Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ord...

In this note we classify all triples (a, b, i) such that there is a convex lattice polygon P with area a, and p respectively i lattice points on the boundary respectively in the interior. The crucial lemma for the classification is the necessity of b ≤ 2 i+7. We sketch three proofs of this fact: the original one by Scott [Sco76], an elementary one, and one using algebraic geometry. As a refinem...

Conditions for the existence of strictly stationary multivariate GARCH processes in the so-called BEKK parametrisation, which is the most general form of multivariate GARCH processes typically used in applications, and for their geometric ergodicity are obtained. The conditions are that the driving noise is absolutely continuous with respect to the Lebesgue measure and zero is in the interior o...

We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to construct models from sub-models, and is implemented as a combination of preand post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the p...

We use an argument of Romans showing that every Virasoro construction leads to realizations of W3, to construct W3 realizations on arbitrary affine Lie algebras. Solutions are presented for generic values of the level as well as for specific values of the level but with arbitrary parameters. We give a detailed discussion of the ŝu(2)l-case. Finally, we discuss possible applications of these rea...

(See e.g. [6] for background.) When X is equipped with a distinguished basis D for its topology, closed under finite meets and joins, one can investigate situations where D is also closed under the implication (2), i.e., where D is a Heyting subalgebra of O (X). Recall that X is a spectral space if it is compact and T0, its collection D of compact open subsets forms a basis which is closed unde...

In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a B...

In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type ofΣ algebra, the seed algebra, which describes exactly the behavior of a process within a labeled transition system. We have shown the possibility of characterizing the bisimulation of two processes with the isomorphism of their corresponding se...

Denotational semantics is the usual mathematical semantics for functional programming languages. It is higher order (H.O.) in the sense that the semantic domain D includes D ! D] as a subdomain. On the other hand, the usual declarative semantics for logic programs is rst order (F.O.) and given by the least Herbrand model. In this paper, we take a restricted kind of H.O. conditional rewriting sy...

An interior point method (IPM) defines a search direction at an interior point of the feasible region. These search directions form a direction field which in turn defines, as the unique solution of a system of ordinary differential equations (ODEs), a curve passing through any interior point. We call such curves off-central paths (the central path is trivial for analysis; our concern is off-ce...