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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A family of Monge-Ampère type operators converging to sigma_k, and their Minkowski problems
sigma_k汇聚 蒙日安培型 算子家族 闵可夫斯基问题
2023/4/17
We introduced a new family of translation invariant geometric measures arising from Integral Geometry of convex bodies. These measures are related to a family of new Monge-Ampère type operators conver...
In this paper we consider both the dynamical and parameter planes for the complex exponential family Eλ(z) = λez where the parameter λ is complex. We show that there are infinitely many curves or “hai...
Our motivation for studying this problem is threefold:
(i) When one fixes r = m = 0, the resulting two parameter family is a normal
form for a codimension two bifurcation within the class of planar ...
How Close a Bataknese One Another?: Study of Indonesian Batak’s Family Tree
family tree batak customary law scale-free network
2015/7/28
The paper conjectures some alternative acquisitions of mathematical models to see the Batak family tree that could enrich our understanding of the anthropological study of Bataknese people. We discuss...
Chaos and Robustness in a Single Family of Genetic Oscillatory Networks
Chaos and Robustness Genetic Oscillatory Networks
2014/12/12
Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological stan...
The number of integer points in a family of anisotropically expanding domains
number of integer points family of anisotropically expanding domains Number Theory
2012/4/17
We investigate the remainder in the asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space, which remain unchanged along some linear subspace and exp...
Numerical analysis of minimal beta-sequences associated with a family of entire functions
Numerical analysis Entire functions Pochhammer polynomials Riemann Xi-function
2011/9/22
Abstract: The Riemann Xi-function Xi(t)=xi(1/2+it) is a particularly interesting member of a broad family of entire functions which can be expanded in terms of symmetrized Pochhammer polynomials depen...
On cyclicity one elliptic islands of the Standard family
elliptic islands the Standard family Dynamical Systems
2011/9/14
Abstract: We study abundance of a special class of elliptic islands (called cyclicity one elliptic islands) for the Standard family of area preserving diffeomorphisms for large parameter values, i.e. ...
On a Devil's staircase associated to the joint spectral radii of a family of pairs of matrices
Joint spectral radius Devil’s staircase finiteness conjecture Sturmian sequence balanced word
2011/9/14
Abstract: The joint spectral radius of a finite set of real d x d matrices is defined to be the maximum possible exponential rate of growth of products of matrices drawn from that set. In previous wor...
The family index theorem and bifurcation of solutions of nonlinear elliptic bvp
Bifurcation Nonlinear Elliptic Boundary Value Problems Fredholm Maps Index Bundle J-homomorphism Family Index Theorem
2011/8/31
Abstract: We obtain some new criteria for bifurcation of solutions of general boundary value problems for nonlinear systems of elliptic partial differential equations which are rather different from t...
The semiclassical limit of focusing NLS for a family of non-analytic initial data
semiclassical limit non-analytic initial data NLS
2011/7/7
The small dispersion limit of the focusing nonlinear Schro\"odinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales....
A note on the border of an exponential family
Algebraic Statistics Convex Support Extended Exponential Family
2011/1/17
Limits of densities belonging to an exponential family appear in many applications, e.g. Gibbs models in Statistical Physics, relaxed combinatorial optimization,coding theory, critical likelihood comp...
A New Family Of Elliptic Curves With Positive Rank arising from Pythagorean Triples
elliptic curves rank pythagorean triples
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves in the form of y2 = x(x−a2)(x−b2) that have positive ranks. We first generate a list of pythagorean triples (a, b, c) ...
A new family of elliptic curves with positive ranks arising from the Heron triangles
Elliptic curves Ranks Torsion group Heron’s Triangle
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves with positive ranks.
Orthogonal polynomials and expansions for a family of weight functions in two variables
Orthogonal polynomials orthogonal expansions Jacobi polynomials
2011/2/25
Orthogonal polynomials for a family of weight functions on [1; 1]2,W ; ; (x; y) = jx + yj2 +1jx yj2 +1(1 x2) (1 y2) ; are studied and shown to be related to ...