A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs

Given an undirected graph G with penalties associated with its vertices and costs associated with its edges, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of G, be it spanning or not. The weight of a PCS tree equals the sum of the costs for its edges plus the sum of the penalties for the vertices of G not spanned by the PCS tree. Accordingly, the Prize Collecting Steiner Problem in Graphs (PCSPG) is to find a PCS tree with the lowest weight. In this paper, after reformulating and re-interpreting a given PCSPG formulation, we use a Lagrangian Non Delayed Relax and Cut (NDRC) algorithm to generate primal and dual bounds to the problem. The algorithm is capable of adequately dealing with the exponentially many candidate inequalities to dualize. It incorporates ingredients such as a new PCSPG reduction test, an effective Lagrangian heuristic and a modification in the NDRC framework that allows duality gaps to be further reduced. The Lagrangian heuristic suggested here dominates their PCSPG counterparts in the literature. The NDRC PCSPG lower bounds, most of the time, nearly matched the corresponding Linear Programming relaxation bounds.     

RBMO(μ)与θ(t)型Calderón-Zygmund算子的交换子的有界性

设μ是Rd上的Randon测度,其唯一需要满足的条件是增长条件:μ(B(x,r))≤Crn对任意x∈Rd,r＞0成立,0＜n≤d.本文中,在这种非双倍测度下证明了RBMO(μ)与θ(t)型Calderón-Zygmund算子的交换子是L∞(μ)到RBMO(μ)有界的,同时还建立了该交换子H1b(μ)到L1(μ)的有界性.     

Investigation of calcium carbonate precipitated in the presence of alkanols

The influence of myristyl alcohol (CH₃(CH₂)₁₃OH), cetyl alcohol (CH₃(CH₂)₁₅OH) and behenyl alcohol (CH₃(CH₂)₂₁OH) on the structure, morphology, size and surface properties of calcium carbonate (CaCO₃) has been investigated. Changes in the nature of the washing solvent, in the C_nOH/Ca²⁺ and CO₃²⁻/Ca²⁺ molar ratios and in temperature have been also evaluated. The sole polymorph produced was rhombohedral calcite. At room temperature, while microspheres composed of submicrocubes were produced at a high molar ratio CO₃²⁻/Ca²⁺ and low CH₃(CH₂)₁₅OH concentration, a stoichiometric molar ratio CO₃²⁻/Ca²⁺ and high CH₃(CH₂)₁₅OH concentration induced the formation of microcubes and microboxes. In the presence of this alkanol (12 % molar) a significant enhancement of the water contact angle (ca. 40 °) resulted in a sample obtained with a stoichiometric CO₃²⁻/Ca²⁺ ratio. These results emphasize the key role played by the three non‐ionic surfactants in the formation of materials with variable crystal shape and wettability and thus technological interest for a range of applications.     

Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images

Effective denoising is vital for proper analysis and accurate quantitative measurements from magnetic resonance (MR) images. Even though many methods were proposed to denoise MR images, only few deal with the estimation of true signal from MR images acquired with phased-array coils. If the magnitude data from phased array coils are reconstructed as the root sum of squares, in the absence of noise correlations and subsampling, the data is assumed to follow a non central-χ distribution. However, when the k-space is subsampled to increase the acquisition speed (as in GRAPPA like methods), noise becomes spatially varying. In this note, we propose a method to denoise multiple-coil acquired MR images. Both the non central-χ distribution and the spatially varying nature of the noise is taken into account in the proposed method. Experiments were conducted on both simulated and real data sets to validate and to demonstrate the effectiveness of the proposed method.     

Non‐Planar Lithium‐Phthalocyanine in the Double Salt (nBu4N)2[Lipc]PF6

We report the synthesis of the diamagnetic double salt bis(tetra(n‐butyl)ammonium) phthalocyanato(2‐)lithate hexafluorophosphate (nBu₄N)₂[Lipc]PF₆ [pc = phthalocyanine, nBu₄N⁺ = tetra(n‐butyl)ammonium] in dme (dme = dimethoxyethane). According to single‐crystal X‐ray diffraction structure analysis [P$\bar{1}$ , a = 8.642(2) Å, b = 12.820(3) Å, c = 15.019(3) Å, α = 83.01(3)°, β = 87.87(3)°, γ = 74.45(3)°, Z = 1, R₁ = 6.4 %], the phthalocyanine building bloc shows a substantial distortion of the macrocyclic ring from planarity. The deviation from D_4h symmetry originates from packing effects induced by the two tetra(n‐butyl)ammonium cations located above and below the macrocycle. DFT structure optimization starting from the experimental non‐planar configuration produces a fully planar complex anion [Lipc]^–.     

氧化镍中非化学计量氧在乙烷氧化脱氢中的作用

以纯ＮｉＯ为模型催化剂考察了乙烷氧化脱氢（ＯＤＨＥ）性能，发现非化学计量氧的存在与反应的活性及选择性密切相关．ＴＧＡ研究结果表明，５００℃制备的样品具有ｘ≈６％的非化学计量氧．Ｈ２ＴＰＲ结果表明，非化学计量氧与晶格氧的可还原性明显不同；Ｏ２ＴＰＤＭＳ又把非化学计量氧区分为两个氧物种，Ｏ－２和Ｏ－（或Ｏ２－２）．脉冲试验结果表明，非化学计量氧对ＯＤＨＥ制乙烯是选择性反应的活性氧物种，晶格氧是完全氧化反应的活性氧物种．一旦催化剂中非化学计量氧耗尽并动用晶格氧时，催化剂便有Ｎｉ０生成，表现出自催化性能，使反应活性迅速提高，但产物均为ＣＯ２，ＣＯ，ＣＨ４等完全燃烧或裂解产物．为保持有较高的乙烯收率，反应处于稳态时Ｎｉ必须处于高价态．电导测定结果表明，优良的ＯＤＨＥ催化剂应有Ｐ型半导性．     

豚草聚合酶链反应产物的高效毛细管电泳检测

利用PE270A－HT型高效毛细管电泳仪,采用无胶筛分电泳,以羟丙基甲基纤维素（HPMC）为筛分介质,对三裂叶豚草（Ambrosia trifida L.)的聚合酶链反应（PCR）产物进行了分离分析,显示了高效、快速、无污染的毛细管电泳技术在植物DNA片段多态性分析方面的巨大的潜力。     

Corrosion Behavior of Aluminum in Non‐Uniform Electric Fields

The present paper discusses the effect of the geometrical structure of the electric fieldon the corrosion of aluminum cathodes by electrolysis of aqueous solutions of sodium chloride. A correlation between the mass of the aluminum dissolved from the cathode and the factors electric current density, distance between the electrodes, electrolysis time and sodium chloride concentration by electrolysis with direct current in electric fields of various geometries was found.     

碳酸钙与碳化硅对室温硫化硅橡胶的补强作用

在有关硅橡胶补强的研究中,人们已经对ＳｉＯ２ 等补强性填料对硅橡胶的补强作用进行了深入的研究,但对非补强填料对室温硫化硅橡胶的补强作用则相对涉及较少．作者研究了ＣａＣＯ３ 和ＳｉＣ 两类非补强性填料以及填料的粒径与分布对室温硫化硅橡胶拉伸强度、断裂伸长率和耐温性能等的影响,发现合适粒径的非补强性填料对室温硫化硅橡胶有较好的补强效果,且在填料粒径及分布匹配时有最好的补强效果,选用ＳｉＣ时还可以有效提高室温硫化硅橡胶的热稳定性．