Schneider’s work on rank functions [17] provides a formal approach to verification of certain properties of a security protocol. However, he illustrates the approach only with a protocol running on a small network; and no help is given with the somewhat hit-and-miss process of finding the rank function that underpins the central theorem. In this paper, we develop the theory to allow for an arbi...

Let F be an algebraic number field. Recently, L. Weng introduced zeta functions of rank n associated to F as a generalization of the Iwasawa-Tate zeta integral from the Arakelov geometric point of view. In the article, we call them the Weng zeta function of rank n. In the case of rank one, the Weng zeta function coincide with the Dedekind zeta function of F . The background and precise definiti...

We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

Schneider’s work on rank functions [14] provides a formal approach to verification of certain properties of a security protocol. However, he illustrates the approach only with a protocol running on a small network; and no help is given with the somewhat hit-and-miss process of finding the rank function which underpins the central theorem. In this paper, we develop the theory to allow for an arb...

A matrix always has a full rank submatrix such that the of this is equal to submatrix. This property one corner stones theory. We call max-full-rank-submatrix property. Tensor ranks play crucial role in low tensor approximation, completion and recovery. However, their theory still not matured yet. Can we set an axiom system for ranks? extend tensors? explore these paper. first propose some axio...