<p style='text-indent:20px;'>In this paper, we explore the period tripling and quintupling renormalizations below <inline-formula><tex-math id="M1">\begin{document}$ C^2 $\end{document}</tex-math></inline-formula> class of unimodal maps. We show that for a given proper scaling data there exists renormalization fixed point on space piece-wise affine maps which are i...

Table 1. Location and spatial distribution of individual vibrissa intrinsic map peaks. ML: lateral distance of map peak relative to the horizontal midline passing through bregma point. RC: caudal distance of map peak relative to bregma. s.d.: standard deviation of the spread of mapped eIOS centroids after affine transformation (cf. figure 4b). s.d.: standard deviation of the spread of mapped eI...

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

We study affine permutation diagrams and their labellings with positive integers. Balanced labellings of a Rothe diagram of a finite permutation were defined by FominGreene-Reiner-Shimozono, and we extend this notion to affine permutations. The balanced labellings give a natural encoding of the reduced decompositions of affine permutations. We show that the sum of weight monomials of the column...

The affine synthesis operator Sc = P j>0 P k∈Z d c j,k ψ j,k is shown to map the coefficient space ℓ p (Z+ × Z d) surjectively onto L p (R d), for p ∈ (0, 1]. Here ψ j,k (x) = | det aj| 1/p ψ(ajx − k) for dilation matrices aj that expand , and the synthesizer ψ ∈ L p (R d) need satisfy only mild restrictions, for example ψ ∈ L 1 (R d) with nonzero integral or else with periodization that is rea...

Abstract For a polygon $$x=(x_j)_{j\in \mathbb {Z}}$$ x = ( j ) ? Z in $$\mathbb {R}^n$$ R n we consider ...

We show how the existence of three objects, $\Omega_{\rm trap}$, ${\bf W}$, and $C$, for a continuous piecewise-linear map $f$ on $\mathbb{R}^N$, implies that has topological attractor with positive Lyapunov exponent. First, trap} \subset \mathbb{R}^N$ is trapping region $f$. Second, W}$ finite set words encodes forward orbits all points in trap}$. Finally, $C T an invariant expanding cone deri...

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

We introduce the notion of a nonlinear splitting on fibre bundle as generalization an Ehresmann connection. present its basic properties and we pay attention to special cases affine, homogeneous principal splittings. explain where splittings appear in context Lagrangian systems Finsler geometry show their relation Routh symmetry reduction, submersive second-order differential equations unreduct...

In this work, we describe a simple and efficient construction of a large subset S of Fp , where p is a prime, such that the set A(S) for any non-identity affine map A over Fp has small intersection with S . Such sets, called affine-evasive sets, were defined and constructed in [ADL14] as the central step in the construction of non-malleable codes against affine tampering over Fp , for a prime p...