bluuebunny/crossref_metadata_2025 huggingface dataset:
Functional expression of NOD2, a novel pattern recognition receptor for bacterial motifs, in primary murine astrocytes
Authors: Sterka David , Rati Dana M. , Marriott Ian
Published: November 2005

There is growing appreciation that resident brain cells can initiate and/or regulate inflammation after trauma or infection in the central nervous system (CNS). Recent studies from our laboratory have begun to shed light on the mechanisms by which astrocytes perceive bacterial challenges by demonstrating the functional expression of Toll‐like receptors (TLR) in this cell type. In the present study, we demonstrate that astrocytes also express members of the novel nucleotide‐binding oligomerization domain (NOD) family of proteins that can serve as cytosolic pattern recognition receptors. We show that isolated cultures of murine astrocytes constitutively express robust levels of NOD2, a molecule that can recognize a minimal peptidoglycan motif. Expression of NOD2 is significantly upregulated after exposure to two disparate and clinically relevant bacterial pathogens of the CNS, Borrelia burgdorferi and Neisseria meningitidis. Similarly, NOD2 protein expression is elevated after exposure to specific bacterial ligands for TLRs. Importantly, we show that astrocytes express Rip2 kinase, an essential downstream effector molecule for NOD‐mediated cell responses, and demonstrate that this expression is upregulated after bacterial challenge. Furthermore, we confirm the functional nature of NOD2 in astrocytes by demonstrating that a specific ligand for this receptor induces significant inflammatory cytokine production and augments immune responses induced by TLR ligation. Taken together, the present demonstration that astrocytes express functional NOD2 proteins may represent a potentially important mechanism by which this glial cell type initiates either protective host responses within the brain or the progression of damaging CNS inflammation. © 2005 Wiley‐Liss, Inc.
Local release of dexamethasone from polymer millirods effectively prevents fibrosis after radiofrequency ablation
Authors: Blanco Elvin , Weinberg Brent D. , Stowe Nicholas T. , Anderson James M. , Gao Jinming
Published: November 2005

Recent studies show that after radiofrequency (RF) ablation, fibrosis occurs at the ablation boundary, hindering anticancer drug transport from a locally implanted polymer depot to the ablation margin, where tumors recur. The purpose of this study is to investigate strategies that can effectively deliver dexamethasone (DEX), an anti‐inflammatory agent, to prevent fibrosis. Polymer millirods consisting of poly(D,L‐lactide‐co‐glycolide) (PLGA) were loaded with either DEX complexed with hydroxypropyl β‐cyclodextrin (HPβ‐CD), or an NaCl and DEX mixture. In vitro release studies show that DEX complexed with HPβ‐CD released 95% of the drug after 4 days, compared to 14% from millirods containing NaCl and DEX. Rat livers underwent RF ablation and received either DEX‐HPβ‐CD‐loaded millirods, PLGA millirods with an intraperitoneal (i.p.) DEX injection, or control PLGA millirods alone. After 8 days in vivo, heightened inflammation and the appearance of a well‐defined fibrous capsule can be observed in both the control experiments and those receiving a DEX injection (0.29 ± 0.08 and 0.26 ± 0.07 mm in thickness, respectively), with minimal inflammation and fibrosis present in livers receiving DEX millirods (0.04 ± 0.01 mm). Results from this study show that local release of DEX prevents fibrosis more effectively than a systemic i.p. injection. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2006
A novel bioactive porous CaSiO3 scaffold for bone tissue engineering
Authors: Ni Siyu , Chang Jiang , Chou Lee
Published: November 2005

The aim of this study was to fabricate bioactive porous CaSiO3 scaffolds and examine their effects on proliferation and differentiation of osteoblast‐like cells. In this study, porous CaSiO3 scaffolds were obtained by sintering a ceramic slip‐coated polymer foam at 1350°C. X‐ray diffraction (XRD) of the scaffolds indicated that the products were essentially pure α‐CaSiO3. The obtained scaffolds had a well‐interconnected porous structure with pore sizes ranging from several micrometers to more than 100 μm and porosities of 88.5 ± 2.8%. The in vitro bioactivity of the scaffolds was investigated by soaking them in simulated body fluid (SBF) for 7 days and then characterizing them by scanning electron microscopy (SEM) and energy‐dispersive spectroscopy (EDS) analysis. The results indicated that hydroxyapatite (HAp) was formed on the surface of the scaffolds. In addition, the scaffolds were incubated in Ringer's solution at 37°C to study the in vitro degradation by measurement of weight loss after incubation, which showed that the CaSiO3 scaffolds were degradable. The cellular responses to the scaffolds were assessed in terms of cell proliferation and differentiation. Osteoblast‐like cells were seeded into the CaSiO3 scaffolds. SEM observations showed that there was significant cell adhesion, as the cells spread and grew in the scaffolds. In addition, the proliferation rate and alkaline phosphatase (ALP) activity of the cells in the scaffolds were improved as compared to the controls. These studies demonstrate initial in vitro cell compatibility and their potential application to bone tissue engineering. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2006
Enhancement of in vivo endothelialization of tissue‐engineered vascular grafts by granulocyte colony‐stimulating factor
Authors: Cho Seung‐Woo , Lim Joung Eun , Chu Hun Su , Hyun Hye‐Jin , Choi Cha Yong , Hwang Ki‐Chul , Yoo Kyung Jong , Kim Dong‐Ik , Kim Byung‐Soo
Published: November 2005

