Exactness, invertibility and the Love Knot

Detecting knot invertibility

We discuss the consequences of the possibility that Vassiliev invariants do not detect knot invertibility as well as the fact that quantum Lie group invariants are known not to do so. On the other hand, finite group invariants, such as the set of homomorphisms from the knot group to M11, can detect knot invertibility. For many natural classes of knot invariants, including Vassiliev invariants a...

Phenomenology of love: The Destructive and Constructive Nature of Love

Love, this eminent humane experience, has been explored not only by writers and poets, but also by philosophers, psychologists and even experimental scientists. This paper aims to discuss a novel aspect in phenomenology of love, as the concept of destructive and constructive nature of love, which is to the best of our knowledge, presented for the first time. The fundamental idea of this paper w...

Deducibility and Exactness

What I intend to show in this short paper is how one can translate in relational terms the concepts of deducibility and exactness which are the result of a sequence of works on homology theory and algebraic topology. As we shall see, we shall obtain as a final product the possibility to associate to an arbitrary binary relation R a difunctional relation R contained in R, in contrast with the di...

A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness

Towards exactness in geomorphometry

Exactness of results of geomorphometric research depends not only on measurement and computational exactness but also on exact definition of measured objects and exactness of interpretation of the geomorphometric variables. The need to consider all aspects of exactness in mutual relationships is exemplified from the use of third order local point-based variables.