Lt. Colonel Rachel (Rae) Diane Landy papers undated, 1913-2000

Rachel Diane Landy Papers consist of correspondence, reminiscences, legal documents, journal, newspaper and magazine articles and color Xerox copies of photographs as well as original photographs. This collection is of value to researchers studying the history of Hadassah and the living conditions and state of medical care in Palestine during the second decade of the 20th century. It is also of interest to researchers studying women in America during the first half of the 20th century who were able to pursue a challenging and productive career and become a leader and innovator in their chosen field. In addition it will be of interest to those researching the graduates of the Cleveland public and professional schools at the end of the 19th and beginning of the 20th centuries, and the Cleveland Jewish community and the George Crile U.S. Army Hospital in Cleveland during the 1940's.

Multipliers of Sobolev spaces

Let Wm,p denote the Sobolev space of functions on Image n whose distributional derivatives of order up to m lie in Lp(Image n) for 1 less-than-or-equals, slant p less-than-or-equals, slant ∞. When 1 < p < ∞, it is known that the multipliers on Wm,p are the same as those on Lp. This result is true for p = 1 only if n = 1. For, we prove that the integrable distributions of order less-than-or-equals, slant1 whose first order derivatives are also integrable of order less-than-or-equals, slant1, belong to the class of multipliers on Wm,1 and there are such distributions which are not bounded measures. These distributions are also multipliers on Lp, for 1 < p < ∞. Moreover, they form exactly the multiplier space of a certain Segal algebra. We have also proved that the multipliers on Wm,l are necessarily integrable distributions of order less-than-or-equals, slant1 or less-than-or-equals, slant2 accordingly as m is odd or even. We have obtained the multipliers from L1(Image n) into Wm,p, 1 less-than-or-equals, slant p less-than-or-equals, slant ∞, and the multiplier space of Wm,1 is realised as a dual space of certain continuous functions on Image n which vanish at infinity.

Construction of Stability Multipliers with Prescribed Phase Characteristics: an Improved Value for $\sigma

For a feedback system consisting of a transfer function $G(s)$ in the forward path and a time-varying gain $n(t)(0 \leqq n(t) \leqq k)$ in the feedback loop, a stability multiplier $Z(s)$ has been constructed (and used to prove stability) by Freedman [2] such that $Z(s)(G(s) + {1 / K})$ and $Z(s - \sigma )(0 < \sigma < \sigma _ * )$ are strictly positive real, where $\sigma _ * $ can be computed from a knowledge of the phase-angle characteristic of $G(i\omega ) + {1 / k}$ and the time-varying gain $n(t)$ is restricted by $\sigma _ * $ by means of an integral inequality. In this note it is shown that an improved value for $\sigma _ * $ is possible by making some modifications in his derivation. ©1973 Society for Industrial and Applied Mathematics.

Lake sediment research as a part of lake management - case studies and implications from southern Finland

In Finland one of the most important current issues in the environmental management is the quality of surface waters. The increasing social importance of lakes and water systems has generated wide-ranging interest in lake restoration and management, concerning especially lakes suffering from eutrophication, but also from other environmental impacts. Most of the factors deteriorating the water quality in Finnish lakes are connected to human activities. Especially since the 1940's, the intensified farming practices and conduction of sewage waters from scattered settlements, cottages and industry have affected the lakes, which simultaneously have developed in to recreational areas for a growing number of people. Therefore, this study was focused on small lakes, which are human impacted, located close to settlement areas and have a significant value for local population. The aim of this thesis was to obtain information from lake sediment records for on-going lake restoration activities and to prove that a well planned, properly focused lake sediment study is an essential part of the work related to evaluation, target consideration and restoration of Finnish lakes. Altogether 11 lakes were studied. The study of Lake Kaljasjärvi was related to the gradual eutrophication of the lake. In lakes Ormajärvi, Suolijärvi, Lehee, Pyhäjärvi and Iso-Roine the main focus was on sediment mapping, as well as on the long term changes of the sedimentation, which were compared to Lake Pääjärvi. In Lake Hormajärvi the role of different kind of sedimentation environments in the eutrophication development of the lake's two basins were compared. Lake Orijärvi has not been eutrophied, but the ore exploitation and related acid main drainage from the catchment area have influenced the lake drastically and the changes caused by metal load were investigated. The twin lakes Etujärvi and Takajärvi are slightly eutrophied, but also suffer problems associated with the erosion of the substantial peat accumulations covering the fringe areas of the lakes. These peat accumulations are related to Holocene water level changes, which were investigated. The methods used were chosen case-specifically for each lake. In general, acoustic soundings of the lakes, detailed description of the nature of the sediment and determinations of the physical properties of the sediment, such as water content, loss on ignition and magnetic susceptibility were used, as was grain size analysis. A wide set of chemical analyses was also used. Diatom and chrysophycean cyst analyses were applied, and the diatom inferred total phosphorus content was reconstructed. The results of these studies prove, that the ideal lake sediment study, as a part of a lake management project, should be two-phased. In the first phase, thoroughgoing mapping of sedimentation patterns should be carried out by soundings and adequate corings. The actual sampling, based on the preliminary results, must include at least one long core from the main sedimentation basin for the determining the natural background state of the lake. The recent, artificially impacted development of the lake can then be determined by short-core and surface sediment studies. The sampling must be focused on the basis of the sediment mapping again, and it should represent all different sedimentation environments and bottom dynamic zones, considering the inlets and outlets, as well as the effects of possible point loaders of the lake. In practice, the budget of the lake management projects of is usually limited and only the most essential work and analyses can be carried out. The set of chemical and biological analyses and dating methods must therefore been thoroughly considered and adapted to the specific management problem. The results show also, that information obtained from a properly performed sediment study enhances the planning of the restoration, makes possible to define the target of the remediation activities and improves the cost-efficiency of the project.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

