相关论文: Rejoinder on "Conjectures on exact solution of thr…
Problems in two axiomatizations of Ja\'skowski's discussive (or discursive) logic D2 are considered. A recent axiomatization of D2 and completeness proof relative to D2's intended semantics seems to be mistaken because some formulas valid…
This mostly expository paper centers on recently proved conjectures in two areas: A) A conjecture of A. Oppenheim on the values of real indefinite quadratic forms at integral points. B) Conjectures of Dani, Raghunathan, and Margulis on…
In the article "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp.2643-2654), published in 2001, we studied the linearizability problem for 3-webs on a 2-dimensional manifold. Four years after the publication of our…
Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the square lattice) from general results on the uniqueness of an…
We reply to the comment of Marinari and Parisi [cond-mat/0002457 v2] on our paper [Phys. Rev. Lett. 83, 5126 (1999) and cond-mat/9906323]. We show that the data in the comment are affected by strong finite-size corrections. Therefore the…
The points raised in the Comment are addressed and except for one error, which will be corrected, the conclusion is that all of our findings are accurate.
W. Zhang's arithmetic fundamental lemma (AFL) is a conjectural identity between the derivative of an orbital integral on a symmetric space with an arithmetic intersection number on a unitary Rapoport-Zink space. In the minuscule case,…
In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.
Rejoinder to "The Future of Indirect Evidence" [arXiv:1012.1161]
A conjecture of Woods from 1972 is disproved.
By extending Lv-Xin-Zhou's first layer formulas of the $q$-Dyson product, we prove Kadell's conjecture for the Dyson product and show the error of his $q$-analogous conjecture. With the extended formulas we establish a $q$-analog of…
In this note, we give item-by-item responses to the criticisms raised in [TZ] by Tehrani ad Zinger on our paper [LR]. We illuminate the main ideas and contributions in [LR] in section 2, itemize the responses to issues raised in [TZ] and…
In this paper, using quaternion arithmetic in the ring of Lipschitz integers, we present a proof of Zh\`i-W\v{e}i S\={u}n's "1-3-5 conjecture" for integral solutions, and for all natural numbers greater than a specific constant. This,…
There are two theories describing the linearizability of 3-webs: one is developed in the article "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp.2643-2654) and another in the article "On the Blaschke conjecture for…
In 2016, Jang and Kim stated a conjecture about the norms of indecomposable integers in real quadratic number fields $\mathbb{Q} \left( \sqrt{D} \right)$ where $D>1$ is a squarefree integer. Their conjecture was later disproved by Kala for…
In their Rejoinder [arXiv:1105.1316v1], Levin and Pakter repeat some of the points raised in their previous Comment [arXiv:1104.0697v1] (already refuted in our first Reply [arXiv:1104.5036v1]), and present some new ones concerning our…
Very recently, a ``Comment'' by Wang [gr-qc/0309003] on a paper by Gon\c{c}alves [Phys. Rev. D {\bf 65}, 084045 (2002)] appeared, claiming that Gon\c{c}alves' analysis of trapped surfaces in certain kinds of cylindrical spacetimes was…
It is shown that the various claims made in the comment by M. Ya. Azbel (physics/0403106) on the two publications Phys. Rev. Lett. 91, 055502 (2003) and Phys. Rev. Lett. 85, 4988 (2000) are invalid. They are a result of a misinterpretation…
In this note, we disprove two Romanov type conjectures posed by Chen.
We make corrections on the paper by Sugino [{\it JHEP} {\bf 0501} (2005) 016].