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Algebraic normal form of a bent function: properties and restrictions
Boolean function bent function linear function
2018/12/3
Maximally nonlinear Boolean functions in nn variables, where n is even, are called bent functions. There are several ways to represent Boolean functions. One of the most useful is via algebraic normal...
We introduce the twisted μ4μ4-normal form for elliptic curves, deriving in particular addition algorithms with complexity 9M+2S9M+2S and doubling algorithms with complexity 2M+5S+2m2M+5S+2m over a bin...
Adaptive and Sophisticated Learning in Repeated Normal Form Games
Adaptive Sophisticated Learning Repeated Normal
2015/7/21
Adaptive and Sophisticated Learning in Repeated Normal Form Games.
New Lattice Based Signature Using The Jordan Normal Form
Lattices Jordan Normal FormDigital Signature Scheme
2013/4/18
In this paper it is shown that the use of Jordan normal form instead of Hermite normal form would improve substantially the efficiency and the security of the lattice based signature scheme. In this s...
Reducing scattering problems under cone potentials to normal form by global canonical transformations
scattering problems cone normal form global canonical transformations Exactly Solvable and Integrable Systems
2012/4/26
We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" $\dot P=0$, $\dot Q=P$, by means of a global canonical transformation $ (P,Q)=A(p,q), p,q\in R^n$, defi...
Normal Form for the Schrödinger equation with analytic non--linearities
Normal Form Schrö dinger equation analytic non--linearities
2011/1/17
We discuss a class of normal forms of the completely resonant non–linear Schr¨odinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study. Further anal...
Construction of the Normal Form for Elliptic Tori in Planetary Systems. Part I: Numerical Validation of the Semi-Analytic Algorithm
Dynamical Systems (math.DS) Chaotic Dynamics (nlin.CD)
2010/11/10
We adapt the Kolmogorov's normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant ellip...
We prove the Poisson geometric version of the Local Reeb Stability (from foliation theory) and of the Slice Theorem (from equivariant geometry),which is also a generalization of Conn’s linearization t...
摘要利用非线整变换,本文推导出了一种只需通过简单代数运算即可算出Hopf分叉Normal Form系数的简单方法,用这种方法求解非线性振动问题,只需把原方程变换成本文讨论的典则形式的一阶微分方程组,然后进行简单的代数运算即可得到原非线性振动方程的解,这种方法简单方便容易掌握。
非半单分叉的Normal Form计算
NormalForm 非半单分叉 最大秩
2007/7/28
摘要在文［１］基础上，提出一种仅知道派生线性系统零实部特征值时求解非线性系统非半单分叉ＮｏｒｍａｌＦｏｒｍ的方法．通过适当的分类，将要求解的线性代数方程组分为若干相互独立的方程组．将所求系数向量按字典序列排列后，各独立方程组的系数矩阵是上三角矩阵．在非共振情形，各系数向量可按反字典序列递推求出．在共振情形，根据文中的二个定理，巧妙地由一简单的常数矩阵的最大秩子矩阵，定位其系数矩阵的满秩子矩阵，解决...