Computation of limit periodic continued fractions. A survey

Over the last 20 years a large number of algorithms has been published to improve the speed and domain of convergence of continued fractions. In this survey we show that these algorithms are strongly related. Actually, they essentially boil down to two main principles.We also prove some results on asymptotic expansions of tail values of limit periodic continued fractions.Dedicated to Luigi Gatteschi on his seventieth birthdayThis research was partially supported by The Norwegian Research Council and by the HMC project ROLLS, under contract CHRX-CT93-0416.     

Modified Three-Dimensional Formulations of Bending Problems of Homogeneous Plates and Beams under Complex Fixing Conditions

Modified three-dimensional formulations of bending problems of homogeneous elastic plates and beams are considered. Modification of the known three-dimensional formulations reduces to using additional constraints imposed on displacement functions. An advantage of the formulations proposed is that complex fixing conditions of plates and beams can be taken into account.     

Fine Dry Grinding of Zeolite in a Laboratory Ball Mill

This paper presents the importance and usage of natural zeolites, which was recently recognized in the industry. Therefore, the grinding properties of natural zeolite were studied with the emphasis on a kinetic study in a ball mill. The experimental mill employed was laboratory sized, 200 mm diameter, 191 mm length, providing a total mill volume of 6000 cm³, with a total mass of 5.62 kg of steel balls of 25 mm diameter with a charge of 20% of the mill volume and with a rotation speed of 76 rpm. The breakage parameters were determined by using single sized feed fractions of ?850+600 μm, ?600+425 μm, and ?425+300 μm for the zeolite samples. The S_i (specific rate of breakage) and B_{i, j} (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distributions by simulation for comparison to the experimental data. From the experimental results, S_i values increased as the feed sizes became coarser, i.e., the highest S_i value was 0.85 min^?1 for ?850+600 μm, while the lowest S_i value was 0.65 min^?1 for ?425+300 μm feed ground in the mill. The B_{i, j} values obtained for the zeolite sample were γ=0.84, ?=0.61, and β=4.25. The breakage parameters obtained showed that the zeolite is broken faster than quartz and slower than calcite and barite in terms of the a_T values reported previously at the same experimental conditions. The simulations of the product size distributions of zeolite were in good agreement with the experimental data using a standard ball mill simulation program. The slowing‐down effect was also seen in the mill after 4 min. of grinding.     

Solid-state Electrochemistry of Gadolinium Hexacyanoferrate Modified Electrode and Electrocatalytic Properties of Gadolinium Hexacyanoferrate

A new electroactive polynuclear inorganic compound of rare earth metal, gadolinium hexacyanoferrate (GdHCF), was prepared and characterized using the techniques of FTIR spectroscopy, thermogravimetric analysis (TG), UV-Vis spectrometry, X-ray photoelectron spectroscopy (XPS), ICP atomic emission spectroscopy, and EDX. The results of ICP atomic emission spectroscopy, EDX, and TGA indicated that the prepared GdHCF sample had a stoichiometry of NaGdFe(CN)₆·12H₂O (when GdHCF was prepared in NaCl solution). The FTIR spectrum of GdHCF showed that there were two types of water molecules in the structure of GdHCF: one was the interstitial water (5 H₂O), which resulted from the association of water due to H-bonding, and the other was water coordinated with Gd (7 H₂O). The results obtained using XPS showed that the oxidation state of Fe and Gd in the GdHCF sample was +2 and +3, respectively. GdHCF was immobilized on the surface of spectroscopically pure graphite (SG) electrode forming the GdHCF/SG electrode, and the solid-state electrochemistry of the resultant electrode was studied using cyclic voltammetry. The cyclic voltammetric results indicated that the GdHCF/SG electrode exhibited a pair of well-defined and stable redox peaks with the formal potential of E^0′=(197±3) mV. The effects of the concentration of the supporting electrolyte on the electrochemical characteristics of GdHCF were studied, and the results showed that the value of E^0′ increased linearly with the activity of the cationic ion of the supporting electrolyte (lga_Na⁺), with a slope of 54.1 mV, which may become a novel method for determining the activity of Na⁺ in solution. Further experimental results indicated that GdHCF had electrocatalytic activities toward the oxidation of dopamine (DA) and ascorbic acid (AA), and the electrocatalytic current increased linearly with the concentration of DA (or AA) in the range of 1.0–10.0 mmol·L^?1 (for DA) or 0.5–20.0 mmol·L^?1 (for AA).     

