Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Cleavage of hemoglobin by hookworm cathespin D aspartic proteases and its potential contribution to host specificity

Hookworms routinely reach the gut of nonpermissive hosts but fail to successfully feed, develop, and reproduce. To investigate the effects of host-parasite coevolution on the ability of hookworms to feed in nonpermissive hosts, we cloned and expressed aspartic proteases from canine and human hookworms. We show here that a cathepsin D-like protease from the canine hookworm Ancylosotoma caninum (Ac-APR-1) and the orthologous protease from the human hookworm Necator americanus (Na-APR-1) are expressed in the gut and probably exert their proteolytic activity extracellularly. Both proteases were detected immunologically and enzymatically in somatic extracts of adult worms. The two proteases were expressed in baculovirus, and both cleaved human and dog hemoglobin (Hb) in vitro. Each protease digested Hb from its permissive host between twofold (whole molecule) and sixfold (synthetic peptides) more efficiently than Hb from the nonpermissive host, despite the two proteases' having identical residues lining their active site clefts. Furthermore, both proteases cleaved Hb at numerous distinct sites and showed different substrate preferences. The findings suggest that the paradigm of matching the molecular structure of the food source within a host to the molecular structure of the catabolic proteases of the parasite is an important contributing factor for host-parasite compatibility and host species range.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) 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 Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Hookworm aspartic protease, Na-APR-2, cleaves human hemoglobin and serum proteins in a host-specific fashion

Hookworms are voracious blood-feeders. The cloning and functional expression of an aspartic protease, Na-APR-2, from the human hookworm Necator americanus are described here. Na-APR-2 is more similar to a family of nematode-specific, aspartic proteases than it is to cathepsin D or pepsin, and the term nemepsins for members of this family of nematode-specific hydrolases is proposed. Na-apr-2 mRNA was detected in blood-feeding, developmental stages only of N. americanus, and the protease was expressed in the intestinal lumen, amphids, and excretory glands. Recombinant Na-APR-2 cleaved human hemoglobin (Hb) and serum proteins almost twice as efficiently as the orthologous substrates from the nonpermissive dog host. Moreover, only 25% of the Na-APR-2 cleavage sites within human Hb were shared with those generated by the related N. americanus cathepsin D, Na-APR-1. Antiserum against Na-APR-2 inhibited migration of 50% of third-stage N. americanus larvae through skin, which suggests that aspartic proteases might be effective vaccines against human hookworm disease.

tRNASer(CGA) differentially regulates expression of wild-type and codon-modified papillomavirus L1 genes

Exogenous transfer RNAs (tRNAs) favor translation of bovine papillomavirus 1 wild-type (wt) L1 mRNA in in vitro translation systems (Zhou et al. 1999, J. Virol., 73, 4972-4982). We, therefore, investigated whether papillomavirus (PV) wt L1 protein expression could be enhanced in eukaryotic cells following exogenous tRNA supplementation. Both Chinese hamster ovary (CHO) and Cos1 cells, transfected with PV1 wt L1 genes, effectively transcribed the genes but did not translate them. However, L1 protein translation was demonstrated following co-transfection with the L1 gene and a gene expressing tRNA(Ser)(CGA). Cell lines, stably transfected with a bovine papillomavirus 1 (BPV1) wt L1 expression construct, produced L1 protein after the transfection of the tRNA(Ser)(CGA) gene, but not following the transfection with basal vectors, suggesting that tRNA(Ser)(CGA) gene enhanced wt L1 translation as a result of endogenous tRNA alterations and phosphorylation of translation initiation factors elF4E and elF2alpha in the tRNA(Ser)(CGA) transfected L1 cell lines. The tRNA(Ser)(CGA) gene expression significantly reduced translation of L1 proteins expressed from codon-modified (HB) PV L1 genes utilizing mammalian preferred codons, but had variable effects on translation of green fluorescent proteins (GFPs) expressed from six serine GFP variants. The changes of tRNA pools appear to match the codon composition of PV wt and HB L1 genes and serine GFP variants to regulate translation of their mRNAs. These findings demonstrate for the first time in eukaryotic cells that translation of the target genes can be differentially influenced by the provision of a single tRNA expression construct.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Crystalloid strong ion difference determines metabolic acid-base change during acute normovolaemic haemodilution

Objective. To study the acid-base effects of crystalloid strong ion difference (SID) during haemodilution. Design. Prospective in vivo study. Setting. University laboratory. Subjects. Anaesthetised, mechanically ventilated Sprague-Dawley rats. Interventions. Rats were studied in seven groups of three. Each group underwent normovolaemic haemodilution with one of seven crystalloids, with SID values from 0 to 40 mEq/l. Six exchanges of 9 ml crystalloid for 3 ml blood were performed. Measurements and main results. [Hb] fell from 142+/-17 to 44+/-10 g/l (p

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

The relative benefits of endurance and strength training on the metabolic factors and muscle function of people with type 2 diabetes mellitus

