Related papers: Computational Holonomy Decomposition of Transforma…
This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…
We describe a mechanism for using discrete symmetries to solve the doublet-triplet splitting problem of four-dimensional supersymmetric GUT's. We present two versions of the mechanism, one via ``deconstruction,'' and one in terms of…
We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It…
In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Topological transitivity is a fundamental notion in topological dynamics and is widely regarded as a basic indicator of global dynamical complexity. For general cellular automata, topological transitivity is known to be undecidable. By…
We extend Dwyer's sharp subgroup homology decomposition of the classifying space of a finite group to arbitrary saturated fusion systems and arbitrary Mackey functors.
Holomorphic functions are amazing because their values in an ever so small disk in the complex plane completely determine the function values at arbitrary points in their maximum possible domain. The process of extending such a function…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group ${\rm GL}(2,{\mathbb C})$ of…
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
We improve on earlier results on the closure under free products of the class of automaton semigroups. We consider partial automata and show that the free product of two self-similar semigroups (or automaton semigroups) is self-similar (an…
We establish a decomposition of stable homology of automorphism groups of free groups with polynomial contravariant coefficients in term of functor homology. This allows several explicit computations, intersecting results obtained by…
Let $G$ be a group which admits the structure of an iterated semidirect product of finitely generated free groups. We construct a finite, free resolution of the integers over the group ring of $G$. This resolution is used to define…
In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…
Hierarchical Finite State Machines (HFSMs) are a standard software-modelling concept which extends the classical Finite State Machine (FSM) notion with the useful abstraction of hierarchical nesting. That is, an HFSM is an FSM whose states…
This paper shows how to construct explicitly an automaton that generates an arbitrary numerical semigroup.
A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow…