A study of second order nonlinear systems

This paper studies a class of second order forced oscillation systems with nonlinear damping and nonlinear restoring forces. The boundedness of the solutions is obtained by recognizing the behavior of the solution path in the phase plane. All solutions are shown to converge to a unique solution provided the characteristics of the nonlinear terms are sufficiently smooth. The convergence of solutions is investigated by studying the asymptotic stability of a second order linear equation with time-varying parameters formed from the nonlinear system. Based on the Second Method of Lyapunov, two different V functions are used to obtain different sufficient conditions on the asymptotic stability of the linear system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32120/1/0000171.pd

Stability and performance analysis of a certain class of nonlinear time varying feedback control systems

The partitioning technique and the state variable approach have been applied to analyze and to study the behaviour of a control system whose dynamic performance can in general be described by a nonlinear differential equation containing some linear, some nonlinear, and a forcing function terms. By placing suitable restrictions on the system equation, it was found that the state variables, which represent the state of the system, belong to an L2 space. Under the assumed restrictions, the admissible system was found to satisfy the definition of asymptotic stability in the sense of Lyapunov. Utilizing two different definitions of the norm, the system trajectory was analyzed. During the interval of operation considered, expressions for the required norms were obtained inside which all possible states of system remain. Included will be found an example to illustrate the method presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32102/1/0000152.pd

An optimal gas-fired heating system

Utilizing a prescribed system configuration, this paper discusses the mathematical models of the system components used and formulates a method for controlling a domestic heating system in accordance to a prescribed criterion. The optimal problem treated is one of reducing the room temperature deviation from a prescribed reference value to zero, while at the same time minimizing the value of some predetermined performance or cost functional J. The development proceeds in essentially five steps. 1. (a) The development of the mathematical models for each of the elements of the heating system;2. (b) Combining the mathematical models into a form which is suitable for the application of optimization techniques;3. (c) Defining an optimization criterion which incorporates the main objective for minimizing room temperature variations with respect to a prescribed reference temperature;4. (d) Choosing the optimization technique best suited for the problem;5. (e) Constructing an optimal control system employing the optimization technique developed.A numerical example compares the performance of the optimal system with a system of the conventional type which can be found in many American homes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32877/1/0000255.pd

Minimum energy problems in Hilbert function space

Minimum energy problems in Hilbert function space are formulated. The methods presented are applicable to both continuous and discrete linear systems. Transformation of a particular operator equation into a set of 2n linear differential equations is described. Applications to physical systems are illustrated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33378/1/0000776.pd

Second surgery for progressive glioblastoma: a multi‐centre questionnaire and cohort‐based review of clinical decision‐making and patient outcomes in current practice

PURPOSE: Glioblastoma prognosis is poor. Treatment options are limited at progression. Surgery may benefit, but no quality guidelines exist to inform patient selection. We sought to describe variations in surgical management at progression, highlight where further evidence is needed, and build towards a consensus strategy. METHODS: Current practice in selection of patients with progressive GBM for second surgery was surveyed online amongst specialists in the UK and Europe. We complemented this with an assessment of practice in a retrospective cohort study from six United Kingdom neurosurgical units. We used descriptive statistics to analyse the data. RESULTS: 234 questionnaire responses were received. Maintaining or improving patient quality of life was key to decision making, with variation as to whether patient age, performance status or intended extent of resection was relevant. MGMT methylation status was not important. Half considered no minimum time after first surgery. 288 patients were reported in the cohort analysis. Median time to second surgery from first surgery 390 days. Median overall survival 815 days, with no association between time to second surgery and time to death (p = 0.874). CONCLUSIONS: This is the most wide-ranging examination of contemporaneous practice in management of GBM progression. Without evidence-based guidelines, the variation is unsurprising. We propose consensus guidelines for consideration, to reduce heterogeneity in decision making, support data collection and analysis of factors influencing outcomes, and to inform clinical trials to establish whether second surgery improves patient outcomes, or simply selects to patients already performing well

Evaluating and Minimizing Distributed Cavity Phase Errors in Atomic Clocks

We perform 3D finite element calculations of the fields in microwave cavities and analyze the distributed cavity phase errors of atomic clocks that they produce. The fields of cylindrical cavities are treated as an azimuthal Fourier series. Each of the lowest components produces clock errors with unique characteristics that must be assessed to establish a clock's accuracy. We describe the errors and how to evaluate them. We prove that sharp structures in the cavity do not produce large frequency errors, even at moderately high powers, provided the atomic density varies slowly. We model the amplitude and phase imbalances of the feeds. For larger couplings, these can lead to increased phase errors. We show that phase imbalances produce a novel distributed cavity phase error that depends on the cavity detuning. We also design improved cavities by optimizing the geometry and tuning the mode spectrum so that there are negligible phase variations, allowing this source of systematic error to be dramatically reduced.Comment: To appear in Metrologi

Molecular Characterisation of Long-Acting Insulin Analogues in Comparison with Human Insulin, IGF-1 and Insulin X10

