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A straightforward way is offered to convert a system of high order linear functional equations of various type into a system of first order equations. [ABSTRACT FROM AUTHOR]

In this paper we find a generalization of the snake lemma and Schanuel's lemma in Hv-modules. We define the isomorph sequences and determine the conditions to split the exact sequences in Hv-modules. Some interesting results on these concepts are given. [ABSTRACT FROM AUTHOR]

Quasi module is an axiomatisation of the hyperspace structure based on a module. We proposed this structure in our paper [2]. It can be thought of as a generalisation of the module structure in the sense that every module can be embedded into a quasi module and every quasi module contains a module. The structure of quasi module is designed on a commutative semigroup with an external ring multiplication and a compatible partial order which has a very intrinsic effect in the entire structure and plays a key role in any development of the theory of quasi module. In this paper we have introduced the concept of exact sequence on quasi modules and proved some Theorems related to exact sequences. [ABSTRACT FROM AUTHOR]

Let V be a vertex operator algebra. The fusion products in this paper are defined by logarithmic intertwining operators. Under this setting, we prove the pure exactness of any extension of the V -module V . Namely, if 0 → Q → ϵ P → ρ V → 0 is a short exact sequence of V -modules and W is a V -module, then 0 → Q ⊠ W → ϵ ⊠ 1 W P ⊠ W → ρ ⊠ 1 W V ⊠ W → 0 is also exact, where we view it as a sequence of g ( V ) -modules. [ABSTRACT FROM AUTHOR]

In this note, a construction of state representations of singular linear time-invariant differential systems is described directly in terms of trajectories. [ABSTRACT FROM AUTHOR]

Abstract: It is shown that every centralizer from any “metric function space” to is continuous at the origin of . As a consequence, every short exact sequence of -modules splits if is a “minimal” function space, and in particular if . There are pairs of Orlicz function spaces such that , but . [Copyright &y& Elsevier]

The paper establishes a relation between exact sequences, parametric finite elements, and perfectly matched layer (PML) techniques. We illuminate the analogy between the Piola-like maps used to define parametric H-, H(curl)-, H(div)-, and L-conforming elements, and the corresponding PML complex coordinates stretching for the same energy spaces. We deliver a method for obtaining PML-stretched bilinear forms (constituting the new weak formulation for the original problem with PML absorbing boundary layers) directly from their classical counterparts. [ABSTRACT FROM AUTHOR]

Benson and Goodearl [Periodic flat modules, and flat modules for finite groups, Pacific J. Math.196(1) (2000) 45-67] proved that if M is a flat module over a ring R such that there exists an exact sequence of R-modules 0 → M → P → M → 0 with P a projective module, then M is projective. The main purpose of this paper is to generalize this theorem to any exact sequence of the form 0 → M → G → M → 0, where G is an arbitrary module over R. Moreover, we seek counterpart entities in the Gorenstein homological algebra of pure projective and pure injective modules. [ABSTRACT FROM AUTHOR]

Abstract: A duality of two categories is introduced. It generalizes the Malcev description of torsion free finite rank abelian groups. An equivalence of two categories is also introduced. It generalizes the Kurosh description of p-primitive groups. The composition of the duality and the equivalence is the duality earlier introduced by W. Wickless and the author. It is shown that the last duality preserves exactness for short exact sequences of homomorphisms. [Copyright &y& Elsevier]

We investigate exactness of long sequences of homology semimodules associated to Schreier short exact sequences of chain complexes of semimodules. [ABSTRACT FROM AUTHOR]