相关论文: Further Improvements on Waring's Problem

This note is the follow up to a paper by M. Waldschmidt.

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued…

We provide conditions on the coefficients of a ternary cubic form that determine its Waring rank.

We obtain some inequalities which are stronger than the Schur majorization inequalities.

We survey recent developments on the Restriction conjecture.

We shortly review the state of art and perspectives of Extended Theories of Gravity.

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…

We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.

We solve the Cauchy problem of the Ward equation with both continuous and discrete scattering data.

In this paper we shall prove a sharpened version of the Finsler-Hadwiger inequality which is a strong generalization of Weitzenbock inequality. After that we give another refinement of this inequality and in the final part we provide some…

Young's integral inequality is complemented with an upper bound to the remainder. The new inequality turns out to be equivalent to Young's inequality, and the cases in which the equality holds become particularly transparent in the new…

In this paper, we will present some results on the counterfeit coins problem in the case of multi-sets.

The extended Wigner's friend problem deals with two Observers each measuring a sealed laboratory in which a friend is making a quantum measurement. We investigate this problem by relying on the basic rules of quantum mechanics as exposed by…

The analysis of papers on usage NMR in quantum computations is provided and the probable direction of the future investigations are considered.

This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness results were…

We highlight some facts about continued fractions of real cubic irrationalities. This may be thought as a small section in a textbook on continued fractions.

We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.

We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results