Modeling rate-controlling solvent effects. The pericyclic meisenheimer rearrangement of N-propargylmorpholine N-oxide

The activation parameters of the pericyclic Meisenheimer rearrangement and a competitive rearrangement of N-propargylmorpholine N-oxide were determined by experimental and computational methods. A number of aprotic and protic solvents of different polarities and hydrogen bond-forming abilities and the roles of electron-pair acceptor additives were investigated. The reaction kinetics were followed by means of NMR. In protic solvents, isotope-labeling experiments revealed a novel inverse secondary kinetic isotope effect (k(H)/k(D) about 0.8) for the rate-determining cyclization step, probably occurring because of a C(sp) --> C(sp(2)) change in hybridization at the reaction center. In molecular computations at the B3LYP/6-31++G(d,p) level of theory, implicit, explicit, and joint explicit-implicit solvent models were used. The explicit-implicit model and molecular dynamic simulations gave the most accurate results. The components of the rate-controlling solvent effect are discussed, and general equations are proposed for accurate prediction of the solvent-dependent activation parameters.     

Isoelectric focusing identification of four freshwater fish commercially labeled "perch"

Isoelectric focusing (IEF) was used to distinguish 4 freshwater fish species that are sold in the European Union under the generic label of "perch": Perca fluviatilis (European perch), Lates niloticus (Nile perch), Stizostedion lucioperca (European pikeperch), and Morone chrysops x saxatilis (Sunshine bass). These species have different commercial values but are easily interchangeable because they are sold already filleted, in view of the numerous bones of the whole fish. IEF of the water-soluble proteins extracted from fish muscle resulted in species-specific patterns. None of the bands was common to all 4 species. Intraspecies polymorphism was low and did not concern the bands identified as characteristic of the species.     

Three-dimensional visualization of protein expression in mouse brain structures using imaging mass spectrometry

We have developed a method to visualize matrix-assisted laser desorption ionization imaging mass spectrometry (MALDI IMS) data aligned with optically determinable tissue structures in three dimensions. Details of the methodology are exemplified using the 3-D reconstruction of myelin basic protein (MBP) in the corpus callosum of a mouse brain. In this procedure, optical images obtained from serial coronal sections are first aligned to each other to reconstruct a surface of the corpus callosum from segmented contours of the aligned images. The MALDI IMS data are then coregistered to the optical images and superimposed into the surface to create the final 3-D visualization. Correlating proteomic data with anatomical structures provides a more comprehensive understanding of healthy and pathological brain functions, and holds promise to be utilized in more complex anatomical arrangements.     

Proteomics of gluten: mapping of the 1Bx7 glutenin subunit in Chinese Spring cultivar by matrix-assisted laser desorption/ionization

The verification of the cDNA-deduced sequence of the high molecular weight glutenin subunit 1Bx7 in Chinese Spring cultivar was achieved by direct matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) analysis of the tryptic fragments. The published sequence of the 1Bx7 subunit contains 5 Lys and 15 Arg residues but, due to the presence of three Arg-Pro bonds, which are generally resistant to cleavage by trypsin, or cleaved to a very limited extent by trypsin, 19 peptides can be predicted. The identification of the tryptic fragments was achieved by direct MALDI-MS analysis by using three different matrices (DHB, SA and HCCA) in combination with the most compatible sample preparation procedures in order to obtain the maximum sequence coverage. MALDI analysis of the 1Bx7 tryptic digest resulted in the identification of the expected peptides and additional fragments arising from non-specific cleavages; the fragments that were not detected are peptides with low mass (from 147.2 to 317.4), so we obtained a sequence coverage of 98.8%. The results reported here also indicated that the sequence of the 1Bx7 subunit from cv. Chinese Spring is different from the cDNA-deduced sequence reported in the literature; in particular, a possible insertion of the hexapeptide QPGQGQ within the sequence Gln630-Tyr725 was suggested. Finally, it is possible to rule out glycosylation of the 1Bx7 subunit, or any other post-translational modification, to within the detection limits of the method.     

Multitiered Supply Chain Networks: Multicriteria Decision—Making Under Uncertainty

In this paper, we present a supply chain network model with multiple tiers of decision-makers, consisting, respectively, of manufacturers, distributors, and retailers, who can compete within a tier but may cooperate between tiers. We consider multicriteria decision-making for both the manufacturers and the distributors whereas the retailers are subject to decision-making under uncertainty since the demands associated with the product are random. We derive the optimality conditions for the decision-makers, establish the equilibrium conditions, and derive the variational inequality formulation. We then utilize the variational inequality formulation to provide both qualitative properties of the equilibrium product shipment, service level, and price pattern and to propose a computational procedure, along with convergence results. This is the first supply chain network model to capture both multicriteria decision-making and decision-making under uncertainty in an integrated equilibrium framework.     

The clamped-plate equation for the limaçon

Hadamard claimed in 1907 that the clamped-plate equation is positivity preserving for domains which are bounded by a Limaçon de Pascal. We will show that this claim is false in its full generality. However, we will also prove that there are nonconvex limaçons for which the clamped-plate equation has the sign-preserving property. In fact we will give an explicit bound for the parameter of the limaçon where sign change may occur. Mathematics Subject Classification (2000) 35J40, 35Q72, 35B50     

Interior penalty method for the indefinite time-harmonic Maxwell equations

Summary In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L²-norm. In particular, the error in the energy norm is shown to converge with the optimal order (h^min{s,}) with respect to the mesh size h, the polynomial degree , and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L²-error is shown to converge with the optimal order (h⁺¹). The theoretical results are confirmed in a series of numerical experiments.Supported by the EPSRC (Grant GR/R76615).Supported by the Swiss National Science Foundation under project 21-068126.02.Supported in part by the Natural Sciences and Engineering Council of Canada.