Results 71 to 80 of about 8,753,370 (220)

The packing chromatic number of the square lattice is at least 12

CoRR, 2010
The packing chromatic number $χ_ρ(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set $V(G)$ can be partitioned into disjoint classes $X_1, ..., X_k$, where vertices in $X_i$ have pairwise distance greater than $i$. For the 2-dimensional square lattice $\mathbb{Z}^2$ it is proved that $χ_ρ(\mathbb{Z}^2) \geq 12$, which improves the ...
Jan Ekstein, Jirí Fiala 0001, Premysl Holub, Bernard Lidický   +3 more
openaire   +2 more sources

Global distribution of avian plumage coloration and patterning: the relative influence of climate, ecology, and sexual selection

Ecography, EarlyView.
Animal coloration exhibits substantial biogeographic variation, reflecting complex adaptations to both abiotic and biotic environments. Although the evolutionary mechanisms underlying avian plumage coloration have been widely studied, geographic variation in plumage patterning has received far less attention.
Yuqing Han, Ying Zeng, Tien Ming Lee, Long Wang, Chen Zeng, Pengfei Fan, Çağan H. Şekercioğlu, Weini Huang, Yang Liu   +8 more
wiley   +1 more source

Dual‐Mode Electrophoretic Displays Enabled by Quantum Dot‐Decorated PR48:2 Pigment Particles and TiO2 for All‐Weather Visibility, Excellent Bistability, and Enhanced Readability

ENERGY &ENVIRONMENTAL MATERIALS, EarlyView.
This study presents a novel quantum dot electrophoretic display (QDEPD), which combines electro‐controlled reflection and optically‐triggered emission to achieve efficient multi‐modal switching within a single pixel. By incorporating multi‐component nanostructures, the system enhances functional integration and multi‐modal response capabilities.
Xingke Zheng, Yun Ye, Hongxing Xie, Yuanyi Liu, Ruihan Lin, Guangyou Liu, Tianyong Guan, Enguo Chen, Tailiang Guo   +8 more
wiley   +1 more source

High‐Strength, Fluorescent, Triboelectric Cellulose Hydrogel‐Derived Plastics Through Molecular Network Engineering for Energy Harvesting and Motion Sensing

ENERGY &ENVIRONMENTAL MATERIALS, EarlyView.
Multifunctional cellulose hydrogel‐derived plastics (FCBPs) are fabricated via a novel molecular network engineering strategy involving epoxy cross‐linking, solvent exchange, and hot‐pressing techniques. The resulting materials exhibit high mechanical strength, excellent thermal/solvent resistance, stable fluorescence, complete biodegradability, and ...
Fuyuan Lu, Yifan Jiao, Yuxuan Chen, Zhezhe Zhou, Gaobo Lou, Caicai Li, Gaojie Jiao, Mark Lynch, Jialong Wen, Xiaochun Zhang, Pingan Song, Dan Sun   +11 more
wiley   +1 more source

The Packing Chromatic Number of Random d-regular Graphs [PDF]

, 2015
Let G = (V (G),E(G)) be a simple graph of order n and let i be a positive integer. Xi superset V (G) is called an i-packing if vertices in Xi are pairwise distance more than i apart. A packing coloring of G is a partition X = {X1,X2,X3, . . .
Clifton, Ann Wells
core   +1 more source

On the Packing Chromatic Number of Trees, Cartesian Products and Some Infinite Graphs

Electronic Notes in Discrete Mathematics, 2008
Abstract A subset A of vertices in a graph G is an r-packing if the distance between every pair of distinct vertices in A is more than r. The packing chromatic number, χ ρ ( G ) , is the smallest k for which there exists some partition V 1 , V 2 , … , V k of the vertex set of G such that V r is an r-packing ...
Douglas F. Rall, Bostjan Bresar, Art S. Finbow, Sandi Klavzar   +3 more
openaire   +1 more source

Packing Chromatic Number of Coronae of Paths and Cycles [PDF]

, 2019
Pakirno kromatično število $chi_{pi}(G)$ grafa $G$ je najmanjši $k$, za katerega lahko poiščemo $k$-pakirno barvanje grafa, torej najmanjši $k$, za katerega obstaja taka funkcija $pi: (G) to [k]$, da iz $pi(u) = pi(v)$ sledi, da je razdalja med $u$ in $v$
Robba, Barbara
core  

Regioselective Oxidative Oligomerization of 2‐Tert‐Butylpyrene Toward Structurally Defined Oligomers and Their Application in Organic Light‐Emitting Diodes

European Journal of Organic Chemistry, EarlyView.
Treatment of 2‐tert‐butylpyrene with Cu2+ afforded structurally well‐defined pyrene oligomers, up to the 13‐mer. Single‐crystal X‐ray diffraction, spectroscopic analyses, and computational studies were conducted to evaluate the properties of the resulting oligopyrenes.
Md Jadu Mia, Daiki Tauchi, Miku Mizoe, Teru Hashimoto, Masashi Hasegawa, Hiroaki Chihara, Hiroto Iwano, Shigeyuki Yagi, Marco Fusè, Giuseppe Mazzeo, Giovanna Longhi, Sergio Abbate, Qingyu Wang, Tamaki Nakano, Ken‐ichi Sugiura   +14 more
wiley   +1 more source

Chromatic roots are dense in the whole complex plane [PDF]

, 2004
I show that the zeros of the chromatic polynomials P-G(q) for the generalized theta graphs Theta((s.p)) are taken together, dense in the whole complex plane with the possible exception of the disc \q - l\ < l.
Sokal, AD
core  

A High‐Efficiency Yet Sustainable Fresh‐Keeping Strategy Inspired by Calyx of Physalis peruviana

Exploration, EarlyView.
This study presents a sprayable, calyx‐inspired food wrap engineered for safety and sustainability using handheld electrospraying. The wrap forms a health‐critical protective barrier with high antiviral and antibacterial efficacy, excellent breathability, and long‐term fresh‐keeping performance.
Yue Zhao, Chengbang Lu, Xiaopeng Bai, Shangyi Wu, Zeyu Wang, Yuqin Hu, Binxin Liang, Danlei Sun, Yunxiang Zhang, Yingning He, Yi Yang, Shengwen Duan, Taolin Sun, Xinjie Wang, Weijie Lan, Hong Zhang, Yang Luo, Xiangyu Liang   +17 more
wiley   +1 more source