Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.

Review of approximate analyses of sheet forming processes

Approximate models are often used for the following purposes: in on-line control systems of metal forming processes where calculation speed is critical; to obtain quick, quantitative information on the magnitude of the main variables in the early stages of process design; to illustrate the role of the major variables in the process; as an initial check on numerical modelling; and as a basis for quick calculations on processes in teaching and training packages. The models often share many similarities; for example, an arbitrary geometric assumption of deformation giving a simplified strain distribution, simple material property descriptions - such as an elastic, perfectly plastic law - and mathematical short cuts such as a linear approximation of a polynomial expression. In many cases, the output differs significantly from experiment and performance or efficiency factors are developed by experience to tune the models. In recent years, analytical models have been widely used at Deakin University in the design of experiments and equipment and as a pre-cursor to more detailed numerical analyses. Examples that are reviewed in this paper include deformation of sandwich material having a weak, elastic core, load prediction in deep drawing, bending of strip (particularly of ageing steel where kinking may occur), process analysis of low-pressure hydroforming of tubing, analysis of the rejection rates in stamping, and the determination of constitutive models by an inverse method applied to bending tests.

Testing the optimality of aggregate consumption decisions: is there rule-of-thumb behavior?

Consumption is an important macroeconomic aggregate, being about 70% of GNP. Finding sub-optimal behavior in consumption decisions casts a serious doubt on whether optimizing behavior is applicable on an economy-wide scale, which, in turn, challenge whether it is applicable at all. This paper has several contributions to the literature on consumption optimality. First, we provide a new result on the basic rule-of-thumb regression, showing that it is observational equivalent to the one obtained in a well known optimizing real-business-cycle model. Second, for rule-of-thumb tests based on the Asset-Pricing Equation, we show that the omission of the higher-order term in the log-linear approximation yields inconsistent estimates when lagged observables are used as instruments. However, these are exactly the instruments that have been traditionally used in this literature. Third, we show that nonlinear estimation of a system of N Asset-Pricing Equations can be done efficiently even if the number of asset returns (N) is high vis-a-vis the number of time-series observations (T). We argue that efficiency can be restored by aggregating returns into a single measure that fully captures intertemporal substitution. Indeed, we show that there is no reason why return aggregation cannot be performed in the nonlinear setting of the Pricing Equation, since the latter is a linear function of individual returns. This forms the basis of a new test of rule-of-thumb behavior, which can be viewed as testing for the importance of rule-of-thumb consumers when the optimizing agent holds an equally-weighted portfolio or a weighted portfolio of traded assets. Using our setup, we find no signs of either rule-of-thumb behavior for U.S. consumers or of habit-formation in consumption decisions in econometric tests. Indeed, we show that the simple representative agent model with a CRRA utility is able to explain the time series data on consumption and aggregate returns. There, the intertemporal discount factor is significant and ranges from 0.956 to 0.969 while the relative risk-aversion coefficient is precisely estimated ranging from 0.829 to 1.126. There is no evidence of rejection in over-identifying-restriction tests.

Gauge formulation for higher order gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=partial derivative F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.

Nonlinear (2+1)-dimensional systems solvable through asymptotic modules

Some nonlinear differential systems in (2+1) dimensions are characterized by means of asymptotic modules involving two poles and a ring of linear differential operators with scalar coefficients.Rational and soliton-like are exhibited. If these coefficients are rational functions, the formalism leads to nonlinear evolution equations with constraints. © 1989.

Gravitational field of a straight cosmic string in the framework of higher-derivative gravity

The gravitational properties of a straight cosmic string are studied in the linear approximation of higher-derivative gravity. These properties are shown to be very different from those found using linearized Einstein gravity: there exists a short range gravitational (anti-gravitational) force in the nonrelativistic limit; in addition, the deflection angle of a light ray moving in a plane orthogonal to the string depends on the impact parameter. © 2008 World Scientific Publishing Company.

Ajustes de modelos não lineares de efeitos fixos, com ponderação e misto

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aspectos clássicos de teorias de segunda ordem

Pós-graduação em Física - IFT

Strong Coupling Isotropization of Non-Abelian Plasmas Simplified

We study the isotropization of a homogeneous, strongly coupled, non-Abelian plasma by means of its gravity dual. We compare the time evolution of a large number of initially anisotropic states as determined, on the one hand, by the full nonlinear Einstein's equations and, on the other, by the Einstein's equations linearized around the final equilibrium state. The linear approximation works remarkably well even for states that exhibit large anisotropies. For example, it predicts with a 20% accuracy the isotropization time, which is of the order of t(iso) less than or similar to 1/T, with T the final equilibrium temperature. We comment on possible extensions to less symmetric situations.

Der Austausch von Carbonylsulfid (COS) zwischen Vegetation und Atmosphäre unter erhöhter CO 2-Umgebungskonzentration

The responses of photosynthetic plant gas exchange, COS uptake and carbonic anhydrase (CA) activity were studied on Quercus ilex (Holm oak), and beech Fagus sylvatica L

Boundary elements in potential and elasticity theory

A general theory that describes the B.I.E. linear approximation in potential and elasticity problems, is developed. A method to tread the Dirichlet condition in sharp vertex is presented. Though the study is developed for linear elements, its extension to higher order interpolation is straightforward. A new direct assembling procedure of the global of equations to be solved, is finally showed.

On Managing Stochastic Decentralized Projects

Thesis (Ph.D.)--University of Washington, 2016-06

Analysis and optimisation of the performance of nonlinear optical communication systems

We investigate the feasibility of simultaneous suppressing of the amplification noise and nonlinearity, representing the most fundamental limiting factors in modern optical communication. To accomplish this task we developed a general design optimisation technique, based on concepts of noise and nonlinearity management. We demonstrate the immense efficiency of the novel approach by applying it to a design optimisation of transmission lines with periodic dispersion compensation using Raman and hybrid Raman-EDFA amplification. Moreover, we showed, using nonlinearity management considerations, that the optimal performance in high bit-rate dispersion managed fibre systems with hybrid amplification is achieved for a certain amplifier spacing – which is different from commonly known optimal noise performance corresponding to fully distributed amplification. Required for an accurate estimation of the bit error rate, the complete knowledge of signal statistics is crucial for modern transmission links with strong inherent nonlinearity. Therefore, we implemented the advanced multicanonical Monte Carlo (MMC) method, acknowledged for its efficiency in estimating distribution tails. We have accurately computed acknowledged for its efficiency in estimating distribution tails. We have accurately computed marginal probability density functions for soliton parameters, by numerical modelling of Fokker-Plank equation applying the MMC simulation technique. Moreover, applying a powerful MMC method we have studied the BER penalty caused by deviations from the optimal decision level in systems employing in-line 2R optical regeneration. We have demonstrated that in such systems the analytical linear approximation that makes a better fit in the central part of the regenerator nonlinear transfer function produces more accurate approximation of the BER and BER penalty. We present a statistical analysis of RZ-DPSK optical signal at direct detection receiver with Mach-Zehnder interferometer demodulation

Classical and technological convergence:beyond the Solow-Swann model

Recent investigations into cross-country convergence follow Mankiw, Romer, and Weil (1992) in using a log-linear approximation to the Swan-Solow growth model to specify regressions. These studies tend to assume a common and exogenous technology. In contrast, the technology catch-up literature endogenises the growth of technology. The use of capital stock data renders the approximations and over-identification of the Mankiw model unnecessary and enables us, using dynamic panel estimation, to estimate the separate contributions of diminishing returns and technology transfer to the rate of conditional convergence. We find that both effects are important.

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

* The author was supported by NSF Grant No. DMS 9706883.