Objective: To compare the effects of a 4-month strength training (ST) versus aerobic endurance training (ET) program on metabolic control, muscle strength, and cardiovascular endurance in subjects with type 2 diabetes mellitus (T2D). Design: Randomized controlled trial. Setting: Large public tertiary hospital. Participants: Twenty-two T21) participants (I I men, I I women; mean age +/- standard error, 56.2 +/- 1.1 y; diabetes duration, 8.8 +/- 3.5y) were randomized into a 4-month ST program and 17 T2D participants (9 men, 8 women; mean age, 57.9 +/- 1.4y; diabetes duration, 9.2 +/- 1.7y) into a 4-month ET program. Interventions: ST (up to 6 sets per muscle group per week) and ET (with an intensity of maximal oxygen consumption of 60% and a volume beginning at 15min and advancing to a maximum of 30min 3X/wk) for 4 months. Main Outcome Measures: Laboratory tests included determinations of blood glucose, glycosylated hemoglobin (Hb A(1c)), insulin, and lipid assays. Results: A significant decline in Hb A, was only observed in the ST group (8.3% +/- 1.7% to 7.1% +/- 0.2%, P=.001). Blood glucose (204 +/- 16mg/dL to 147 +/- 8mg/dL, P <.001) and insulin resistance (9.11 +/- 1.51 to 7.15 +/- 1.15, P=.04) improved significantly in the ST group, whereas no significant changes were observed in the ET group. Baseline levels of total cholesterol (207 +/- 8mg/dL to 184 +/- 7mg/dL, P <.001), low-density lipoprotein cholesterol (120 +/- 8mg/dL to 106 +/- 8mg/dL, P=.001), and triglyceride levels (229 +/- 25mg/dL to 150 +/- 15mg/dL, P=.001) were significantly reduced and high-density lipoprotein cholesterol (43 +/- 3mg/dL to 48 +/- 2mg/dL, P=.004) was significantly increased in the ST group; in contrast, no such changes were seen in the ET group. Conclusions: ST was more effective than ET in improving glycemic control. With the added advantage of an improved lipid profile, we conclude that ST may play an important role in the treatment of T2D.

On the existence of solutions to boundary value problems on time scales

This work formulates existence theorems for solutions to two-point boundary value problems on time scales. The methods used include maximum principles, a priori bounds and topological degree theory.

Carotid artery intimal medial thickness, brachial artery flow-mediated vasodilation and cardiovascular risk factors in diabetic and non-diabetic indigenous Australians

Background: Indigenous Australians are at high risk for cardiovascular disease and type 2 diabetes. Carotid artery intimal medial thickness (CIMT) and brachial artery flow-mediated vasodilation (FMD) are ultrasound imaging based surrogate markers of cardiovascular risk. This study examines the relative contributions of traditional cardiovascular risk factors on CIMT and FMD in adult Indigenous Australians with and without type 2 diabetes mellitus. Method: One hundred and nineteen Indigenous Australians were recruited. Physical and biochemical markers of cardiovascular risk, together with CIMT and FMD were meausred for all subjects. Results: Fifty-three Indigenous Australians subjects (45%) had type 2 diabetes mellitus. There was a significantly greater mean CIMT in diabetic versus non-diabetic subjects (p = 0.049). In the non-diabetic group with non-parametric analyses, there were significant correlations between CIMT and: age (r = 0.64, p < 0.001), systolic blood pressure (r = 0.47, p < 0.001) and non-smokers (r = -0.30, p = 0.018). In the diabetic group, non-parametric analysis showed correlations between CIMT, age (r = 0.36, p = 0.009) and duration of diabetes (r = 0.30, p = 0.035) only. Adjusting forage, sex, smoking and history of cardiovascular disease, Hb(A1c) became the sole significant correlate of CIMT (r = 0.35,p = 0.01) in the diabetic group. In non-parametric analysis, age was the sole significant correlate of FMD (r = -0.31,p = 0.013), and only in non-diabetic subjects. Linear regression analysis showed significant associations between CIMT and age (t = 4.6,p < 0.001), systolic blood pressure (t = 2.6, p = 0.010) and Hb(A1c) (t = 2.6, p = 0.012), smoking (t = 2.1, p = 0.04) and fasting LDL-cholesterol (t = 2.1, p = 0.04). There were no significant associations between FMD and examined cardiovascular risk factors with linear regression analysis Conclusions: CIMT appears to be a useful surrogate marker of cardiovascular risk in this sample of Indigenous Australian subjects, correlating better than FMD with established cardiovascular risk factors. A lifestyle intervention programme may alleviate the burden of cardiovascular disease in Indigenous Australians by reducing central obesity, lowering blood pressure, correcting dyslipidaemia and improving glycaemic control. CIMT may prove to be a useful tool to assess efficacy of such an intervention programme. (c) 2004 Elsevier Ireland Ltd. All rights reserved.