Let Ω⊂Cm be an open, connected and bounded set A(Ω) a function algebra of holomorphic functions on Ω. Suppose that M is reproducing kernel Hilbert module over A(Ω). In this article, we first obtain model for the quotient modules obtained from submodules in vanishing to order k along smooth irreducible complex analytic Z⊂Ω codimension at least 2, assuming Cowen-Douglas class This used show such ...

In this paper we prove a higher differentiability result for the solutions to class of obstacle problems in formmin⁡{∫ΩF(x,Dw)dx:w∈Kψ(Ω)} where ψ∈W1,p(x)(Ω) is fixed function called and Kψ(Ω)={w∈W01,p(x)(Ω)+u0:w≥ψa.e. Ω} admissible functions, suitable boundary value u0. We deal with convex integrand F which satisfies p(x)-growth conditions|ξ|p(x)≤F(x,ξ)≤C(1+|ξ|p(x)),p(x)>1.

We present several characterizations of uo-convergent nets or sequences in spaces continuous functions C(Ω), Cb(Ω), C0(Ω), and C∞(Ω), extending results [11]. In particular, it is shown that a sequence uo-converges iff converges pointwise on co-meagre set. also characterize order bounded sets functions. This leads to convergence.

Let (M,I,Ω) be a holomorphically symplectic manifold equipped with holomorphic Lagrangian fibration π:M↦X, and η closed form of Hodge type (1,1)+(2,0) on X. We prove that Ω′:=Ω+π⁎η is again form, for another complex structure I′, which uniquely determined by Ω′. The corresponding deformation structures called “degenerate twistorial deformation”. map π respect to this new structure, X the fibers...

 The study aims to determine the influence of frying (shallow and deep) with olive, canola and sunflower oil on fatty acid composition of silver carp. Frying by olive oil and canola oil increased the monounsaturated fatty acids (MUFA) significantly (p<0.05) that consequently decreased saturated fatty acids (SFA), polyunsaturated fatty acids (PUFA) and ω-3 fatty acids. Frying by sunflow...

In this appendix we show that 1 2 ∆ F (θ)∆ is a second order Taylor approximation of D KL (p(θ)p(θ + ∆)). First, let g q (θ) :=D KL (qp(θ)) = ω∈Ω q(ω) ln q(ω) p(ω|θ). We begin by deriving equations for the Jacobian and Hessian of g q at θ: ∂g q (θ) ∂θ = ω∈Ω q(ω) p(ω|θ) q(ω) ∂ ∂θ q(ω) p(ω|θ) = ω∈Ω q(ω) p(ω|θ) q(ω) −q(ω) ∂p(ω|θ) ∂θ p(ω|θ) 2 = ω∈Ω − q(ω) p(ω|θ) ∂p(ω|θ) ∂θ , (4) and so: ∂ 2 g q (θ)...

the tenacity of a graph g, t(g), is dened by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we dene τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph&apos;s...