A New Proof of Szemerédi's Theorem for Arithmetic Progressions of Length Four

((Without abstract)) Submitted: November 1997, Final version: May 1998     

高能重离子碰撞中正负荷电粒子比单事例起伏研究

用强子和弦级联模型,JPCIAE及相应的Monte Carlo事例产生器,研究相对论性核–核碰撞中有限快度区间内正负荷电粒子比单事例起伏与能量、中心度、共振态衰变及快度间隔的关系.JPCIAE模型能够较好地符合CERN/SPS能区Pb+Pb碰撞的实验结果.本文还用此模型预言了RHIC能区Au+Au碰撞和ALICE能区Pb+Pb碰撞中的正负荷电粒子比单事例起伏.可以看出碰撞能量、中心度、共振态衰变及快度间隔对正负荷电粒子比单事例起伏的影响都不大.     

Linear Forms and Higher-Degree Uniformity for Functions On {\mathbb{F}^{n}_{p}}

In [GW1] we began an investigation of the following general question. Let L ₁, . . . , L _m be a system of linear forms in d variables on Fⁿ_p{F^n_p}, and let A be a subset of Fⁿ_p{F^n_p} of positive density. Under what circumstances can one prove that A contains roughly the same number of m-tuples L ₁(x ₁, . . . , x _d ), . . . , L _m (x ₁, . . . , x _d ) with x₁,?, x_d ? \mathbb Fⁿ_p{x_1,\ldots, x_d \in {\mathbb F}^n_p} as a typical random set of the same density? Experience with arithmetic progressions suggests that an appropriate assumption is that ||A - d1||_U^k{||A - \delta 1||_{U{^k}}} should be small, where we have written A for the characteristic function of the set A, δ is the density of A, k is some parameter that depends on the linear forms L ₁, . . . , L _m , and || ·||_U^k{|| \cdot ||_U{^k}} is the kth uniformity norm. The question we investigated was how k depends on L ₁, . . . , L _m . Our main result was that there were systems of forms where k could be taken to be 2 even though there was no simple proof of this fact using the Cauchy–Schwarz inequality. Based on this result and its proof, we conjectured that uniformity of degree k − 1 is a sufficient condition if and only if the kth powers of the linear forms are linearly independent. In this paper we prove this conjecture, provided only that p is sufficiently large. (It is easy to see that some such restriction is needed.) This result represents one of the first applications of the recent inverse theorem for the U ^k norm over Fⁿ_p{F^n_p} by Bergelson, Tao and Ziegler [TZ2], [BTZ]. We combine this result with some abstract arguments in order to prove that a bounded function can be expressed as a sum of polynomial phases and a part that is small in the appropriate uniformity norm. The precise form of this decomposition theorem is critical to our proof, and the theorem itself may be of independent interest.     

Theoretical Study of Hydrated Cd~（2＋） Interactions with Guanine

Theoretical study was performed to investigate how the hydration of cadmium ca-tion influences the structure and properties of guanine.The aqueous environment was simulated by both explicit solvent(1-5 water molecules) model and implicit solvent model.For complexes in which Cd2+ attached to the N(7) and O(6) sites of guanine,energy analysis together with the Natural Bonding Orbital(NBO) analysis were performed to elucidate the bonding characteristics in detail.The most stable structures are penta-coordinate complexes without aqua ligand located at the guanine site.Higher number of water ligands corresponds to higher stabilization energies.Average bonding energies of G-Cd increase with the number of water molecules.Bonding energies of water ligands depend on its position in the complexes.The charge distribution of guanine changed with increasing the number of water ligands,which may also influence the base-pairing pattern of guanine.There is positive charge transfer from guanine to aqua ligand as the number of the hydration waters increases.IEFPCM optimization has results comparable to the [CdG(H2O)5]2+ structure 5a.     

