Related papers: Comment on "Two notes on imbedded prime divisors"
The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.
This note presents criteria in terms of Bernoulli numbers for a number to be simultaneously a Wilson prime and a Lerch prime.
We apply the Inclusion-Exclusion Principle to a unique pair of prime number subsequences to determine whether these subsequences form a small set or a large set and thus whether the infinite sum of the inverse of their terms converges or…
The problem of embedding an ample semigroup in an inverse semigroup as a (2, 1, 1)-type subalgebra is known to be undecidable. In this article, we investigate the problem for certain classes of ample semigroups. We also give examples of…
We show in this comment that the results obtained in a recent work by Yi et al. [Phys. Rev. Lett. 92, 150406 (2004)] are quantitatively not correct and the proposed subsystem Berry phase is not well-defined.
We prove a new equidistribution estimate for the divisor function in arithmetic progression to moduli that have two small factors. We give two applications. First, we show an asymptotic formula for the divisor function over arithmetic…
The proofs of Theorem 1.1 and Theorem 1.5(2) in the authors' paper 'The Hasse norm principle for abelian extensions' are incorrect. We point out the mistakes and provide correct proofs, using techniques of the original paper.
In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.
Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.
Please goto the "Note Added" part of v6, quant-ph/0501143
This addendum contains results about the inversion number and major index polynomials for permutations avoiding 321 which did not fit well into the original paper. In particular, we consider symmetry, unimodality, behavior modulo 2, and…
In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…
In this note, we give the possible revised version of the unique solvability conditions for the two incorrect results that appeared in the published paper by Wu et al. (Appl Math Lett 76:195-200, 2018).
The classes of two theta divisors on an abelian variety in the naive Grothendieck ring of varieties need not be congruent modulo the class of the affine line.
Tight and essentially tight modules generalize weakly injective modules. Essential tightness requires embeddings to be essential. This restriction makes the two notions totally different. In this note, we investigate cases when those two…
Answering a question by Honsell and Plotkin, we show that there are two equations between lambda terms, the so-called subtractive equations, consistent with lambda calculus but not simultaneously satisfied in any partially ordered model…
In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if $M\geq 5$ is an integer and the integers $a$ and $b$ are relatively prime to $M$ and satisfy $1\leq a<b<M/2$, and the…
We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.
We establish an explicit inequality for the number of divisors of an integer $n$. It uses the size of $n$ and its number of distinct prime divisors.
We obtain a new bound on the second moment of modified shifted convolutions of the generalized 3-fold divisor function, and show that, for applications, the modified version is sufficient.