Properly efficient and efficient solutions for vector maximization problems in euclidean space

AbstractRecently Benson proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone K is any nontrivial, closed convex cone. We give an equivalent definition of his notion of proper efficiency. Our definition, by means of perturbation of the cone K, seems to offer another justification of Benson's choice above Borwein's extension of Geoffrion's concept. Our result enables one to prove some other theorems concerning properly efficient and efficient points. Among these is a connectedness result

From simple to complicated:Noncausal bounded input, bounded output stability in linear discrete time models in the deterministic and stochastic cases

We consider the question of bounded input, bounded output stability for time-invariant linear systems with a finite dimensional state space and with time axis , i.e., all the integers. Our approach also includes the stochastic ARMA models. We do not assume that the inputs are necessarily nonanticipating, and in this respect our results differ from most existing ones. Similar results have been given by Hannan and Deistler and by Brockwell and Davis. Our approach is polynomial-algebra-oriented, and does not use strictly rational functions

Weakly Equivalent Arrays

The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and extensionality axioms originally proposed by McCarthy. Various filters are used to limit the number of axiom instantiations while preserving completeness. We present an algorithm that lazily instantiates lemmas based on weak equivalence classes. These lemmas are easier to interpolate as they only contain existing terms. We formally define weak equivalence and show correctness of the resulting decision procedure

Biodegradable hollow fibres for the controlled release of drugs

Biodegradable hollow fibres of poly-l-lactic acid (PLLA) filled with a suspension of the contraceptive hormone levonorgestrel in castor oil were implanted subcutaneously in rats to study the rate of drug release, rate of biodegradation and tissue reaction caused by the implant. The in vivo drug release was compared with the release in vitro using different release media. Fibres, disinfected with alcohol showed a zero-order release, both in vitro and in vivo, for over 6 months. Fibres, either γ-sterilized or disinfected with alcohol were harvested at time intervals ranging from 1 d to 6 months after implantation. Molecular weights of PLLA, tensile strengths, and remaining amounts of drug were determined as a function of time.\ud \ud The tissue reaction can be described as a very moderate foreign body reaction with the initial presence of macrophages, which are gradually replaced by fibroblasts which form a collagen capsule. Molecular weight determinations of PLLA showed a decrease from an initial Mw of 1.59x10 5 to 5.5 × 10 4 in 4 months (after alcohol sterilization). A gradual decrease in fibre strength with time was observed which did not significantly impair the release rate of levonorgestrel

Nonperturbative study of generalized ladder graphs in a \phi^2\chi theory

The Feynman-Schwinger representation is used to construct scalar-scalar bound states for the set of all ladder and crossed-ladder graphs in a \phi^2\chi theory in (3+1) dimensions. The results are compared to those of the usual Bethe-Salpeter equation in the ladder approximation and of several quasi-potential equations. Particularly for large couplings, the ladder predictions are seen to underestimate the binding energy significantly as compared to the generalized ladder case, whereas the solutions of the quasi-potential equations provide a better correspondence. Results for the calculated bound state wave functions are also presented.Comment: 5 pages revtex, 3 Postscripts figures, uses epsf.sty, accepted for publication in Physical Review Letter

Relativistic bound-state equations in three dimensions

Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the relative four-momentum. In the absence of negative-energy states, the kernels of the three-dimensional equations derived by this technique may be represented as sums of time-ordered perturbation theory diagrams. Consequently, such equations have two major advantages over quasi-potential equations: they may easily be written down in any Lorentz frame, and they include the meson-retardation effects present in the original four-dimensional equation. Secondly, a simple four-dimensional equation with the correct one-body limit is obtained by a reorganization of the generalized ladder Bethe-Salpeter kernel. Thirdly, our approach to deriving three-dimensional equations is applied to this four-dimensional equation, thus yielding a retarded interaction for use in the three-dimensional bound-state equation of Wallace and Mandelzweig. The resulting three-dimensional equation has the correct one-body limit and may be systematically improved upon. The quality of the three-dimensional equation, and our general technique for deriving such equations, is then tested by calculating bound-state properties in a scalar field theory using six different bound-state equations. It is found that equations obtained using the method espoused here approximate the wave functions obtained from their parent four-dimensional equations significantly better than the corresponding quasi-potential equations do.Comment: 28 pages, RevTeX, 6 figures attached as postscript files. Accepted for publication in Phys. Rev. C. Minor changes from original version do not affect argument or conclusion