We define a convex extension of a lower-semicontinuous function to be a convex function that is identical to the given function over a pre-specified subset of its domain. Convex extensions are not necessarily constructible or unique. We identify conditions under which a convex extension can be constructed. When multiple convex extensions exist, we characterize the tightest convex extension in a...

ARGUMENTATION An (abstract) argumentation framework [1] (AF) is a pair 〈A,Σ〉, where A is a set of arguments and Σ ⊆ A×A is a set of attacks. – It allows representing dialogues, making decisions, and handling inconsistency; – An AF can be viewed as a direct graph, whose nodes are arguments and whose edges are attacks. SEMANTICS FOR AFS An argumentation semantics specifies the criteria for identi...

0 −→ c −→ g1 φ1 −→g −→ 0 such that c ⊆ Z(g1), the center of g̃. A morphism of central extensions is a Lie algebra homomorphism ψ : g1 → g2 such that φ2ψ = φ1. A universal central extension is a central extension g̃ such that there is a unique morphism from g̃ to every other central extension of g. The Schur multiplier is the kernel of the universal central extension of g. It classifies the project...

The study assessed farmers’ perception of effectiveness of agricultural extension agents in Anambra State, Nigeria. The population of the study comprised all contact farmers and extension agents in Anambra State. Multi-stage, purposive and simple random sampling techniques were used to select 200 respondents comprising 160 farmers and 40 extension agents. Data for the study were collected throu...

Compartmentalised extension prohibits the uptake of new technology thereby inhibiting agricultural growth. Extension services aimed at increased agricultural growth should have a market-led and evidence-based pluralistic advisory system that is coordinated by the government’s Agricultural and Technical Services division in response to the needs of farmers. This study sought to assess extension ...

Here, we present a novel method for SNP genotyping based on protease-mediated allele-specific primer extension (PrASE), where the two allele-specific extension primers only differ in their 3'-positions. As reported previously [Ahmadian,A., Gharizadeh,B., O'Meara,D., Odeberg,J. and Lundeberg,J. (2001), Nucleic Acids Res., 29, e121], the kinetics of perfectly matched primer extension is faster th...

In this paper, we consider fractional differential equations with the new derivative involving a nonsingular kernel, namely, Caputo-Fabrizio derivative. Using successive approximation method, prove an extension of Picard-Lindelöf existence and uniqueness theorem for derivative, which gives set conditions, under initial value problem has unique solution.

An extension of the GCED matrices from domain natural integers to unique factorization is given. The structure these type defined on both arbitrary sets and GCED-closed are presented. Moreover, we present exact expressions for determinant inverse such matrices. domains Gaussian polynomials over finite fields used illustrate work.