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In 1974, Jeffrey Rauch proposed the hot spot conjecture for the second eigenfunctions of the Neumann eigenvalue problems. We will recall some of its development and related studies in recent years. We...
This paper considers nonparametric and semiparametric regression models subject to monotonicity constraint. We use bagging as an alternative approach to Hall and Huang (2001). Asymptotic properties of...
Fast gradient methods are known to be non-monotone algorithms, and oscillations typically occur around the solution. To avoid this behavior, we propose in this paper a fast gradient method with restar...
It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decrease with the sample size. The proofs are based on fine propert...
Abstract: Graph pebbling considers the problem of transforming configurations of discrete pebbles to certain target configurations on the vertices of a graph, using the so-called pebbling move. This p...
Abstract: A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence...
Abstract: We prove the existence of minimizers of a class of multi-constrained variational problems in which the non linearity involved does not sat- isfy compactness, monotonicity, neither symmetry p...
We introduce the notion of ratio monotonicity for polynomials with nonnegative coefficients, and we show that for n ≥ 6, the q-derangement numbers Dn(q) are strictly ratio monotone, except for the las...
We prove new l'Hopital rules for monotonicity valid on an arbitrary time scale. Both delta and nabla monotonic l'Hopital rules are obtained. As an example of application, we give some new upper and lo...
The ratio monotonicity of a polynomial is a stronger property than log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing coefficients. We prove the ratio monotone property of P(x ...
This article relies on [15] that the author wrote with Gang Tian and Xiaodong Wang. In view of Hamilton's important work on the Ricci flow and Perelman's paper on the Ricci flow where he developes the...
In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that the...
We study a certain monotonicity property of ratios of means, which we call a strong inequality. These strong inequalities were recently shown to be related to the so-called relative metric. We also us...

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