Multiphoton Phosphorescence of Simple Ketones by Visible-light Excitation and Its Consideration for Active Sensing in Space

Journal of Fluorescence - Acetone and butanone were seen to emit blue light around 450 nm when excited in the green by a high intensity pulsed laser. The pathway of this anti-Stokes...     

Photooxidations of 2-(γ,ε-dihydroxyalkyl) furans in water: synthesis of DE-bicycles of the pectenotoxins

Photooxygenations of 2-(γ,ε-dihydroxyalkyl) furans in H(2)O followed by in situ reduction and ketalization affords, in one synthetic operation, DE-bicyclic ketals of the pectenotoxins.     

Removing ruthenium residues from olefin metathesis reaction products

Olefin metathesis has revolutionized the way chemists design and synthesize molecules, mostly due to the development of well-defined ruthenium catalysts with high oxygen-, moisture-, and functional-group tolerance. However, the complete removal of residual ruthenium after the end of a metathesis reaction often imposes significant challenges. This Minireview summarizes the strategies for the sequestration of ruthenium impurities from olefin metathesis post-reaction mixtures, thus comprising a practical guide for synthetic chemists employing ruthenium-catalyzed metathesis reactions in the synthesis of organic or polymeric materials.     

An optimal Hardy–Morrey inequality

In this work we improve the sharp Hardy inequality in the case p?>?n by adding an optimal weighted H?lder seminorm. To achieve this we first obtain a local improvement. We also obtain a refinement of both the Sobolev inequality for p?>?n and the Hardy inequality, the latter having the best constant.     

Liquid chromatography–mass spectrometry based global metabolite profiling: A review

Untargeted, global metabolite profiling (often described as metabonomics or metabolomics) represents an expanding research topic and is, potentially, a major pillar for systems biology studies. To obtain holistic metabolic profiles from complex samples, such as biological fluids or tissue extracts, requires powerful, high resolution and information-rich analytical methods and for this spectroscopic technologies are generally used. Mass spectrometry, coupled to liquid chromatography (LC–MS), is increasingly being used for such investigations as a result of the significant advances in both technologies over the past decade. Here we try to critically review the topic of LC–MS-based global metabolic profiling and describe and compare the results offered by different analytical strategies and technologies. This review highlights the current challenges, limitations and opportunities of the current methodology.     

A singular function boundary integral method for elliptic problems with singularities

In this work we present a singular function boundary integral method for elliptic problems with boundary singularities. In this method, the approximation is constructed from the truncated asymptotic expansion for the solution near the singular point and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. The resulting discrete problem is posed and solved on the boundary of the domain, away from the point of singularity. We are able to show that the method approximates the generalized stress intensity factors, i.e. the coe cients in the asymptotic expansion, at an exponential rate. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the blow-up set of the Yang–Mills flow on Kähler surfaces

The Yang–Mills flow on a Kähler surface with holomorphic initial data converges smoothly away from a singular set determined by the Harder–Narasimhan– Seshadri filtration of the initial holomorphic bundle.     

Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians

Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the Grothendieck Quot Scheme. The latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by Bradlow. This gives an effective way of computing certain intersection numbers (known as ``Gromov invariants') on the space of holomorphic maps into Grassmannians. We carry out these computations in the case where the Riemann surface has genus one.

     

Forcing Divergence When the Supremum Is Not Integrable

If a sequence of functions (f_n) has an integrable supremum and converges almost everywhere, then an operator sequence (T_n) will yield a sequence (T_nf_n) that converges almost everywhere too, under some very general assumptions about the sequence (T_n). However, if the supremum of (f_n) is not integrable then this can fail to be the case. It is shown that if a sequence of functions (f_n)has a supremum sup_n |f_n| that is not integrable, then one can always construct a variety of sequences of positive contractions (T_n) such that lim sup |T_n f_n| = ∞ a.e. These operators can be conditional expectations with respect to an increasing sequence of finite σ-algebras, the conditional expectation with respect to one fixed σ-algebra, or averages with respect to a measure-preserving transformation. General discussion of these constructions, history of previous results of this type, and some open questions are also given.