Arithmetically Cohen-Macaulay bundles on complete intersection varieties of sufficiently high multidegree

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.

Harvesting undelimbed Scots pine (Pinus sylvestris L.) from first thinnings for integrated production of kraft pulp and energy

The present study evaluates the feasibility of undelimbed Scots pine (Pinus sylvestris L.) for integrated production of pulp and energy in a kraft pulp mill from the technical, economic and environmental points of view, focusing on the potential of bundle harvesting. The feasibility of tree sections for pulp production was tested by conducting an industrial wood-handling experiment, laboratory cooking and bleaching trials, using conventional small-diameter Scots pine pulpwood as a reference. These trials showed that undelimbed Scots pine sections can be processed in favourable conditions as a blend with conventional small-diameter pulpwood without reducing the pulp quality. However, fibre losses at various phases of the process may increase when using undelimbed material. In the economic evaluation, both pulp production and wood procurement costs were considered, using the relative wood paying capability of a kraft pulp mill as a determinant. The calculations were made for three Scots pine first-thinning stands with the breast-height diameter of the removal (6 12 cm) as the main distinctive factor. The supply chains included in the comparison were based on cut-to-length harvesting, whole-tree harvesting and bundle harvesting (whole-tree bundling). With the current ratio of pulp and energy prices, the wood paying capability declines with an increase in the proportion of the energy fraction of the raw material. The supply system based on the cut-to-length method was the most efficient option, resulting in the highest residual value at stump in most cases. A decline in the pulp price and an increase in the energy price improved the competitiveness of the whole-tree systems. With short truck transportation distances and low pulp prices, however, the harvesting of loose whole trees can result in higher residual value at stump in small-diameter stands. While savings in transportation costs did not compensate for the high cutting and compaction costs by the second prototype of the bundle harvester, an increase in transportation distances improved its competitiveness. Since harvesting undelimbed assortments increases nutrient export from the site, which can affect soil productivity, the whole-tree alternatives included in the present study cannot be recommended on infertile peatlands and mineral soils. The harvesting of loose whole trees or bundled whole trees implies a reduction in protective logging residues and an increase in site traffic or payloads. These factors increase the risk of soil damage, especially on peat soils with poor bearing capacity. Within the wood procurement parameters which were examined, the CO2 emissions of the supply systems varied from 13 27 kg m3. Compaction of whole trees into bundles reduced emissions from transportation by 30 39%, but these reductions were insufficient to compensate for the increased emissions from cutting and compaction.

Hydrogen Storage Capacity of Carbon-Foams: Grand Canonical Monte Carlo Simulations

Hydrogen storage in the three-dimensional carbon foams is analyzed using classical grand canonical Monte Carlo simulations. The calculated storage capacities of the foams meet the material-based DOE targets and are comparable to the capacities of a bundle of well-separated similar diameter open nanotubes. The pore sizes in the foams are optimized for the best hydrogen uptake. The capacity depends sensitively on the C-H-2 interaction potential, and therefore, the results are presented for its ``weak'' and ``strong'' choices, to offer the lower and upper bounds for the expected capacities. Furthermore, quantum effects on the effective C-H-2 as well as H-2-H-2 interaction potentials are considered. We find that the quantum effects noticeably change the adsorption properties of foams and must be accounted for even at room temperature.

A classification of homogeneous operators in the Cowen-Douglas class

An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc D is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous holomorphic Hermitian vector bundles over D, the ones corresponding to operators in the Cowen-Douglas class B-n(D) are identified. The classification of homogeneous operators in B-n(D) is completed using an explicit realization of these operators. We also show how the homogeneous operators in B-n(D) split into similarity classes. (C) 2011 Elsevier Inc. All rights reserved.

Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

The stability of transmembrane helices: A molecular dynamics study on the isolated helices of bacteriorhodopsin

Bacteriorhodopsin (bR) continues to be a proven testing ground for the study of integral membrane proteins (IMPs). It is important to study the stability of the individual helices of bR, as they are postulated to exist as independently stable transmembmne helices (TMHs) and also for their utility as templates for modeling other IMPs with the postulated seven-helix bundle topology. Toward this purpose, the seven helices of bR have been studied by molecular dynamics simulation in this study. The suitability of using the backbone-dependent rotamer library of side-chain conformations arrived at from the data base of globular protein structures in the case TMHs has been tested by another set of ? helix simulations with the side-chain orientations taken from this library. The influence of the residue's net charge oil the helix stability was examined by simulating the helices III, IV, and VI (from both of the above sets of helices) with zero net charge on the side chains. The results of these 20 simulations demonstrate in general the stability of the isolated helices of bR in conformity with the two-stage hypothesis of IMP folding. However, the helices I, II, V, and VII are more stable than the other three helices. The helical nature of certain regions of III, IV, and VI are influenced by factors such as the net charge and orientation of several residues. It is seen that the residues Arg, Lys, Asp, and Glu (charged residues), and Ser, Thr, Gly, and Pro, play a crucial role in the stability of the helices of bR. The backbone-dependent rotamer library for the side chains is found to be suitable for the study of TMHs in IMP. (C) 1996 John Wiley & Sons, Inc.

Flat connections, geometric invariants and energy of harmonic functions on compact Riemann surfaces

A geometric invariant is associated to the space of fiat connections on a G-bundle over a compact Riemann surface and is related to the energy of harmonic functions.

Spectral asymptotics of the Helmholtz model in fluid-solid structures

A model representing the vibrations of a coupled fluid-solid structure is considered. This structure consists of a tube bundle immersed in a slightly compressible fluid. Assuming periodic distribution of tubes, this article describes the asymptotic nature of the vibration frequencies when the number of tubes is large. Our investigation shows that classical homogenization of the problem is not sufficient for this purpose. Indeed, our end result proves that the limit spectrum consists of three parts: the macro-part which comes from homogenization, the micro-part and the boundary layer part. The last two components are new. We describe in detail both macro- and micro-parts using the so-called Bloch wave homogenization method. Copyright (C) 1999 John Wiley & Sons, Ltd.

Allosteric Communication in Cysteinyl tRNA Synthetase A NETWORK OF DIRECT AND INDIRECT READOUT

Protein structure networks are constructed for the identification of long-range signaling pathways in cysteinyl tRNA synthetase (CysRS). Molecular dynamics simulation trajectory of CysRS-ligand complexes were used to determine conformational ensembles in order to gain insight into the allosteric signaling paths. Communication paths between the anticodon binding region and the aminoacylation region have been identified. Extensive interaction between the helix bundle domain and the anticodon binding domain, resulting in structural rigidity in the presence of tRNA, has been detected. Based on the predicted model, six residues along the communication paths have been examined by mutations (single and double) and shown to mediate a coordinated coupling between anticodon recognition and activation of amino acid at the active site. This study on CysRS clearly shows that specific key residues, which are involved in communication between distal sites in allosteric proteins but may be elusive in direct structure analysis, can be identified from dynamics of protein structure networks.

Synthesis and characterization of self-assembled nanofiber-bundles of V(2)O(5): their electrochemical and field emission properties

High-quality self-assembled V(2)O(5) nanofiber-bundles (NBs) are synthesized by a simple and direct hydrothermal method using a vanadium(V) hydroxylamido complex as a vanadium source in the presence of HNO(3). The possible reaction pathway for the formation of V(2)O(5) NBs is discussed and demonstrated that HNO(3) functions both as an oxidizing and as an acidification agent. V(2)O(5) NBs are single-crystals of an orthorhombic phase that have grown along the [010] direction. A bundle is made of indefinite numbers of homogeneous V(2)O(5) nanofibers where nanofibers have lengths up to several micrometres and widths ranging between 20 and 50 nm. As-prepared V(2)O(5) NBs display a high electrochemical performance in a non-aqueous electrolyte as a cathode material for lithium ion batteries. Field emission properties are also investigated which shows that a low turn-on field of similar to 1.84 V mu m(-1) is required to draw the emission current density of 10 mu Lambda cm(-2).

