In this article, we have introduced the idea of statistically convergent generalized difference lacunary double sequence spaces 2 [ ( , , , )] n w M p q θ Δ , 2 0 [ ( , , , )] n w M p q θ Δ and defined over a semi norm space (X, q). Also we have study some basic properties and obtained some inclusion relations between them.

We classify the holomorphic structures of the tangent vertical bundle Θ of the twistor fibration of a quaternionic manifold (M, Q) of dimension 4n ≥ 8. Using a Penrose transform we show that, when (M, Q) is compact and admits a compatible quaternionic-Kähler metric of negative scalar curvature, Θ admits no global non-trivial holomorphic sections with respect to any of its holomorphic structures...

Theorem 1 There exists a 1/3 6 pc 6 2/3 such that θ(p) = 0 for p < pc and θ(p) > 0 for p > pc. Proof: First, we show that for p < 1/3, θ(p) = 0. Let σ(n) denote the number of self-avoiding (consisting of distinct vertices and edges) paths of length n in L starting at the origin. σ(n) is unknown but a simple bound is σ(n) 6 4 · 3 since at each step there are 3 choices of directions, except for t...

We present a method for active object segmentation based on integration of several cues; image point positions, binocular disparities and pixel colours. It serves as a framework for generation of object hypotheses of previously unseen objects in natural indoor scenes. The appearance, 3D shape and size of objects are modelled in an iterative manner using an approximate Expectation-Maximisation (...

After discussing the intrinsic ambiguity in determining the light quark mass ratio mu/md, we reexamine the recent proposal that this ambiguity can be resolved by applying the QCD multipole expansion for the heavy quarkonium decays. It is observed that, due to instanton effects, some matrix elements which have been ignored in previous works can give a significant contribution to the decay amplit...

We present first results of a simultaneous atmospheric turbulence measurement campaign at the Calar Alto (Spain) 1.23 m and 3.5 m telescopes. A SCIDAR instrument and the Calar Alto Adaptive Optics system ALFA were used at the 1.23 m and 3.5 m telescopes respectively to determine essential turbulence parameters like the Fried parameter r 0 , the isoplanatic angle θ 0 , and, in the case of SCIDAR...

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [

3.1 Maximum likelihood estimates — in exponential families. Let (X, B) be a measurable space and {P θ , θ ∈ Θ} a measurable family of laws on (X, B), dominated by a σ-finite measure v. Let f (θ, x) be a jointly measurable version of the density (dP θ /dv)(x) by Theorem 1.3.3. For each x ∈ X, a maximum likelihood estimate (MLE) of θ is any θ ˆ = θ ˆ (x) such that f (ˆ θ, x) = sup{f (φ, x) : φ ∈ ...

In this note, we prove that for every θ ≥ 115 121 and x ≥ x0(θ), the short interval (x, x + xθ] contains at least one prime number of the form p = 1+m2 +n2 with (m,n) = 1. This improves a similar result due to Huxley and Iwaniec, which requires θ ≥ 99 100 . §