We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various areas, such as number theory, combinatorics and mathematical physics.

This note revisits the identification theorems of Brown (1983) and Roehrig (1988). We describe an error in the proofs of the main identification theorems in these papers, and provide an important counterexample to the theorems on the identification of the reduced form. Specifically, the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions of t...

In this paper, we have studied the Henstock - Kurzweil integral which is a generalized Riemann means. Hen-stock natural extension of integral. We defined Banach space valued function with respect to bounded variation an real increasing function. investigated elementary properties variation. proved convergence theorems and Saks lemma functions vari-ation. Equi-integrability equi-integrable theor...

In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic MALLP, which is the linear fragment (without structural rules) of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories C−/C+ of an ambient ∗-autonomous category C (with products). Similar structures were first introduced by ...

Abstract We present an abstract development of Gödel’s incompleteness theorems, performed with the help Isabelle/HOL proof assistant. analyze sufficient conditions for applicability our theorems to a partially specified logic. In addition usual benefits generality, perspective enables comparison between alternative approaches from literature. These include Rosser’s variation first theorem, Jero...