Related papers: A note on the Tikhonov theorem on an infinite inte…

We provide a direct proof of Agafonov's theorem which states that finite state selection preserves normality. We also extends this result to the more general setting of shifts of finite type by defining selections which are compatible the…

In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].

We propose a framework for temporal quantum theories for the purpose of describing states and observables associated with extended regions of space time quantum mechanically. The proposal is motivated by Isham's history theories. We discuss…

The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.

This paper considers the problem of finite-time stability for stochastic nonlinear systems. A new Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing…

We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

In this note, we prove an $L^2$ Hartogs-type extension theorem for unbounded domains.

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The…

This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.

This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually finite amenable group.

We give a rigorous proof for the linear stability of the Skyrmion. In addition, we provide new proofs for the existence of the Skyrmion and the GGMT bound.

In this paper, we present a short proof of Halin's grid theorem.

The classical theorems about singular perturbation reduction (due to Tikhonov and Fenichel) are concerned with convergence on a compact time interval (in slow time) as a small parameter approaches zero. For unbounded time intervals…

In this article, we study an inverse problem consisting in the identification of a space-time dependent source term in the Ginzburg-Landau equation from final-time observations. We adopt a weak-solution framework and analyze Tikhonov's…

The aim of this note is to give a proof of the Schottky theorem in general domains in $\mathbb{C}^n$. The proof is short and works for the cases $n = 1$ and $n > 1$ at the same time.

The purpose of this note is to give an (esentially optimal) effective version of Matsusaka's Big theorem for smooth projective surfaces.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We present a new fundamental intuition for why the Kemeny feature of a Markov chain is a constant. This new perspective has interesting further implications

We state a version of the P=?NP problem for infinite time Turing machines. It is observed that P not= NP for this version.