Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Cerimetry in non-aqueous media - Oxidation of oxalic acid through the intermediate formation of ceric oxalate

It was found that ceric oxalate is an intermediate product in the oxidation of oxalic acid by ammonium hexanitrato cerate in solvents such as acetonitrile, and a mixture of acetonitrile and glacial acetic acid. Conditions for the formation of ceric oxalate and its decomposition into carbon dioxide and cerous oxalate have been studied. An analytical method for the estimation of oxalic acid in non-aqueous media has been evolved based on this reaction.

Searching the inclusive ℓγE̸T+b-quark signature for radiative top quark decay and non-standard-model processes

In a search for new phenomena in a signature suppressed in the standard model of elementary particles (SM), we compare the inclusive production of events containing a lepton, a photon, significant transverse momentum imbalance (MET), and a jet identified as containing a b-quark, to SM predictions. The search uses data produced in proton-antiproton collisions at 1.96 TeV corresponding to 1.9 fb-1 of integrated luminosity taken with the CDF detector at the Fermilab Tevatron. We find 28 lepton+photon+MET+b events versus an expectation of 31.0+4.1/-3.5 events. If we further require events to contain at least three jets and large total transverse energy, simulations predict that the largest SM source is top-quark pair production with an additional radiated photon, ttbar+photon. In the data we observe 16 ttbar+photon candidate events versus an expectation from SM sources of 11.2+2.3/-2.1. Assuming the difference between the observed number and the predicted non-top-quark total is due to SM top quark production, we estimate the ttg cross section to be 0.15 +- 0.08 pb.

Free vibrations of non-linear cubic spring mass systems in the presence of coulomb damping

An exact solution for the free vibration problem of non-linear cubic spring mass system with Coulomb damping is obtained during each half cycle, in terms of elliptic functions. An expression for the half cycle duration as a function of the mean amplitude during the half cycle is derived in terms of complete elliptic integrals of the first kind. An approximate solution based on a direct linearization method is developed alongside this method, and excellent agreement is obtained between the results gained by this method and the exact results. © 1970 Academic Press Inc. (London) Limited.

Minimizing total weighted tardiness on a batch-processing machine with non-agreeable release times and due dates

This study considers the scheduling problem observed in the burn-in operation of semiconductor final testing, where jobs are associated with release times, due dates, processing times, sizes, and non-agreeable release times and due dates. The burn-in oven is modeled as a batch-processing machine which can process a batch of several jobs as long as the total sizes of the jobs do not exceed the machine capacity and the processing time of a batch is equal to the longest time among all the jobs in the batch. Due to the importance of on-time delivery in semiconductor manufacturing, the objective measure of this problem is to minimize total weighted tardiness. We have formulated the scheduling problem into an integer linear programming model and empirically show its computational intractability. Due to the computational intractability, we propose a few simple greedy heuristic algorithms and meta-heuristic algorithm, simulated annealing (SA). A series of computational experiments are conducted to evaluate the performance of the proposed heuristic algorithms in comparison with exact solution on various small-size problem instances and in comparison with estimated optimal solution on various real-life large size problem instances. The computational results show that the SA algorithm, with initial solution obtained using our own proposed greedy heuristic algorithm, consistently finds a robust solution in a reasonable amount of computation time.

