Observation of geometric phases for mixed states using NMR interferometry

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.     

The dual-site alternating cyclocopolymerization of 1,3-butadiene with ethylene

The copolymerization of ethylene with 1,3-butadiene was studied with the series of ansa-metallocenes Me2Si(Cp)(9-Flu)ZrCl2 (1), Me2Si(1-Ind)(9-Flu)ZrCl2 (2), and Me2Si(9-Flu)2ZrCl2 (3) with methylaluminoxane (MAO) as cocatalyst. The catalyst 2/MAO yields a cyclocopolymer composed of two ethylene monomer units for every one butadiene in a novel periodic architecture of 1,2-enchained cyclopentane units separated by three methylenes. The high butadiene content in the copolymer and the high selectivity for alternating cyclocopolymerization to form methylene-1,2-cyclopentane units implicate a dual-site mechanism where butadiene and ethylene are enchained at different coordination sites.     

Solid phase synthesis of carbocyclic l-2'-deoxynucleosides

[reaction: see text] Carbocyclic L-2'deoxynucleosides 17 were synthesized on solid phase in four steps from the appropriately protected intermedate 11. The Mitsunobu reaction was used as a condensation method between the carbocyclic moiety and heterocyclic bases. The regioselectivity of the carbocyclic nucleosides was compared between the solid and solution phase syntheses.     

On Some Three-Color Ramsey Numbers

 In this paper we study three-color Ramsey numbers. Let K _i,j denote a complete i by j bipartite graph. We shall show that (i) for any connected graphs G ₁, G ₂ and G ₃, if r(G ₁, G ₂)≥s(G ₃), then r(G ₁, G ₂, G ₃)≥(r(G ₁, G ₂)−1)(χ(G ₃)−1)+s(G ₃), where s(G ₃) is the chromatic surplus of G ₃; (ii) (k+m−2)(n−1)+1≤r(K _1,k , K _1,m , K _n )≤ (k+m−1)(n−1)+1, and if k or m is odd, the second inequality becomes an equality; (iii) for any fixed m≥k≥2, there is a constant c such that r(K _k,m , K _k,m , K _n )≤c(n/logn), and r(C _2m , C _2m , K _n )≤c(n/logn) ^m/(m−1) for sufficiently large n. Received: July 25, 2000 Final version received: July 30, 2002 RID="*" ID="*" Partially supported by RGC, Hong Kong; FRG, Hong Kong Baptist University; and by NSFC, the scientific foundations of education ministry of China, and the foundations of Jiangsu Province Acknowledgments. The authors are grateful to the referee for his valuable comments. AMS 2000 MSC: 05C55     

Guided-wave multiwavelength polarization-insensitive processing module for a parallel multicomparand perfect-match algorithm

We present a design for a planar guided-wave polarization-insensitive (intensity-based) optoelectronics module that provides a parallel perfect-match search for database and text processing. The module is based on a content-addressable memory model for parallel information retrieval. We propose the use of planar guided-wave optics with multiwavelength processing to achieve a substantially high degree of performance and parallelism. Based on initial performance analysis, the proposed module is capable of achieving an aggregate processing speed of 10(12) bits/s.     

Engineering of a two-step purification strategy for a panel of monoclonal immunoglobulin M directed against undifferentiated human embryonic stem cells

A two-step purification strategy comprising of polyethylene glycol (PEG) precipitation and anion-exchange chromatography was developed for a panel of monoclonal immunoglobulin M (IgM) (pI 5.5–7.7) produced from hybridoma cultures. PEG precipitation was optimized with regards to concentration, pH and mixing. For anion-exchange chromatography, different resins were screened of which Fractogel EMD, a polymer grafted porous resin had the highest capacity. Despite its significantly slower mass transfer, the binding capacity was still higher compared to a convection driven resin (monolith). This purification strategy was successfully demonstrated for all 9 IgMs in the panel. In small scale most antibodies could be purified to >95% purity with the exception of two which gave a lower final purity (46% and 85%). The yield was dependent on the different antibodies ranging from 28% to 84%. Further improvement of recovery and purity was obtained by the digestion of DNA present in the hybridoma supernatant using an endonuclease, benzonase. So far this strategy has been applied for the purification of up to 2 l hybridoma supernatants.     

Determination of rare earth elements in hot spring water and crater lake water samples by neutron activation analysis incorporating coprecipitation process using aluminium as a collector

Hot spring water and crater lake water samples were analyzed for their rare earth elements: (REE's) by neutron activation method, which, in the irradiation, sample preparation, incorporated a coprecipitation process in which aluminium was used as a collector. Ten REE's, La, Ce, Sm, Eu, Gd, Tb, Dy, Tm, Yb and Lu, were consequently detected and determined at the ppb level with satisfactory precision. It was shown that the aluminium coprecipitation is effective in enhancing concentrations of the REE's and reducing the amounts of interfering nuclides before neutron irradiation.     

On the use of fuzzy inference techniques in assessment models: part I—theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.     

Double shearography for engineering metrology: optical and digital approach

This paper presents a double shearographic configuration based on the optical method by using two Michelson interferometers in tandem. The problems associated with the extraction of second order derivatives by optical means and a comparison with the proposed novel approach by digital means are discussed in this paper.