In recent years, categorists have come up with some very interesting ways of looking at algebraic constructions and algebraic objects. But most of what they write on this is technical and aimed at other categorists. I shall sketch some of these ideas here, emphasizing concrete examples, for the algebraist with a reasonable foundation in category theory (familiarity with adjoint functors and col...

We condense the theory of blockchains down to a simple and compact set four type equations (Idealised EUTxO), an algebraic characterisation (abstract chunk systems), exhibit adjoint pair functors between them. This gives novel account essential mathematical structures underlying blockchain technology, such as Bitcoin.

Let G be a reductive algebraic group of Q-rank one associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a torsion-free arithmetic subgroup. Let d be the cohomological dimension of Γ. We present an algorithm to compute the action of the Hecke operators on H(Γ;Z). This generalizes the classical modular symbol algorithm, when Γ ⊂ SL2(Z), to a setting including Bianchi gro...

This paper introduces sufficient and necessary conditions with respect to the fuzzy operators considered in a multi-adjoint frame under which the standard combinations of multiadjoint sufficiency, possibility and necessity operators form (antitone or isotone) Galois connections. The underlying idea is to study the minimal algebraic requirements so that the concept-forming operators (defined usi...

A linear completely nonhomogeneous generally nonlocal multipoint problem is investigated for a fourth-order differential equation with generally nonsmooth coefficients satisfying some general conditions such as pintegrability and boundedness. A system of five integro-algebraic equations called an adjoint system is introduced for this problem. A concept of a Green functional is introduced as a s...

In this paper we propose a new method based on adjoint systems for parametric sensitivity analysis of DAE’s. This method is employed in a series of experiments, and the results are compared with the estimation of sensitivity by a finite differences method, widely used because of the simplicity of its implementation. In addition, we propose a method extension based on the use of estimation funct...

We consider some geometric aspects of regular Sturm-Liouville problems. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of Sturm-Liouville eigenvalues on the boundary condition, and reveals many new properties of these eigenvalues. In particular, the eigenvalues for separated boundary conditions and thos...

Let d ≥ 1, and let α be an expansive Z-action by continuous automorphisms of a compact abelian group X with completely positive entropy. Then the group ∆α(X) of homoclinic points of α is countable and dense in X, and the restriction of α to the α-invariant subgroup ∆α(X) is a Z-action by automorphisms of ∆α(X). By duality, there exists a Z-action α∗ by automorphisms of the compact abelian group...