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Infinite-Order Differential Operators in the Module of Formal Generalized Functions and in a Ring of Formal Power Series
We obtain the general form of continuous linear map**s acting in the module of formal generalized functions over a commutative ring and commuting...
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Factorizing formal contexts from closures of necessity operators
Factorizing datasets is an interesting process in a multitude of approaches, but many times it is not possible or efficient the computation of a...
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Multisummability of Formal Solutions for a Family of Generalized Singularly Perturbed Moment Differential Equations
The notion of moment differentiation is extended to the set of generalized multisums of formal power series via an appropriate integral...
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An explicit example of an iteration group in the ring of formal power series
We give an example of some iteration group in a ring of formal power series over a field of characteristic 0. It allows us to obtain an explicit...
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Summability of Transseries Solution of Non-integrable Hamiltonian System
This paper studies the summability of the transseries solution of a nonintegrable Hamiltonian system. Since our system has a resonance and is not...
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Linear Differential Equation with Inhomogeneity in the Form of a Formal Power Series Over a Ring with Non-Archimedean Valuation
Consider a linear inhomogeneous differential equation of the m th order with constant coefficients from the valuation ring K of a non-Archimedean...
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On formal normal forms of holomorphic germs at super-saddle fixed points
We consider a class of holomorphic skew product germs at super-saddle fixed points, which formally conjugate to their normal forms. We give necessary...
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Convergence of Formal Solutions to the Second Member of the Fourth Painlevé Hierarchy in a Neighborhood of Zero
AbstractThe second member of the fourth Painlevé hierarchy is considered. Convergence of certain power asymptotic expansions in a neighborhood of...
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An Invitation to Formal Power Series
This is an account on the theory of formal power series developed entirely without any analytic machinery. Combining ideas from various authors we...
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A Matrix Method for Detecting Formal Solutions to the Problem of Algebraic Synthesis of a Finite-State Machine with a Datapath of Transitions
For a finite-state machine with a datapath of transitions, a new method for detecting formal solutions to an algebraic synthesis problem is proposed....
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Formal Proofs in Mathematical Practice
Over the past half-century, formal, machine-executable proofs have been developed for an impressive range of mathematical theorems. Formalists argue...
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On Existence and Uniqueness of Formal Power Series Solutions of Algebraic Ordinary Differential Equations
Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be...
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A note on badly approximable systems of linear forms over a field of formal series
We prove that the set of badly approximable systems of M linear forms in N variables over the field of formal power series is hyperplane absolute...
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On the summability and convergence of formal solutions of linear q-difference-differential equations with constant coefficients
We consider the Cauchy problem for homogeneous linear q -difference-differential equations with constant coefficients. We characterise convergent, k -su...
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On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics
We provide families of compact astheno-Kähler nilmanifolds and we study the behaviour of the complex blowup of such manifolds. We prove that the...
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Continuity of Formal Power Series Products in Nonlinear Control Theory
Formal power series products appear in nonlinear control theory when systems modeled by Chen–Fliess series are interconnected to form new systems. In...
