A weak law for normed weighted sums of random elements in rademacher type p banach spaces

For weighted sums Σ_{j = 1}ⁿa_jV_j of independent random elements {V_n, n ≥ 1} in real separable, Rademacher type p (1 ≤ p ≤ 2) Banach spaces, a general weak law of large numbers of the form (Σ_{j = 1}ⁿa_jV_j − v_n)/b_n →^p 0 is established, where {v_n, n ≥ 1} and b_n → ∞ are suitable sequences. It is assumed that {V_n, n ≥ 1} is stochastically dominated by a random element V, and the hypotheses involve both the behavior of the tail of the distribution of |V| and the growth behaviors of the constants {a_n, n ≥ 1} and {b_n, n ≥ 1}. No assumption is made concerning the existence of expected values or absolute moments of the {V_n, n >- 1}.     

A modification of Crum's method

A generalization of Crum's method is proposed that makes it possible to construct new examples of Sturm-Liouville operators with spectrum that can be exactly calculated.Institute of Methamatics of the Ufa Scientific Center, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 3, pp. 323–330, December, 1994.     

Light charged particle release in252Cf spontaneous fission: Tripartition versus fragment de-excitation

Double-differential emission probabilities P (E, θ) in angle θ and energy E of protons, tritons, and α-particles were measured in the case of spontaneous fission of²⁵²Cf. A detector system consisting of position-sensitive parallel-plate avalanche counters (PPAC) and ΔE?E-telescopes allowed a coincidence measurement of fission fragments (FF) and light charged particles (LCP) in the whole region from 0 deg. to 180 deg. with respect to the light-fragment direction. Previous results for α-particle emission were confirmed. The background contributions for protons are discussed in detail. For proton emission the background arising from (n, p)-reactions was measured and compared with a corresponding Monte-Carlo simulation of elastic (n, p)-clusions. Unlike for tritons and a-particles the P (E, θ) distribution for protons does not show equatorial peaking in 0 between 80 deg. and 90 deg. and contradicts classical scission point emission. The proton distribution, however, agrees with fragment de-excitation calculations in the framework of the cascade evaporation model (CEM) whereas an analogous calculation forα-particles completely fails. Upper limits for an additional scission component of proton emission are given.     

Analysis of a statistical multiplexer with generalized periodic sources

We provide solution techniques for the analysis of multiplexers with periodic arrival streams, which accurately account for the effects of active and idle periods and of gradual arrival. In the models considered in this paper, it is assumed that each source alternates (periodically) between active and idle periods of fixed durations. Incoming packets are transmitted on the network link and excess information is stored in the multiplexing buffer when the aggregate input rate exceeds the capacity of the link. We are interested in the probability distribution of the buffer content for a given network link speed as a function of the number of sources and their characteristics, i.e., rate and duration of idle and active periods. We derive this distribution from two models: discrete time and continuous time systems. Discrete time systems operate in a slotted fashion, with a slot defining the base unit for data generation and transmission. In particular, in each slot the link is capable of transmitting one data unit and conversely an active source generates one data unit in that time. The continuous time model of the paper falls in the category of fluid models. Compared to previous works we allow a more general model for the periodic packet arrival process of each source. In discrete time, this means that the active period of a source can now extend over several consecutive slots instead of a single slot as in previous models. In continuous time, packet arrivals are not required to be instantaneous, but rather the data generation process can now take place over the entire duration of the active period. In both cases, these generalizations allow us to account for the progressive arrival of source data as a function of both the source speed and the amount of data it generates in an active period.This work was done while at the IBM T.J. Watson Research Center.This work was done while at the IBM T.J. Watson Research Center.Part of the work was done while visiting the IBM T.J. Watson Research Center.     

Substituted 2,5-Diaryl-2H-Tetrazoles

Elimination of nitrogen from diaryl substituted 2H-tetrazoles during the first step of thermal decomposition yields diphenylnitrileimines. In spite of the. drastic reaction conditions of the melt, they react relatively selective, giving two main products, the 1,2,4,5-tetrazines and 1,2,4-triazoles (together more than 70%). The triazoles are formed if the separation of nitrenes from the nitrileimine is favoured. Therefore, the mass losses found for the first step exceed the values calculated for N₂ only. The product mixture after the first TG step was investigated by the title methods, and especially by means of computer-aided MS analysis.     

System size and energy dependence of jet-induced hadron pair correlation shapes in Cu+Cu and Au+Au collisions at square root sNN=200 and 62.4 GeV

We present azimuthal angle correlations of intermediate transverse momentum (1-4 GeV/c) hadrons from dijets in Cu+Cu and Au+Au collisions at square root sNN=62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from Delta phi=pi in central and semicentral collisions in all the systems. The broadening and peak location are found to depend upon the number of participants in the collision, but not on the collision energy or beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to Cherenkov gluon radiation models.