Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

We define the Virasoro algebra action on imaginary Verma modules for affine and construct an analogue of the Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a realization of imaginary Verma modules in terms of sums of partial differential operators.

Induced Modules for Affine Lie Algebras

We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra P(ps), P subset of P(ps). The structure of P-induced modules in this case is fully determined by the structure of P(ps)-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. Konig, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].

Équations différentielles issues des vecteurs singuliers des représentations de l'algèbre de Virasoro

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

Functional microarray analysis suggests repressed cell-cell signaling and cell survival-related modules inhibit progression of head and neck squamous cell carcinoma

Background: Cancer shows a great diversity in its clinical behavior which cannot be easily predicted using the currently available clinical or pathological markers. The identification of pathways associated with lymph node metastasis (N+) and recurrent head and neck squamous cell carcinoma (HNSCC) may increase our understanding of the complex biology of this disease. Methods: Tumor samples were obtained from untreated HNSCC patients undergoing surgery. Patients were classified according to pathologic lymph node status (positive or negative) or tumor recurrence (recurrent or non-recurrent tumor) after treatment (surgery with neck dissection followed by radiotherapy). Using microarray gene expression, we screened tumor samples according to modules comprised by genes in the same pathway or functional category. Results: The most frequent alterations were the repression of modules in negative lymph node (N0) and in non-recurrent tumors rather than induction of modules in N+ or in recurrent tumors. N0 tumors showed repression of modules that contain cell survival genes and in non-recurrent tumors cell-cell signaling and extracellular region modules were repressed. Conclusions: The repression of modules that contain cell survival genes in N0 tumors reinforces the important role that apoptosis plays in the regulation of metastasis. In addition, because tumor samples used here were not microdissected, tumor gene expression data are represented together with the stroma, which may reveal signaling between the microenvironment and tumor cells. For instance, in non-recurrent tumors, extracellular region module was repressed, indicating that the stroma and tumor cells may have fewer interactions, which disable metastasis development. Finally, the genes highlighted in our analysis can be implicated in more than one pathway or characteristic, suggesting that therapeutic approaches to prevent tumor progression should target more than one gene or pathway, specially apoptosis and interactions between tumor cells and the stroma.

INTEGRABLE MODULES FOR AFFINE LIE SUPERALGEBRAS

Irreducible nonzero level modules with finite-dimensional weight spaces are discussed for nontwisted affine Lie superalgebras. A complete classification of such modules is obtained for superalgebras of type A(m, n)(boolean AND) and C(n)(boolean AND) using Mathieu's classification of cuspidal modules over simple Lie algebras. In other cases the classification problem is reduced to the classification of cuspidal modules over finite-dimensional cuspidal Lie superalgebras described by Dimitrov, Mathieu and Penkov. Based on these results a. complete classification of irreducible integrable (in the sense of Kac and Wakimoto) modules is obtained by showing that any such module is of highest weight, in which case the problem was solved by Kac and Wakimoto.

Folding, calcium binding, and structural characterization of a concatemer of the first and second ligand-binding modules of the low-density lipoprotein receptor

The ligand-binding domain of the low-density lipoprotein (LDL) receptor is comprised of seven tandemly repeated ligand-binding modules, each being approximately 40 amino acids long and containing six conserved cysteine residues. We have expressed and characterized a concatemer of the first two modules (LB1 and LB2) of the human LDL receptor. Oxidative folding of the recombinant concatemer (rLB(1-2)), in the presence of calcium ions, gave a single dominant isomer with six disulfide bonds. Peptic cleavage of the short Linker region that connects the last cysteine residue of LB1 and the first cysteine residue of LB2 yielded two discrete fragments, thus excluding the presence of intermodule disulfide bonds. The N-terminal module, LB1, reacted with a conformation-specific monoclonal antibody (IgG-C7) made to LB1 in the native LDL receptor. From this, we concluded that the first module was correctly folded, with the same set of disulfide bonds as LB1 of the LDL receptor. The disulfide bond connections of LB2 were identified from mass spectral analysis of fragments formed by digestion of the C-terminal peptic fragment with elastase. These data showed that the disulfide bonds of LB2 connected Cys(I) and Cys(III), Cys(II) and Cys(V), and Cys(IV) and Cys(VI). This pattern is identical to that found for recombinant LB1 and LB2. The concatemer has two high-affinity calcium-binding sites, one per module. An analysis of the secondary chemical shifts of C alpha protons shows that the conformations of LB1 and LB2 in the concatemer are very similar to those of the individual modules, with no evidence for strong interactions between the two modules.

