Related papers: String Diagrammatic Electrical Circuit Theory
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…
Nested graphs have been used in different applications, for example to represent knowledge in semantic networks. On the other hand, graphs with cycles are really important in surface reconstruction, periodic schedule and network analysis.…
Digital circuits, despite having been studied for nearly a century and used at scale for about half that time, have until recently evaded a fully compositional theoretical in which arbitrary circuits may be freely composed together without…
The scope of this paper is to determine the generalized form for equivalent tension generator theorem (Helmholtz-Thevenin theorem) for three-phase electrical circuit. Any complicated electrical power systems we can reduce depending on any…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…
The diagrammatic theory is proposed for the strongly correlated impurity Anderson model. The strongly correlated impurity electrons are hybridized with free conduction electrons. For this system the new diagrammatic approach is formulated.…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
We introduce a general diagrammatic theory of digital circuits, based on connections between monoidal categories and graph rewriting. The main achievement of the paper is conceptual, filling a foundational gap in reasoning syntactically and…
One-dimensional atomic mixtures of fermions can effectively realize spin chains and thus constitute a clean and controllable platform to study quantum magnetism. Such strongly correlated quantum systems are also of sustained interest to…
Except for Koshy who devotes seven pages to applications of Fibonacci Numbers to electric circuits, most books and the Fibonacci Quarterly have been relatively silent on applications of graphs and electric circuits to Fibonacci numbers.…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of…
Classical solutions describing strings endowed with an electric charge and carrying a constant electromagnetic current are constructed within the bosonic sector of the Electroweak Theory. For any given ratio of the Higgs boson mass to W…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
Applied category theory provides powerful mathematical tools for modelling processes and their composition. Symmetric monoidal categories, which involve series and parallel composition, are particularly well-suited for describing the…
The strong coupling Eliashberg theory plus vertex correction is used to calculate maps of transition temperature (Tc) in parameter-space characterizing superconductivity. Based on these Tc maps, crossover behaviors are found when…
This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The…
As digitization in engineering progressed, circuit diagrams (also referred to as schematics) are typically developed and maintained in computer-aided engineering (CAE) systems, thus allowing for automated verification, simulation and…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…