Fractional partial differential equations with boundary conditions

We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posedness of the associated Cauchy problems in $C_0(\mathrm{\Omega })$ and $L_1(\mathrm{\Omega })$. In order to do so we develop a new method of embedding finite state Markov processes into Feller processes on bounded domains and then show convergence of the respective Feller processes. This also gives a numerical approximation of the solution. The proof of well-posedness closes a gap in many numerical algorithm articles approximating solutions to fractional differential equations that use the Lax–Richtmyer Equivalence Theorem to prove convergence without checking well-posedness.     

An iterative method for solving the stable subspace of a matrix pencil and its application

This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a semigroup property depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order.     

区间合成模糊对策

给出了一种新的合成模糊对策模型——区间合成模糊对策,研究了区间合成模糊对策的区间稳定集、区间核心、区间Shapley值、区间Banzhaf-Coleman势指标以及与子区间模糊对策的关系。区间合成模糊对策作为一种特殊的模糊数合成模糊对策,对于研究其它具有模糊数的模糊合成对策有一定的参考价值。     

Isotope Studies of Hydrogen and Oxygen in Ground Ice - Experiences with the Equilibration Technique

Abstract

Equilibration technique suitable for a large amount ofsamples is described for hydrogen and oxygen isotope analyses of ground ice, especially ice wedges, including the sampling strategy and the analytical procedure as well as the calibration of the Finnigan MAT Delta-S mass spectrometer in June, 1999. Since for future analyses of ice wedges, a higher sampling resolution with limited sample volume is required, the limit of the equliibration technique for small water samples size of between 0.05 and 5 ml was checked. For water samples smaller than 1ml, corresponding to a molar ratio [H₂O]/[H₂] of smaller than 0.994, a balance correction has to be applied. The experimental errors due to partial evaporation during evacuation, the balance calcultion of the isotope equilibration process, the linearity as well as memory effects of the mass spectrometer for smaples with large differences in δ¹⁸O and δD are tackled in this paper. In the polar regions of Northern Siberia without Late Pleistocene and Holocene glaciation, ground ice is used as an archive for paleoclimate studies. First results of stable isotope measurements on ice wedges clearly show a shift towards heavier isotopes and thus warmer winter temperatures as well as a change in the source of the precipitation between Late Pleistocene and Holocene. These results indicate the high potential of ground ice for paleoclimate studies.     

Determining the content and 13C abundance of total dissolved carbon in water samples by TOC analyser-mass spectrometer coupling

A combined system consisting of a TOC analyser connected to a quadrupole MS was recently described as a way of measuring the N content and the ¹⁵N abundance of total dissolved nitrogen in aqueous samples. This work examines whether this combination of instruments can also be used for the ¹³C determination of the total dissolved carbon in aqueous samples. A level of precision good for ¹³C-enriched samples was achieved with a relative standard deviation of <3%. By using an isotope ratio MS instead of the quadrupole MS employed here, TOC-MS coupling also ought to be suitable for determining natural ¹³C abundances.     

Stable categories of higher preprojective algebras

We introduce (n+1)$(n+1)$-preprojective algebras of algebras of global dimension n$n$. We show that if an algebra is n$n$-representation-finite then its (n+1)$(n+1)$-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)$(n+1)$-preprojective algebra is (n+1)$(n+1)$-Calabi–Yau, and, more precisely, it is the (n+1)$(n+1)$-Amiot cluster category of the stable n$n$-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)$(n+1)$-cluster tilting object. We show that even if the (n+1)$(n+1)$-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}$n\in \{1,2\}$) the results above still hold for the stable category of Cohen–Macaulay modules.     

A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces

We introduce a new technique for proving the classical stable manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the convergence of a canonical sequence of “finite time local stable manifolds” which are related to the dynamics of a finite number of iterations.