Related papers: Mathematical structure of unit systems
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as…
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
For a given family of similar shapes, what we call a "unit shape" strongly analogizes the role of the unit circle within the family of all circles. Within many such families of similar shapes, we present what we believe is naturally and…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
In classical physics, a single measurement can in principle reveal the state of a system. However, quantum theory permits numerous non-equivalent measurements on a physical system, each providing only limited information about the state.…
We survey some basic mathematical structures, which arguably are more primitive than the structures taught at school. These structures are orders, with or without composition, and (symmetric) monoidal categories. We list several `real life'…
Well-structured systems, aka WSTSs, are computational models where the set of possible configurations is equipped with a well-quasi-ordering which is compatible with the transition relation between configurations. This structure supports…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
The most standard description of symmetries of a mathematical structure produces a group. However, when the definition of this structure is motivated by physics, or information theory, etc., the respective symmetry objects might become more…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
The argument of physical dimension/units is applied to electrical switched circuits, making the topic of the nonlinearity of such circuits simpler. This approach is seen against the background of a more general outlook (IEEE CAS MAG, III,…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
We investigate unification of two systems of identical elements having different dimensions which may be of interest for both physics and economics. Characteristic parameters as well as explicit formulae for the temperature (in economics -…