Related papers: A correction to: Rational and nearly rational vari…

We correct the statements and proofs of the (auxiliary) Propositions 4.1 and 4.2 of our paper `Evaluation of motivic functions, non-nullity, and integrability in fibers' in Advances in Mathematics, Vol. 409, Part A, Paper No. 108635, 29…

In this brief reply we point out to some misconceptions in C.Camacho's comment (cond-mat/9701210).

We study strong approximation for some algebraic varieties over which are defined using norm forms over the rationals. This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg.

Completeness and transitivity are standard rationality conditions in economics. However, under ambiguity, decision makers sometimes violate these requirements because of the difficulty of forming accurate predictions about ambiguous events.…

We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.

An error in the author's paper (Functiones et Approximatio, 37 . pp. 203-211) is corrected.

Good quality explanations strengthen the understanding of language models and data. Feature attribution methods, such as Integrated Gradient, are a type of post-hoc explainer that can provide token-level insights. However, explanations on…

There is a serious mistake in the proof.

We prove some extensions of Andrews inequality.

We establish a conjecture of Mumford characterizing rationally connected complex projective manifolds in several cases.

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.

We describe a rational, but low resolution model of probability.

We correct a statement of a theorem on characterisation of the (c)-regularity we gave in Topology 37 (1998), 45--62. This theorem was used in the paper in the proof of two theorems on the (c)-regular stratification. In this note we give a…

In the paper [Hong-Shi Zong, Wei-Min Sun, Phys. Lett. B 640 (2006) 196], the authors claim that our proof of the inconsistency of the ladder approximation to QCD [Phys. Lett. B 611 (2005) 129] was incorrect. However, their claim is based on…

Citations are updated; referred papers are increased. An error right after the eq.~(27) is corrected, and several chages (not serious) are made.

A simple application of the semipositivity.

The aim is to correct part of the Remark 3 of my paper "On regular, intra-regular ordered semigroups" in Pure Math. Appl. (PU.M.A.) 4, no. 4 (1993), 447--461. On this occasion, some further results and the similarity between the…

Let $Z$ be a projective geometrically integral algebraic variety. This paper is concerned with estimating the number of rational points on $Z$ which have height at most $B$. The bounds obtained are uniform in varieties of fixed degree and…

We correct some tables and figures in [A.P. Bustamante and R.C. Calleja, Physica D: Nonlinear Phenomena, 395 (2019), pp. 15-23, arXiv:1712.05476]. We also report on the new computations that verify the accuracy of the data and extend the…

We extend the Cone Theorem of the Log Minimal Model Program to log varieties with arbitrary singularities.