Successful reconstruction of large‐diameter blood vessel in humans has been demonstrated using the tissue engineering technique, but improvement in patency of small‐diameter bioartificial vascular graft remains a great challenge. This study reports that granulocyte colony‐stimulating factor (G‐CSF) can enhance in vivo endothelialization of tissue‐engineered vascular grafts, which could be used to improve patency of small‐diameter vascular graft. Vascular grafts were tissue engineered with decellularized canine abdominal aortas and canine autologous bone marrow–derived cells. Prior to cell seeding onto decellularized graft matrices, bone marrow–derived cells were induced to differentiate into endothelial cells and smooth muscle cells. The cell‐seeded vascular grafts were implanted into the abdominal aortas of bone marrow donor dogs. Before and after graft implantation, G‐CSF was administered subcutaneously to the dogs (n = 3). The grafts implanted into the dogs not receiving G‐CSF were used as controls (n = 3). Eight weeks after implantation, grafts in both groups showed regeneration of vascular tissues including endothelium and smooth muscle. Importantly, endothelium formation was more extensive in the G‐CSF–treated grafts than in the control grafts, as assessed with reverse transcription polymerase chain reaction, western blot, and immunohistochemistry. In addition, intimal hyperplasia was significantly reduced in the G‐CSF–treated grafts compared to the control grafts. This study suggests that G‐CSF administration could be applied to improve patency of small‐diameter tissue‐engineered vascular grafts. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2006
Morphological features of ovine embryonic lung fibroblasts cultured on different bioactive scaffolds
Authors: Moscato S. , Cascone M. G. , Lazzeri L. , Danti S. , Mattii L. , Dolfi A. , Bernardini N.
Published: November 2005

Tissue regeneration with autologous cell transplantation is one of the most important goals in clinical research. In this field, the development of bioactive materials that provide microenvironments for cell–matrix interactions mimicking biological conditions is required. In recent years, many synthetic materials have been developed as scaffolds and many procedures for the surface modification of these materials have been applied using biological molecules. In this study, we analyzed the morphology and the molecule production by ovine embryonic lung fibroblasts cultured on three different sponge‐like matrices based on poly(L‐lactic acid) (PLLA): agarose/PLLA, crosslinked and uncrosslinked gelatin/PLLA. The matrices were produced by using an emulsion freeze‐drying method leading to the formation of sponge‐like materials with high porosity and with interconnection between the pores. In vitro MTT test demonstrated that transplanted cells were viable and metabolically active. Morphological analysis revealed that fibroblasts adhered to and penetrated the polymeric structures. Moreover, all the different matrices supported fibroblast production of proteoglycans, glycoproteins, and matrix molecules such as elastin, collagen I, and fibronectin. These data suggest that the tested bioactive scaffolds may support the growth and extracellular matrix molecule production of fibroblasts allowing in vitro connective tissue regeneration. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res, 2006
Sensitivity to implant materials in patients undergoing total hip replacement
Authors: Granchi Donatella , Cenni Elisabetta , Trisolino Giovanni , Giunti Armando , Baldini Nicola
Published: November 2005