Inverse Problem for Fractional Brownian Motion with Discrete Data

The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

Integral Transformations of Volterra Gaussian Processes

We study integral representations of Gaussian processes with a pre-specified law in terms of other Gaussian processes. The dissertation consists of an introduction and of four research articles. In the introduction, we provide an overview about Volterra Gaussian processes in general, and fractional Brownian motion in particular. In the first article, we derive a finite interval integral transformation, which changes fractional Brownian motion with a given Hurst index into fractional Brownian motion with an other Hurst index. Based on this transformation, we construct a prelimit which formally converges to an analogous, infinite interval integral transformation. In the second article, we prove this convergence rigorously and show that the infinite interval transformation is a direct consequence of the finite interval transformation. In the third article, we consider general Volterra Gaussian processes. We derive measure-preserving transformations of these processes and their inherently related bridges. Also, as a related result, we obtain a Fourier-Laguerre series expansion for the first Wiener chaos of a Gaussian martingale. In the fourth article, we derive a class of ergodic transformations of self-similar Volterra Gaussian processes.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Transfer of Dietary Plant Natural Flavor Compounds From Essential Oils to Maternal Fluids in Pigs

Fetal flavor conditioning during the perinatal stage could be essential at the time of the weaning to reduce the stress and improve the feed intake in pigs. The transfer of flavor compounds from maternal diet to amniotic fluid and milk has been shown in behavioral experiments, but not through analytical procedures such as gas chromatography–mass spectrometry (GC–MS). The aim of the experiment was to trace the principal essential oils compounds supplied in the diet in maternal fluids. Twenty Large White sows around their 104th gestational day were allocated to individual farrowing crates. Two groups of 10 sows were fed either a standard gestation diet or the same diet supplemented with a mix of 8 essential oils at a rate of 1kg/ton during the last 10 days of gestation. At approximately the 113th gestational day, animals were individually treated with 10mg of Lutalyse IM was to induce farrowing. Fresh amniotic fluid was collected during the farrowing in 100-mL glass bottles and immediately stored at −20 °C freezer. During the second lactation day, 10–20 IU of Oxytocin IM was administered to each sow to facilitate collection of milk samples in 20-mL glass bottles. The samples were stored at −20 °C until analyzed by GC–MS. The presence of significant amounts of principal components of all the essential oils except one were found in the milk and amniotic fluid samples of the treated sows relative to the control sows. Our data prove the transfer of selected dietary flavors to maternal fluids and sets the scenario for further trials to manipulate postweaning behavior in piglets.

Isotope shifts and hyperfine structure in the 555.8-nm S-1(0) -> P-3(1) line of Yb

We apply our technique of using a Rb-stabilized ring-cavity resonator to measure the frequencies of various spectral components in the 555.8-nm 1S0-->3P1 line of Yb. We determine the isotope shifts with 60 kHz precision, which is an order-of-magnitude improvement over the best previous measurement on this line. There are two overlapping transitions, 171Yb(1/2-->3/2) and 173Yb(5/2-->3/2), which we resolve by applying a magnetic field. We thus obtain the hyperfine constants in the 3P1 state of the odd isotopes with a significantly improved precision. Knowledge of isotope shifts and hyperfine structure should prove useful for high-precision calculations in Yb necessary to interpret ongoing experiments testing parity and time-reversal symmetry violation in the laws of physics.

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

A new type of high-order elements based on the mesh-free interpolations

We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].

Nanoindentation study on germania-doped silica glass preforms: evidence for the compaction-densification model of photosensitivity

Nanoindentation technique was employed to measure the changes in mechanical properties of a glass preform subjected to different levels of UV exposure. The results reveal that short-term exposure leads to an appreciable increase in the Young's modulus (E), suggesting the densification of the glass, confirming the compaction-densification model. However, on prolonged exposure, E decreases, which provides what we believe to be the first direct evidence of dilation in the glass leading into the Type IIA regime. The present results rule out the hypothesis that continued exposure leads to an irreversible compaction and prove that index modulation regimes are intrinsic to the glass matrix.