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

USING FLUORESCENT AND NON-FLUORESCENT STEROLS TO STUDY RAFTS AND INTRACELLULAR CHOLESTEROL TRANSPORT IN MAMMALIAN CELLS

Cholesterol is an essential component in the membranes of most eukaryotic cells, in which it mediates many functions including membrane fluidity, permeability and the formation of ordered membrane domains. In this work a fluorescent and a non-fluorescent cholesterol analog were characterized as tools to study cholesterol. Next, these analogs were used to study two specific cell biological processes that involve cholesterol, i.e. the structure and function of ordered membrane domains/rafts and intracellular cholesterol transport. The most common method for studying ordered membrane domains is by disrupting them by cholesterol depletion. Because cholesterol depletion affects many cellular functions besides those mediated by membrane domains, this procedure is highly unspecific. The cellular exchange of cholesterol by desmosterol as a tool to study ordered membrane domains was characterized. It turned out that the ability of desmosterol to form and stabilize membrane domains in vitro was weaker compared to cholesterol. This result was reinforced by atomistic scale simulations that indicated that desmosterol has a lower ordering effect on phospholipid acyl chains. Three procedures were established for exchanging cellular cholesterol by desmosterol. In cells in which desmosterol was the main sterol, insulin signaling was attenuated. The results suggest that this was caused by desmosterol destabilizing membrane rafts. Contrary to its effect on ordered membrane domains it was found that replacing cholesterol by desmosterol does not change cell growth/viability, subcellular sterol distribution, Golgi integrity, secretory pathway, phospholipid composition and membrane fluidity. Together these results suggest that exchanging cellular cholesterol by desmosterol provides a selective tool for perturbing rafts. Next, the importance of cholesterol for the structure and function of caveolae was analyzed by exchanging the cellular cholesterol by desmosterol. The sterol exchange reduced the stability of caveolae as determined by detergent resistance of caveolin-1 and heat resistance of caveolin-1 oligomers. Also the sterol exchange led to aberrations in the caveolar structure; the morphology of caveolae was altered and there was a larger variation in the amount of caveolin-1 molecules per caveola. These results demonstrate that cholesterol is important for caveolar stability and structural homogeneity. In the second part of this work a fluorescent cholesterol analog was characterized as a tool to study cholesterol transport. Tight control of the intracellular cholesterol distribution is essential for many cellular processes. An important mechanism by which cells regulate their membrane cholesterol content is by cholesterol traffic, mostly from the plasma membrane to lipid droplets. The fluorescent sterol probe BODIPY-cholesterol was characterized as a tool to analyze cholesterol transport between the plasma membrane, the endoplasmic reticulum (ER) and lipid droplets. The behavior of BODIPY-cholesterol was compared to that of natural sterols, using both biochemical and live-cell microcopy assays. The results show that the transport kinetics of BODIPY-cholesterol between the plasma membrane, the ER and lipid droplets is similar to that of unesterified cholesterol. Next, BODIPY-cholesterol was utilized to analyze the importance of oxysterol binding protein related proteins (ORPs) for cholesterol transport between the plasma membrane, the ER, and lipid droplets in mammalian cells. By overexpressing all human ORPs it turned out that especially ORP1S and ORP2 enhanced sterol transport from the plasma membrane to lipid droplets. Our results suggest that the increased sterol transport takes place between the plasma membrane and ER and not between the ER and lipid droplets. Simultaneous knockdown of ORP1S and ORP2 resulted in a moderate but significant inhibition of sterol traffic from the plasma membrane to ER and lipid droplets, suggesting a physiological role for these ORPs in this process. The two phenylalanines in an acidic tract (FFAT) motif in ORPs, which mediates interaction with vesicle associated membrane protein associated proteins (VAPs) in the ER, was not necessary for mediating sterol transport. However, VAP silencing slowed down sterol transport, most likely by destabilizing ORPs containing a FFAT motif.

The role of selected non-timber forest products for rural areas in Laos: Case studies in Ban Napo and Ban Kouay communities

Non-timber forest products (NTFPs) are one of the major income sources for the rural population of Laos. An exploratory study was conducted to determine the role of non-timber forest products for rural communities of the study area. The study was carried out in two villages viz. Ban Napo and Ban Kouay of Sangthong district between January and March 2010. A semi-structured questionnaire was used to gather data from the respondents. Twenty-five respondents from each village were chosen based on their involvement in NTFPs collection and marketing activities. Statistically significant NTFPs income differences were not found between the villages and age groups of the respondents, however, significant differences were found in the annual incomes between farms size of the respondents. This study also analyzed the value chain structure of the three (See khai’ ton, Bamboo mats and Incense sticks) important non-timber forest products and the interactions between the actors in the case study areas. Barriers to entry the market, governance and upgrading possibilities have been discussed for each of the value chains. Comparison of unit prices at different levels of the value chains indicated uneven income distribution in favour of the intermediaries, factories and foreign buyers. The lack of capital, marketing information and negotiation skills restricted the villagers to increase their income. However, all the respondents have shown their satisfaction with their income from NTFPs.