Sensitivity to implant materials is an unpredictable event, which may contribute to the process leading to the failure of the total hip replacement (THR). The aim of the current study was to investigate the informative power of skin testing in detecting the sensitization to the implant components in patients undergoing THR. A consecutive series of 223 patients was enrolled in the study, including 66 candidates to THR, 53 with stable implant, and 104 with THR loosening. The patch testing was performed by using the most relevant components of cobalt‐based alloys (CoCrMo), Ti‐based alloys (TiAlV), and bone cements. The frequency of positive patch testing in preimplant patients did not differ from that observed after THR. Patients with CoCrMo‐failed implant showed a significant low frequency of nickel‐positive skin reaction, while patients with TiAlV‐THR had a high incidence of vanadium‐positive patch testing. The panel of haptens showed a good performance in the identification of patients known to have a contact dermatitis. With regard to the THR outcome, patch testing was not able to discriminate between stable and failed implant. Sensitivity to at least one hapten, namely bone cement, as well as the positive medical history of hypersensitivity, influenced negatively the THR survival. Our results show the reliability of patch testing for investigating the sensitivity to implant components. The cause–effect relationship between sensitization and negative outcome cannot be established, but the shorter lifespan of THR in patients who have a positive patch testing supports the significant role of this event in contributing to the implant failure. © 2005 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2006
Aid and growth in Sub‐Saharan Africa: accounting for transmission mechanisms
Authors: Gomanee Karuna , Girma Sourafel , Morrissey Oliver
Published: November 2005

This paper is a contribution to the literature on aid and growth. Despite an extensive empirical literature in this area, existing studies have not addressed directly the mechanisms via which aid should affect growth. We identify investment as the most significant transmission mechanism, and also consider effects through financing imports and government consumption spending. With the use of residual generated regressors, we achieve a measure of the total effect of aid on growth, accounting for the effect via investment. Pooled panel results for a sample of 25 Sub‐Saharan African countries over the period 1970 to 1997 point to a significant positive effect of foreign aid on growth, ceteris paribus. On average, each one percentage point increase in the aid/GNP ratio contributes one‐quarter of one percentage point to the growth rate. Africa's poor growth record should not therefore be attributed to aid ineffectiveness. Copyright © 2005 John Wiley & Sons, Ltd.
Palaeoenvironmental evolution and sea‐level fluctuations along the southeastern Pampa grasslands coast of Argentina during the Holocene
Authors: Vilanova Isabel , Prieto Aldo R. , Espinosa Marcela
Published: November 2005

Holocene pollen and diatom analyses and complementary data from δ18O and δ13C, malacology and sedimentology have provided a detailed record of vegetation history and palaeoenvironmental change at arroyo Las Brusquitas, on the southeastern coast of the pampas of Argentina especially in relation to past sea levels. Holocene palaeosalinity trends were estimated by Detrended Correspondence Analysis and by salinity indexes based on pollen and diatom data. As a consequence of sea‐level rise from the postglacial an extensive wave‐cut platform formed over which Holocene infilling sequences were deposited unconformably. In these sequences, variation in pollen and diatom assemblages occurred in agreement with changes in mollusc diversity and abundance, isotope values, and sediment deposits. Between ca. 6700 and 6190 14C yr BP (6279–6998 cal. yr BP) saline conditions predominated in an environment highly influenced by tides and salt water during the Holocene sea‐level highstand. Between ca. 6200 and 3900 14C yr BP (4235–4608 cal. yr BP) shallow brackish water bodies formed surrounded by saltmarsh vegetation that became more widespread from 5180 14C yr BP (5830–6173 cal. yr BP) to 3900 14C yr BP in relation to a sea‐level stabilisation period within the regression phase. Less saline conditions marked by frequent variations in salinity predominated between ca. 3900 and 2040 yr 14C BP (1830–2160 cal. yr BP). The intertidal saltmarsh environment changed into a brackish marsh dominated by freshwater conditions and sporadic tidal influence. Halophytic vegetation increased towards ca. 200014C yr BP indicating that saline conditions may be due to either desiccation or an unusually high tide range with rare frequency. After ca. 2000 14C yr BP the sedimentary sequences were buried by aeolian sand dunes. Changes in Holocene vegetation and environments in Las Brusquitas area are in agreement with data obtained from various southeastern coastal sites of the Pampa grasslands. Copyright © 2005 John Wiley & Sons, Ltd.
Singularity functions at axisymmetric edges and their representation by Fourier series
Authors: Heinrich Bernd
Published: November 2005

The regularity of solutions of the Dirichlet problem for the Poisson equation in three‐dimensional axisymmetric domains with reentrant edges is studied by means of Fourier series. The decomposition of the 3D problem into variational equations in 2D, a priori estimates of their solutions, a theorem of Riesz–Fischer type and two singularity functions (of tensor and non‐tensor product type) are given.
Optimal control for parabolic systems with competitive interactions
Authors: Lenhart S. , Protopopescu V.
Published: November 2005

We consider a two‐dimensional parabolic system with general competitive interactions as a two‐player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.
Local existence of solutions of impedance initial‐boundary value problem for non‐linear Maxwell equations
Authors: Picard R. H. , Zajaczkowski W. M.
Published: November 2005

