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Abstract  

An exponential inequality for the tail of the conditional expectation of sums of centered independent random variables is obtained. This inequality is applied to prove analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for conditional expectations. As corollaries we obtain certain strong theorems for the generalized allocation scheme and for the nonuniformly distributed allocation scheme.

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Abstract  

The Pauli channel acting on 2 × 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M n is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings M nM n are constructed such that the restriction to the subalgebras are depolarizing channels. The result is the necessary and sufficient condition of complete positivity. The main examples appear on bipartite systems.

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In a recent paper the authors have studied the role of author self-citations within the process of documented scientific communication. Two important regularities such as the relative fast ageing of self-citations with respect to foreign citations and the “square-root law” characterising the conditional expectation of self-citations for given number of foreign citation have been found studying the phenomenon of author self-citations at the macro level. The goal of the present paper is to study the effect of author self-citations on macro indicators. The analysis of citation based indicators for 15 fields in the sciences, social sciences and humanities substantiates that at this level of aggregation there is no need for any revision of national indicators and the underlying journal citation measures in the context of excluding self-citations.

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This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (1985) in multiple regression problems in groundwater monitoring data analysis. This special inverse nonparametric approach can be applied easily for estimating the optimal transformations of different groundwater monitoring data from the Bükk Mountains to obtain maximum correlation between observed aquifer variables. The approach does not require a priori assumptions of a mathematical form, and the optimal transformations are derived solely based on the groundwater data set. The advantages and applicability of the proposed approach to solve different multiple regression problems in hydrogeology or in groundwater management are illustrated by means of case studies from a Hungarian karst aquifer. It is demonstrated that the ACE method has certain advantages in some fitting problems of groundwater science over the traditional multiple regression.In the past, different groundwater monitoring data (like groundwater level, groundwater temperature and conductance, etc.) had been used for groundwater management purposes in the Bükk Mountains. One of the difficulties in earlier approaches has been the need to make some kind of assumption of the expected mathematical forms among the investigated reservoir and petrophysical variables. By using nonparametric regression, the need to assume a specific form of model is avoided, and a clearer vision of the relationships between aquifer parameters can be revealed in the Bükk Mountains, where karst water is the main source of potable water supply. Complex monitoring data from the Bükk Mountains were analyzed using the ACE inverse method, and results were verified successfully against quantitative and qualitative field observations.

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measures of noncompactness and interpolation spaces Serdica Math. J. 32 179 – 184 . [6] Brooks , J. K. , Dinculeanu , N. 1979 Conditional expectation and weak and strong compactness in

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46 Goldstein, S. , Conditional expectation and stochastic integrals in non-commutative L p -spaces, Math. Proc. Cambridge Philos. Soc. 110 (1991), 365–383. MR 92k

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