Related papers: Reply to Hagen & Sudarshan's Comment

Let $A$ be an algebra and let $f$ be a nonconstant noncommutative polynomial. In the first part of the paper, we consider the relationship between $[A,A]$, the linear span of commutators in $A$, and span$f(A)$, the linear span of the image…

We argue that, in the recent letter by A. Danan et al. [PRL 111, 240402 (2013), arXiv:1304.7469], if weak measurements are performed such that complete destructive interference is not disturbed, claims such as "some photons have been inside…

Certain Hamiltonians based on two coupled quantum mechanical spins exhibit degenerate eigenvalues despite having no obvious non-abelian symmetries. Operators acting to permute the degenerate states do not have a simple form when expressed…

We prove a strengthened form of a conjecture of Sun on a determinant attached to a binary quadratic form. Let $n>3$ and let $c,d\in\Z$. If $n$ is composite, then \[ \det\big[(i^2+cij+dj^2)^{n-2}\big]_{0\leq i,j\leq n-1}\equiv 0\pmod {n^2}…

In this paper, we prove that Gorenstein projective conjecture is left and right symmetric and the co-homology vanishing condition can not be reduced in general. Moreover, the Gorenstein projective conjecture is proved to be true for…

The non-relativistic hydrogen atom and the Zwanziger problem have the same dynamical symmetry for bound and scattering states.We show that this is also true for a Hilbert space which is non-commutative in co-ordinates. The group structure…

Reflective equilibrium between physics and philosophy, and between GR and particle physics, is fruitful and rational. I consider the virtues of simplicity, conservatism, and conceptual coherence, along with perturbative expansions. There…

Benenti et al. recently submitted a Comment (arXiv:0912.3667) on our work "Coherent Ratchets in Driven Bose-Einstein condensates". We show that the main claim of the Comment is wrong, and correct some other misunderstandings presented…

We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that,…

If $X = V(f) \subset \mathbb P^N$ is a reduced complex hypersurface, the hessian of $f$ (or by abusing the terminology the hessian of $X$) is the determinant of the matrix of the second derivatives of the form $f$, that is the determinant…

In a recent paper, Struyve et al. [Struyve W, De Baere W, De Neve J and De Weirdt S 2003 J. Phys. A 36 1525] attempted to show that the thought experiment proposed in [Golshani M and Akhavan O 2001 J. Phys. A 34 5259, quant-ph/0103101]…

This paper is a response to an article (R. de la Madrid, Journal of Physics A: Mathematical and General, 39,9255-9268 (2006)) recently published in Journal of Physics A: Mathematical and Theoretical. The article claims that the theory of…

Let $\mathcal P(S)$ be the semigroup obtained by equipping the family of all non-empty subsets of a (multiplicatively written) semigroup $S$ with the operation of setwise multiplication induced by $S$ itself. We call a subsemigroup $P$ of…

In the recent progress [BE1], [M], [Z1] and [Z2], the well-known Jacobian conjecture ([BCW], [E]) has been reduced to a problem on HN (Hessian nilpotent) polynomials (the polynomials whose Hessian matrix are nilpotent) and their (deformed)…

We consider subelliptic equations in non divergence form of the type $Lu = \sum a_{ij} X_jX_iu=0$, where $X_j$ are the Grushin vector fields, and the matrix coefficient is uniformly elliptic. We obtain a scale invariant Harnack's inequality…

We discuss a difference between the rational and the real non-vanishing conjecture for pseudo-effective log canonical divisors of log canonical pairs. We also show the log non-vanishing theorem for rationally connected varieties under…

In lines 8-11 of \cite[pp. 2977]{Lu} we wrote: "For integer $m\ge 3$, if $M$ is $C^m$-smooth and $C^{m-1}$-smooth $L:\R\times TM\to\R$ satisfies the assumptions (L1)-(L3), then the functional ${\cal L}_\tau$ is $C^2$-smooth, bounded below,…

John Morgan and G,Tian pointed out a mistake in the concluding argument for our paper entitled "$C_1$ in [2] is zero", which was recently published in arXiv:1512.02098. We hereby acknowledge this mistake and correct the computation, leading…

We comment on the paper by Benayoun, DelBuono, Eidelman, Ivanchenko, and O'Connell [Phys. Rev. {\bf D 59}, 114027 (1999)]. We show that the decay $\phi\to\pi^0\gamma$ is absent in model of the nonet symmetry and SU(3) breaking suggested by…

We show Kantor's conjecture (1974) holds in rank 4. This proves both the sticky matroid conjecture of Poljak and Turzik (1982) and the whole Kantor's conjecture, due to an argument of Bachem, Kern, and Bonin, and an equivalence argument of…