relations between them, period mappings for -constant families of singularities, and Torelli theorems are discussed.     

Factors influencing chromatographic data in fast gas chromatography with on‐column injection

The use of larger volume injection with on‐column injection and fast GC commercial instrumentation was evaluated with the model mixture of n‐alkanes of a broad range of volatility (C₁₀–C₂₈). The presented configuration allows introduction of 40–80‐fold larger sample volumes without any distortion of peak shapes compared to “usual” fast GC set‐ups using narrow‐bore columns. A normal‐bore retention gap (1–5 m×0.32 mm ID) was coupled to a narrow‐bore (5 m×0.1 mm ID×0.4 μm film thickness) analytical column using a standard press‐fit connector. The connection was tight and reliable, and hence suitable for hydrogen as carrier gas. The effect of pre‐column and analytical column connector, injection volume, pre‐column length, column inlet pressure, and analyte volatility on peak shape, peak broadening, and focusing are discussed. The precision of chromatographic data measurements and peak capacity under optimised temperature programmed conditions for fast separations with large volume injection were found to be very good. The presented fast GC set‐up with on‐column injection extends the applicability of the technique to trace analysis.     

On rigidity of affine surfaces

Rigidity of nondegenerate Blaschke surfaces in is studied. The rigidity criteria are given in terms of , where is the curvature of the Blaschke connection . If the rank of is 2, then the surface is rigid. If , it is nonrigid. In the case where the rank of is 1 there are both rigid and nonrigid surfaces. This case is discussed for various types of surfaces.

     

Cosmological solutions for the coupled Einstein-Yang-Mills-Higgs equations

The coupled system of Einstein-Yang-Mills-Higgs equations is solved numerically for a Robertson-Walker symmetric universe. The open universe must be excluded because, for this situation, the coupled system is unable to produce energy-momentum densityT in agreement with the Robertson-Walker symmetry. For the closed universe, inflation solutions do occur if an early re-collapse is avoided by suitable choice of the initial conditions. The energy exchange between the minimally coupled Higgs and Yang-Mills subsystems is very small so that the inflating power of the Higgs field cannot be disturbed by the presence of the Yang-Mills field. After the inflation phase the influence of the Yang-Mills field is completely negligible (cosmic no-hair theorem).     

Holomorphic flat projective structures on projective threefolds

Here we classify projective 3-folds with a holomorphic flat projective structure and Kodaira dimension 1 or 2.The author was partially supported by MURST and GNSAGA of CNR (Italy).     

Reflection positivity, rank connectivity, and homomorphism of graphs

It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and exponential rank connectivity. In terms of statistical physics, this can be viewed as a characterization of partition functions of vertex coloring models.

     

Itô maps and analysis on path spaces

We consider versions of Malliavin calculus on path spaces of compact manifolds with diffusion measures, defining Gross–Sobolev spaces of differentiable functions and proving their intertwining with solution maps, , of certain stochastic differential equations. This is shown to shed light on fundamental uniqueness questions for this calculus including uniqueness of the closed derivative operator d and Markov uniqueness of the associated Dirichlet form. A continuity result for the divergence operator by Kree and Kree is extended to this situation. The regularity of conditional expectations of smooth functionals of classical Wiener space, given , is considered and shown to have strong implications for these questions. A major role is played by the (possibly sub-Riemannian) connections induced by stochastic differential equations: Damped Markovian connections are used for the covariant derivatives.     

多局部残差连接注意网络的图像去模糊

针对现有的基于卷积神经网络的图像去模糊算法存在图像纹理细节恢复不清晰的问题,提出了一种基于多局部残差连接注意网络的图像去模糊算法。首先,采用一个卷积层进行浅层特征提取;其次,设计了一种新的基于残差连接和并行注意机制的多局部残差连接注意模块,用于消除图像模糊并提取上下文信息;再次,采用一个基于扩张卷积的成对连接模块进行细节恢复;最后,利用一个卷积层重建清晰图像。实验结果表明：在GoPro数据集上的PSNR (peak signal to noise ratio)和SSIM (structure similarity)分别为31.83 dB、0.927 5,在定性和定量两方面都表明所提方法能够有效地恢复模糊图像的纹理细节,网络性能优于对比方法。     

基于集对分析联系数的区间数型水环境质量综合评价模型及其应用

水环境质量综合评价具有不确定性,其待评价水质监测值及评价标准是区间数.针对待评价水质监测值与水环境质量评价标准不能直接比较大小的问题,根据区间数的误差分布形式,提出一种基于集对分析联系数的区间数型水环境质量综合评价模型.模型定义了两个联系数之间的加权海明距离,用水环境质量评价标准组成标准联系数,待评价水质监测值组成待评价联系数,通过计算待评价联系数与标准联系数的加权联系数海明距离,根据a+bi型联系数大小比较法则,综合判定待评价水质级别.以浑河沈阳东陵大桥处实测水质部分结果评价为例进行计算分析,并与其它方法得到的结果进行了对比,得到的结果一致.     

Generic injectivity and stability of inverse problems for connections

We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a compact Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral geometry question of some attenuated geodesic ray transform through a pseudolinearization argument. We show injectivity (up to natural obstructions) and stability estimates for both the linear and nonlinear problems for generic simple metrics and generic connections and Higgs fields, including the real-analytic ones. We consider the problems on simple manifolds to make the exposition of the main ideas clear and concise, many results of this paper still hold under some assumptions weaker than simplicity.