Regular singular points of a system of homogeneous linear differential equations of the first order.

"From Proceedings of the American Academy of Arts and Sciences, v.38, no. 9, Oct. 1902."

Parametric Optimization of Inductively Driven Liner Compression Driver System

Thesis (Master's)--University of Washington, 2016-06

Interactions at the head-tape interface of a linear tape system

Many of the recent improvements in the capacity of data cartridge systems have been achieved through the use of narrower tracks, higher linear densities and continuous servo tracking with multi-channel heads. These changes have produced new tribological problems at the head/tape interface. It is crucial that the tribology of such systems is understood and this will continue since increasing storage capacities and faster transfer rates are constantly being sought. Chemical changes in the surface of single and dual layer MP tape have been correlated to signal performance. An accelerated tape tester, consisting of a custom made cycler ("loop tester"), was used to ascertain if results could be produced that were representative of a real tape drive system. A second set of experiments used a modified tape drive (Georgens cycler), which allowed the effects of the tape transport system on the tape surface to be studied. To isolate any effects on the tape surface due to the head/tape interface, read/write heads were not fitted to the cycler. Two further sets of experiments were conducted which included a head in the tape path. This allowed the effects of the head/tape interface on the physical and chemical properties of the head and tape surfaces to be investigated. It was during the final set of experiments that the effect on the head/tape interface, of an energised MR element, was investigated. The effect of operating each cycler at extreme relative humidity and temperature was investigated through the use of an environmental chamber. Extensive use was made of surface specific analytical techniques such as XPS, AFM, AES, and SEM to study the physical and chemical changes that occur at the head/tape interface. Results showed that cycling improved the signal performance of all the tapes tested. The data cartridge drive belt had an effect on the chemical properties of the tape surface on which it was in contact. Also binder degradation occurred for each tape and appeared to be greater at higher humidity. Lubricant was generally seen to migrate to the tape surface with cycling. Any surface changes likely to affect signal output occurred at the head surface rather than the tape.

Wave chaotic behaviour generated by linear systems

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time. © 2008 Springer Science+Business Media, LLC.

System identification of linear vibrating structures

Methods of dynamic modelling and analysis of structures, for example the finite element method, are well developed. However, it is generally agreed that accurate modelling of complex structures is difficult and for critical applications it is necessary to validate or update the theoretical models using data measured from actual structures. The techniques of identifying the parameters of linear dynamic models using Vibration test data have attracted considerable interest recently. However, no method has received a general acceptance due to a number of difficulties. These difficulties are mainly due to (i) Incomplete number of Vibration modes that can be excited and measured, (ii) Incomplete number of coordinates that can be measured, (iii) Inaccuracy in the experimental data (iv) Inaccuracy in the model structure. This thesis reports on a new approach to update the parameters of a finite element model as well as a lumped parameter model with a diagonal mass matrix. The structure and its theoretical model are equally perturbed by adding mass or stiffness and the incomplete number of eigen-data is measured. The parameters are then identified by an iterative updating of the initial estimates, by sensitivity analysis, using eigenvalues or both eigenvalues and eigenvectors of the structure before and after perturbation. It is shown that with a suitable choice of the perturbing coordinates exact parameters can be identified if the data and the model structure are exact. The theoretical basis of the technique is presented. To cope with measurement errors and possible inaccuracies in the model structure, a well known Bayesian approach is used to minimize the least squares difference between the updated and the initial parameters. The eigen-data of the structure with added mass or stiffness is also determined using the frequency response data of the unmodified structure by a structural modification technique. Thus, mass or stiffness do not have to be added physically. The mass-stiffness addition technique is demonstrated by simulation examples and Laboratory experiments on beams and an H-frame.

Fiber optical parametric amplifier performance in a 1-Tb/s DWDM communication system

We have reduced signal-signal four-wave mixing crosstalk in a fiber optical parametric amplifier (OPA) by using a short nonlinear fiber for the gain medium and a high-power pump. This allowed us to obtain less than 1 dB penalty for amplification of 26 dense wavelength-division multiplexed (WDM) channels modulated at 43.7Gb/s return to zero-differential phase-shift keying, with the OPA placed between transmitter and receiver. We then used the same OPA in several different roles for a long-haul transmission system. We did not insert the OPA within the loop, but investigated this role indirectly by using equivalent results for small numbers of loop recirculations. We found that standard erbium-doped fiber amplifiers currently hold an advantage over this OPA, which becomes negligible for long distances. This paper shows that at this time OPAs can handle amplification of WDM traffic in excess of 1 Tb/s with little degradation. It also indicates that with further improvements, fiber OPAs could be a contender for wideband amplification in future optical communication networks.

A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space

2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94.

Evaluation on a 60 GHz radio over fiber system employing photonic up conversion and optically beam formed linear array antenna for broadband indoor access

In this study, two linear coplanar array antennas based on Indium Phosphide (InP) substrate are designed, presented and compared in terms of bandwidth and gain. Slot introduction in combination with coplanar structure is investigated, providing enhanced antenna gain and bandwidth at the 60 GHz frequency band. In addition the proposed array antennas are evaluated in terms of integration with a high-speed photodiode and investigated in terms of matching, providing a bandwidth that reaches 2 GHz. Moreover a potential beam forming scenario combined with photonic up-conversion scheme has been proposed. © 2013 IEEE.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.