AIMS/HYPOTHESIS: There is controversy with respect to molecular characteristics of insulin analogues. We report a series of experiments forming a comprehensive characterisation of the long acting insulin analogues, glargine and detemir, in comparison with human insulin, IGF-1, and the super-mitogenic insulin, X10. METHODS: We measured binding of ligands to membrane-bound and solubilised receptors, receptor activation and mitogenicity in a number of cell types. RESULTS: Detemir and glargine each displayed a balanced affinity for insulin receptor (IR) isoforms A and B. This was also true for X10, whereas IGF-1 had a higher affinity for IR-A than IR-B. X10 and glargine both exhibited a higher relative IGF-1R than IR binding affinity, whereas detemir displayed an IGF-1R:IR binding ratio of ≤ 1. Ligands with high relative IGF-1R affinity also had high affinity for IR/IGF-1R hybrid receptors. In general, the relative binding affinities of the analogues were reflected in their ability to phosphorylate the IR and IGF-1R. Detailed analysis revealed that X10, in contrast to the other ligands, seemed to evoke a preferential phosphorylation of juxtamembrane and kinase domain phosphorylation sites of the IR. Sustained phosphorylation was only observed from the IR after stimulation with X10, and after stimulation with IGF-1 from the IGF-1R. Both X10 and glargine showed an increased mitogenic potency compared to human insulin in cells expressing many IGF-1Rs, whereas only X10 showed increased mitogenicity in cells expressing many IRs. CONCLUSIONS: Detailed analysis of receptor binding, activation and in vitro mitogenicity indicated no molecular safety concern with detemir

Seasonal differences in leaf-level physiology give lianas a competitive advantage over trees in a tropical seasonal forest

Lianas are an important component of most tropical forests, where they vary in abundance from high in seasonal forests to low in aseasonal forests. We tested the hypothesis that the physiological ability of lianas to fix carbon (and thus grow) during seasonal drought may confer a distinct advantage in seasonal tropical forests, which may explain pan-tropical liana distributions. We compared a range of leaf-level physiological attributes of 18 co-occurring liana and 16 tree species during the wet and dry seasons in a tropical seasonal forest in Xishuangbanna, China. We found that, during the wet season, lianas had significantly higher CO2 assimilation per unit mass (Amass), nitrogen concentration (Nmass), and δ13C values, and lower leaf mass per unit area (LMA) than trees, indicating that lianas have higher assimilation rates per unit leaf mass and higher integrated water-use efficiency (WUE), but lower leaf structural investments. Seasonal variation in CO2 assimilation per unit area (Aarea), phosphorus concentration per unit mass (Pmass), and photosynthetic N-use efficiency (PNUE), however, was significantly lower in lianas than in trees. For instance, mean tree Aarea decreased by 30.1% from wet to dry season, compared with only 12.8% for lianas. In contrast, from the wet to dry season mean liana δ13C increased four times more than tree δ13C, with no reduction in PNUE, whereas trees had a significant reduction in PNUE. Lianas had higher Amass than trees throughout the year, regardless of season. Collectively, our findings indicate that lianas fix more carbon and use water and nitrogen more efficiently than trees, particularly during seasonal drought, which may confer a competitive advantage to lianas during the dry season, and thus may explain their high relative abundance in seasonal tropical forests

Is there a common water-activity limit for the three domains of life?

Archaea and Bacteria constitute a majority of life systems on Earth but have long been considered inferior to Eukarya in terms of solute tolerance. Whereas the most halophilic prokaryotes are known for an ability to multiply at saturated NaCl (water activity (a w) 0.755) some xerophilic fungi can germinate, usually at high-sugar concentrations, at values as low as 0.650-0.605 a w. Here, we present evidence that halophilic prokayotes can grow down to water activities of <0.755 for Halanaerobium lacusrosei (0.748), Halobacterium strain 004.1 (0.728), Halobacterium sp. NRC-1 and Halococcus morrhuae (0.717), Haloquadratum walsbyi (0.709), Halococcus salifodinae (0.693), Halobacterium noricense (0.687), Natrinema pallidum (0.681) and haloarchaeal strains GN-2 and GN-5 (0.635 a w). Furthermore, extrapolation of growth curves (prone to giving conservative estimates) indicated theoretical minima down to 0.611 a w for extreme, obligately halophilic Archaea and Bacteria. These were compared with minima for the most solute-tolerant Bacteria in high-sugar (or other non-saline) media (Mycobacterium spp., Tetragenococcus halophilus, Saccharibacter floricola, Staphylococcus aureus and so on) and eukaryotic microbes in saline (Wallemia spp., Basipetospora halophila, Dunaliella spp. and so on) and high-sugar substrates (for example, Xeromyces bisporus, Zygosaccharomyces rouxii, Aspergillus and Eurotium spp.). We also manipulated the balance of chaotropic and kosmotropic stressors for the extreme, xerophilic fungi Aspergillus penicilloides and X. bisporus and, via this approach, their established water-activity limits for mycelial growth (∼0.65) were reduced to 0.640. Furthermore, extrapolations indicated theoretical limits of 0.632 and 0.636 a w for A. penicilloides and X. bisporus, respectively. Collectively, these findings suggest that there is a common water-activity limit that is determined by physicochemical constraints for the three domains of life