Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Jacob Plaut Family Collection Interview Disc circa 1930-1940

Private press aluminum phonographic record sent to Jakob Plaut in Berlin by his sons Günther and Walter in Maine, United States, on his 58th birthday with their birthday wishes and an interview. Each side is only a few minutes long.

Middleware for Mobile Sensing Applications in Urban Environments

Sensor networks represent an attractive tool to observe the physical world. Networks of tiny sensors can be used to detect a fire in a forest, to monitor the level of pollution in a river, or to check on the structural integrity of a bridge. Application-specific deployments of static-sensor networks have been widely investigated. Commonly, these networks involve a centralized data-collection point and no sharing of data outside the organization that owns it. Although this approach can accommodate many application scenarios, it significantly deviates from the pervasive computing vision of ubiquitous sensing where user applications seamlessly access anytime, anywhere data produced by sensors embedded in the surroundings. With the ubiquity and ever-increasing capabilities of mobile devices, urban environments can help give substance to the ubiquitous sensing vision through Urbanets, spontaneously created urban networks. Urbanets consist of mobile multi-sensor devices, such as smart phones and vehicular systems, public sensor networks deployed by municipalities, and individual sensors incorporated in buildings, roads, or daily artifacts. My thesis is that "multi-sensor mobile devices can be successfully programmed to become the underpinning elements of an open, infrastructure-less, distributed sensing platform that can bring sensor data out of their traditional close-loop networks into everyday urban applications". Urbanets can support a variety of services ranging from emergency and surveillance to tourist guidance and entertainment. For instance, cars can be used to provide traffic information services to alert drivers to upcoming traffic jams, and phones to provide shopping recommender services to inform users of special offers at the mall. Urbanets cannot be programmed using traditional distributed computing models, which assume underlying networks with functionally homogeneous nodes, stable configurations, and known delays. Conversely, Urbanets have functionally heterogeneous nodes, volatile configurations, and unknown delays. Instead, solutions developed for sensor networks and mobile ad hoc networks can be leveraged to provide novel architectures that address Urbanet-specific requirements, while providing useful abstractions that hide the network complexity from the programmer. This dissertation presents two middleware architectures that can support mobile sensing applications in Urbanets. Contory offers a declarative programming model that views Urbanets as a distributed sensor database and exposes an SQL-like interface to developers. Context-aware Migratory Services provides a client-server paradigm, where services are capable of migrating to different nodes in the network in order to maintain a continuous and semantically correct interaction with clients. Compared to previous approaches to supporting mobile sensing urban applications, our architectures are entirely distributed and do not assume constant availability of Internet connectivity. In addition, they allow on-demand collection of sensor data with the accuracy and at the frequency required by every application. These architectures have been implemented in Java and tested on smart phones. They have proved successful in supporting several prototype applications and experimental results obtained in ad hoc networks of phones have demonstrated their feasibility with reasonable performance in terms of latency, memory, and energy consumption.

Role of Capping Ligands on the Nanoparticles in the Modulation of Properties of a Hybrid Matrix of Nanoparticles in a 2D Film and in a Supramolecular Organogel

We incorporate various gold nanoparticles (AuNPs) capped with different ligands in two-dimensional films and three-dimensional aggregates derived from N-stearoyl-L-alanine and N-lauroyl-L-alanine, respectively. The assemblies of N-stearoyl-L-alanine afforded stable films at the air-water interface. More compact assemblies were formed upon incorporation of AuNPs in the air-water interface of N-stearoyl-L-alanine. We then examined the effects of incorporation of various AuNPs functionalized with different capping ligands in three-dimensional assemblies of N-lauroyl-L-alanine, a compound that formed a gel in hydrocarbons. The profound influence of nanoparticle incorporation into physical gels was evident from evaluation of various microscopic and bulk properties. The interaction of AuNPs with the gelator assembly was found to depend critically on the capping ligands protecting the Au surface of the gold nanoparticles. Transmission electron microscopy (TEM) showed a long-range directional assembly of certain AuNPs along the gel fibers. Scanning electron microscopy (SEM) images of the freeze-dried gels and nanocomposites indicate that the morphological transformation in the composite microstructures depends significantly on the capping agent of the nanoparticles. Differential scanning calorimetry (DSC) showed that gel formation from sol occurred at a lower temperature upon incorporation of AuNPs having capping ligands that were able to align and noncovalently interact with the gel fibers. Rheological studies indicate that the gel-nanoparticle composites exhibit significantly greater viscoelasticity compared to the native gel alone when the capping ligands are able to interact through interdigitation into the gelator assembly. Thus, it was possible to define a clear relationship between the materials and the molecular-level properties by means of manipulation of the information inscribed on the NP surface.

Spray deposition of exfoliated MoS2 flakes as hole transport layer in perovskite-based photovoltaics

We propose the use of solution-processed molybdenum disulfide (MoS2) flakes as hole transport layer (HTL) for metal-organic perovskite solar cells. MoS2 bulk crystals are exfoliated in 2-propanol and deposited on perovskite layers by spray coating. We fabricated cells with glass/FTO/compact-TiO2/mesoporous-TiO2/CH3NH3PbI3/spiro- OMeTAD/Au structure and cells with the same structure but with MoS2 flakes as HTL instead of spiro-OMeTAD, the most widely used HTL. The electrical characterization of the cells with MoS2 as HTL show promising power conversion efficiency -η- of 3.9% with respect to cells with pristine spiro-OMeTAD (η=3.1%). Endurance test on 800-hour shelf life has shown higher stability for the MoS2–based cells (ΔPCE/PCE=-17%) with respect to the doped spiro-OMeTAD-based one (ΔPCE/PCE =-45%). Further improvements are expected with the optimization of the MoS2 deposition process

FSK bursts for efficient clutter rejection

The clutter-rejection properties of compact f.s.k. bursts with amplitude modulation are investigated. A procedure for computer-aided design of such signals is given. The loss of clutter performance on constraining the individual pulse amplitudes to be equal is evaluated.

Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.