Longest cycles in almost regular 3-partite tournaments

If D is a digraph, then we denote by V(D) its vertex set. A multipartite or c-partite tournament is an orientation of a complete c-partite graph. The global irregularity of a digraph D is defined by

     

Spectral characteristics of 2-(4′-amino-3-pyridyl)benzimidazole: Effects of solvent and acid or base concentration

Spectral characteristics of 2-(4′-amino-3-pyridyl)benzimidazole (4-A3PyBI) have been studied in different solvents, as well as at different acid or base concentrations using absorption, fluorescence excitation and fluorescence spectroscopy. Excited singlet state (S₁) lifetimes for each species were measured using nanosecond time-dependent spectrofluorimeter. AM1 semi-empirical and density functional theoretical (DFT) calculations were performed on each species for the spectral assignment. From the above results it is concluded that 4-A3PyBI exists only in the amine form. First protonation occurs at pyridineN- atom and second protonation at the benzimidazole (BI)N- atom. When dication (DC) species is excited, two emission bands are observed, having the same fluorescence excitation spectra, suggesting the same ground state (S₀) precursor. Short wavelength (SW) emission band is assigned to the π-π* transition and long wavelength (LW) emission to the charge transfer transition. First deprotonation in S₀ state occurs from >N-H moiety, whereas in S₁ state it is from -NH₂ group. Monoanion (MA) so formed in S₁ state is non-fluorescent. Dianion (DA) is formed by further deprotonating >N-H moiety in S₁ state and it is fluorescent. pK_a values were determined and discussed.     

An almost periodic noncommutative Wiener's Lemma

We develop a theory of almost periodic elements in Banach algebras and present an abstract version of a noncommutative Wiener's Lemma. The theory can be used, for example, to derive some of the recently obtained results in time-frequency analysis such as the spectral properties of the finite linear combinations of time-frequency shifts.     

A note on the (G′/G)-expansion method again

We report an observation on two recent analytic methods; the (G′/G)-expansion method and the simplest equation method.     

On transitive topological group actions

We prove a general theorem on transitive topological group actions that give rise to almost ?ech-complete homogeneous spaces. This theorem implies the known open mapping theorems whose proof is a Baire category argument. As an application, we prove the uniform generalized Schönflies theorem generalizing Wright (1969) [19, Theorem 3].     

Codimension and projective dimension up to symmetry

Symmetric ideals in increasingly larger polynomial rings that form an ascending chain are investigated. We focus on the asymptotic behavior of codimensions and projective dimensions of ideals in such a chain. If the ideals are graded it is known that the codimensions grow eventually linearly. Here this result is extended to chains of arbitrary symmetric ideals. Moreover, the slope of the linear function is explicitly determined. We conjecture that the projective dimensions also grow eventually linearly. As part of the evidence we establish two non-trivial lower linear bounds of the projective dimensions for chains of monomial ideals. As an application, this yields Cohen–Macaulayness obstructions.     

Lelong–Poincaré formula in symplectic and almost complex geometry

In this paper, we present two applications of the theory of singular connections developed by Harvey and Lawson (1993). The first one is a version of the Lelong–Poincaré formula with estimates for sections of vector bundles over an almost complex manifold. The second one is a convergence theorem for divisors associated to a general family of symplectic submanifolds constructed by Donaldson (1996) (the case of hypersurfaces) and by Auroux in (1997) (for arbitrary dimensional submanifolds).     

非对合剩余格的正规双极值模糊理想

本文对非对合剩余格的双极值模糊理想问题作进一步深入研究.引入了非对合剩余格的正规双极值模糊理想概念, 考察了其性质并获得了其若干等价刻画.同时, 给出了两类特殊的双极值模糊理想的定义, 分别称为极大双极值模糊理想和完全正规双极值模糊理想并讨论了它们的性质和相互关系.这些工作为进一步揭示非对合剩余格的结构特征拓展了研究思路.     

Superconcentration,and randomized Dvoretzky's theorem for spaces with 1-unconditional bases

Let n be a sufficiently large natural number and let B be an origin-symmetric convex body in ${\mathbb{R}}^n$in the ?-position, and such that the space $({\mathbb{R}}^n,{6?6}_B)$ admits a 1-unconditional basis. Then for any $\epsilon \in (0,1/2]$, and for random $c\epsilon \log ?n/\log ?\frac{1}{\epsilon }$-dimensional subspace E distributed according to the rotation-invariant (Haar) measure, the section $B\cap E$ is $(1+\epsilon )$-Euclidean with probability close to one. This shows that the “worst-case” dependence on ε in the randomized Dvoretzky theorem in the ?-position is significantly better than in John's position. It is a previously unexplored feature, which has strong connections with the concept of superconcentration introduced by S. Chatterjee. In fact, our main result follows from the next theorem: Let B be as before and assume additionally that B has a smooth boundary and ${\mathbb{E}}_{{\gamma }_n}{6?6}_B\le n^c{\mathbb{E}}_{{\gamma }_n}{6{\mathrm{grad}}_B(?)6}_2$ for a small universal constant $c>0$, where ${\mathrm{grad}}_B(?)$ is the gradient of ${6?6}_B$ and ${\gamma }_n$ is the standard Gaussian measure in ${\mathbb{R}}^n$. Then for any $p\in [1,c\log ?n]$ the p-th power of the norm ${6?6}_B^p$ is $\frac{C}{\log ?n}$-superconcentrated in the Gauss space.     

L-预余拓扑空间中的理想

说明L-预余拓扑空间是L-余拓扑空间的推广;定义L-预余拓扑空间中理想间的强弱关系并给出一些相关结论;讨论L-预余拓扑空间中极大理想的性质.