Recent articles have addressed the problem to construct the confidence intervals for the mean of a normal distribution where the parameter space is restricted, see for example Wang [Confidence intervals for the mean of a normal distribution with restricted parameter space. Journal of Statistical Computation and Simulation, Vol. 78, No. 9, 2008, 829–841.], we derived, in this paper, analytic exp...

We revisit fixed-parameter tractability, fixed-parameter reducibility and kernelizability. The standard formulations of their definitions are enhanced for greater correctness from a structural complexity point of view. Doing so makes clear the distinction between fixed-parameter reducibility and kernelizability. Additionally, these time based definitions are augmented with space based counterpa...

Consider the problem of sequentially testing a null hypothesis vs an alternative hypothesis when the risk function is a linear combination of probability of error in the terminal decision and expected sample size (i.e., constant cost per observation.) Assume that the parameter space is the union of null and alternative, the parameter space is convex, the intersection of null and alternative is ...

In this paper we introduce a parameter ω∞ in the space of functions L0. The parameter measures the lack of equimeasurability using a sequence of functions which controls the oscillations of every function of a given subset of L0. We estimate the Hausdorff measure of noncompactness in terms of ω∞ and the parameter σ (see [3]) and characterize the totally bounded subsets of L0. A criterion of com...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.