Related papers: Une note sur l'article de S. Takahashi
We prove that the bounded arithmetic theory $S^1_2$ is consistent with EXP $\not\subseteq$ P/poly. More generally, we show that certain separations of $V^1_2$ from a theory $T$ imply the consistency of $T$ with EXP $\not\subseteq$ P/poly.…
We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity. We show that these conditions are directly related to important conjectures in number theory coming from…
We present a unified approach for determining and proving obstructions to small-time local controllability of scalar-input control systems. Our approach views obstructions to controllability as resulting from interpolation inequalities…
We provide a short proof of the necessity of Crawley-Boevey's condition in his solution to the Deligne-Simpson problem. The proof relies on the local neighbourhood theorem for $2$-Calabi-Yau categories due to Davison together with…
We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.
Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,\ldots, z_n\in \Omega$ and $w_1,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the $Pick\, interpolation\, problem$ asks when there is a…
We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation.…
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…
We give a counterexample to Theorem 9 in [T.K. Subrahmonian Moothathu, Syndetically proximal pairs, J. Math. Anal. Appl. 379 (2011) 656--663]. We also provide sufficient conditions for the conclusion of Theorem 9 to hold.
We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.
We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.
In this paper we will explore the 2D system describing trapped ionic system in the quadrapole field with a superposition of rationally symmetric hexapole and octopole fields for meromorphic integrability. We use the Lyapunov's and…
We induce a Poisson algebra $\{\cdot,\cdot\}_{\mathcal{C}_{n,N}}$ on the configuration space $\mathcal{C}_{n,N}$ of $N$ twisted polygons in $\mathbb{RP}^{n-1}$ from the swapping algebra \cite{L12}, which is found coincide with…
In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna-Pick interpolation problem for analytic functions with positive real parts on the open unit disc. As consequences, we deduce some results concerning…
We derive a generalized Pohozhaev's identity for radial solutions of $p$-Laplace equations, by using the approach in [5], thus extending the work of H. Br\'{e}zis and L. Nirenberg [2], where this identity was implicitly used for the Laplace…
Although it is important both in theory as well as in applications, a theory of Birkhoff interpolation with main emphasis on the shape of the set of nodes is still missing. Although we will consider various shapes (e.g. we find all the…
This paper extends the results of the previous paper designated I hereafter in which the one- and two-soiton solutions of the Degasperis-Procesi(DP) equation were obtained and their peakon limit was considered. Here, we present the general…
Strengthening of two Clarkson-McCarthy inequalities with several operators is established. These not only confirm a conjecture of the author in [Israel J. Math. 2024], but also improve results of Hirazallah-Kittaneh in [Integral Equations…
We introduce Nevanlinna--Pick norms associated with finite families of characters in a commutative semisimple Banach algebra and study the class $NP_\infty$, where all such norms are minimal. Our main result is a topological rigidity…
We prove a Noether-type symmetry theorem and a DuBois-Reymond necessary optimality condition for nabla problems of the calculus of variations on time scales.