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.

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters is an element of and lambda respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Lambda(1) x A(2) -> 2(X) for such parametric implicit vector equilibrium problems. (c) 2005 Elsevier 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.

Measurement-based teleportation along quantum spin chains

We examine the teleportation of an unknown spin-1/2 quantum state along a quantum spin chain with an even number of sites. Our protocol, using a sequence of Bell measurements, may be viewed as an iterated version of the 2-qubit protocol of C. H. Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)]. A decomposition of the Hilbert space of the spin chain into 4 vector spaces, called Bell subspaces, is given. It is established that any state from a Bell subspace may be used as a channel to perform unit fidelity teleportation. The space of all spin-0 many-body states, which includes the ground states of many known antiferromagnetic systems, belongs to a common Bell subspace. A channel-dependent teleportation parameter O is introduced, and a bound on the teleportation fidelity is given in terms of O.

Control of vector-borne disease by genetic manipulation of insect populations: technological requirements and research priorities

The possibility of controlling vector-borne disease through the development and release of transgenic insect vectors has recently gained popular support and is being actively pursued by a number of research laboratories around the world. Several technical problems must be solved before such a strategy could be implemented: genes encoding refractory traits (traits that render the insect unable to transmit the pathogen) must be identified, a transformation system for important vector species has to be developed, and a strategy to spread the refractory trait into natural vector populations must be designed. Recent advances in this field of research make it seem likely that this technology will be available in the near future. In this paper we review recent progress in this area as well as argue that care should be taken in selecting the most appropriate disease system with which to first attempt this form of intervention. Much attention is currently being given to the application of this technology to the control of malaria, transmitted by Anopheles gambiae in Africa. While malaria is undoubtedly the most important vector-borne disease in the world and its control should remain an important goal, we maintain that the complex epidemiology of malaria together with the intense transmission rates in Africa may make it unsuitable for the first application of this technology. Diseases such as African trypanosomiasis, transmitted by the tsetse fly, or unstable malaria in India may provide more appropriate initial targets to evaluate the potential of this form of intervention.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

Long-Term Effects of Specific Stabilizing Exercises for First-Episode Low Back Pain

Study Design. A randomized clinical trial with 1-year and 3-year telephone questionnaire follow-ups. Objective. To report a specific exercise intervention’s long-term effects on recurrence rates in acute, first-episode low back pain patients. Summary of Background Data. The pain and disability associated with an initial episode of acute low back pain (LBP) is known to resolve spontaneously in the short-term in the majority of cases. However, the recurrence rate is high, and recurrent disabling episodes remain one of the most costly problems in LBP. A deficit in the multifidus muscle has been identified in acute LBP patients, and does not resolve spontaneously on resolution of painful symptoms and resumption of normal activity. Any relation between this deficit and recurrence rate was investigated in the long-term. Methods. Thirty-nine patients with acute, first-episode LBP were medically managed and randomly allocated to either a control group or specific exercise group. Medical management included advice and use of medications. Intervention consisted of exercises aimed at rehabilitating the multifidus in cocontraction with the transversus abdominis muscle. One year and three years after treatment, telephone questionnaires were conducted with patients. Results. Questionnaire results revealed that patients from the specific exercise group experienced fewer recurrences of LBP than patients from the control group. One year after treatment, specific exercise group recurrence was 30%, and control group recurrence was 84% (P , 0.001). Two to three years after treatment, specific exercise group recurrence was 35%, and control group recurrence was 75% (P , 0.01). Conclusion. Long-term results suggest that specific exercise therapy in addition to medical management and resumption of normal activity may be more effective in reducing low back pain recurrences than medical management and normal activity alone. [Key Words: multifidus, low back pain, rehabilitation]

Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces

In the present paper, we establish two fixed point theorems for upper semicontinuous multivalued mappings in hyperconvex metric spaces and apply these to study coincidence point problems and minimax problems. (C) 2002 Elsevier Science (USA). 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.

The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

Longitudinal excursion and strain in the median nerve during novel nerve gliding exercises for carpal tunnel syndrome

Nerve and tendon gliding exercises are advocated in the conservative and postoperative management of carpal tunnel syndrome (CTS). However, traditionally advocated exercises elongate the nerve bedding substantially, which may induce a potentially deleterious strain in the median nerve with the risk of symptom exacerbation in some patients and reduced benefits from nerve gliding. This study aimed to evaluate various nerve gliding exercises, including novel techniques that aim to slide the nerve through the carpal tunnel while minimizing strain (sliding techniques). With these sliding techniques, it is assumed that an increase in nerve strain due to nerve bed elongation at one joint (e.g., wrist extension) is simultaneously counterbalanced by a decrease in nerve bed length at an adjacent joint (e.g., elbow flexion). Excursion and strain in the median nerve at the wrist were measured with a digital calliper and miniature strain gauge in six human cadavers during six mobilization techniques. The sliding technique resulted in an excursion of 12.4 mm, which was 30% larger than any other technique (p 0.0002). Strain also differed between techniques (p 0.00001), with minimal peak values for the sliding technique. Nerve gliding associated with wrist movements can be considerably increased and nerve strain substantially reduced by simultaneously moving neighboring joints. These novel nerve sliding techniques are biologically plausible exercises for CTS that deserve further clinical evaluation. © 2007 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 25:972-980, 2007

A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.