Local existence of solutions of a mixed problem for non‐linear Maxwell equations is proved. The solution is so regular that its third derivatives are from L2. However, the considered problem is characteristic we were able to obtain necessary estimate because compatibility conditions were used.
Existence of a solution for a lubrication problem in elastic journal‐bearing devices with thin bearing
Authors: Bayada G. , Durany J. , Vázquez C.
Published: November 2005

A particular elastohydrodynamic lubrication problem is modelled in this work. The presence of elasticity, lubrication and cavitation calls for a non‐linear coupled system of variational equations. The existence of a solution is deduced by means of a constructive algorithm that decouples biharmonic equation of the elastic hinged plate and the lubrication‐cavitation Elrod‐Adams free boundary problem.
Boundary layer resolution in hierarchical plate modelling
Authors: Schwab C.
Published: November 2005

The dimensional reduction of an elliptic model boundary value problem on a thin, plate‐like domain of thickness 2d is analysed. A class of lower‐dimensional models with variable model orders in the interior and near the boundary of the plate is investigated and it is shown that for a sufficiently large model order in a O(d∣ln d∣)‐neighbourhood of the edge the hierarchical models compensate for the boundary layers of the exact solution—in the sense that their asymptotic rate of convergence as d → 0 is the same as the optimal one for compatible, layer‐free solutions.
Uniqueness theorems for a nonlinear Tricomi problem and the related evolution problem
Authors: Lar'kin N. A. , Schneider M.
Published: November 2005

We consider an initial‐boundary value problem for the non‐linear evolution equation

equation image

in a cylinder Qt = Ω × (0, t), where T[u] = yuxx + uyy is the Tricomi operator and l(u) a special differential operator of first order. In [10] we proved the existence of a generalized solution of problem (1) and the existence of a generalized solution of the corresponding stationary boundary value problem (non‐linear Tricomi problem)

equation image

In this paper we give sufficient conditions for the uniqueness of these solutions.
Assessment of glutamate and glutamine contribution to in vivo N‐acetylaspartate quantification in human brain by 1H‐magnetic resonance spectroscopy
Authors: Clementi Valeria , Tonon Caterina , Lodi Raffaele , Malucelli Emil , Barbiroli Bruno , Iotti Stefano
Published: November 2005

N‐Acetylaspartate (NAA) is one of the most important metabolites detectable by brain 1H‐MRS being considered an index of neuronal integrity. At the low magnetic field used in most clinical settings β,γ‐glutamate/glutamine (Glx) resonances are very close and partially overlap the methyl‐NAA resonance interfering with NAA quantification especially at low TE and in the presence of increased Glx signals. NAA overestimation due to Glx on a set of model solutions containing NAA, glutamate, and glutamine in variable amounts was evaluated and the result tested in vivo in six healthy controls and five age‐ and sex‐matched patients with hepatic encephalopathy (HE), the latter having an increased Glx content. A method to assess in vivo the NAA overestimation caused by Glx is proposed. A perfect match was obtained between the assessment of Glx contamination on the NAA of healthy controls and that obtained on the model solutions. However, a substantial difference in NAA overestimation was found between controls and HE patients that cannot be explained by our model. An interpretative hypothesis is provided. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
T2† measurement during acute cerebral ischemia by Carr‐Purcell MRI at 4T
Authors: Nikolova Simona , Hughes Sarah , Bartha Robert
Published: November 2005

Metabolic and structural changes occur in brain tissue within minutes of ischemia. The adiabatic multi‐echo (Carr‐Purcell) localization pulse sequence LASER has shown promise in detecting tissue contrast changes within the first hour of ischemia. The purpose of this initial study was to combine the LASER localization sequence with fast 3D echo‐planar imaging (EPI) to quantify the regional apparent transverse relaxation (T2†) in a rabbit model of acute embolic ischemia at 4 Tesla. Carr‐Purcell T2†‐weighted images were acquired at 7 different echo‐times and used to estimate T2† in both cortex and striatum. In ischemic tissue identified by 2,3,5 ‐ triphenyltetrazolium chloride (TTC) staining, the T2† increased by approximately 31% after 1 hour of ischemia and remained elevated until study completion at 4 h of ischemia. Lesion volume, defined as the number of pixels with T2† greater than 90 ms, increased by 40% between 1 and 4 h after induction of ischemia. Carr‐Purcell LASER‐EPI T2†‐weighted images show promise in detecting early tissue changes in focal cerebral ischemia. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Single heartbeat cardiac tagging for the evaluation of transient phenomena
Authors: Herzka Daniel A. , Derbyshire J. Andrew , Kellman Peter , McVeigh Elliot R.
Published: November 2005

