In this paper, we investigate the existence of extension operators fromW (Ω) toW (R) (1 < p < ∞) for a class of tree-shaped domains Ω with a self-similar fractal boundary previously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the results of Jones imply that there exist such extension operators for all p ∈ [1,∞]. In the case when the fractal boundary self-inte...

The linear extension diameter of a finite poset P is the maximum distance between a pair of linear extensions of P, where the distance between two linear extensions is the number of pairs of elements of P appearing in different orders in the two linear extensions. We prove a formula for the linear extension diameter of the Boolean Lattice and characterize the diametral pairs of linear extension...

BACKGROUND The appropriate elbow position of short-segment nerve conduction study (SSNCS) to diagnose cubital tunnel syndrome (CubTS) is still controversial. The goal of this study was to determine the effect of different elbow positions at full extension and 70° flexion on SSNCS in CubTS. METHODS In this cross-sectional study, the clinical data of seventy elbows from 59 CubTS patients betwee...

OBJECTIVE To quantify changes in the diameter of the vertebral canal with flexion and extension in the cervical vertebral column. STUDY DESIGN Cadaveric biomechanical study. SAMPLE POPULATION Cadaveric canine cervical vertebral column (n = 16 dogs). METHODS All vertebral columns were evaluated with MRI. Group 1 consisted of 8 normal vertebral columns. Group 2 included 8 vertebral columns ...

In probability theory, Bayesian statistics, artificial intelligence and database theory the minimum cross-entropy principle is often used to estimate a distribution with a given set P of marginal distributions under the proportionality assumption with respect to a given “prior” distribution q. Such an estimation problem admits a solution if and only if there exists an extension of P that is dom...

We present two prudent semantics within Dung’s theory of argumentation. They are based on two new notions of extension, referred to as p-extension and c-extension. Two arguments cannot belong to the same p-extension whenever one of them attacks indirectly the other one. Two arguments cannot belong to the same c-extension whenever one of them indirectly attacks a third argument while the other o...

Let K ≤ F be a normal field extension. Put S := S(K,F) and P := P(K,F). Let K ≤ E ≤ S. (a) We will show that S(E,F) = S. Let a ∈ S. Then a is separable over K. By 5.2.20, a is also separable over E, so a ∈ S(E,F) and S ⊆ S(E,F). Now note that E is a separable extension of K because E ≤ S. Let a ∈ S(E,F). Since a is separable over E, E(a) is a separable extension of E. Thus, K ≤ E ≤ E(a) is a se...

The present research is conducted to find out the services and facilities of tobacco companies in promotion of tobacco crop in Malakand division of Khyber Pakhtunkhwa, Pakistan. A multi-stage sampling technique applied for selection sample size. In this method, 135 tobacco growers were selected from fifteen villages of tobacco growers. The principle researcher interviewed selected respondents f...

‎We present a Picone's identity for the‎ ‎$mathcal{A}_{p(x)}$-Laplacian‎, ‎which is an extension of the classic‎ ‎identity for the ordinary Laplace‎. ‎Also‎, ‎some applications of our‎ ‎results in Sobolev spaces with variable exponent are suggested.

This study examined the accuracy between extension professionals and farmers regarding their perceptions of privatization and commercialization of agricultural extension services. The study was carried out in Delta State, Nigeria and it had a sample size of 224 respondents comprising of 134 extension professionals of the Delta State Agricultural Programme (DTADP) and 90 farmers that were random...