Acute Triangulations of the Cuboctahedral Surface

In this paper we prove that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore, we show that both bounds are the best possible.Comment: 16 pages, 8 figures, presented on CGGA201

SparseGAN: Sparse Generative Adversarial Network for Text Generation

It is still a challenging task to learn a neural text generation model under the framework of generative adversarial networks (GANs) since the entire training process is not differentiable. The existing training strategies either suffer from unreliable gradient estimations or imprecise sentence representations. Inspired by the principle of sparse coding, we propose a SparseGAN that generates semantic-interpretable, but sparse sentence representations as inputs to the discriminator. The key idea is that we treat an embedding matrix as an over-complete dictionary, and use a linear combination of very few selected word embeddings to approximate the output feature representation of the generator at each time step. With such semantic-rich representations, we not only reduce unnecessary noises for efficient adversarial training, but also make the entire training process fully differentiable. Experiments on multiple text generation datasets yield performance improvements, especially in sequence-level metrics, such as BLEU

NANOCOMPOSITES OF POLY(LACTIC ACID) REINFORCED WITH CELLULOSE NANOFIBRILS

A chemo-mechanical method was used to prepare cellulose nanofibrils dispersed uniformly in an organic solvent. Poly(ethylene glycol) (PEG 1000) was added to the matrix as a compatibilizer to improve the interfacial interaction between the hydrophobic poly(lactic acid) (PLA) and the hydrophilic cellulose nanofibrils. The composites obtained by solvent casting methods from N,N-Dimethylacetamide (DMAc) were characterized by tensile testing machine, atomic force microscope (AFM), scanning electron microscope (SEM), and Fourier transform infrared spectroscopy (FT-IR). The tensile test results indicated that, by adding PEG to the PLA and the cellulose nanofibrils matrix, the tensile strength and the elongation rate increased by 56.7% and 60%, respectively, compared with the PLA/cellulose nanofibrils composites. The FT-IR analysis successfully showed that PEG improved the intermolecular interaction, which is based on the existence of inter-molecular hydrogen bonding among PLA, PEG, and cellulose nanofibrils

Hexakis(dimethyl­ammonium) di-μ6-oxido-tetra-μ3-oxido-tetra­deca-μ2-oxido-octa­oxidodeca­vanadate(V) monohydrate

In the title compound, (C2H8N)6[V10O28]·H2O, the [V10O28]6− polymetalate anion has crystallographic mirror symmetry with six V atoms and 12 O atoms lying on the mirror plane. Each of the VV atoms adopts a distorted octa­hedral geometry. Eight terminal O atoms are bonded to VV atoms with double bonds and the others act as bridging atoms. In the crystal structure, a network of N—H⋯O and O—H⋯O hydrogen bonds helps to establish the packing