On an Example of Rutkowski and Schröder

An ultrafilter construction is used to show that a certain infinite product of ordered sets with FPP, while connected, does not itself have FPP.     

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.     

A rapid method for cross-species quantitation of apolipoproteins A1, B48 and B100 in plasma by ultra-performance liquid chromatography/tandem mass spectrometry

Apolipoprotein B100 (apoB100) and apolipoprotein A1 (apoA1) are the primary protein components of low density lipoprotein (LDL) and high density lipoprotein (HDL) particles, respectively, and plasma levels of these proteins are associated with risks of cardiovascular disease. Existing apoB100 quantitation methods for animal models have been limited to affinity capture techniques such as enzyme-linked immunosorbent assay (ELISA) and Western blot which require specialized reagents for each species and in many cases are not readily available. Here we demonstrate a single translatable ultra-performance liquid chromatography/tandem mass spectrometry (UPLC/MS/MS) assay that is fast and robust and can be used to measure apolipoprotein concentrations in plasma for six species. When possible, peptide sequences that are conserved across species were identified for this assay. The sample preparation is limited and can be carried out in 96-well microtiter plates and thus allows for multiplexed preparation of samples for analysis of large numbers of samples in a short time frame when combined with UPLC/MS/MS. Separation and quantitation of the tryptic peptides is carried out at 700 μL/min using a 1.7 μm core shell C18 column (2.1 × 50 mm). The chromatography is designed for the analysis of over 100 samples per day, and the UPLC run is less than 10 min. This assay is capable of supporting cardiovascular research by providing a single assay to measure critical biomarkers across multiple species without the need for antibodies, and does so in a high-throughput manner.     

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.     

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.     

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.