Stable hydrogen isotope ratios of lignin methoxyl groups as a palaeoclimate proxy

• Stable isotope ratios of organic compounds are valuable tools for determining the geographical origin, identity, authenticity or history of samples from a vast range of sources such as sediments, plants and animals, including humans. • Hydrogen isotope ratios (d2H values) of methoxyl groups in lignin from wood of trees grown in different geographical areas were measured using compound-specificpyrolysis isotope ratio mass spectrometry analysis. • Lignin methoxyl groups were depleted in 2H relative to both meteoric water andwhole wood. A high correlation (r2=0.91) was observed between the d2 H valuesof the methoxyl groups and meteoric water, with a relatively uniform fractionation of –216±19 recorded with respect to meteoric water over a range of d2H values from –110 in northern Norway to + 20‰ in Yemen. Thus, woods from northernlatitudes can be clearly distinguished from those from tropical regions. By contrast, the d2H values of bulk wood were only relatively poorly correlated (r 2 = 0.47) with those of meteoric water. • Measurement of the d 2H values of lignin methoxyl groups is potentially a powerful tool that could be of use not only in the constraint of the geographical origin of lignified material but also in paleoclimate, food authenticity and forensic investigations.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

An infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes

An example is constructed of an infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes.

Universal Abelian topological groups

A topological group G is said to be universal in a class K of topological groups if G is an element of K and if for every group H is an element of K there is a subgroup K of G that is isomorphic to H as a topological group. A group is constructed that is universal in the class of separable metrizable topological Abelian groups.

Counterexample to Peano's theorem in infinite-dimensional F '-spaces

Let $E$ be a nonnormable Frechet space, and let $E'$ be the space of all continuous linear functionals on $E$ in the strong topology. A continuous mapping $f : E' \to E'$ such that for any $t_0\in R$ and $x_0\in E'$, the Cauchy problem $\dot x= f(x)$, x(t_0) = x_0$ has no solutions is constructed.