Double complexes and vanishing of Novikov cohomology

We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that a finitely dominated cochain complex over a Laurent polynomial ring has trivial (positive and negative) Novikov cohomology.

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

State detection of bond wires in IGBT modules using eddy current pulsed thermography

Insulated gate bipolar transistor (IGBT) modules are important safety critical components in electrical power systems. Bond wire lift-off, a plastic deformation between wire bond and adjacent layers of a device caused by repeated power/thermal cycles, is the most common failure mechanism in IGBT modules. For the early detection and characterization of such failures, it is important to constantly detect or monitor the health state of IGBT modules, and the state of bond wires in particular. This paper introduces eddy current pulsed thermography (ECPT), a nondestructive evaluation technique, for the state detection and characterization of bond wire lift-off in IGBT modules. After the introduction of the experimental ECPT system, numerical simulation work is reported. The presented simulations are based on the 3-D electromagnetic-thermal coupling finite-element method and analyze transient temperature distribution within the bond wires. This paper illustrates the thermal patterns of bond wires using inductive heating with different wire statuses (lifted-off or well bonded) under two excitation conditions: nonuniform and uniform magnetic field excitations. Experimental results show that uniform excitation of healthy bonding wires, using a Helmholtz coil, provides the same eddy currents on each, while different eddy currents are seen on faulty wires. Both experimental and numerical results show that ECPT can be used for the detection and characterization of bond wires in power semiconductors through the analysis of the transient heating patterns of the wires. The main impact of this paper is that it is the first time electromagnetic induction thermography, so-called ECPT, has been employed on power/electronic devices. Because of its capability of contactless inspection of multiple wires in a single pass, and as such it opens a wide field of investigation in power/electronic devices for failure detection, performance characterization, and health monitoring. 

Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Evaluation of predicted network modules in yeast metabolism using NMR-based metabolite profiling

Genome-scale metabolic models promise important insights into cell function. However, the definition of pathways and functional network modules within these models, and in the biochemical literature in general, is often based on intuitive reasoning. Although mathematical methods have been proposed to identify modules, which are defined as groups of reactions with correlated fluxes, there is a need for experimental verification. We show here that multivariate statistical analysis of the NMR-derived intra- and extracellular metabolite profiles of single-gene deletion mutants in specific metabolic pathways in the yeast Saccharomyces cerevisiae identified outliers whose profiles were markedly different from those of the other mutants in their respective pathways. Application of flux coupling analysis to a metabolic model of this yeast showed that the deleted gene in an outlying mutant encoded an enzyme that was not part of the same functional network module as the other enzymes in the pathway. We suggest that metabolomic methods such as this, which do not require any knowledge of how a gene deletion might perturb the metabolic network, provide an empirical method for validating and ultimately refining the predicted network structure.

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

Intelligent Assembly Time Analysis Using a Digital Knowledge-Based Approach

The implementation of effective time analysis methods fast and accurately in the era of digital manufacturing has become a significant challenge for aerospace manufacturers hoping to build and maintain a competitive advantage. This paper proposes a structure oriented, knowledge-based approach for intelligent time analysis of aircraft assembly processes within a digital manufacturing framework. A knowledge system is developed so that the design knowledge can be intelligently retrieved for implementing assembly time analysis automatically. A time estimation method based on MOST, is reviewed and employed. Knowledge capture, transfer and storage within the digital manufacturing environment are extensively discussed. Configured plantypes, GUIs and functional modules are designed and developed for the automated time analysis. An exemplar study using an aircraft panel assembly from a regional jet is also presented. Although the method currently focuses on aircraft assembly, it can also be well utilized in other industry sectors, such as transportation, automobile and shipbuilding. The main contribution of the work is to present a methodology that facilitates the integration of time analysis with design and manufacturing using a digital manufacturing platform solution.