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...

Objects dual to graded algebras are subproduct systems of linear spaces, a purely algebraic counterpart of a notion introduced recently in the context of noncommutative dynamics (Shalit and Solel [5], Bhat and Mukherjee [2]). A complete classification of these objects in the lowest nontrivial dimension is given in this work, triggered by a question of Bhat [1].

What is the minimal algebraic structure to reason about information flow? Do we really need the full power of Boolean algebras with co-closure and de Morgan dual operators? Howmuch canweweaken and still be able to reason about multi-agent scenarios in a tidy compositional way? This paper provides some answers.

An “automatic continuity” question has naturally occurred since Roger Howe established the local theta correspondence over R: Does the algebraic version of local theta correspondence over R agree with the smooth version? We show that the answer is yes, at least when the concerning dual pair has no quaternionic type I irreducible factor.

An adaptive algorithm based on the dual Youla-Kucera parametrization is introduced enabling simple closed-loop identification and adaptation of a class of symmetric MIMO systems. The methodology exploits the algebraic approach to control system design. Necessary conditions for usage of the developed method are discussed and results are presented for the case of coupled drives control. Copyright...

Let G(K) be the group of K-rational points of a connected adjoint simple algebraic group over a nonarchimedean local field K. In this paper we classify the unipotent representations of G(K) in terms of the geometry of the Langlands dual group. This was known earlier in the special case where G(K) is an inner form of a split group.

An analogue of the genuinely nonlinear character of an one-dimensional simple waves solution is identified and essentially used in the construction of some multidimensional extensions (simple waves solutions, regular interactions of simple waves solutions). A class of exact multidimensional gasdynamic solutions is constructed whose interactive elements are regular. Some specific aspects of Burn...

7 This paper deals with a particular question—When do powersets in lattice-valued mathematics form algebraic theories (ormonads) in clone form?Our approach in this and related papers is to consider “powersets over objects” in the ground categories Set and Set×C 9 from the standpoint of algebraic theories in clone form (C is a particular subcategory of the dual of the category of semi-quantales)...

The joint invariants of a pair of coplanar conics has been widely used in recent vision literature. In this paper, the algebraic invariant of a pair of non-coplanar conics in space is concerned. The algebraic invariant of a pair of non-coplanar conics is rst derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space conics. Then, this al...