A Compact and Compliant External Pipe-Crawling Robot

The focus of this paper is on the practical aspects of design, prototyping, and testing of a compact, compliant external pipe-crawling robot that can inspect a closely spaced bundle of pipes in hazardous environments and areas that are inaccessible to humans. The robot consists of two radially deployable compliant ring actuators that are attached to each other along the longitudinal axis of the pipe by a bidirectional linear actuator. The robot imitates the motion of an inchworm. The novel aspect of the compliant ring actuator is a spring-steel compliant mechanism that converts circumferential motion to radial motion of its multiple gripping pads. Circumferential motion to ring actuators is provided by two shape memory alloy (SMA) wires that are guided by insulating rollers. The design of the compliant mechanism is derived from a radially deployable mechanism. A unique feature of the design is that the compliant mechanism provides the necessary kinematic function within the limited annular space around the pipe and serves as the bias spring for the SMA wires. The robot has a control circuit that sequentially activates the SMA wires and the linear actuator; it also controls the crawling speed. The robot has been fabricated, tested, and automated. Its crawling speed is about 45 mm/min, and the weight is about 150 g. It fits within an annular space of a radial span of 15 mm to crawl on a pipe of 60-mm outer diameter.

Resolution of Singularities for a Class of Hilbert Modules

Let M be the completion of the polynomial ring C(z) under bar] with respect to some inner product, and for any ideal I subset of C (z) under bar], let I] be the closure of I in M. For a homogeneous ideal I, the joint kernel of the submodule I] subset of M is shown, after imposing some mild conditions on M, to be the linear span of the set of vectors {p(i)(partial derivative/partial derivative(w) over bar (1),...,partial derivative/partial derivative(w) over bar (m)) K-I] (., w)vertical bar(w=0), 1 <= i <= t}, where K-I] is the reproducing kernel for the submodule 2] and p(1),..., p(t) is some minimal ``canonical set of generators'' for the ideal I. The proof includes an algorithm for constructing this canonical set of generators, which is determined uniquely modulo linear relations, for homogeneous ideals. A short proof of the ``Rigidity Theorem'' using the sheaf model for Hilbert modules over polynomial rings is given. We describe, via the monoidal transformation, the construction of a Hermitian holomorphic line bundle for a large class of Hilbert modules of the form I]. We show that the curvature, or even its restriction to the exceptional set, of this line bundle is an invariant for the unitary equivalence class of I]. Several examples are given to illustrate the explicit computation of these invariants.

Monopoles on S-F(2) from the fuzzy conifold

The intersection of the conifold z(1)(2) + z(2)(2) + z(3)(2) = 0 and S-5 is a compact 3-dimensional manifold X-3. We review the description of X-3 as a principal U(1) bundle over S-2 and construct the associated monopole line bundles. These monopoles can have only even integers as their charge. We also show the Kaluza-Klein reduction of X-3 to S-2 provides an easy construction of these monopoles. Using the analogue of the Jordan-Schwinger map, our techniques are readily adapted to give the fuzzy version of the fibration X-3 -> S-2 and the associated line bundles. This is an alternative new realization of the fuzzy sphere S-F(2) and monopoles OH it.

EXTENSIONS OF VECTOR BUNDLES WITH APPLICATION TO NOETHER-LEFSCHETZ THEOREMS

Given a smooth, projective variety Y over an algebraically closed field of characteristic zero, and a smooth, ample hyperplane section X subset of Y, we study the question of when a bundle E on X, extends to a bundle epsilon on a Zariski open set U subset of Y containing X. The main ingredients used are explicit descriptions of various obstruction classes in the deformation theory of bundles, together with Grothendieck-Lefschetz theory. As a consequence, we prove a Noether-Lefschetz theorem for higher rank bundles, which recovers and unifies the Noether-Lefschetz theorems of Joshi and Ravindra-Srinivas.

Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (S*)(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E-T corresponding to the operator T in the Cowen-Douglas class B-1() which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B-1() for a bounded domain in C-m.