Many cardiac abnormalities are of a transient nature, creating a beat‐to‐beat variation in myocardial function. This work presents the cardiac imaging technique for the measurement of regional function during transient cardiac phenomena. All information necessary for the reconstruction of a cine loop is acquired within a single heartbeat, avoiding the temporal blurring introduced by segmented imaging due to the assumption of cardiac cycle periodicity. This method incorporates a gradient‐optimized, high‐efficiency EPI‐SSFP sequence and TSENSE parallel imaging. For acquisitions with readout resolutions of 128,160, 192, and 256 points, the technique produced images with average temporal resolution of 35, 39, 43, and 52 ms and average spatial resolutions of 2.65, 2.12, 1.77, and 1.32 mm in the readout direction, respectively, and 2.88 and 2.08 mm in the phase encode direction for acceleration rates of 3 and 4, respectively. Local apparent strains in the single slice and measurements of ventricular end‐systolic and end‐diastolic areas were used as quantitative measures to validate the single heartbeat technique. To demonstrate the utility of the sequence, movie loops were acquired for multiple heartbeats in non‐breath‐held acquisitions as well as during a Valsalva maneuver. A heartbeat‐interleaved acquisition allowed for the reconstruction of nonaccelerated images from R contiguous heartbeats. Images reconstructed from such data displayed tag blurring and reduced tag persistence due to motion and interheartbeat variability. Images acquired during the Valsalva maneuver demonstrated apparent beat‐to‐beat variability, visible both in the images and as changing strain patterns and ventricular volumes. Magn Reson Med, 2005. Published 2005 Wiley‐Liss, Inc.
Quantitative assessment of coronary artery plaque vulnerability by high‐resolution magnetic resonance imaging and computational biomechanics: A pilot study ex vivo
Authors: Zheng Jie , El Naqa Issam , Rowold Faith E. , Pilgram Thomas K. , Woodard Pamela K. , Saffitz Jeffrey E. , Tang Dalin
Published: November 2005

The risk of atherosclerotic plaque disruption is thought to be closely related to plaque composition and rupture triggers such as external mechanical forces. The purpose of this study was to integrate MR imaging and computational techniques for the quantification of plaque vulnerability with morphologic data and biomechanical stress/strain distributions that were all based on high‐resolution MR images of coronary artery plaque specimens ex vivo. Twenty‐two coronary artery plaque specimens were selectively collected from 10 cadavers. Multislice T2‐weighted spin echo images were acquired with a resolution of 100 × 100 μm2. Histopathological images were used as the gold standard for the identification of plaque components and vulnerability. Plaque components were classified on MR images, and the stress/strain components were calculated with a two‐dimensional computational model with fluid–structure interactions. As expected, vulnerable plaques appeared to result from a large lipid pool, a thin fibrous cap, and some critical stress/strain conditions. An empiric vulnerability marker was derived and was closely related to the vulnerability score that was determined through pathologic examination. Noninvasive quantification of the MR contrast and mechanical properties of plaque may provide a comprehensive biomarker for the assessment of vulnerability of atherosclerotic plaques. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
The concept of special inner products for deriving new conjugate gradient‐like solvers for non‐symmetric sparse linear systems
Authors: Meyer Arnd
Published: November 2005

Yserentant's and Bramble/Pasciak/Xu's hierarchical preconditioners only require the hierarchical node connection of a finite element grid. So they could be applied to nonsymmetric FE‐systems too, having a symmetric preconditioner. We investigate the question whether this fact could be useful in the CG‐like iterative methods. The main key is the consideration of an appropriate choice of the inner product defined in the N‐vector space. It is shown, how the inner product influences the formulas of the methods, the rate of convergence and some other properties.
Equivalence of conditions for convergence of iterative methods for singular equations
Authors: Szyld Daniel B.
Published: November 2005

Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operators.
Diagonally compensated reduction and related preconditioning methods
Authors: Axelsson O. , Kolotilina L.
Published: November 2005

When solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M‐matrices (H‐matrices). In some application areas, however, the arising coefficient matrices are not H‐matrices. This is the case, for instance, when higher‐order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M‐matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described.
Algebraic multilevel iteration method for Stieltjes matrices
Authors: Axelsson O. , Neytcheva M.
Published: November 2005

The numerical solution of elliptic selfadjoint second‐order boundary value problems leads to a class of linear systems of equations with symmetric, positive definite, large and sparse matrices which can be solved iteratively using a preconditioned version of some algorithm. Such differential equations originate from various applications such as heat conducting and electromagnetics. Systems of equations of similar type can also arise in the finite element analysis of structures.

