Let {p θ , θ ∈ Θ} be a family of probability densities with respect to µ where Θ is an open subinterval (finite, infinite or semi-infinite) of the real line. The Fisher Information for this family is defined by: I(θ) := E θ ∂ ∂θ log p θ (X) 2 Note that the densities p θ can be on arbitrary spaces; the only condition for defining I(θ) is that θ is real. The function ∂ ∂θ log p θ (X) is called th...

We give different characterizations of the classes Plogi(NP), which are located between Θ2 and ∆2 . First we show that these classes are equal to the classes AC i−1(NP). Second we prove that they are also equivalent to certain binary search classes over NP. Third we show that they can be characterized as the classes defined by circuits of size O(log n) with NP oracle gates. All the proofs given...

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

In this paper, we introduce the condition of θ-locality which can be used as a substitute for microcausality in quantum field theory on noncommutative spacetime. This condition is closely related to the asymptotic commutativity which was previously used in nonlocal QFT. Heuristically, it means that the commutators of observables behave at large spacelike separation like exp(−|x − y|2/θ), where ...

We introduce a new class of functions called θ-precontinuous functions which is contained in the class of weakly precontinuous (or almost weakly continuous) functions and contains the class of almost precontinuous functions. It is shown that the θprecontinuous image of a p-closed space is quasi H-closed. 2000 Mathematics Subject Classification. 54C08.