Bounds and Constructions for Two‐Dimensional Variable‐Weight Optical Orthogonal Codes

Optical orthogonal codes (1D constant‐weight OOCs or 1D CWOOCs) were first introduced by Salehi as signature sequences to facilitate multiple access in optical fibre networks. In fiber optic communications, a principal drawback of 1D CWOOCs is that large bandwidth expansion is required if a big number of codewords is needed. To overcome this problem, a two‐dimensional (2D) (constant‐weight) coding was introduced. Many optimal 2D CWOOCs were obtained recently. A 2D CWOOC can only support a single QoS (quality of service) class. A 2D variable‐weight OOC (2D VWOOC) was introduced to meet multiple QoS requirements. A 2D VWOOC is a set of 0, 1 matrices with variable weight, good auto, and cross‐correlations. Little is known on the construction of optimal 2D VWOOCs. In this paper, new upper bound on the size of a 2D VWOOC is obtained, and several new infinite classes of optimal 2D VWOOCs are obtained.     

一类自相似集重分形分支的量纲

本文首先定义具有量纲函数的重分形测度,然后证明当Euclid空间中的两个重分形测度具有等价的量纲函数时,它们也等价.进一步,对于直线上满足强分离条件(SSC)的自相似集,在某些加倍条件下,本文给出判断其重分形分支的量纲函数的充要条件.     

最优(m,n,4,1)光正交签名码的进一步结果

为支持高速多址网络中二维图像的传输,Kitayama首次提出码分多址并行图像传输系统的概念.作为码分多址并行图像传输系统的首选光地址码,光正交签名码(OOSPC)是一族具有良好相关性的Hamming重量为k的m×n(0,1)-矩阵.用Θ(m,n,k,λ)表示所有参数为(m,n,k,λ)的OOSPC中码字容量可能的最大值,则称码字容量为Θ(m,n,k,λ)的(m,n,k,λ)-OOSPC是最优的.本文将针对满足下列条件之一的正整数m和n:(1)mn≡8,16(mod 24),gcd(m,n,2)=2,且mn≡16(mod 32)和gcd(m,n,4)=2不同时成立,其中m和n的所有奇素因子均模6余1;(2)mn≡0(mod 24)且gcd(m,n,6)=2,证明Θ(m,n,4,1)=|mn-1/12|,即构造码字容量为|mn-1/12|的最优(m,n,4,1)-OOSPC.     

Performance of columns packed with the new shell particles,Kinetex-C18

The performance of the new Kinetex-C₁₈ column was investigated. Packed with a new brand of porous shell particles, this column has an outstanding efficiency. Once corrected for the contribution of the instrument extra column volume, the minimum values of the reduced plate heights for a number of low molecular weight compounds (e.g., anthracene and naphtho[2,3-a]pyrene) were between 1.0 and 1.3, breaking the legendary record set 3 years ago by Halo-C₁₈ packed columns. The liquid-solid mass transfer of proteins (e.g., insulin and lyzozyme) is exceptionally fast on Kinetex-C₁₈ much faster than on the Halo-C₁₈ column. The different contributions of dispersion and mass transfer resistances to the column efficiency were determined and discussed. The possible reasons for this extremely high column efficiency are discussed.     

The off-line group seat reservation problem

In this paper we address the problem of assigning seats in a train for a group of people traveling together. We consider two variants of the problem. One is a special case of two-dimensional knapsack where we consider the train as having fixed size and the objective is to maximize the utilization of the seats in the train. The second is a special case of two-dimensional bin packing where all requests must be accommodated while trying to minimize the number of passenger cars needed. For both variants of the problem we present a number of bounds and develop exact algorithms. Computational results are presented for various instances based on realistic data, and from the packing literature adapted to the problems addressed.     

Polymorph‐Dependent Green,Yellow, and Red Emissions of Organic Crystals for Laser Applications

Color tuning of organic solid‐state luminescent materials remains difficult and time‐consuming through conventional chemical synthesis. Herein, we reported highly efficient polymorph‐dependent green (P1), yellow (P2), and red (P3) emissions of organic crystals made by the same molecular building blocks of 4‐(2‐{4‐[2‐(4‐diphenylamino‐phenyl)‐vinyl]‐phenyl}‐vinyl)‐benzonitrile (DOPVB). Single‐crystal X‐ray diffraction (XRD) and spectroscopic data reveal that all three polymorphs follow the herringbone packing motif in H‐type aggregations. On the one hand, from P1, P2 to P3, the reduced pitch translation along π stacks increases the intermolecular interactions between adjacent molecules, therefore leading to gradually red‐shifted emissions from 540, 570 to 614 nm. On the other hand, the edge‐to‐face arrangement and large roll translations avoid strong π–π overlap, making P1, P2 and P3 highly emissive with record‐high solid‐state fluorescence quantum yields of 0.60, 0.98, and 0.68, respectively. Furthermore, the optically allowed 0–1 transitions of herringbone H‐aggregates of P1, P2 and P3 naturally provide a four‐level scheme, enabling green and yellow amplified spontaneous emissions (ASE) with very low thresholds.     

A Response to “On method overfitting”

If special-purpose methods can be overfitted to benchmarks, so can general methods.     

Packing manner of graft copolymers with rigid‐rod main chains and amorphous‐crystalline diblock copolymers as side chains

We have investigated the morphology and packing manner of graft copolymers consisting of rigid‐rod‐like poly(γ‐benzyl L ‐glutamate) (PBLG) main chains and grafted diblock copolymers of amorphous poly(propylene glycol) (PPG) and crystalline poly(ethylene glycol) (PEG). The results of differential scanning calorimetry and wide‐angle X‐ray scattering measurements for graft copolymers with higher side‐chain volume fractions suggest that the rodlike main chains and crystallized PEG chains exist in segregated domains. Small‐angle X‐ray scattering profiles for these samples show diffraction intensity maxima accompanied by higher order peaks, the positions of which suggest the formation of an ordered layered structure. From these observations, the graft copolymers are estimated to form repeated layered structure consisting of segregated PBLG, PPG, and PEG layers. A proposed model for molecular packing of the graft copolymers is consistent with the experimental observation that the repeating distance for the layered structure decreases with an increase in the volume fraction of side chains. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1904–1912, 2002     

Synthesis of poly(2‐vinyl pyridine)‐b‐poly(n‐hexyl isocyanate) amphiphilic coil‐rod block copolymer by anionic polymerization

A well‐defined amphiphilic coil‐rod block copolymer, poly(2‐vinyl pyridine)‐b‐poly(n‐hexyl isocyanate) (P2VP‐b‐PHIC), was synthesized with quantitative yields by anionic polymerization. A low reactive one‐directional initiator, potassium diphenyl methane (DPM‐K), was very effective in polymerizing 2‐vinyl pyridine (2VP) without side reactions, leading to perfect control over molecular weight and molecular weight distribution over a broad range of initiator and monomer concentration. Copolymerization of 2VP with n‐hexyl isocyanate (HIC) was carried out in the presence of sodium tetraphenyl borate (NaBPh₄) to prevent backbiting reactions during isocyanate polymerization. Terminating the living end with a suitable end‐capping agent resulted in a P2VP‐b‐PHIC coil‐rod block copolymer with controlled molecular weight and narrow molecular weight distribution. Cast film from a chloroform solution of P2VP‐b‐PHIC displayed microphase separation, characteristic of coil‐rod block copolymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 607–615, 2005