We discuss a recursive method constructing preconditioners to a symmetric, positive definite matrix. An algebraic multilevel technique based on partitioning of the matrix in two by two matrix block form, approximating some of these by other matrices with more simple sparsity structure and using the corresponding Schur complement as a matrix on the lower level, is considered.

The quality of the preconditioners is improved by special matrix polynomials which recursively connect the preconditioners on every two adjoining levels. Upper and lower bounds for the degree of the polynomials are derived as conditions for a computational complexity of optimal order for each level and for an optimal rate of convergence, respectively.

The method is an extended and more accurate algebraic formulation of a method for nine‐point and mixed five‐ and nine‐point difference matrices, presented in some previous papers.
On the convergence of difference schemes for a heat conduction equation
Authors: Andreev Andrey , Juboury Hussain
Published: November 2005

Sufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.
On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling
Authors: Freund Roland W. , Hochbruck Marlis
Published: November 2005

Recently, Freund and Nachtigal proposed the quasi‐minimal residual algorithm (QMR) for solving general nonsingular non‐Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose‐free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov‐subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.
A fast minimal residual algorithm for shifted unitary matrices
Authors: Jagels Carl F. , Reichel Lothar
Published: November 2005

A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non‐Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.
Efficient reduction algorithms for bordered band matrices
Authors: van Huffel Sabine , Park Haesun
Published: November 2005

Various plane rotation patterns are presented, which provide stable algorithms for reducing a b‐band matrix bordered by p rows and/or columns to (b + p)‐band form. These schemes generalize previously presented O(N2) reduction algorithms for matrices of order N, b = 1, and p = 1 to the reduction of more general b‐band, p‐bordered matrices where b ≥ 1 and p ≥ 1. Moreover, by splitting the matrix into two similarly structured submatrices and chasing nonzeros to the corners in two directions, the newly proposed patterns reduce the number of required rotations and hence the computational cost by one half compared to the other existing one‐way chasing algorithms. Symmetric, as well as more general matrices, are considered. An example of the first type is the symmetric arrowhead matrix that arises in solving inverse eigenvalue problems. Examples of the second type are found in updating the singular value decomposition (SVD) and the partial SVD.
Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
Authors: Druskin Vladimir , Knizhnerman Leonid
Published: November 2005

Many researchers are now working on computing the product of a matrix function and a vector, using approximations in a Krylov subspace. We review our results on the analysis of one implementation of that approach for symmetric matrices, which we call the spectral lanczos decomposition method (SLDM).

We have proved a general convergence estimate, relating SLDM error bounds to those obtained through approximation of the matrix function by a part of its Chebyshev series. Thus, we arrived at effective estimates for matrix functions arising when solving parabolic, hyperbolic and elliptic partial differential equations. We concentrate on the parabolic case, where we obtain estimates that indicate superconvergence of SLDM. For this case a combination of SLDM and splitting methods is also considered and some numerical results are presented.

We implement our general estimates to obtain convergence bounds of Lanczos approximations to eigenvalues in the internal part of the spectrum. Unlike Kaniel‐Saad estimates, our estimates are independent of the set of eigenvalues between the required one and the nearest spectrum bound.

We consider an extension of our general estimate to the case of the simple Lanczos method (without reorthogonalization) in finite computer arithmetic which shows that for a moderate dimension of the Krylov subspace the results, proved for the exact arithmetic, are stable up to roundoff.
Progress in the numerical solution of the nonsymmetric eigenvalue problem
Authors: Bai Zhaojun
Published: November 2005

With the growing demands from disciplinary and interdisciplinary fields of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper we examine the state of the art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.
On Parlett's matrix norm inequality for the Cholesky decomposition
Authors: Edelman Alan , Mascarenhas Walter F.
Published: November 2005

We show that a certain matrix norm ratio studied by Parlett has a supermum that is O(\documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[\sqrt n \] $\end{document}) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2‐norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.
Optimal backward perturbation bounds for the linear least squares problem
Authors: Waldén Bertil , Karlson Rune , Sun Ji‐Guang
Published: November 2005

Let A be an m × n matrix, b be an m‐vector, and x̃ be a purported solution to the problem of minimizing ‖b — Ax‖2. We consider the following open problem: find the smallest perturbation E of A such that the vector x̃ exactly minimizes ‖b — (A+E)x‖2. This problem is completely solved when E is measured in the Frobenius norm. When using the spectral norm of E, upper and lower bounds are given, and the optimum is found under certain conditions.
On the solution of block Hessenberg systems
Authors: Stewart G. W.
Published: November 2005

