We show that every semi-abelian category, as defined by Palamodov, possesses a maximal exact structure in the sense of Quillen and that the exact structure of a quasi-abelian category is a special case thereof.

Turetzkii [Uchenye Zapiski, Vypusk 1 (149) (1959), 31–55, (English translation in East J. Approx. 11 (2005) 337–359)] considered quadrature rules of interpolatory type with simple nodes, with maximal trigonometric degree of exactness. For that purpose Turetzkii made use of orthogonal trigonometric polynomials of semi–integer degree. Ghizzeti and Ossicini [Quadrature Formulae, Academie-Verlag, B...

In this paper it is shown how non-pointed exactness provides a framework which allows a simple categorical treatment of the basics of KuroshAmitsur radical theory in the non-pointed case. This is made possible by a new approach to semi-exactness, in the sense of the first author, using adjoint functors. This framework also reveals how categorical closure operators arise as radical theories.

Abstract Social work practice is a constantly evolving, evidence-based profession. As an explanation of client ‘presenting problems’, social incorporates Q sort via Rogers’ client-centred/humanism. mathematical tool that enables incremental step by the profession at-large towards scientific exactness. Absent sort, as practice, well-respected critics have commenced to denigrate semi-profession i...

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

We propose to use Grothendieck institutions based on 2categorical diagrams as a basis for heterogeneous specification. We prove a number of results about colimits and (some weak variants of) exactness. This framework can also be used for obtaining proof systems for heterogeneous theories involving institution semi-morphisms.

We introduce a software system for semi-automatic segmentation of the patellar cartilage. By providing tools for sub-pixel accurate edge tracing, automatic contour completion, and adequate visualization we achieve a remarkable speed-up of the physician’s segmentation process. Our results show the exactness that can be reached for cartilage segmentation if expertise and automation are merged in ...

In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty funct...

If A is a small category and E a Grothendieck topos, the Kan extension LanF of a flat functor F : A → E along any functor A → D preserves whatever finite limits may exist in D; this is a well known fundamental result in topos theory. We shall present a metamathematical argument to derive out of this some other left exactness results, for Kan extensions with values in a (possibly large) site E. ...