Factoring periodic maps into Dehn twists

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\ge 1$. In this paper, we develop various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy. As applications, we develop methods for factoring certain roots of Dehn twists as words in Dehn twists. We will also show the existence of conjugates of periodic maps of order 4g and $4g+2$, for $g\ge 2$, whose product is pseudo-Anosov.     

On co-σ-porosity of the parameters with dense critical orbits for skew tent maps and matching on generalised β-transformations

We prove that the critical point and the point 1 have dense orbits for Lebesgue-a.e., parameter pairs in the two-parameter skew tent family and generalised $\beta$-transformations. As an application, we show that for the generalised $\beta$-transformation with the tribonacci number as slope, there is matching (i.e., $T^n\left(0\right)=T^n\left(1\right)$ for some $n\ge 1$) for Lebesgue-a.e. translation parameter.     

Order and chaos in a three dimensional galaxy model

We explore the orbital dynamics of a realistic three dimensional model describing the properties of a disk galaxy with a spherically symmetric central dense nucleus and a triaxial dark matter halo component. Regions of phase space with regular and chaotic motion are identified depending on the parameter values for triaxiality of the dark matter halo and for breaking the rotational symmetry. The four dimensional Poincaré map of the three degrees of freedom system is analyzed by a study of its restriction to various two dimensional invariant subsets of its domain.     

Using store level scanner data to improve category management decisions: Developing positioning maps

This paper provides evidence of the usefulness of aggregated point-of-sale scanner data to infer the positioning of competing brands, providing valuable information for category management and hence facilitating decision making. Specifically, the authors propose a methodology to study the internal market structure based on market share models with latent heterogeneity when only macro-level time series data (not individual choices) are available. The proposed approach assumes a multidimensional decomposition, latent in the preference structure that is implicit to these types of models. By empirically applying this approach, the authors (1) simultaneously identify both latent dimensions of competing brands and latent segments with different brand preferences, (2) explain the competitive positioning of brands without using disaggregated consumer panel data, and (3) achieve greater predictive performance. The findings offer insights to academics and practitioners interested in improving the practice of category management.     

The Mazur product map on Hardy-type sequence spaces

We study certain Hardy-type sequence spaces Hp and , 1?p?∞, which are analogues of ?^∞ and c₀, respectively. We show that the Mazur product is not onto for every p∈(1,∞) with q=p⁻¹(p−1). We present corollaries for spaces defined via weighted ?p seminorms and for c₀. The latter corollary provides a new solution of Mazur's Problem 8 in the Scottish Book.     

On Characterizing the Solution Sets of Pseudoinvex Extremum Problems

In this paper, we study the minimization of a pseudoinvex function over an invex subset and provide several new and simple characterizations of the solution set of pseudoinvex extremum problems. By means of the basic properties of pseudoinvex functions, the solution set of a pseudoinvex program is characterized, for instance, by the equality , for each feasible point x, where is in the solution set. Our study improves naturally and extends some previously known results in Mangasarian (Oper. Res. Lett. 7: 21–26, 1988) and Jeyakumar and Yang (J. Opt. Theory Appl. 87: 747–755, 1995). This research was partially supported by National Natural Science Foundation of China Grants No. 10771228 and 10831009.     

Maps preserving scrambling index

In this paper we characterize bijective linear maps on matrices over semirings that preserve scrambling index.     

Frankel's theorem in the symplectic category

We prove that if an -dimensional torus acts symplectically on a -dimensional symplectic manifold, then the action has a fixed point if and only if the action is Hamiltonian. One may regard it as a symplectic version of Frankel's theorem which says that a Kähler circle action has a fixed point if and only if it is Hamiltonian. The case of is the well-known theorem by McDuff.

     

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

We study the nullcone in the multi-vector representation of the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.     

Binder melt: Quantification using SEM/EDS and its effects on composite solid propellant combustion

The present study reports the development of a novel technique to quantify binder melt on the surface of the propellant. Non-aluminized AP-HTPB propellants of 86% particulate loading are used to illustrate the technique. Elemental maps of unburnt and extinguished propellant surface are obtained using EDS (Energy Dispersive Spectroscopy). Overlap between the elements is identified and the elemental maps are processed to calculate AP and binder area exposed in unburnt and extinguished samples. The AP area exposed is found to be around 72.3% and 63.3% for unburnt and extinguished samples, respectively, indicating a reduction in AP exposed area with extinguished samples. This has been attributed to the binder melt discussed in literature but never quantified. Simulations have been carried out to analyze and understand the effects of this binder melt. A random packing algorithm is used to simulate propellant packs. Also, a methodology to account for binder melt layer is introduced and is used to capture AP exposed areas. Effect of binder melt in propellants with different solid loading and varying particle size is discussed. It is shown that fine AP particles are more prone to being covered by binder melt than the coarse AP particles. A possible explanation to the behavior of plateau burning propellants observed in literature has been provided through this analysis.