On Measuring the Efficiency of Kernel Operators in L p (R d )

It is well known that it is possible to enhance the approximation properties of a kernel operator by increasing its support size. There is an obvious tradeoff between higher approximation order of a kernel and the complexity of algorithms that employ it. A question is then asked: how do we compare the efficiency of kernels with comparable support size? We follow Blu and Unser and choose as a measure of the efficiency of the kernels the first leading constant in a certain error expansion. We use time domain methods to treat the case of globally supported kernels in L _p (R ^d), 1≤p≤∞.

     

Water – A key parameter in the stability of anion exchange membrane fuel cells

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A Pd/C‐CeO2 Anode Catalyst for High‐Performance Platinum‐Free Anion Exchange Membrane Fuel Cells

One of the biggest obstacles to the dissemination of fuel cells is their cost, a large part of which is due to platinum (Pt) electrocatalysts. Complete removal of Pt is a difficult if not impossible task for proton exchange membrane fuel cells (PEM‐FCs). The anion exchange membrane fuel cell (AEM‐FC) has long been proposed as a solution as non‐Pt metals may be employed. Despite this, few examples of Pt‐free AEM‐FCs have been demonstrated with modest power output. The main obstacle preventing the realization of a high power density Pt‐free AEM‐FC is sluggish hydrogen oxidation (HOR) kinetics of the anode catalyst. Here we describe a Pt‐free AEM‐FC that employs a mixed carbon‐CeO₂ supported palladium (Pd) anode catalyst that exhibits enhanced kinetics for the HOR. AEM‐FC tests run on dry H₂ and pure air show peak power densities of more than 500 mW cm^?2.     

Character sets of strings

Given a string S over a finite alphabet Σ, the character set (also called the fingerprint) of a substring S^′ of S is the subset CΣ of the symbols occurring in S^′. The study of the character sets of all the substrings of a given string (or a given collection of strings) appears in several domains such as rule induction for natural language processing or comparative genomics. Several computational problems concerning the character sets of a string arise from these applications, especially:

(1) Output all the maximal locations of substrings having a given character set.

(2) Output for each character set C occurring in a given string (or a given collection of strings) all the maximal locations of C.

Denoting by n the total length of the considered string or collection of strings, we solve the first problem in Θ(n) time using Θ(n) space. We present two algorithms solving the second problem. The first one runs in Θ(n²) time using Θ(n) space. The second algorithm has Θ(n|Σ|log|Σ|) time and Θ(n) space complexity and is an adaptation of an algorithm by Amir et al. [A. Amir, A. Apostolico, G.M. Landau, G. Satta, Efficient text fingerprinting via Parikh mapping, J. Discrete Algorithms 26 (2003) 1–13].     

Multilevel preconditioning for partition of unity methods: some analytic concepts

This paper is concerned with the construction and analysis of multilevel Schwarz preconditioners for partition of unity methods applied to elliptic problems. We show under which conditions on a given multilevel partition of unity hierarchy (MPUM) one even obtains uniformly bounded condition numbers and how to realize such requirements. The main anlytical tools are certain norm equivalences based on two-level splits providing frames that are stable under taking subsets. This work has been supported in part by the European Community’s Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY), by the Leibniz-Programme of the German Research Foundation (DFG), and by the SFB 401 funded by DFG.     

Anisotropic Meshless Frames on ℝ n

We present a construction of anisotropic multiresolution and anisotropic wavelet frames based on multilevel ellipsoid covers (dilations) of ℝ ⁿ . The wavelets we construct are C ^∞ functions, can have any prescribed number of vanishing moments and fast decay with respect to the anisotropic quasi-distance induced by the cover. The dual wavelets are also C ^∞, with the same number of vanishing moments, but with only mild decay with respect to the quasi-distance. An alternative construction yields a meshless frame whose elements do not have vanishing moments, but do have fast anisotropic decay.     

Nanoparticle dispersion laser

Lasing action from a dispersion of nanoparticles is reported for the first time to our knowledge. The nanoparticles are Nd(2)O(3) modified with dimethyldichlorosilane (DMDCS) in dimethylsulfoxide. The laser was pumped with a pulsed laser at 802 nm and yielded 2.7 mJ with a slope efficiency of 50%. This was compared to a standard Nd-doped phosphate glass that yielded very similar results in the same setup.     

Fast index for approximate string matching

We present an index that stores a text of length n such that given a pattern of length m, all the substrings of the text that are within Hamming distance (or edit distance) at most k from the pattern are reported in $O(m+\log \log n+\text{\#}\text{matches})$ time (for constant k). The space complexity of the index is $O(n^{1+?})$ for any constant $?>0$.     

Anionic oligomerization of dimethyl itaconate

Methanolic solutions of alkali metal and magnesium methoxides were used as initiators for the oligomerization of dimethyl itaconate in methanol, DMF and DMSO. The yield of oligomers was higher in the aprotic solvents. The oligomeric mixtures contained a preponderance of trimer, the structure of which was elucidated by mass spectrometry as a cyclohexane derivative. The oligomers contained no methoxyl end-groups, and initiation is postulated to be an acid-base reaction, in which the allylic hydrogen α- to the carbonyl is abstracted. This belief was supported by the fact that the use of sodium naphthalene and triethylamine as initiators gave the same oligomers. The trimer was tested as a plasticizer.