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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Monotonicity of the second Neumann eigenfunction in symmetry domain
对称域 第二个 诺依曼特征函数 单调性
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2023/4/18
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...
Nonparametric and Semiparametric Regressions Subject to Monotonicity Constraints: Estimation and Forecasting
Nonlinearity Nonparametric regression Semiparametric regression Local mono- tonicity Bagging
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2016/1/25
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...
Monotonicity and restart in fast gradient methods
flat gradient algorithm oscillation values
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2015/8/7
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...
Monotonicity in the Sample Size of the Length of Classical Confidence Intervals
Gamma function Location and scale parameters Stochastic monotonicity
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2012/3/1
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...
Counterexamples to a Monotonicity Conjecture for the Threshold Pebbling Number
combinatorics probability theory graph theory graph pebbling pebbling number pebbling threshold
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2011/9/20
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...
Almgren-type monotonicity methods for the classification of behavior at corners of solutions to semilinear elliptic equations
Almgren monotonicity formula semilinear elliptic equations conical boundary points
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2011/9/19
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...
Existence of Minimizers of a class of multi-constrained variationnal problems in the absence of compactness, symmetry and monotonicity
Minimizers multi-constrained variationnal problems absence of compactness symmetry and monotonicity
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2011/8/23
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...
The Ratio Monotonicity of the q-Derangement Numbers
q-derangement number spiral property log-concavity ratio monotone property
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2014/6/3
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...
L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
L'Hopital-Type Rules Quantum Calculus
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2010/11/24
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...
Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences
log-concavity ratio monotonicity Boros-Moll polynomials
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2014/6/3
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 ...
Perelman's Monotonicity Formula and Applications
Ricci flow smooth convergence
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2010/2/26
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...
The Ratio Monotonicity of the Boros-Moll Polynomials
ratio monotone property spiral property unimodality log-concavity Jacobi polynomials Boros-Moll polynomials
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2014/6/3
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...
A Monotonicity Property of Power Means
Arithmetic mean Geometric mean Monotonicity Power means
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2008/7/3
A Monotonicity Property of Power Means.
A Monotonicity Property of Ratios of Symmetric Homogeneous Means
Monotonicity Strong inequalities Extended mean values Gini's mean Seiffert's mean Relative metrics
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2008/7/3
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...
A Monotonicity Property of the Gamma Function
Gamma function Strictly completely monotone
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2008/7/3
A Monotonicity Property of the Gamma Function