Localization in Abelian Categories

We construct a generic Hall algebra of the Kronecker algebra and prove that its twisted version is a polynomial algebra in infinitely many variables over the twisted generic composition algebra. The variables are explicitly given as some central elements in the generic Hall algebra.

Thus, we obtain generic versions in the Kronecker case of theorems by Hua-Xiao and Sevenhant-Van den Bergh.     

Two variations of Boas–Fu–Straube’s deflation identity

In this article, we investigate deflation type identities of the Bergman kernel functions. The first identity of this kind was obtained by Boas, Fu, and Straube in 1999. It was generalized by the author of the present article in 2015. In 2017, Beberok also obtained a deflation type identity for certain Reinhardt domains. In this article, we introduce the Roos domains which include all domains considered in these three works as special cases. We establish two variations of deflation type identities for Roos domains.     

Extending Coggia–Couvreur attack on Loidreau’s rank-metric cryptosystem

Designs, Codes and Cryptography - A recent paper by Coggia and Couvreur presents a polynomial time key-recovery attack on Loidreau’s encryption scheme, based on rank-metric codes, for some...     

Remarks on Rawnsley’s $$\varvec{\varepsilon }$$ε -function on the Fock–Bargmann–Hartogs domains

In this paper, we mainly study a family of unbounded non-hyperbolic domains in $$\mathbb {C}^{n+m}$$, called Fock–Bargmann–Hartogs domains $$D_{n,m}(\mu )$$ ($$\mu >0$$) which are defined as a Hartogs type domains with the fiber over each $$z\in \mathbb {C}^{n}$$ being a ball of radius $$e^{-\frac{\mu }{2} {\Vert z\Vert }^{2}}$$. The purpose of this paper is twofold. Firstly, we obtain necessary and sufficient conditions for Rawnsley’s $$\varepsilon $$-function $$\varepsilon _{(\alpha ,g)}(\widetilde{w})$$ of $$\big (D_{n,m}(\mu ), g(\mu ;\nu )\big )$$ to be a polynomial in $$\Vert \widetilde{w}\Vert ^2$$, where $$g(\mu ;\nu )$$ is a Kähler metric associated with the Kähler potential $$\nu \mu {\Vert z\Vert }^{2} -\ln (e^{-\mu {\Vert z\Vert }^{2}}-\Vert w\Vert ^2)$$. Secondly, using above results, we study the Berezin quantization on $$D_{n,m}(\mu )$$ with the metric $$\beta g(\mu ;\nu )$$$$(\beta >0)$$.     

The role of a nation’s culture in the country’s governance: Stochastic frontier analysis

Central European Journal of Operations Research - What role does culture play in determining institutions in a country? This paper argues that the establishment of institutions is a process...     

Schlichting’s theorem for approximate subgroups

We prove Schlichting’s theorem for approximate subgroups: if $${\mathcal {X}}$$ is a uniform family of commensurable approximate subgroups in some ambient group, then there exists an invariant approximate subgroup commensurable with $${\mathcal {X}}$$.     

Kurdyka–Łojasiewicz Exponent via Inf-projection

Foundations of Computational Mathematics - Kurdyka–Łojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In...     

A Menon-type identity using Klee’s function

Czechoslovak Mathematical Journal - Menon’s identity is a classical identity involving gcd sums and the Euler totient function φ. A natural generalization of φ is the Klee’s...     

Box-counting by Hölder’s traveling salesman

We provide a sufficient Dini-type condition for a subset of a complete, quasiconvex metric space to be covered by a Hölder curve. This implies in particular that if the upper box-counting dimension is less than $$d \ge 1$$, then it can be covered by an $$\frac{1}{d}$$-Hölder curve. On the other hand, for each $$1\le d <2$$ we give an example of a compact set in the plane with lower box-counting dimension equal to zero and upper box-counting dimension equal to d, just failing the above Dini-type condition, that can not be covered by a countable collection of $$\frac{1}{d}$$-Hölder curves.     

Hua’s theorem on five squares of primes

We give an alternative proof of Hua’s theorem that each large N≡5 (mod 24) can be written as a sum of five squares of primes. The proof depends on an estimate of exponential sums involving the Möbius function.     

Radon’s construction and matrix relations generating syzygies

Monatshefte für Mathematik - Let $$\varPi _n$$ be the set of bivariate polynomials of degree not greater than n. A $$\varPi _n$$-correct set of nodes is a set such that the Lagrange...     

Bertram’s pairs trading strategy with bounded risk

Central European Journal of Operations Research - Finding Bertram’s optimal trading strategy for a pair of cointegrated assets following the Ornstein–Uhlenbeck price difference process...     

Constraint-Preserving Hybrid Finite Element Methods for Maxwell’s Equations

Foundations of Computational Mathematics - Maxwell’s equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux...     

Means,Milne’s inequality,and quadrilateral area

Aequationes mathematicae - We discuss Milne’s inequality and apply it to the sides of a convex quadrilateral to derive an approximation to the area of the quadrilateral via arithmetic and...     

A generalization of Halphén’s formula for derivatives

We present a generalization of Halphén’s formula on the higher order derivatives of     

Newton’s Method for Solving Generalized Equations Without Lipschitz Condition

Journal of Optimization Theory and Applications - This paper aims to establish higher order convergence of the (inexact) Newton’s method for solving generalized equations composed of the sum...     

A variant of Yano’s extrapolation theorem on Hardy spaces

In this note, a variant of Yano’s classical extrapolation theorem for sublinear operators acting on analytic Hardy spaces over the torus is obtained.     

Fridman’s Invariant,Squeezing Functions,and Exhausting Domains

We show that if a bounded domain Ω is exhausted by a bounded strictly pseudoconvex domain D with C2 boundary, then Ω is holomorphically equivalent to D or the unit ball, and show that a bounded domain has to be holomorphically equivalent to the unit ball if its Fridman’s invariant has certain growth condition near the boundary.