Random-order bin packing

The average-case analysis of algorithms usually assumes independent, identical distributions for the inputs. In [C. Kenyon, Best-fit bin-packing with random order, in: Proc. of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 1996, pp. 359–364] Kenyon introduced the random-order ratio, a new average-case performance metric for bin packing heuristics, and gave upper and lower bounds for it for the Best Fit heuristics. We introduce an alternative definition of the random-order ratio and show that the two definitions give the same result for Next Fit. We also show that the random-order ratio of Next Fit equals to its asymptotic worst-case, i.e., it is 2.     

On a method of Pollaczek

In 1952, F. Pollaczek gave a method for finding the distribution of the maximal partial sum of mutually independent and identically distributed random variables. In this paper, Pollaczek's results are extended, and the extended results are applied in theory of queues for finding the distribution of the waiting time for single server queues.     

Katalytischer Nachweis und Bestimmung von Jodspuren mit Hilfe der 3,3′-Dimethylnaphthidin-Hydrogenperoxid-Reaktion

Zusammenfassung Die 3,3-Dimethylnaphthidin-Wasserstoffperoxid-Redoxreaktion wird von Jodid sehr stark katalysiert. Damit kann man bei Anwesenheit von Ameisensäure Jodid selbst in einer Grenzkonzentration von 0,002g/ml nachweisen bzw bestimmen. Dazu eignet sich die Simultankomparationsmethode. Im Konzentrationsbereich von 0,1 bis 0,01g J^–/5 ml beträgt der relative Fehler 3%. Ag⁺, Hg²⁺ oder Bi³⁺ dürfen nicht anwesend sein; andere störende Ionen können mit ÄDTA bzw. Weinsäure maskiert werden.

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Catalytic detection and determination of traces of iodine by means of the 3,3-dimethylnaphthidine-hydragen peroxide reaction

Summary The 3,3-dimethylnaphthidine-hydrogen peroxide redox reaction is strongly catalysed by iodide. Therefore, if formic acid is present, iodide itself may be detected or determined in a limiting concentration of 0.002g/ml. The simultaneous comparation method is appropriate here. In the concentration region from 0.1 to 0.01g I^–/5 ml, the relative error is 3%. Ag⁺, Hg²⁺ or Bi³⁺ may not be present. Other interfering ions can be masked with EDTA or tartaric acid.

     

A correction to and improvement of ‘Strong approximations of some biometric estimates under random censorship’

Summary In the proof of the main result of the original paper there is an error. Instead of repairing that proof to get just the original result, at the critical spot we improve the proof and obtain a much better result. In particular, we approximate the product-limit and empirical cumulative hazard processes by suitable copies of the corresponding limiting Gaussian processes with rates of approximation that on appropriate fixed half lines reduce to the rates of Komlós, Major and Tusnády for the uncensored empirical process.     

The rate of strong uniform consistency for the multivariate product-limit estimator

The general asymptotic order of magnitude is determined for the maximal deviation of the multivariate product-limit estimate from the estimated survival function on R^k. This order depends on the joint behavior of the censoring and censored distributions in a well-defined way. Corresponding to specific joint behaviors, several lim sup results are deduced generalizing everything that is known in the univariate case. The results are also extended for the variable censoring model.     

On generalized Dedekind sums

In this paper we give a simple proof for the reciprocity formula for the generalized Dedekind sums and derive an explicit expression for these sums.     

Air-breathing laminar flow-based microfluidic fuel cell

This communication reports the design and characterization of an air-breathing laminar flow-based microfluidic fuel cell (LFFC). The performance of previous LFFC designs was cathode-limited due to the poor solubility and slow transport of oxygen in aqueous media. Introduction of an air-breathing gas diffusion electrode as the cathode addresses these mass transfer issues. With this design change, the cathode is exposed to a higher oxygen concentration, and more importantly, the rate of oxygen replenishment in the depletion boundary layer on the cathode is greatly enhanced as a result of the 4 orders of magnitude higher diffusion coefficient of oxygen in air as opposed to that in aqueous media. The power densities of the present air-breathing LFFCs are 5 times higher (26 mW/cm2) than those for LFFCs operated using formic acid solutions as the fuel stream and an oxygen-saturated aqueous stream at the cathode ( approximately 5 mW/cm2). With the performance-limiting issues at the cathode mitigated, these air-breathing LFFCs can now be further developed to fully exploit their advantages of direct control over fuel crossover and the ability to individually tailor the chemical composition of the cathode and anode media to enhance electrode performance and fuel utilization, thus increasing the potential of laminar flow-based fuel cells.