Simultaneously continuous retraction and Bishop-Phelps-Bollob\'as type theorem

We study the existence of a retraction from the dual space $X^*$ of a (real or complex) Banach space $X$ onto its unit ball $B_{X^*}$ which is uniformly continuous in norm topology and continuous in weak-$*$ topology. Such a retraction is called a uniformly simultaneously continuous retraction. It is shown that if $X$ has a normalized unconditional Schauder basis with unconditional basis constant 1 and $X^*$ is uniformly monotone, then a uniformly simultaneously continuous retraction from $X^*$ onto $B_{X^*}$ exists. It is also shown that if $\{X_i\}$ is a family of separable Banach spaces whose duals are uniformly convex with moduli of convexity $\delta_i(\varepsilon)$ such that $\inf_i \delta_i(\varepsilon)>0$ and $X= \left[\bigoplus X_i\right]_{c_0}$ or $X=\left[\bigoplus X_i\right]_{\ell_p}$ for $1\le p<\infty$, then a uniformly simultaneously continuous retraction exists from $X^*$ onto $B_{X^*}$. The relation between the existence of a uniformly simultaneously continuous retraction and the Bishsop-Phelps-Bollob\'as property for operators is investigated and it is proved that the existence of a uniformly simultaneously continuous retraction from $X^*$ onto its unit ball implies that a pair $(X, C_0(K))$ has the Bishop-Phelps-Bollob\'as property for every locally compact Hausdorff spaces $K$. As a corollary, we prove that $(C_0(S), C_0(K))$ has the Bishop-Phelps-Bollob\'as property if $C_0(S)$ and $C_0(K)$ are the spaces of all real-valued continuous functions vanishing at infinity on locally compact metric space $S$ and locally compact Hausdorff space $K$ respectively.Comment: 15 page

Energy harvesting using a modified rectangular cymbal transducer based on 0.71Pb(Mg[sub ⅓]Nb[sub ⅔])O₃–0.29PbTiO₃ single crystal

2009-2010 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Towards a Neural Graphics Pipeline for Controllable Image Generation

In this paper, we leverage advances in neural networks towards forming a neural rendering for controllable image generation, and thereby bypassing the need for detailed modeling in conventional graphics pipeline. To this end, we present Neural Graphics Pipeline (NGP), a hybrid generative model that brings together neural and traditional image formation models. NGP decomposes the image into a set of interpretable appearance feature maps, uncovering direct control handles for controllable image generation. To form an image, NGP generates coarse 3D models that are fed into neural rendering modules to produce view-specific interpretable 2D maps, which are then composited into the final output image using a traditional image formation model. Our approach offers control over image generation by providing direct handles controlling illumination and camera parameters, in addition to control over shape and appearance variations. The key challenge is to learn these controls through unsupervised training that links generated coarse 3D models with unpaired real images via neural and traditional (e.g., Blinn-Phong) rendering functions, without establishing an explicit correspondence between them. We demonstrate the effectiveness of our approach on controllable image generation of single-object scenes. We evaluate our hybrid modeling framework, compare with neural-only generation methods (namely, DCGAN, LSGAN, WGAN-GP, VON, and SRNs), report improvement in FID scores against real images, and demonstrate that NGP supports direct controls common in traditional forward rendering. Code is available at http://geometry.cs.ucl.ac.uk/projects/2021/ngp

Magnetoelectric effect in laminate composite of magnets/0.7Pb(Mg[sub ⅓]Nb[sub ⅔])O₃-0.3PbTiO₃ single crystal

Author name used in this publication: Siu Wing OrAuthor name used in this publication: Helen Lai Wa Chan2005-2006 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Enhanced magnetoelectric effect in longitudinal-transverse mode Terfenol-D/Pb(Mg[sub ⅓]Nb[sub ⅔])O₃-PbTiO₃ laminate composites with optimal crystal cut

Author name used in this publication: Siu Wing OrAuthor name used in this publication: Helen Lai Wa Chan2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Magnetoelectric effect from mechanically mediated torsional magnetic force effect in NdFeB magnets and shear piezoelectric effect in 0.7Pb(Mg[sub ⅓]Nb[sub ⅔])O₃-0.3PbTiO₃ single crystal

Author name used in this publication: Siu Wing OrAuthor name used in this publication: Helen Lai Wa Chan2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Converse magnetoelectric effect in laminated composites of PMN-PT single crystal and Terfenol-D alloy

Author name used in this publication: Siu Wing OrAuthor name used in this publication: Helen Lai Wa Chan2005-2006 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Additional dc magnetic field response of magnetostrictive/piezoelectric magnetoelectric laminates by Lorentz force effect

Author name used in this publication: Siu Wing OrAuthor name used in this publication: Helen Lai Wa Chan2006-2007 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

High magnetoelectric effect in laminated composites of giant magnetostrictive alloy and lead-free piezoelectric ceramic

Author named used in this publication: Siu Wing OrAuthor named used in this publication: Helen Lai Wa Chan2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe