Some facets of the simple plant location polytope

We relate the simple plant location problem to the vertex packing problem and derive several classes of facets of their associated integer polytopes.This work was supported by NSF Grant ENG 79-02506.     

High-Performance Organic Solar Cells Containing Pyrido[2,3-b]quinoxaline-Core-Based Small-Molecule Acceptors with Optimized Orbit Overlap Lengths and Molecular Packing

The central core in A-DA₁D-A-type small-molecule acceptor (SMAs) plays an important role in determining the efficiency of organic solar cells (OSCs), while the principles governing the efficient design of SMAs remain elusive. Herein, we developed a series of SMAs with pyrido[2,3-b]quinoxaline (PyQx) as new electron-deficient unit by combining with the cascade-chlorination strategy, namely Py1, Py2, Py3, Py4 and Py5. The introduction of chlorine atoms reduces the intramolecular charge transfer effects but elevates the LUMO values. Density functional theory (DFT) reveals that Py2 with ortho chlorine substituted PyQx and Py5 with two chlorine atoms yield larger dipole moments and smaller π⋅⋅⋅π stacking distances, as compared with the other three acceptors. Moreover, Py2 shows the strongest light absorption capability induced by extended orbit overlap lengths and more efficient packing structures in the dimers. These features endow the best device performance of Py2 due to the better molecular packing and aggregation behaviors, more suitable domain sizes with better exciton dissociation and charge recombination. This study highlights the significance of incorporating large dipole moments, small π⋅⋅⋅π stacking distances and extended orbit overlap lengths in dimers into the development of high-performance SMAs, providing insight into the design of efficient A-DA₁D-A-type SMAs for OSCs.     

Complete Peripheral Fluorination of the Small-Molecule Acceptor in Organic Solar Cells Yields Efficiency over 19 %

Due to the intrinsically flexible molecular skeletons and loose aggregations, organic semiconductors, like small molecular acceptors (SMAs) in organic solar cells (OSCs), greatly suffer from larger structural/packing disorders and weaker intermolecular interactions comparing to their inorganic counterparts, further leading to hindered exciton diffusion/dissociation and charge carrier migration in resulting OSCs. To overcome this challenge, complete peripheral fluorination was performed on basis of a two-dimensional (2D) conjugation extended molecular platform of CH-series SMAs, rendering an acceptor of CH8F with eight fluorine atoms surrounding the molecular backbone. Benefitting from the broad 2D backbone, more importantly, strengthened fluorine-induced secondary interactions, CH8F and its D18 blends afford much enhanced and more ordered molecular packings accompanying with enlarged dielectric constants, reduced exciton binding energies and more obvious fibrillary networks comparing to CH6F controls. Consequently, D18:CH8F-based OSCs reached an excellent efficiency of 18.80 %, much better than that of 17.91 % for CH6F-based ones. More excitingly, by employing D18-Cl that possesses a highly similar structure to D18 as a third component, the highest efficiency of 19.28 % for CH-series SMAs-based OSCs has been achieved so far. Our work demonstrates the dramatical structural multiformity of CH-series SMAs, meanwhile, their high potential for constructing record-breaking OSCs through peripheral fine-tuning.     

Droplet structure instability in concentrated emulsions

Dynamic rheological measurements are reported on concentrated emulsions of monodispersed sodium dodecyl sulfate-stabilized polydimethylsiloxane droplets with different cross-linking levels (i.e., controllable deformability and either viscous or viscoelastic) and over a volume fraction range 0.5 to 0.72. Emulsion structure instability is revealed at a volume fraction of 0.7 and is represented by an anomalously low G(')/G(') crossover stain, gamma(co) (G('), elastic modulus; G('), viscous modulus). This phenomenon is independent of the droplet cross-linking level and not observable for hard-sphere silica sols of volume fractions from 0.54 to 0.63. It is suggested that the structural instability arises from deformation-induced formation of "slip planes" between droplet layers specific to the repulsive droplets at the specific volume fraction, which may be dependent on the droplet packing configurations for the given polydispersity of the system. The gamma(co) value may be considered as an in situ index of the structural stability and interdroplet interaction balance in concentrated emulsions.     

装箱问题的算法及最新进展

装箱问题在经济社会发展中扮演着重要的角色,该问题研究的是寻找较好的布局方式,尽可能实现利益的最大化.装箱问题具有NP-难性质,其理论和应用研究存在一定的挑战,但因其有广泛的应用背景而受到研究者高度的关注.本文主要总结近几十年来装箱问题的研究成果,特别针对一维、二维和三维单目标装箱问题和算法,以及多目标装箱问题的算法进行概括和总结,并提出装箱问题算法上有待进一步的研究工作.     

NiO、CuO在γ-Al2O3表面分布问题的探究——第21届全国化学竞赛决赛第6题的解析

对一个全国高中化学竞赛(决赛)试题晶体部分NiO、CuO在γ-Al2O3表面的分布问题进行分析、探究,并对试题问题的设置进行了整合重组和新的设计.     

Effects of Different Amount of Crystalline Solvate Molecules on Solid Structures and Photophysical Properties of a Platinum(II) Moiety with 4,4′‐Dibromo‐2,2′‐Bipyridine Ligand

A platinum(II) complex Pt(DiBrbpy)Cl₂ ( 1 ) based on 4,4′‐dibromo‐2,2′‐bipyridine ligand was synthesized and characterized. Interestingly, two solvated phases of 1 with different amounts of crystalline CH₂Cl₂ molecules, 1· 1/3(CH₂Cl₂) (yellow) and 1· 3/2(CH₂Cl₂) (red), were obtained. In the solid state, 1· 1/3(CH₂Cl₂) exhibits a 3D supramolecular structure based on Pt(DiBrbpy)Cl₂ monomer and emits a weak yellow luminescence at 541 nm (579, sh). In contrast, 1· 3/2(CH₂Cl₂) displays a 2D layer structure based on Pt(DiBrbpy)Cl₂ dimeric units and has a strong red luminescence centered at 624 nm. The results show that crystalline solvate molecule amount can not only influence the packing structures but also photophysical properties of the platinum moiety in solid state. Furthermore, the absorption and luminescence spectra of both phases were studied by TD‐DFT calculations.     

Packing directed cycles efficiently

Let G be a simple digraph. The dicycle packing number of G, denoted ν_c(G), is the maximum size of a set of arc-disjoint directed cycles in G. Let G be a digraph with a nonnegative arc-weight function w. A function ψ from the set C of directed cycles in G to R₊ is a fractional dicycle packing of G if ∑_e∈C∈Cψ(C)?w(e) for each e∈E(G). The fractional dicycle packing number, denoted , is the maximum value of ∑_C∈Cψ(C) taken over all fractional dicycle packings ψ. In case w≡1 we denote the latter parameter by .Our main result is that where n=|V(G)|. Our proof is algorithmic and generates a set of arc-disjoint directed cycles whose size is at least ν_c(G)-o(n²) in randomized polynomial time. Since computing ν_c(G) is an NP-Hard problem, and since almost all digraphs have ν_c(G)=Θ(n²) our result is a FPTAS for computing ν_c(G) for almost all digraphs.The result uses as its main lemma a much more general result. Let F be any fixed family of oriented graphs. For an oriented graph G, let ν_F(G) denote the maximum number of arc-disjoint copies of elements of F that can be found in G, and let denote the fractional relaxation. Then, . This lemma uses the recently discovered directed regularity lemma as its main tool.It is well known that can be computed in polynomial time by considering the dual problem. We present a polynomial algorithm that finds an optimal fractional dicycle packing. Our algorithm consists of a solution to a simple linear program and some minor modifications, and avoids using the ellipsoid method. In fact, the algorithm shows that a maximum fractional dicycle packing with at most O(n²) dicycles receiving nonzero weight can be found in polynomial time.     

An investigation into two bin packing problems with ordering and orientation implications

This paper considers variants of the one-dimensional bin packing (and stock cutting) problem in which both the ordering and orientation of items in a container influences the validity and quality of a solution. Two new real-world problems of this type are introduced, the first that involves the creation of wooden trapezoidal-shaped trusses for use in the roofing industry, the second that requires the cutting and scoring of rectangular pieces of cardboard in the construction of boxes. To tackle these problems, two variants of a local search-based approximation algorithm are proposed, the first that attempts to determine item ordering and orientation via simple heuristics, the second that employs more accurate but costly branch-and-bound procedures. We investigate the inevitable trade-off between speed and accuracy that occurs with these variants and highlight the circumstances under which each scheme is advantageous.     

The multiple container loading cost minimization problem

In the shipping and transportation industry, there are several types of standard containers with different dimensions and different associated costs. In this paper, we examine the multiple container loading cost minimization problem (MCLCMP), where the objective is to load products of various types into containers of various sizes so as to minimize the total cost. We transform the MCLCMP into an extended set cover problem that is formulated using linear integer programming and solve it with a heuristic to generate columns. Experiments on standard bin-packing instances show our approach is superior to prior approaches. Additionally, since the optimal solutions for existing test data is unknown, we propose a technique to generate test data with known optimal solutions for MCLCMP.