This paper describes a divide‐and‐conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.
Optimal algebraic multilevel preconditioning for local refinement along a line
Authors: Margenov S. , Maubach J.
Published: November 2005

The application of some recently proposed algebraic multilevel methods for the solution of two‐dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.
Peaceman—Rachford procedure and domain decomposition for finite element problems
Authors: Layton William J. , Rabier Patrick J.
Published: November 2005

This paper presents a general method to associate the operator splitting for the Peaceman—Rachford procedure with a decomposition of the domain in problems arising from finite element discretization of partial differential equations. The algorithm is provably convergent without any symmetry requirement. Moreover, this method possesses the significant advantage of making the linear systems of the Peaceman—Rachford iteration block diagonal and therefore perfectly appropriate for parallel processing. Not only is sparsity not affected but a reduction of the bandwidth occurs. In fact, for appropriate choices of nonconforming finite element spaces, this method makes directly possible elementwise processing. This option remains available in general for higher‐dimensional problems by applying the splitting algorithm recursively. Practical implementation requires nothing more than the standard finite element assembly procedure and some bookkeeping to relate a few different orderings of the nodes. In addition to all these attractive features, the method is rapidly convergent and remains highly competitive even when used on a serial machine.
Multilevel preconditioners for discretizations of the biharmonic equation by rectangular finite elements
Authors: Oswald Peter
Published: November 2005

Recently, some new multilevel preconditioners for solving elliptic finite element discretizations by iterative methods have been proposed. They are based on appropriate splittings of the finite element spaces under consideration, and may be analyzed within the framework of additive Schwarz schemes. In this paper we discuss some multilevel methods for discretizations of the fourth‐order biharmonic problem by rectangular elements and derive optimal estimates for the condition numbers of the preconditioned linear systems. For the Bogner–Fox–Schmit rectangle, the generalization of the Bramble–Pasciak–Xu method is discussed. As a byproduct, an optimal multilevel preconditioner for nonconforming discretizations by Adini elements is also derived.
Finite element procedures for strain estimations of sheet metal forming parts
Authors: Guo Y. Q. , Batoz J. L. , Detraux J. M. , Duroux P.
Published: November 2005

A finite element algorithm is developed to predict the strain distribution of sheet forming parts and to evaluate their formability at the design stage. The algorithm is simply called the inverse approach since we know the positions of the material points on the final product and we determine the positions of the corresponding material points in the initial blank. This is also a direct algorithm which avoids the path dependent incremental procedure of plasticity and contact. This paper presents some theoretical aspects related to the large logarithmic strains with membrane triangular elements, the deformation theory of plasticity, the isotropic and anisotropic material properties of metal sheets and the non‐linear solution techniques. Some particular problems are also studied, such as the influence of friction forces under the punch and blankholders, the ‘optimization’ of the initial blank's contour and the deep drawing in several steps. The results are compared with those obtained by experiments and by the more classical incremental approach.
Application of the finite element method to the simulation of sheet forming processes: Comparison of calculations and experiments
Authors: Keck P. , Wilhelm M. , Lange K.
Published: November 2005

Elastic‐plastic finite element calculations have been carried out to analyse sheet forming processes such as hydrostatic bulging of circular and rectangular blanks and the axisymmetric stretching of sheets (with different punch radii). The results, partly obtained by different finite element models, are compared with experimental data. It could be shown that, regarding the examples considered, experiments and calculations fit well and that a more sophisticated modelling of the contact boundary conditions improves the accuracy of the results. As a first attempt to handle more complex sheet forming operations, the deep drawing of a rectangular cup has been analysed. A summary of the theoretical background as well as some comments on the solution method and the implementation are given.
Finite element simulation of three‐dimensional deformation in shape rolling
Authors: Mori K. , Osakada K.
Published: November 2005

A method for simulating three‐dimensional steady‐state deformation in shape rolling with grooved rolls by the rigid‐plastic finite element method is proposed. For the three‐dimensional element mesh, contact of the nodal points with the roll surface and detachment from the surface are judged in each step of calculation. The boundary conditions of metal flow along the curved roll surface and of friction between the roll and the workpiece are dealt with at each node over the interface. Complex steady‐state deformation in shape rolling is simulated by using the non‐steady‐state scheme and the remeshing technique. As examples of simulation, rolling processes of bars and beams with grooved rolls are chosen. The deforming shape, the rolling torque, the roll separating force and the distributions of stress and strain in the workpiece are computed.
Optimal placement of actuators and sensors in control‐augmented structural optimization
Authors: Sepulveda Abdon E. , Schmit Lucien A.
Published: November 2005

