Related papers: Harder-Narasimhan theory
We formulate and discuss a general axiomatic theory of arbitrary objects. This theory is expressed in a simple first-order language without modal operators, and it is governed by classical logic.
We present a theory of lazy imperative timing.
We present a proof of Hadamard Inverse Function Theorem by the methods of Variational Analysis, adapting an idea of I. Ekeland and E. Sere.
Instead of developing a customized typed lambda-calculus for each theory, we attempt to design a general parametric calculus that permits to express the proofs of any theory. This way, the problem of expressing proofs in the lambda-calculus…
The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. The textbook proof of the result, as well as one of the original proofs by Hardy, refers to the…
Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian…
In this paper, we estabish an analogue of Hardy's theorem and Miyachi's theorem for the Clifford-Fourier transform.
The existence of non-trivial IR and UV fixed points in gauge theories as a function of the number of fermion flavors and bare coupling is discussed in the light of recent work. It is pointed out that in fact only a small subset of potential…
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We give an elementary proof to Hasse theorem.
We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.
The theory of freely-propagating massless higher spins is usually formulated via gauge fields and parameters subject to trace constraints. We summarize a proposal allowing to forego them by introducing only a pair of additional fields in…
An algebraic deformation theory of coalgebra morphisms is constructed.
The theory of the on-shell Sudakov form factor to all order of logarithms is explained.
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the…
A solution is given to a conjecture proposed by Y. Wigderson and A. Wigderson concerning a "Heisenberg-like" uncertainty principle. This is an old article already published in 2022.
We show that the imperceptibility of several existing linguistic steganographic systems (Fang et al., 2017; Yang et al., 2018) relies on implicit assumptions on statistical behaviors of fluent text. We formally analyze them and empirically…
An algebraic deformation theory of dialgebra morphisms is obtained.
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
In 2010, Invent. Math., Ershov and Jaikin-Zapirain proved Kazhdan's property (T) for elementary groups. This expository article focuses on presenting an alternative simpler proof of that. Unlike the original one, our proof supplies no…