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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convexity, Uniqueness, and Stability of the Regular Shock Reflection-diffraction Problem
规则冲击 反射衍射问题 凸性 唯一性 稳定性
2023/4/17
We will talk about our recent results on the convexity, uniqueness, and stability of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The appr...
The geometry of groups satisfying weak almost-convexity or weak geodesic-combability conditions
almost-convexity geodesic-combability
2015/8/26
We examine the geometry of the word problem of two different types groups: those satisfying weak almost-convexity conditions and those admitting geodesic combings whose width satisfy minimally restric...
Convexity of Optimal Control over Networks with Delays and Arbitrary Topology
Delays Arbitrary Topology
2015/6/19
We consider the design of optimal controllers for a networked system (or a spatio-temporal system), where the dynamics of each subsystem may affect those of other subsystems with some propagation dela...
Non-Convexity Of The Dimension Function For SierpiNski Pedal
Moran Equation SierpiNski Pedal
2012/8/10
We disprove the conjecture of the paper [5] on the Schur-convexity
of the dimension function for the family of Sierpi磏ski pedal triangles.
We also show that this function is not convex and the relat...
Local convexity properties of Apollonian and Seittenranta's metric balls
Apollonian distance Seittenranta’s distance metric ball local convexity
2012/4/17
We consider local convexity properties of the Apollonian and the Seittenranta's metric balls. The Apollonian metric balls are considered in the twice punctured space, convex and starlike domains. The ...
Radius of Close-to-convexity of Harmonic Functions
Coefficient inequality partial sums radius of univalence analytic univalent convex and starlike harmonic functions
2011/8/24
Abstract: Let ${\mathcal H}$ denote the class of all normalized complex-valued harmonic functions $f=h+\bar{g}$ in the unit disk ${\mathbb D}$, and let $K=H+\bar{G}$ denote the harmonic Koebe function...
Generalized convexity and the existence of finite time blow-up solutions for an evolutionary problem
Finite time blow-up solutions p-Laplacian generalized convexity regularly varying functions
2011/9/22
Abstract: In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann-Robin boundary conditions, for $p$-Laplacian, has finite time blow-up solutions.
Convexity of Workload Autocorrelation in a Stationary Single Server Queue with Independent Increment Input
Convexity of Workload Autocorrelation Independent Increment Input Probability
2011/8/26
Abstract: We propose a method based on probabilistic arguments to study the convexity of the autocorrelation function of processes associated with a single server queue. To illustrate the power of the...
The 2-log-convexity of the Apéry Numbers
Apery numbers log-convexity 2-log-convexity infinite log-convexity
2014/6/3
We present an approach to proving the 2-log-convexity of sequences satisfying three-term recurrence relations. We show that the Apéry numbers, the Cohen-Rhin numbers, the Motzkin numbers, the Fine num...
NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems
NP-hardness of Deciding Convexity of Quartic Polynomials Related Problems
2011/1/19
We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time)
algorithm that can decide whether a multivariate polynomial of degree four (or higher even
degree) is globa...
A note on convexity and starshapedness
Convex sets wn-convex sets starshaped sets affine sets
2010/11/1
We establish sufficient and necessary conditions for a set to be affine or convex. The concepts of weak near convexity and affine starshapedness are studied. A characterization of the (affine) kernel ...
Convexity of Momentum Maps: A Topological Analysis
Convexity of Momentum Maps Topological Analysis
2010/11/15
We extend the Local-to-Global-Principle used in the proof of convexity theorems for momentum maps to not necessarily closed maps $f\colon X\ra Y$ whose target space $Y$ carries a convexity structure ...
We give a survey of basic results on the cut norm and cut metric for graphons (and sometimes more general kernels), with emphasis on the equivalence problem. The main results are not new, but we add v...
Hermite-Hadamard Type Inequalities via (α,m)- Convexity
Convexity Hermite-Hadamard inequality H¨older’s integral inequality
2010/12/13
In this paper, we establish some integral inequalities for functions whose second derivatives in absolute value are ( ,m)− convex.
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
Restricted strong convexity weighted matrix completion Optimal bounds with noise
2010/12/3
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case.We analyze the associated random ob...