Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

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.

Inference of phylogeny and taxonomy within the Didymozoidae (Digenea) from the second internal transcribed spacer (ITS2) of ribosomal DNA

DNA sequences of the second internal transcribed spacer (ITS2) of ribosomal DNA (rDNA) were determined for 11 species from four genera of Didymozoinae (Indodidymozoon, Helicodidymozoon, Rhopalotrema and Neometadidymozoon) and a species of the Lecithasteridae, Lecithaster stellatus. Sequences were used to test the validity of species recognised on morphological criteria and to infer phylogenetic relationships. Sequences of the 11 didymozoids differed by 0.5% to 19%. Our phylogenetic analyses: (i) indicate that species in the genera Helicodidymozoon and Rhopalotrema are a monophyletic group; (ii) support separation of the genus Helicodidymozoon from the genera Indodidymozoon and Neometadidymozoon; and (iii) support recognition of Rhopalotrema as a genus distinct from Neometadidymozoon. We found the gonochoristic species, I. pearsoni and I. suttiei, to be genetically similar to the hermaphroditic species in the genus Indodidymozoon and found no evidence to indicate that they belong in a separate genus.

A second Candida albicans resistance gene (Carg2) regulates tissue damage, but not fungal clearance, in sub-lethal murine systemic infection

The severity of systemic infection with the yeast Candida albicans has been shown to be under complex genetic control. C57/L mice carry an allele that is associated with an increase in tissue destruction when compared with C57BI/6 mice; however, the gene affects only the severity of tissue lesions, and does not influence the magnitude of the fungal burden in either kidney or brain. Studies in [C57/L x C57BI/6]F1 hybrid mice, and [C57/L x C57BI/6]F1 x C57/L backcross mice, demonstrated that the gene behaves as a simple Mendelian co-dominant. (C) 1998 Academic Press.

Quantum technology: the second quantum revolution

We are currently in the midst of a second quantum revolution. The first quantum revolution gave us new rules that govern physical reality. The second quantum revolution will take these rules and use them to develop new technologies. In this review we discuss the principles upon which quantum technology is based and the tools required to develop it. We discuss a number of examples of research programs that could deliver quantum technologies in coming decades including: quantum information technology, quantum electromechanical systems, coherent quantum electronics, quantum optics and coherent matter technology.

A second known species of Eratomyia Amorim & Rindal (Diptera, Rangomaramidae, Chiletrichinae) from Colombia

A second species of the genus Eratomyia Amorim & Rindal-E. risaralda, sp. n.-is described from Risaralda, Colombia, based on one male and three females. The female of Eratomyia is described for the first time. A number of striking modifications in the female terminalia shared with Chiletricha Chandler support the hypothesis that they are sister genera within the Rangomaramidae. The position of Chiletricha and Eratomyia within the Chiletrichinae is discussed.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

Existence results for abstract impulsive second-order neutral functional differential equations

We establish the existence of mild solutions for a class of impulsive second-order partial neutral functional differential equations with infinite delay in a Banach space. (C) 2009 Published by Elsevier Ltd

Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local mild solutions, the existence of global mild solutions and the existence of asymptotically almost periodic solutions.

Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system. (C) 2008 Elsevier Ltd. All rights reserved.

Existence of solutions for second order partial neutral functional differential equations

We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with unbounded delay in a Banach space.