The Gold Partition Conjecture for 6-Thin Posets

We consider the Gold Partition Conjecture (GPC) that implies the 1/3–2/3 Conjecture. We prove the GPC in the case where every element of the poset is incomparable with at most six others. The proof involves the extensive use of computers. This paper contains results obtained using computer resources of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM), University of Warsaw.     

Skew partitions in perfect graphs

We discuss some new and old results about skew partitions in perfect graphs.     

Growth behavior of Cu/Al intermetallic compounds in hot‐dip aluminized copper

Hot‐dipped aluminum copper with plating auxiliary KF is introduced in this work. In this study, the intermetallic layer thickness varies with dipping temperature and time in a linear relationship. The main phases are identified to be CuAl₂ and K₃AlF₆ by means of X‐ray diffraction. The reaction equations are deduced according to the elements concentration gradient in cross section. The copper diffusion rate in liquid Al is calculated to be 1.13 × 10⁻¹² m²/s by Fick's second law in semi‐infinite solid model, and the obtained conductivity is 1.758–1.767 × 10⁻² Ω mm²/m. The results indicate that the interfacial bonding is in a good state and plating auxiliary KF aqueous solution. can significantly improve the substrate wettability. The appropriate hot‐dipping condition for the samples is 953–973 K for 4–8 s. Copyright © 2009 John Wiley & Sons, Ltd.     

A new family of low wear,low coefficient of friction polymer blend based on polytetrafluoroethylene and an aromatic thermosetting polyester

To improve the wear resistance of polytetrafluoroethylene (PTFE), a crosslinked aromatic thermosetting polyester (ATSP) has been blended directly with PTFE. Cured ATSP powder which was directly synthesized as a cured powder form was used for this application. Because of the similar processing temperature range of cured ATSP and PTFE, composites within the entire composition range were successfully prepared by blending these two powders using a hot press. Tribological pin‐on‐disk tests (composite pins sliding against gray cast iron disks) showed improvement on friction coefficient of all composites and much less wear than pure PTFE. The composites survived at contact pressures of 7 MPa, which is higher than either pure PTFE or pure ATSP could sustain. With an increase in the amount of ATSP in the composites, storage modulus, and glass transition temperature were higher, and the wear resistance was enhanced. SEM images helped provide explanations for the unusually low mean wear rates that were observed for these composite samples. Copyright © 2008 John Wiley & Sons, Ltd.     

An illustrated theory of hyperbolic virtual polytopes

The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.      

Points of Bounded Height on Equivariant Compactifications of Vector Groups, I

We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane.     

On a cycle partition problem

Let G be any graph and let c(G) denote the circumference of G. We conjecture that for every pair c₁,c₂ of positive integers satisfying c₁+c₂=c(G), the vertex set of G admits a partition into two sets V₁ and V₂, such that V_i induces a graph of circumference at most c_i, i=1,2. We establish various results in support of the conjecture; e.g. it is observed that planar graphs, claw-free graphs, certain important classes of perfect graphs, and graphs without too many intersecting long cycles, satisfy the conjecture.This work is inspired by a well-known, long-standing, analogous conjecture involving paths.     

Cn中有界域的Bergman核函数的零点问题

多复变数空间Cn中有界域的Bergman核函数的零点问题集中表现为陆启铿猜想.陆启铿猜想是波兰数学家M.Skwarczynski对陆启铿1966年的一篇文章中关于Bergman核函数的零点问题而命名的,至今已经40年了.该猜想已写入了多复变函数论的多本专著,引起很多数学家的兴趣而研究之,已经成为多复变函数论中的一个活跃的研究方向.本文简述了陆启铿猜想的最初含意,综述了迄今为止关于有界域的Bergman核函数有无零点的各种研究成果以及所用的思想和方法.特别对近来出现的陆启铿猜想的新研究领域进行了较详细的阐述并在最后提出了关于陆启铿猜想的6个Open Problems,希望国内的年轻数学家对陆启铿猜想感到兴趣而研究之.     

Quantification of Polycyclic Aromatic Hydrocarbons in Avian Dried Blood Spots by Ultra-performance Liquid Chromatography with Simple Liquid Extraction and Phospholipid Solid-phase Extraction Preparation

Here, a simple, reliable method for the quantification of the 16 EPA priority polycyclic aromatic hydrocarbons in dried blood spots is outlined using liquid extraction and phospholipid solid-phase sample cleanup coupled with analysis by ultra-performance liquid chromatography with ultraviolet–visible detection. Whole blood spotted on Whatman FTA cards was efficiently quantified by extraction into acidified methanol and passed through a phospholipid solid-phase extraction well plate before injection into a liquid chromatography under reverse-phase conditions. The analyte recoveries in quality control samples ranged from 63.4 to 104.1%, with relative standard deviations from 0.48 to 2.04%. These figures of merit are comparable with measurements in whole blood or serum using similar techniques. The method detection limits were from 45.0?ng·g^?1 for benzo[g,h,i]perylene to 118.7?ng·g^?1 for chrysene, with matrix spike recoveries from 64.3 to 99.4%, demonstrating acceptable sensitivity and low matrix interference. With a simple liquid extraction approach and short 16-min liquid chromatography, the dried blood spots were effectively and rapidly analyzed.     

Pressurised hot water extraction followed by simultaneous derivatization and headspace solid-phase microextraction and gas chromatography-tandem mass spectrometry for the determination of aliphatic primary amines in sewage sludge

In this paper we describe an environmentally friendly and sensitive method for the determination of ten primary amines in sewage sludge. The method is based on pressurised hot water extraction (PHWE) followed by simultaneous derivatization with pentafluorobenzaldehyde (PFBAY) and headspace solid-phase microextraction (HS-SPME) and subsequent gas-chromatography ion-trap tandem mass spectrometry (GC-IT-MS-MS) analysis. The influence of the main factors on the PHWE of sludge was optimized by a central composite design. For all species the optimal conditions were water at pH 4 as the extracting solvent, an extraction temperature of 100 °C and an extraction time of 15 min. The separation and detection of the ten amines by GC-IT-MS-MS took just 10 min and the entire process took approximately 1 h. Repeatability and reproducibility between days, expressed as RSD (%) (n = 5), were less than 19 and 24%, respectively. The average limit of detection (LOD) was of 65 μg kg⁻¹ s (range found 9-135) and the average limit of quantification (LOQ) was of 230 μg kg⁻¹ (range found 50-450) of dry weight (d.w.). Under optimized conditions we used this method to determine the compounds in industrial and municipal sewage sludge samples and in sludge from a potable water treatment plant. Methylamine and isobutylamine showed the highest levels in one of the industrial sewage sludge samples (404 and 543 mg kg⁻¹ (d.w.), respectively). To our knowledge, this paper presents for the first time the determination of ten primary amines in sewage sludge samples using PHWE.