Analysis Of Several Variables Research Articles

Perturbation of Invariant Subspaces

The questions of how perturbation of an operator affects its invariant subspaces have raised a substantial amount of interest, especially in the Ž w x . finite dimensions see, e.g., 5, 10]12 and the references given there . It turns out that linear perturbation of the operator gives rise to an analytic perturbation of the projection on its invariant subspace under some reasonable conditions. Although the question of estimating the norms of the terms of the Taylor series’ expansion of this projection-valued function does have some applications in numerical analysis, it seems to be studied w x less frequently. For instance, in 12 the matrix algebra approach combined with complex analysis in several variables was used to get existence and analyticity of the perturbed projection. The terms were obtained as well, using specially developed formulas for their direct computation. However, we find it hard to see that these estimates are good enough to ensure the convergence of this series, let alone to give an estimate of its radius of convergence. In this article we propose a different approach to the subject which achieves the two goals at one stroke and, we believe, with better results. Namely, we study the problem in terms of operator-valued analytic functions, thus reducing the problem to solving an algebraic Riccati-type equation. In order to solve it we extend in Sections 2 and 3 somewhat the Ž usual methods to our case see the comments about the meaning of . ‘‘usual’’ in the last paragraph of the introduction . The main result, given in Section 4, is the estimates of the radius of convergence and of the terms. The estimates are clearly good enough to yield an estimated radius of

Optimal interval for triple-lumen catheter changes: a decision analysis.

A survey of 53 university and community hospitals revealed that 73% of the institutions had no standard policy for the replacement of triple-lumen catheters (TLCs). Since the maintenance of a TLC in place for a prolonged period may lead to infectious complications, it appeared warranted that standards of management be developed. A decision-tree model was constructed for evaluating the optimal time for changing a TLC that would minimize infection. Cost estimates and health effects at three-, five-, and ten-day change intervals were considered for catheter insertion and complications resulting from such insertion. The results suggested that prophylactic catheter changes should occur no later than every five days, provided that there are no signs of infection. However, sensitivity analysis of several variables suggested that individual institutions should establish policy timing changes based upon careful interpretation of their own data. A model was developed to assist in determining the optimal time to change a TLC based upon such data.

The effect of maternal bearing-down efforts on arterial umbilical cord pH and length of the second stage of labor

This study was conducted to compare two types of maternal bearing-down techniques as they relate to the fetal and maternal outcomes of arterial umbilical cord blood pH and length of the second stage of labor. A convenience sample was drawn from the laboring women at a 305-bed medical center who met specific inclusion criteria. Women self-selected to one of two bearing-down groups: spontaneous or Valsalva. Subjects were given specific instructions for the chosen method. The Valsalva group was comprised of 14 subjects, and the spontaneous group was comprised of 16 subjects. The groups were found to be comparable after analysis of several variables. Results of statistical analysis using t-test indicated that, in this small sample, there is no relationship between the second stage bearing-down method and arterial umbilical cord blood pH or length of the second stage of labor. These findings support the conclusions of several studies: using the spontaneous bearing-down method does not have a deleterious effect upon the mother or the fetus. Several recommendations are made for future research based on methodological issues raised during this study.

Spectral properties of Schrödinger operators with magnetic fields for a spin [formula omitted] particle

We discuss the spectral properties of Schrödinger operators with magnetic fields, especially for a spin 1 2 particle. We are interested in the essential spectrum and the discrete spectrum. We classified the spectrum by the asymptotic behavior of the magnetic field at infinity. Our main tools are the supersymmetry and the complex analysis in several variables. We show that 0 is an eigenvalue with infinite multiplicity under suitable conditions.

Comparative Structural Life Assessment of Patrol Boat Bottom Plating

The estimation of an absolute life expectancy of a structure is a complex process and the results are expected to have relatively large levels of uncertainty. In this study, a comparative analysis is undertaken between two different patrol boats. This is an approach which results in a higher confidence level because certain factors common to both boats can be eliminated by assuming them to be at constant normal levels. The study is limited to the critical forward bottom plating and takes into account the differences in material, plate dimensions, operational profile, structure and loading of the two vessels. Two failure modes, plastic plate deformation and fatigue, are considered, and a novel approach to plate wastage is included. Many factors affect the structural life of a vessel. They include structural type, operational profile, structural details, loads, inspection and maintenance, design methods, safety factors, corrosion, and environmental factors. There are three types of uncertainty associated with these factors; namely, physical randomness, statistical uncertainties, and model uncertainties. The method described is designed to address these uncertainties. The objective of the paper is to present the reliability-based structural life assessment method, and then to use it to evaluate and compare the structural performance of the forward bottom plating of the two patrol boats. The results of the evaluation are presented in the form of graphs and tables in order to facilitate the comparative evaluation. The method is performed within a computer-based format which allows parametric sensitivity analysis of several variables including the size of the plating panel, thickness, operational profile and loading. The sensitivity of the structural life expectancy of the forward bottom plating to variations in these parameters is evaluated.

A several complex variables approach to feedback stabilization of linear neutral delay-differential systems

In this paper we consider the problem of uniform asymptotic stabilization of neutral delay differential systems by a suitable choice of linear feedback law, where the controller is static and at timet 0 has full knowledge ofx(t 0) ∈ ℝ n as well asx(t 0 − d) for finitely many delays present in the system. Using complex analysis in several variables in a Banach algebra context we present a solution to this problem in the form of a sufficient condition for the existence of such a stabilizing feedback gain. This condition is a weak form of (algebraic) reachability together with a condition, which we call resolvability, on the solution of an associated algebraic Riccati equation. In the case of commensurable delays our results apply to neutral systems having aD-operator which is stable in the sense of Cruz and Hale. In the non-commensurate case, our results hold for systems with aD-operator satisfying a stronger condition on the spectrum of the evolution equation, which we call formal stability. A graphical criterion, in the spirit of the multi-dimensional Nyquist theory, is presented for formal stability ofD. We find these results especially interesting in light of recent work [39] which shows that, for a special class of systems, formal stability is necessary for stabilization by a feedback gain of the type considered here. This, in fact, gives a counterexample [39] to the well known condition of Pandolfi [40]. Included among our results is an extension to the neutral case of the result in [11] which states that if the pointwise Kronecker indices are constant then the system is feedback equivalent to a delay-free system. As corollaries to this result we obtain some existing results [33] on canonical forms for time-delay systems, and, in addition, exhibit a large class of systems which are resolvable.

An Introduction to Complex Analysis in Several Variables, by L. Hormander. Van Nostrand, University series in higher Mathematics, 1966. 208 pages. $8.20.

An Introduction to Complex Analysis in Several Variables, by L. Hormander. Van Nostrand, University series in higher Mathematics, 1966. 208 pages. $8.20.