相关论文: Some consequences of the Karpenko-Merkurjev theore…

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John's theorem and in the form…

We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

The inevitability of Chern--Simons terms in constructing a variety of physical models, and the mathematical advances they in turn generate, illustrates the unexpected but profound interactions between the two disciplines.

Nikolai Durov introduced the theory of generalized rings and schemes to study Arakelov geometry in an alternative algebraic framework, and introduced the residue field at the infinite place. We show an elementary algebraic approach to…

In this paper, we establish some new fixed point theorems and coincidence point theorems for essential distances and $e^{0}$-metrics which generalize and improve Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point…

Sufficient ultraspherical multiplier criteria are refined in such a way that they are comparable with necessary multiplier conditions. Also new necessary conditions for Jacobi multipliers are deduced which, in particular, imply known Cohen…

Kapranov Theorem is a well known generalization of Newton-Puiseux theorem for the case of several variables. This theorem is stated mainly in the context of tropical geometry. We present a new, constructive proof, that also characterizes…

The paper continues our previous work [7] on the radius of subregularity that was initiated by Asen Dontchev. We extend the results of [7] to general Banach/Asplund spaces and to other classes of perturbations, and sharpen the coderivative…

Theory of $n$-complements with applications is presented.

Gromov \cite{Gr$_1$} and Dranishnikov \cite{Dr$_1$} introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we…

We construct a counterexamples in dimensions $n>3$ to Gromov's conjecture \cite{Gr1} that the macroscopic dimension of rationally essential $n$-dimensional manifolds equals $n$.

Recent progress in the theory of hadrons containing a single heavy quark is reviewed. Particular attention is paid to those aspects that bear on the determination of the magnitudes of the Cabibbo--Kobayashi--Maskawa matrix elements $V_{cb}$…

In this note we prove the Borel Conjecture for closed, irreducible and sufficiently collapsed three-dimensional Alexandrov spaces. We also pose several questions related to characterization of fundamental groups of three-dimensional…

This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recent years. The paper surveys classical and…

A brief presentation of basics of the theory of Tchebycheff and Markov systems of functions and its applications to extremal problems for integrals of such functions is given. The results, as well as all the necessary definitions, are…

In this paper, we establish an analogue of the Fundamental Theorem of Algebra for polynomial matrix equations, where both the coefficient matrices and the unknown matrix are $Q$-circulant matrices. This result generalizes Abramov's result…

We prove a generalisation of the Khukhro--Makarenko theorem on large characteristic subgroups with laws. This general fact implies new results on groups, algebras, and even graphs and other structures. Concerning groups, we obtain, e.g., a…

In this paper, we first derive an inequality involving central moments for n real numbers, which in turn provides an extension of Theorem 2.2 of Wolkowicz and Styan [18]. Furthermore, we present refinements of various inequalities obtained…