The rank of a commutative cancellative semigroup

Summary For a commutative cancellative semigroup S, we define the rank of S intrinsically. This definition implies that the rank of S equals the usual rank of its group of quotients. We also characterize the rank in terms of embeddability into a rational vector space of the greatest power cancellative image of S.     

Chemo- and regioselective cyclohydrocarbonylation of alpha-keto alkynes catalyzed by a zwitterionic rhodium complex and triphenyl phosphite

alpha-Keto alkynes react with CO and H(2) in the presence of catalytic quantities of the zwitterionic rhodium complex (eta(6)-C(6)H(5)BPh(3))(-)Rh(+)(1,5-COD) and triphenyl phosphite affording either the 2-, 2(3H)-, or 2(5H)-furanones in 61-93% yields. The cyclohydrocarbonylation is readily accomplished using substrates containing alkyl, aryl, vinyl, and alkoxy groups at the acetylenic terminal, as well as a variety of primary, secondary, and tertiary alkyl, aryl, and heteroaryl groups connected to the ketone functionality. Structural and electronic properties present in the starting materials mediate the chemo- and regioselectivity of the reaction.     

Simultaneous representations in categories of algebras

Hedrlin and Pultr proved that every small category is isomorphic to a full subcategory of the category Alg (Δ) of all algebras of type Δ whenever the sum ∑Δ of their arities satisfies ∑Δ>2. This article deals with simultaneous representation in categories of algebras, a generalization of the related question: given a subcategory k′ of a small category k, when does there exist an extension Δ′ of a type Δ with ∑Δ?2 such that k′ is a full subcategory of Alg(Δ′) while the Alg (Δ)-redacts of algebras representing k′ determine a category isomorphic to k? We characterize simultaneous representability by algebras and their reducts completely, and show that it is closely related to Isbell's dominion. A consequence of the main result states that algebraically representable pairs (k′, k) of one-object categories k′ k are exactly those for which k′ coincides with its dominion in k, and provides an alternative characterization of the dominion. Simultaneous representability by partial algebras is not subject to any such restriction.     

Near varieties of idempotent generated completely simple semigroups

Algebra universalis - Completely simple semigroups form a variety if we consider them as algebras with multiplication and inversion. A near variety of idempotent generated completely simple...     

Generation of fluorescent adducts of malondialdehyde and amino acids: toward an understanding of lipofuscin

Lipofuscin is a yellow-brown, highly fluorescent pigment that undergoes an age-related progressive accumulation in animal cells, mainly in postmitotic cells. It is a heterogeneous, high-molecular weight material associated with proteins, lipids and nucleic acids. Lipofuscin is implicated in many aspects of human health, including aging, oxidative stress, macular degeneration, lipid peroxidation, atherosclerosis, dementia (Alzheimer's Disease) and diseases associated with prions. Although the fluorescent properties of lipofuscin have long been recognized, neither histologists nor chemists have yet isolated the pigments themselves or characterized their optical properties. We have prepared lipofuscinlike species by reacting malondialdehyde (MDA) with cysteine (Cys). MDA:Cys adducts 3:2 and 2:2 are two of those that have been identified among the many that were present in the reaction. Whereas previous attempts to synthesize lipofuscinlike species resulted in compounds that were either nonfluorescent or emitted principally in the blue, the MDA:Cys adducts reported in this study are not only fluorescent but also emit over a broader range.     

A Canonical Directly Infinite Ring

Let be the set of nonnegative integers and the ring of integers. Let be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of all matrices in with only a finite number of nonzero entries and the subring of generated by the identity matrix. Regular elements are also described. We characterize all ideals of , show that all ideals are finitely generated and that not all ideals of are principal. Some general ring theoretic properties of are also established.     

Continuous glucose monitoring by means of mid-infrared transmission laser spectroscopy in vitro

The continuous surveillance of glucose concentration reduces short-term risks and long-term complications for people with diabetes mellitus, a disorder of glucose metabolism. As a first step towards the continuous monitoring of glucose, reagent-free transmission spectroscopy in the mid-infrared region has been carried out in vitro using a quantum cascade laser and an optical silver halide fiber. A 30 μm gap in the fiber allowed for transmission spectroscopy of aqueous glucose solutions at a wavelength of 9.69 μm, which is specific to a molecular vibration of glucose. A noise-equivalent concentration as low as 4 mg/dL was achieved at an average power of 1.8 mW and an integration time of 50 s. This is among the most precise of glucose measurements using mid-infrared spectroscopy. Even with the very low average laser power of 0.07 mW the sensitivity of previous results (using a fiber optical evanescent field analysis) has been improved upon by almost one order of magnitude. Finally, the impact of potentially interfering substances such as other carbohydrates was analyzed.     

Identities without the star for *-bands

Adair determined the lattice of varieties of *-bands and provided a single identity for each of them. We construct a new set of identities for the same purpose. Both of these systems involve at least one variable which is starred. Using the second system of identities, we show that the system of identities constructed by Gerhard and the author for varieties of bands also represents a set of identities determining the varieties of *-bands. The same type of result is proved for varieties of band monoids and varieties of *-band monoids using the results of two papers by Wismath.Presented by R. W. Quackenbush.