Related papers: On a convexity problem
It is shown that the question raised in Section 5.7 of [1] has an affirmative answer.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
In this article we proved an interesting property of the class of continuous convex functions. This leads to the form of pre-Hermite-Hadamard inequality which in turn admits a generalization of the famous Hermite-Hadamard inequality. Some…
In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.
Following the overall strategy of the paper ``Convex hypersurfaces in contact topology" by Ko Honda and Yang Huang on contact convexity in high dimensions, we present a simplified proof of their main result.
It is shown that the results of ref [1] are consistent.
Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)
We consider several appearances of the notion of convexity in Greek antiquity, more specifically in mathematics and optics, in the writings of Aristotle, and in art. The final version of this article will appear in the book `Geometry in…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
This paper has been withdrawn: it has been merged with the preprint to which it refers.
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
In the authors' previous works, novel finite element formulations for the contact interaction of slender beams have been proposed. In their recent article "Consistent Development of a Beam-To-Beam Contact Algorithm via the Curve to Solid…
Here we give further evidences to support our scaling relation described in our previous paper [cond-mat/0006459, Phys. Rev. Lett. Vol.85, pp.1238 (2000)].
We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also…
This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…
This paper is a continuation of our earlier work "[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]", where compactness results were…
We consider a sub-class of the $f$-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or $\kappa$-convex divergences. We derive new and old relationships, based on convexity arguments, between…
This is a Response to a recent Comment [F.Y. Wu et al., Phil. Mag. 88, 3093 (2008), arXiv:0811.3876] on the conjectured solution of the three-dimensional (3D) Ising model [Z.D. Zhang, Phil. Mag. 87, 5309 (2007), arXiv:0705.1045]. Several…
We review the results of our previous publication [Phys. Rev. D63, 116001 (2001); hep-ph/0012226] in the light of recent calculations and comments.
This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.