Preparation and Storage of Silver Nanoparticles in Aqueons Polymers

以水溶性聚合物为保护剂,采用化学还原法制备了银纳米粒子,分别利用透射电子显微镜、紫外可见光谱、同步光散射光谱等手段对其进行了表征,并探索了制备银纳米粒子的最佳实验条件。通过将银纳米粒子-聚合物溶液进行脱水,得到含有银纳米粒子的固态聚合物膜。将固态聚合物膜重新溶解于水,其水溶液的紫外可见光谱与脱水前的溶液进行了比较,发现两者性质并无明显差异。因此,将银纳米粒子分散固定在聚合物膜中是一种崭新而有效的银纳米粒子制备和存储方法。     

Identification of Novel Inhibitors of Escherichia coli DNA Ligase (LigA)

Present in all organisms, DNA ligases catalyse the formation of a phosphodiester bond between a 3′ hydroxyl and a 5′ phosphate, a reaction that is essential for maintaining genome integrity during replication and repair. Eubacterial DNA ligases use NAD⁺ as a cofactor and possess low sequence and structural homology relative to eukaryotic DNA ligases which use ATP as a cofactor. These key differences enable specific targeting of bacterial DNA ligases as an antibacterial strategy. In this study, four small molecule accessible sites within functionally important regions of Escherichia coli ligase (EC-LigA) were identified using in silico methods. Molecular docking was then used to screen for small molecules predicted to bind to these sites. Eight candidate inhibitors were then screened for inhibitory activity in an in vitro ligase assay. Five of these (geneticin, chlorhexidine, glutathione (reduced), imidazolidinyl urea and 2-(aminomethyl)imidazole) showed dose-dependent inhibition of EC-LigA with half maximal inhibitory concentrations (IC₅₀) in the micromolar to millimolar range (11–2600 µM). Two (geneticin and chlorhexidine) were predicted to bind to a region of EC-LigA that has not been directly investigated previously, raising the possibility that there may be amino acids within this region that are important for EC-LigA activity or that the function of essential residues proximal to this region are impacted by inhibitor interactions with this region. We anticipate that the identified small molecule binding sites and inhibitors could be pursued as part of an antibacterial strategy targeting bacterial DNA ligases.     

Nuclear Liquid-Gas Phase Transition Shown in Multifragment ation

The Incomplete-Fusion-nagmentation Model has been used to reproduce nicely the experimental evidence of liquid-gas phase transition probed in the reaction of Au + Au at 600A MeV. The analysis of the relative yields of decay modes for the projectile remnant as a function of bound> shows clearly the competition and transformation processes of various decay modes of projectile remnant with decreasing of bound>. The agreement between theoretical and experimental results for the anaJysis of relative yield of decay modes indicates that the experimental evidence of liquid-gas phase transition is composed of the decay mode transformations.     

STUDY ON TARGET RESIDUES FROM THE INTERACTION OF COPPER WITH 44MeV/A12C IONS

Cross sections and average forward ranges were determined for 35 target residues from the interaction of copper with 44MeV/A¹²C ions with nuclear chemistry techniques.From these data the isobaric yield distribution,the mass yield distribution and the longitudinal momentum transfer were obtained.The mass yield distribution and the isobaric yield distribution are in good agreement with those calculated from a modified statistical model and corresponding Monte Carlo technique.     

STUDY OF πNN VERTEX FROM HADRON AND QUARK POINT OF VIEW

we have identified the first-order mixing amplitude of πNN process described by the hadron model with the second-order mixing amplitude of the same process described by the quark model.Then the expression for the coupling constant f_π of the πNN vertex with different quark wave functions and gluon propagators in different approximations has been derived. The calculation results of f_π have been compared with experimental data.     

Strangeness production in pA and AA collisions at 158 A GeV

LUCIAE, a hadronic and string cascade model and its corresponding event generator are used to analyse strangeness production singly and multiply in p-Pb and Pb-Pb collisions at 158 A GeV. Spectra of multiplicity and transverse mass for single (Λ, Λ) and multiple (Ξ-, Ξ-, Ω-, Ω-) strangeness are given. In LUCIAE model it suggests a physical mechanism, i.e. the dependence of the strange quark suppression factor on incident energy, projectile mass and centrality of colliding system might result in increase of yield of strange particles with increasing the above three parameters. Calculations from the model reconstruct well the WA97 experimental data: increase of yield of strange particles with increasing centrality and increase of strangeness enhancement with increasing number of strange quarks, in relativistic nucleus-nucleus collisions.