A control‐augmented structural synthesis methodology is presented in which actuator and sensor placement is treated in terms of (0, 1) variables. Structural member sizes and control variables are treated simultaneously as design variables. A multiobjective utopian approach is used to obtain a compromise solution for inherently conflicting objective functions such as structural mass, control effort and number of actuators. Constraints are imposed on natural frequencies, peak transient displacements and accelerations, peak actuator forces and dynamic stability as well as controllability and observability of the system. The combinatorial aspects of the mixed (0, 1)‐continuous variable design optimization problem are made tractable by combining approximation concepts with branch and bound techniques. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.
Incompressibility without tears—HOW to avoid restrictions of mixed formulation
Authors: Zienkiewicz O. C. , Wu J.
Published: November 2005

The severe restrictions of the Babuška‐Brezzi stability criteria permit only a limited number of interpolations for velocities (displacements) and pressure to be used for incompressible behaviour. These restrictions preclude the use of many useful elements. We show in this paper how such difficulties can be side‐stepped by seeking the steady state solution through the use of various time marching schemes. This permits a simple iterative approach to incompressible (or nearly incompressible) problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow, etc.
Fourth order Runge‐Kutta method in 2d for linear boundary value problems
Authors: Demendy Zoltan
Published: November 2005

The standard formulae of the fourth order Runge‐Kutta method are transformed into a finite difference equation which allow us to solve linear boundary value problems. This equation is manipulated further and extended into 2D for solving second order linear partial differential equations. The various transformations result in four equations for the two first derivatives, mixed second derivative and the function value in the depicted point of the mesh. Each of these quantities is expressed by the linear combination of values of the function given in the eight nearest nodes around the depicted node. Explicit formulation of the equations for corner, boundary, symmetry and internal nodes is given. The results of the new computer code are compared with an analytical result and precise measurements, as well as a FEM calculation. It is concluded, for the specific example investigated, that the new method is about ten or more times precise than the FEM with the same number of elements. The major merit of the method lies in the fact that it can be implemented on personal computers.
Adaptive analysis of thin shells using facet elements
Authors: Hinton E. , Özakça M. , Rao N. V. R.
Published: November 2005

An adaptive mesh refinement (AMR) procedure is used in static thin shell analysis using triangular facet shell elements. The procedure described herein uses the h‐version of adaptive refinement based on an error estimate determined by using the best guess values of bending moments and membrane forces obtained from a previous solution. It includes the use of a relaxation factor to achieve better convergence. Some examples are presented to illustrate this method. The results obtained are compared with those of uniform mesh refinement (UMR).
Conjugate progector preconditioning for the solution of contact problems
Authors: Dostál Zdeněk
Published: November 2005

We present a new algorithm for numerical solution of contactproblems without friction. The method is based on enhancing conjugate projector preconditioning into the standard conjugate gradient method for the solution of quadratic programming problems with inequality constraints. We show that the algorithm is correct and discuss the efficiency of the algorithm. The relation of the algorithm to the domain decomposition methods is also explained. The paper is supplied with numerical experiment.
Grapplings with the simulation of non‐Newtonian flows in polymer processing
Authors: Shen Shan‐Fu
Published: November 2005

In computational mechanics, flow simulation of polymer processing not only must deal with exotic constitutive behaviour and complex geometry, but often faces the presence of moving free boundaries. The cavity‐filling of injection moulding, treated as a Stefan problem, could be better attacked, computationally, by a fixed‐domain approach after a Baiocchi transformation. For thermosetting materials, modelling the rheology and the chemical reaction needs the kinematics in the meniscus region behind the moving front. The fluid mechanics, however, touches on the unresolved question of the moving contact point, fundamental to wetting phenomena. Aspects of particular interest to polymer processing are reviewed. In spite of the imperfections, the simulation of the ASTM standard ‘spiral‐mould test’ for thermosets has recently proved promising as an inverse problem to characterize the rheology of a commercial fast‐reacting thermosetting material. The key was to match the simulation only to portions of the data that were least influenced by the uncertainties.
Numerical simulation of unsteady multiphase pipeline flow with virtual mass effect
Authors: Bournaski E.
Published: November 2005

Multiphase solid–liquid pipeline flow with small quantities of free gas is treated in the paper. A 1‐D separated unsteady flow model with liquid and gas virtual mass effect is described. A stable numerical method for the model equations based on the characteristics method is developed. Some accurate iteration procedures at every grid point for the solution of the algebraic equations are shown. The wave speed for flow in a pipeline worked out on the basis of this theoretical model shows a good correspondence with experimental results for two‐ and three‐phase mixtures.