Some Paranormed Difference Sequence Spaces of Order mm Derived by Generalized Means and Compact Operators

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from $l(r, s, t, p; \Delta^{(m)})$ to $l_{\infty}, l_1$. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of some matrix operators on the BK space $l_{p}(r, s, t ;\Delta^{(m)})$ by applying the Hausdorff measure of noncompactness.Comment: Please withdraw this paper as there are some logical gap in some results. 20 pages. arXiv admin note: substantial text overlap with arXiv:1307.5883, arXiv:1307.5817, arXiv:1307.588

Shape Generation using Spatially Partitioned Point Clouds

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in reasonably good correspondences across all shapes. We then use PCA analysis to derive a linear shape basis across the spatially partitioned points, and optimize the point ordering by iteratively minimizing the PCA reconstruction error. Even with the spatial sorting, the point clouds are inherently noisy and the resulting distribution over the shape coefficients can be highly multi-modal. We propose to use the expressive power of neural networks to learn a distribution over the shape coefficients in a generative-adversarial framework. Compared to 3D shape generative models trained on voxel-representations, our point-based method is considerably more light-weight and scalable, with little loss of quality. It also outperforms simpler linear factor models such as Probabilistic PCA, both qualitatively and quantitatively, on a number of categories from the ShapeNet dataset. Furthermore, our method can easily incorporate other point attributes such as normal and color information, an additional advantage over voxel-based representations.Comment: To appear at BMVC 201

A New Design of Ultra-Flattened Near-zero Dispersion PCF Using Selectively Liquid Infiltration

The paper report new results of chromatic dispersion in Photonic Crystal Fibers (PCFs) through appropriate designing of index-guiding triangular-lattice structure devised, with a selective infiltration of only the first air-hole ring with index-matching liquid. Our proposed structure can be implemented for both ultra-low and ultra-flattened dispersion over a wide wavelength range. The dependence of dispersion parameter of the PCF on infiltrating liquid indices, hole-to-hole distance and air-hole diameter are investigated in details. The result establishes the design to yield a dispersion of 0+-0.15ps/ (nm.km) in the communication wavelength band. We propose designs pertaining to infiltrating practical liquid for near-zero ultra-flat dispersion of D=0+-0.48ps/ (nm.km) achievable over a bandwidth of 276-492nm in the wavelength range of 1.26 {\mu}m to 1.80{\mu}m realization.Comment: 6 pages, 13 figures, 1 tabl