相关论文: Further Improvements on Waring's Problem

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…

We describe the difficulties that advanced undergraduate and graduate students have with quantum measurement within the standard interpretation of quantum mechanics. We explore the possible origins of these difficulties by analyzing student…

We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann…

In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…

Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…

The aim of this paper is to analyze the weighted KyFan inequality proposed in [11]. A number of numerical simulations involving the exponential weighted function is given. We show that in several cases and types of examples one can imply an…

Waring problem for homogeneus forms asks for additive decomposition of a form $f$ into powers of linear forms. A classical problem is to determine when such a decomposition is unique. In this paper I answer this question when the degree of…

We present some recent results on the existence of solutions of the Schr\"odinger flows, and pose some problems for further research.

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.

Some Titchmarsh results following Gram's law are improved in this paper.

This review aims to provide a comprehensive update on the progress made on the Sequential Testing problem (STP) in the last 20 years after the review, [1] was published. Many studies have provided new theoretical results, extensions of the…

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

In this paper we provide an application to the Neumann problem of a recent three critical points theorem.

In this talk, I summarize the status of our understanding of the puzzle of large gauge invariance at finite temperature.

We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.

The aim of the present paper is to give extensions of the cosine-sine functional equation.

New cases of the multiplicity conjecture are considered.

Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined.

In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.