Related papers: On three duality results

The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.

In this note, we investigate J.-C. Liu's work on truncated Gauss' square exponent theorem and obtain more truncations. We also discuss some possible multiple summation extensions of Liu's results.

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

An inequality concerning ratios of gamma functions is proved. This answers a question of Guo and Qi (2003).

In the paper "The relativistic Doppler effect: when a zero-frequency shift or a red shift exists for sources approaching the observer, Ann. Phys. (Berlin) 523, No. 3, 239-246 (2011), DOI 10.1002/andp.201000099 by C. Wang the use of an…

In this note we rectify the proof of Theorem 3.11 in [arXiv:2403.02876]. We also present a set of examples at the end discussing various cases.

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).

A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…

In prior work we have introduced an asymptotic threshold of sufficient randomness for causal inference from observational data. In this paper we extend that prior work in three main ways. First, we show how to empirically estimate a lower…

We prove a duality theorem for graded algebras over a field that implies several known duality results : graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and…

The aim of this article is twofold: first, improve the multiplicity estimate obtained by the second author for Drinfeld quasi-modular forms; and then, study the structure of certain algebras of "almost-$A$-quasi-modular forms"

We find it absurd that Walliser [1] essentially used the same analysis and obtained identical results as reported in [3], yet arrived at different conclusions. Namely, based on an incomplete theory and using erroneous arguments, he not only…

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems,…

This is a reply to Muff, S. et al. (2022) Rewriting results sections in the language of evidence, Trends in Ecology & Evolution 37, 203-210.

A number of authors have recently pointed out inconsistencies of results obtained with the Huang-Yang multipolar pseudo-potential for low-energy scattering [K. Huang and K. C. Yang, Phys. Rev. A, v 105, 767 (1957); later revised in K.…

Recently, Bradley studied partial sums of multiple q-zeta values and proved a duality result. In this paper, we present a generalization of his result.

We reply to the comment by Ying Zhang and S. Das Sarma on our PRL 94, 226405 (2005).

The aim of this note is to prove the analogue of Poincar\'e duality in the chiral Hodge cohomology.

Du, Kakade, Wang, and Yang recently established intriguing lower bounds on sample complexity, which suggest that reinforcement learning with a misspecified representation is intractable. Another line of work, which centers around a…