ITERATIVE APPROXIMATION OF FIXED POINTS OF NON-LIPSCHITZIAN ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS

The purpose of this paper is to investigate the problem of approximating fixed points of non-Lipschitizian asymptotically pseudocontractive mappings in an arbitrary real Banach space by the modified Ishikawa iterative sequences with errors.     

New poly(butylene succinate)/layered silicate nanocomposites. II. Effect of organically modified layered silicates on structure,properties, melt rheology,and biodegradability

A series of new poly(butylene succinate) (PBS)/layered silicate nanocomposites were prepared successfully by simple melt extrusion of PBS and organically modified layered silicates (OMLS). Three different types of OMLS were used for the preparation of nanocomposites: two functionalized ammonium salts modified montmorillonite and a phosphonium salt modified saponite. The structure of the nanocomposites in the nanometer scale was characterized with wide-angle X-ray diffraction and transmission electron microscopic observations. With three different types of layered silicates modified with three different types of surfactants, the effect of OMLS in nanocomposites was investigated by focusing on four major aspects: structural analysis, materials properties, melt rheological behavior, and biodegradability. Interestingly, all these nanocomposites exhibited concurrent improvements of material properties when compared with pure PBS. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3160–3172, 2003     

多壁碳纳米管膜湿敏特性的研究

研究了多壁碳纳米管(MWNTs)薄膜的湿敏特性，实验所用的多壁碳纳米管是用热灯丝化学气相沉积法(CVD)合成的.分别对未修饰和修饰的多壁碳纳米管膜温度和湿度特性进行研究后发现，修饰的多壁碳纳米管对温度和湿度非常敏感，且对湿度的响应时间和恢复时间短，重复性好.而未修饰的多壁碳纳米管对温度和湿度不太敏感.对修饰多壁碳纳米管的湿敏特性进行了理论分析，给出了其理论表示式. 关键词： 多壁碳纳米管 化学修饰 湿敏特性 物理吸附     

Fabrication of Zeolite A Rods with Irregular Macropores by Self-assembly of Zeolite A Microcrystals Using Microwave-assisted Hydrothermal Synthesis

Zeolite A rods by self-assembly of zeolite A microcrystal were successfully synthesized by microwave-assisted hydrotherrnal synthesis. The average size of zeolite crystals consisting of self-assembling materials was about 300 nm and the length of zeolite rods was in the range of 15--30μm.     

Selective quenching of tryptophanyl fluorescence in bovine serum albumin by the iodide ion

Modified Stern-Volmer equation is obeyed by bovine serum albumin (BSA)-iodide system showing selective quenching of tryptophanyl fluorescence of BSA. The fraction of accessible protein fluorescence is 0.56 and the effective Stern-Volmer constant is 290 M^-1 at pH 7.4 in 0.005 M phosphate buffer at 25°C. Collisional quenching is operative both in the BSA -I⁻¹ system and the model system, tryptophan-I⁻¹. It is supported by the observed relationship between the ratio of quenching rate constants (k _q ) and diffusion coefficients and alsok _q with bulk viscosity.     

Miscible blends of modified poly(aryl ether ketones) with aromatic polyimides

The phase behavior of binary blends of poly(ether ether ketone) (PEEK), sulfonated PEEK, and sulfamidated PEEK with aromatic polyimides is reported. PEEK was determined to be immiscible with a poly(amide imide) (TORLON 4000T). Blends of sulfonated and sulfamidated PEEK with this poly(amide imide), however, are reported here to be miscible in all proportions. Blends of sulfonated PEEK and a poly(ether imide) (ULTEM 1000) are also reported to be miscible. Spectroscopic investigations of the intermolecular interactions suggest that formation of electron donoracceptor complexes between the sulfonated/sulfamidated phenylene rings of the PEEKs and the n-phenylene units of the polyimides are responsible for this miscibility. © 1993 John Wiley & Sons, Inc.