Evolution Of The Deaths Registry System In Brazil: Associations With Changes In The Mortality Profile, Under-registration Of Death Counts, And Ill-defined Causes Of Death.

This paper examines the spatial pattern of ill-defined causes of death across Brazilian regions, and its relationship with the evolution of completeness of the deaths registry and changes in the mortality age profile. We make use of the Brazilian Health Informatics Department mortality database and population censuses from 1980 to 2010. We applied demographic methods to evaluate the quality of mortality data for 137 small areas and correct for under-registration of death counts when necessary. The second part of the analysis uses linear regression models to investigate the relationship between, on the one hand, changes in death counts coverage and age profile of mortality, and on the other, changes in the reporting of ill-defined causes of death. The completeness of death counts coverage increases from about 80% in 1980-1991 to over 95% in 2000-2010 at the same time the percentage of ill-defined causes of deaths reduced about 53% in the country. The analysis suggests that the government's efforts to improve data quality are proving successful, and they will allow for a better understanding of the dynamics of health and the mortality transition.

Comparative In vitro Mechanical Evaluation Of Techniques Using A 2.0 mm Locking Fixation System For Simulated Fractures Of The Mandibular Body.

To perform a comparative evaluation of the mechanical resistance of simulated fractures of the mandibular body which were repaired using different fixation techniques with two different brands of 2.0 mm locking fixation systems. Four aluminum hemimandibles with linear sectioning simulating a mandibular body fracture were used as the substrates and were fixed using the two techniques and two different brands of fixation plate. These were divided into four groups: groups I and II were fixed with one four-hole plate, with four 6 mm screws in the tension zone and one four-hole plate, with four 10 mm screws in the compression zone; and groups III and IV were fixed with one four-hole plate with four 6 mm screws in the neutral zone. Fixation plates manufactured by Tóride were used for groups I and III, and by Traumec for groups II and IV. The hemimandibles were submitted to vertical, linear load testing in an Instron 4411 servohydraulic mechanical testing unit, and the load/displacement (3 mm, 5 mm and 7 mm) and the peak loads were measured. Means and standard deviations were evaluated applying variance analysis with a significance level of 5%. The only significant difference between the brands was seen at displacements of 7 mm. Comparing the techniques, groups I and II showed higher mechanical strength than groups III and IV, as expected. For the treatment of mandibular linear body fracture, two locking plates, one in the tension zone and another in the compression zone, have a greater mechanical strength than a single locking plate in the neutral zone.

Influência da idade no comportamento da frequência cardíaca na transição repouso-exercício: uma análise por deltas e regressão linear

BACKGROUND: Changes in heart rate during rest-exercise transition can be characterized by the application of mathematical calculations, such as deltas 0-10 and 0-30 seconds to infer on the parasympathetic nervous system and linear regression and delta applied to data range from 60 to 240 seconds to infer on the sympathetic nervous system. The objective of this study was to test the hypothesis that young and middle-aged subjects have different heart rate responses in exercise of moderate and intense intensity, with different mathematical calculations. METHODS: Seven middle-aged men and ten young men apparently healthy were subject to constant load tests (intense and moderate) in cycle ergometer. The heart rate data were submitted to analysis of deltas (0-10, 0-30 and 60-240 seconds) and simple linear regression (60-240 seconds). The parameters obtained from simple linear regression analysis were: intercept and slope angle. We used the Shapiro-Wilk test to check the distribution of data and the t test for unpaired comparisons between groups. The level of statistical significance was 5%. RESULTS: The value of the intercept and delta 0-10 seconds was lower in middle age in two loads tested and the inclination angle was lower in moderate exercise in middle age. CONCLUSION: The young subjects present greater magnitude of vagal withdrawal in the initial stage of the HR response during constant load exercise and higher speed of adjustment of sympathetic response in moderate exercise.

Ressonância não linear de uma bússola em campos magnéticos

Fenômenos oscilatórios e ressonantes são explorados em vários cursos experimentais de física. Em geral os experimentos são interpretados no limite de pequenas oscilações e campos uniformes. Neste artigo descrevemos um experimento de baixo custo para o estudo da ressonância em campo magnético da agulha de uma bússola fora dos limites acima. Nesse caso, termos não lineares na equação diferencial são responsáveis por fenômenos interessantes de serem explorados em laboratórios didáticos.

Development of a Multicommutated Flow System with Chemiluminometric Detection for Quantification of Gentamicin in Pharmaceuticals

A new flow procedure based on multicommutation with chemiluminometric detection was developed to quantify gentamicin sulphate in pharmaceutical formulations. This approach is based on gentamicin's ability to inhibit the chemiluminometric reaction between luminol and hypochlorite in alkaline medium, causing a decrease in the analytical signal. The inhibition of the analytical signal is proportional to the concentration of gentamicin sulphate, within a linear range of 1 to 4 mu g mL(-1) with a coefficient variation <3%. A sample throughput of 55 samples h(-1) was obtained. The developed method is sensitive, simple, with low reagent consumption, reproducible, and inexpensive, and when applied to the analysis of pharmaceutical formulations (eye drops and injections) it gave results with RSD between 1.10 and 4.40%.