We propose a subvolume method to study the $\theta$ dependence of free energy density four-dimensional SU($N$) Yang-Mills theory on lattice. As an attempt, is first applied SU(2) at $T=1.2\,T_c$ understand systematics method. then proceed calculation vacuum and obtain qualitatively different from high temperature case. The numerical results combined with theoretical requirements provide evidenc...

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 ...