NMR structure and backbone dynamics of a concatemer of epidermal growth factor homology modules of the human low-density lipoprotein receptor

The ligand-binding region of the low-density lipoprotein (LDL) receptor is formed by seven N-terminal, imperfect, cysteine-rich (LB) modules. This segment is followed by an epidermal growth factor precursor homology domain with two N-terminal, tandem, EGF-like modules that are thought to participate in LDL binding and recycling of the endocytosed receptor to the cell surface. EGF-A and the concatemer, EGF-AB, of these modules were expressed in Escherichia coli. Correct protein folding of EGF-A and the concatemer EGF-AB was achieved in the presence or absence of calcium ions, in contrast to the LB modules, which require them for correct folding. Homonuclear and heteronuclear H-1-N-15 NMR spectroscopy at 17.6 T was used to determine the three-dimensional structure of the concatemer. Both modules are formed by two pairs of short, anti-parallel beta -strands. In the concatemer, these modules have a fixed relative orientation, stabilized by calcium ion-binding and hydrophobic interactions at the interface. N-15 longitudinal and transverse relaxation rates, and {H-1}-N-15 heteronuclear NOEs were used to derive a model-free description of the backbone dynamics of the molecule. The concatemer appears relatively rigid, particularly near the calcium ion-binding site at the module interface, with an average generalized order parameter of 0.85 +/- 0.11. Some mutations causing familial hypercholesterolemia may now be rationalized. Mutations of D41, D43 and E44 in the EGF-B calcium ion-binding region may affect the stability of the linker and thus the orientation of the tandem modules. The diminutive core also provides little structural stabilization, necessitating the presence of disulfide bonds. The structure and dynamics of EGF-AB contrast with the N-terminal LB modules, which require calcium ions both for folding to form the correct disulfide connectivities and for maintenance of the folded structure, and are connected by highly mobile linking peptides. (C) 2001 Academic Press.

Parallel simulation system for earthquake generation: Fault analysis modules and parallel coupling analysis

Solid earth simulations have recently been developed to address issues such as natural disasters, global environmental destruction and the conservation of natural resources. The simulation of solid earth phenomena involves the analysis of complex structures including strata, faults, and heterogeneous material properties. Simulation of the generation and cycle of earthquakes is particularly important, but such simulations require the analysis of complex fault dynamics. GeoFEM is a parallel finite-element analysis system intended for solid earth field phenomena problems. This paper describes recent development in the GeoFEM project for the simulation of earthquake generation and cycles.

Power Electronics Didactic Modules for Direct Current Machine Control

Several didactic modules for an electric machinery laboratory are presented. The modules are dedicated for DC machinery control and get their characteristic curves. The didactic modules have a front panel with power and signal connectors and can be configurable for any DC motor type. The three-phase bridge inverter proposed is one of the most popular topologies and is commercially available in power package modules. The control techniques and power drives were designed to satisfy static and dynamic performance of DC machines. Each power section is internally self-protected against misconnections and short-circuits. Isolated output signals of current and voltage measurements are also provided, adding versatility for use either in didactic or research applications. The implementation of such modules allowed experimental confirmation of the expected performance.

Lightweight amorphous silicon photovoltaic modules on flexible plastic substrate

Solar cells on lightweight and flexible substrates have advantages over glass-or wafer-based photovoltaic devices in both terrestrial and space applications. Here, we report on development of amorphous silicon thin film photovoltaic modules fabricated at maximum deposition temperature of 150 degrees C on 100 mu m thick polyethylene-naphtalate plastic films. Each module of 10 cm x 10 cm area consists of 72 a-Si:H n-i-p rectangular structures with transparent conducting oxide top electrodes with Al fingers and metal back electrodes deposited through the shadow masks. Individual structures are connected in series forming eight rows with connection ports provided for external blocking diodes. The design optimization and device performance analysis are performed using a developed SPICE model.

Embedding instruments & modules into an IEEE1451-FPGA-Based Weblab infrastructure

Adopting standard-based weblab infrastructures can be an added value for spreading their influence and acceptance in education. This paper suggests a solution based on the IEEE1451.0 Std. and FPGA technology for creating reconfigurable weblab infrastructures using Instruments and Modules (I&Ms) described through standard Hardware Description Language (HDL) files. It describes a methodology for creating and binding I&Ms into an IEEE1451-module embedded in a FPGA-based board able to be remotely controlled/accessed using IEEE1451-HTTP commands. At the end, an example of a step-motor controller module bond to that IEEE1451-module is described.