实二次域上理想类的zeta-函数在-1处的值

用连分数给出了实二次域理想类的zeta-函数-1处值的一个具体的计算公式.     

Computing Zeta Functions of Kummer Curves via Multiplicative Characters

We present a practical polynomial-time algorithm for computing the zeta function of a Kummer curve over a finite field of small characteristic. Such algorithms have recently been obtained using a method of Kedlaya based upon Monsky–Washnitzer cohomology, and are of interest in cryptography. We take a different approach. The problem is reduced to that of computing the L-function of a multiplicative character sum. This latter task is achieved via a cohomological formula based upon the work of Dwork and Reich. We show, however, that our method and that of Kedlaya are very closely related.Dedicated to the memory of Gian-Carlo Rota     

Zeta regularized determinants for conic manifolds

We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ-determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant.     

One-Parameter Fixed-Point Theory and Gradient Flows of Closed 1-Forms

We use the one-parameter fixed-point theory of Geoghegan and Nicas to get information about the closed orbit structure of transverse gradient flows of closed 1-forms on a closed manifold M. We define a noncommutative zeta function in an object related to the first Hochschild homology group of the Novikov ring associated to the 1-form and relate it to the torsion of a natural chain homotopy equivalence between the Novikov complex and a completed simplicial chain complex of the universal cover of M.     

Polyethylene compounds with antimicrobial surface properties

The present study aims at antimicrobial polyethylene surfaces. To achieve this, LLDPE was compounded with the polymeric biocide poly(2-tert-butylaminoethyl) methacrylate TBAM (bulk modification with 1.5-5.0 wt.% of TBAM). Surfaces of these polymer compounds were then subjected to microbial assays. Using standard methods the colony forming units (CFU) for Escherichia coli and Staphylococcus aureus were determined on these surfaces. In all cases, polyethylene surfaces with highly antimicrobial properties were achieved. An average reduction of 10⁴ CFU ml⁻¹ compared to neat LLDPE was achieved. The surfaces of these LLDPE/TBAM compounds were assessed by electrokinetic (zeta potential) measurements. The results indicate a relation between the antimicrobial activity and the zeta-potential of the polymer compounds. Moreover, the antimicrobial compounds were investigated towards biofilm formation. Compared to pristine LLDPE, the surfaces of the polymer compounds showed less adhering biofilm after a testing period of 16 weeks.     

Convergence of dynamical zeta functions

I study poles and zeros of zeta functions in one-dimensional maps. Numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function: this describes convergence of the calculations of the first zero, which is generally the physically interesting quantity. Some remarks on how these results should generalize to zeta functions of dynamical systems with pruned symbolic dynamics and in higher dimensions follow.     

Effect of solution chemistry on the surface charge of polymeric reverse osmosis and nanofiltration membranes

A streaming potential analyzer has been used to investigate the effect of solution chemistry on the surface charge of four commercial reverse osmosis and nanofiltration membranes. Zeta potentials of these membranes were analyzed for aqueous solutions of various chemical compositions over a pH range of 2 to 9. In the presence of an indifferent electrolyte (NaCl), the isoelectric points of these membranes range from 3.0 to 5.2. The curves of zeta potential versus solution pH for all membranes display a shape characteristic of amphoteric surfaces with acidic and basic functional groups. Results with salts containing divalent ions (CaCl₂, Na₂SO₄, and MgSO₄) indicate that divalent cations more readily adsorb to the membrane surface than divalent anions, especially in the higher pH range. Three sources of humic acid, Suwannee River humic acid, peat humic acid, and Aldrich humic acid, were used to investigate the effect of dissolved natural organic matter on membrane surface charge. Other solution chemistries involved in this investigation include an anionic surfactant (sodium dodecyl sulfate) and a cationic surfactant (dodecyltrimethylammonium bromide). Results show that humic substances and surfactants readily adsorb to the membrane surface and markedly influence the membrane surface charge.     

Negative adsorption due to electrostatic exclusion of micelles

Interactions of surfactants with solid substrates are important in the controlling of processes such as flotation, coating, flocculation and sedimentation. These interactions usually lead to adsorption on solids, but can also result in an exclusion of the reagents with dire consequences. In this work electrostatic exclusion of negatively charged dodecylbenzene sulfonate micelles from quartz/water, Bio-Sil/water and alumina/water interfaces has been investigated as a function of pH and ionic strength. Measurable negative adsorption of these surfactants from similarly charged solid/liquid interface was observed in the micellar region. In the case of porous samples with large surface area, comparison of pore size with the micelle size is necessary to avoid any erroneous conclusions regarding the role of electrostatic exclusion in a given system. A theoretical model for the electrostatic exclusion of micelles is developed and used to calculate the adsorption of negatively charged dodecylbenzene sulfonate on negatively charged quartz (pH 7), silica (Bio-Sil A, pH 3) and alumina (pH 11) in the micellar concentration region. The micellar exclusion values calculated using the model are in excellent agreement with the experimental results.     

STABILITY OF POLY（N,N＇-METHYLENEBISACRYLAMIDE-co-4-VINYLPYRIDINE） MICROGEL DISPERSION AND ADJUSTMENT OF THE HYDROPHOBICITY IN THE MICROGELS

In the UV-Vis spectra of pure light-scattering systems, there is an exponential relationship between absorbance and wavelength （A = Kλ^-n）. Here, the exponent n is named as flocculation-coagulation parameter. In the present paper, the effects of different additives on the stability of poly（N,N＇-methylenebisacrylamide-co-4-vinylpyridine） （poly（Bis-co-4-VP）） microgel dispersion were studied in detail via this parameter. The results showed that the stability of the dispersion mainly comes from the ionization of pyridine groups, making the microgel positively charged on its surface. This was confirmed by the measurement of Zeta potential and the result of conductometric titration. The result of fluorescence analysis indicated that the hydrophobicity in the microgels is enhanced with the increase in total 4-VP unit content.     

α-Al2O3纳米粒子对Co-Ni合金异常共沉积电化学行为的影响

为了研究在电化学复合共沉积过程中,惰性纳米粒子和金属离子、电极表面的相互作用,以及由此产生的对合金电化学共沉积行为的影响.本文从两个吸附过程出发: 电解液中的金属离子和H＋在纳米粒子表面的吸附；纳米粒子迁移到阴极表面,在电极表面的吸附.采用Zeta电势和稳态极化以及电化学交流阻抗（EIS）研究了纳米Al2O3粒子和电解液中的金属离子，和电极表面的相互作用,进而分析了纳米粒子对Co2＋和Ni2＋还原沉积的影响规律.通过对阻抗数据的拟合,讨论了Al2O3纳米粒子对等效电路中各物理参数的影响.在H＋和不同金属离子在纳米粒子上发生竞争吸附的基础上,提出了纳米粒子和合金共沉积的可能反应历程.