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It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
This short note first develops a general formalism for globally removing a factor from an obstruction theory. This formalism is then applied to give a construction of a reduced obstruction theory on the moduli of maps from a curve to a…
We prove a general version of the classical Perron-Frobenius convergence property for reducible matrices. We then apply this result to reducible substitutions and use it to produce limit frequencies for factors and hence invariant measures…
Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem of congruence commutators for loops relates generators of the…
As an extension of our previous study, we derive slow-roll conditions for multiple scalar fields which are non-minimally coupled with gravity and for generalized gravity theories of the form $f(\phi,R)$. We provide simple formulae of the…
Armendariz and semicommutative rings are generalizations of reduced rings. In \cite{IN}, I.N. Herstein introduced the notion of a hypercenter of a ring to generalize the center subclass. For a ring $R$, an element $a \in R$ is called…
This paper generalizes the results in [30] concerning feedback stabilization of target states for N-level quantum angular momentum systems undergoing quantum non-demolition measurements (QND) in absence of the knowledge about initial states…
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are…
Pearl's front-door criterion provides a set of sufficient conditions for estimating the total causal effect from observational data in the presence of latent confounding, using the functional P(y | do(x := x*)) = \sum_z P(z | x*) \sum_x P(y…
For single input single output systems, we give a refinement of the generalized chordal metric. Our metric is given in terms of coprime factorizations, but it coincides with the extension of Vinnicombe's nu-metric given in earlier work by…
Conditional models with one pair of conditional and conditioned factors in Mukerjee et al. (2017) are extended to two pairs in this paper. The extension includes the parametrization, effect hierarchy, sufficient conditions for universal…
We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…
After the language of module and theirs morphisms, this short course presents matricial calculus and determinants in a commutative ring as appliction of ``remarquable identities'' in the ring of polynomials with integer coefficients with…
We numerically study the magnetization of small metallic clusters. The magnetic susceptibility is enhanced for lower electronic densities due to the stronger influence of electron-electron interactions. The magnetic susceptibility…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
In high-energy processes which are sensitive to small transverse momenta, individual contributions from collinear and soft momentum regions are not separately well-defined in dimensional regularization. A simple possibility to solve this…
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
Feedback asymptotic stabilization of control systems is an important topic of control theory and applications. Broadly speaking, if the system $\dot{x} = f(x,u)$ is locally asymptotically stabilizable, then there exists a feedback control…