An orthomodular lattice

An orthomodular lattice is constructed by taking a homomorphic image of the ortholattice obtained from a certain orthogonality relation on an infinite set.Presented by B. Jónsson.This research was supported by N.S.E.R.C. grant 0041702.     

Notes on sectionally complemented lattices. III

Summary In a recent survey article, G. Grätzer and E. T. Schmidt raise the problem when is the ideal lattice of a sectionally complemented chopped lattice sectionally complemented. The only general result is a 1999 lemma of theirs, stating that if the finite chopped lattice is the union of two ideals that intersect in a two-element ideal U, then the ideal lattice of M is sectionally complemented. In this paper, we present examples showing that in many ways their result is optimal. A typical result is the following: For any finite sectionally complemented lattice U with more than two elements, there exists a finite sectionally complemented chopped lattice M that is (i) the union of two ideals intersecting in the ideal U; (ii) the ideal lattice of M is not sectionally complemented.     

Fixed Points and Products: Width 3

Order - If P and X are ordered sets with the fixed point property, does P×X have the fixed point property? In case one of P and X is finite the answer is yes. Here we answer the question...     

The strong fixed point property for small sets

It is shown that every partially ordered set with the fixed point property and with ten or fewer elements actually has the strong fixed point property.Supported by NSERC Operating Grant A7884.Supported by NSERC Operating Grant 41702.     

Notes on sectionally complemented lattices. IV How far does the Atom Lemma go?

There are two results in the literature that prove that the ideal lattice of a finite, sectionally complemented, chopped lattice is again sectionally complemented. The first is in the 1962 paper of G. Grätzer and E. T. Schmidt, where the ideal lattice is viewed as a closure space to prove that it is sectionally complemented; we call the sectional complement constructed then the 1960 sectional complement. The second is the Atom Lemma from a 1999 paper of the same authors that states that if a finite, sectionally complemented, chopped lattice is made up of two lattices overlapping in an atom and a zero, then the ideal lattice is sectionally complemented. In this paper, we show that the method of proving the Atom Lemma also applies to the 1962 result. In fact, we get a stronger statement, in that we get many sectional complements and they are rather close to the componentwise sectional complement.     

Interlaboratory comparison of pesticide recovery from water using solid-phase extraction disks and gas chromatography

An interlaboratory study was conducted to assess the suitability of C18 solid-phase extraction disks to retain and ship different pesticides from water samples. Surface and deionized water samples were fortified with various pesticides and extracted using C18 disks. Pesticides were eluted from disks and analyzed in-house, or disks were sent to another laboratory where they were eluted and analyzed. Along with the disks, a standard pesticide solution in methanol was also shipped to be used for fortification, extraction, and analysis. The highest recovery from deionized or surface water using shipped disks was obtained for cyanazine (>97%), followed by metalaxyl (>96%), and atrazine (>92%). Although <40% of the bifenthrin, chlorpyrifos, and chlorothalonil fortified in surface water was recovered from shipped disks, recoveries from deionized water were >70%. From in-house eluted disks, bifenthrin and chlorpyrifos were recovered at 118 and 105%, whereas chlorothalonil showed 71% recovery, indicating that poor recovery from surface water was due to loss during shipping rather than low retention by the C18 disks. There was no consistent relationship between recovery from C18 disk and physicochemical properties for the pesticides included in this study. For most of the 13 pesticides tested, there were no differences in recovery between in-house extracted disks and shipped disks, indicating the suitability of disks to concentrate and transport pesticides extracted from water samples.     

Sample introduction techniques for microfabricated separation devices

A great deal of progress has been made toward the development of the micro total analysis system (micro-TAS) since its inception in 1990. A wide variety of applications, including genomics, proteomics and drug discovery, have prompted the development of analytical methods capable of very high throughput while maintaining low cost. The micro-TAS concept addresses both of these requirements. Electrophoresis has been a key element in the development of the micro-TAS. Most chemical and biochemical assays utilize a separation component at some point during analysis. Genomics, in particular, depends almost exclusively on electrophoresis for size-based separations of DNA. This review examines sample introduction into microfabricated electrophoretic devices, or chips, primarily for DNA analysis. Sample introduction is an important component of these systems and is an essential process for making chip electrophoresis a widely applicable analytical technique. Specific issues, such as automation, the delivery of large numbers of samples to microfabricated devices and injection of picoliter-sized sample plugs into a separation lanes on chips, are presented.