Showing papers on "Constant (mathematics) published in 1993"

Lipschitzian optimization without the Lipschitz constant

Abstract: We present a new algorithm for finding the global minimum of a multivariate function subject to simple bounds. The algorithm is a modification of the standard Lipschitzian approach that eliminates the need to specify a Lipschitz constant. This is done by carrying out simultaneous searches using all possible constants from zero to infinity. On nine standard test functions, the new algorithm converges in fewer function evaluations than most competing methods. The motivation for the new algorithm stems from a different way of looking at the Lipschitz constant. In particular, the Lipschitz constant is viewed as a weighting parameter that indicates how much emphasis to place on global versus local search. In standard Lipschitzian methods, this constant is usually large because it must equal or exceed the maximum rate of change of the objective function. As a result, these methods place a high emphasis on global search and exhibit slow convergence. In contrast, the new algorithm carries out simultaneous searches using all possible constants, and therefore operates at both the global and local level. Once the global part of the algorithm finds the basin of convergence of the optimum, the local part of the algorithm quickly and automatically exploits it. This accounts for the fast convergence of the new algorithm on the test functions.

One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable

Abstract: A one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka. An internal variable ap proach is used to deri...

Constant depth circuits, Fourier transform, and learnability

Abstract: In this paper, Boolean functions in ,4C0 are studied using harmonic analysis on the cube. The main result is that an ACO Boolean function has almost all of its "power spectrum" on the low-order coefficients. An important ingredient of the proof is Hastad's switching lemma (8). This result implies several new properties of functions in -4C(': Functions in AC() have low "average sensitivity;" they may be approximated well by a real polynomial of low degree and they cannot be pseudorandom function generators. Perhaps the most interesting application is an O(n POIYIOg(n ')-time algorithm for learning func- tions in ACO. The algorithm observes the behavior of an AC'" function on O(nPO'Y'Og(n)) randomly chosen inputs, and derives a good approximation for the Fourier transform of the function. This approximation allows the algorithm to predict, with high probability, the value of the function on other randomly chosen inputs.

Adaptive current control

Abstract: Closed-loop control of current through a load through pulse-width modulated application of a substantially constant supply voltage across the load, wherein a duty cycle turn-on time is adjusted according to the result of a comparison between a commanded minimum current level and a sensed minimum current through the load during a cycle.

Precautionary Savings and the Permanent Income Hypothesis

Abstract: This paper derives the explicit solution of a dynamic stochastic optimal consumption problem for infinitely-lived agents whose preferences exhibit, in the presence of non-diversifiable labour income uncertainty, a constant elasticity of intertemporal substitution and constant absolute risk aversion. The constancy of the elasticity of intertemporal substitution, which implies that marginal utility at zero consumption is infinite, guarantees that the non-negativity constraint on consumption is never binding along the optimal path. The assumption of constant absolute risk aversion allows an explicit computation of human wealth, and provides a simple representation of the precautionary savings motive.

The Constant Flux: A Study of Class Mobility in Industrial Societies

Abstract: This is a study of social mobility within the developing class structures of modern industrial societies based on a unique data-set constructed by John Goldthorpe and Robert Erikson. The focus is on the experience of European nations - western and eastern - in the period of the `long boom' following the Second World War; but the book also devotes separate chapters to examining the experience of the USA, Australia, and Japan. The authors combine historical and statistical approaches in their analysis of both trends in mobility and of cross-national similarities and differences. They show that wide variation at the level of actually observed mobility coexists with a surprising degree of constancy and commonality in underlying patterns of social fluidity. The empirical results of their study serve as the basis for a critical re-examination of current theories of mobility and for raising more general issues of the proper concerns and methods of comparative macro-sociology. This book is intended for teachers and postgraduates in sociology, social and economic history, social stratification, and the sociology of industrial societies.

The development of variable-step symplectic integrators with application to the two-body problem

Abstract: The authors develop and test variable step symplectic Runge–Kutta–Nystrom algorithms for the integration of Hamiltonian systems of ordinary differential equations. Numerical experiments suggest that, for symplectic formulae, moving from constant to variable stepsizes results in a marked decrease in efficiency. On the other hand, symplectic formulae with constant stepsizes may outperform available standard (nonsymplectic) variable-step codes. For the model situation consisting in the long-time integration of the two-body problem, our experimental findings are backed by theoretical analysis.

Integration Graphs: A Class of Decidable Hybrid Systems

Abstract: Integration Graphs are a computational model developed in the attempt to identify simple Hybrid Systems with decidable analysis problems. We start with the class of constant slope hybrid systems (cshs), in which the right hand side of all differential equations is an integer constant. We refer to continuous variables whose right hand side constants are always 1 as timers. All other continuous variables are called integrators. The first result shown in the paper is that simple questions such as reachability of a given state are undecidable for even this simple class of systems.

Exact solutions of topologically massive gravity with a cosmological constant

Abstract: Exact solutions of the Deser-Jackiw-Templeton field equations including a cosmological constant are presented. They generalize the finite-action homogeneous, anisotropic vacuum solutions of topologically massive gravity. We find that only Vuorio-type solutions, where any two of the constant scale factors coincide, admit a cosmological constant. One of these solutions can be dressed up to yield a two parameter black hole solution of topologically massive gravity.

S-matrix for generalized Landau-Zener problem

Abstract: The Schrodinger equation i Psi =(A+Bt) Psi with constant Hermitian matrices A and B is studied. In the form where B is diagonalized, this equation is a generalization of the Landau-Zener problem to an arbitrary number of crossing energy levels. An approach-the independent crossing approximation-leading to a partial understanding of the general case in terms of the two-level problem is introduced. It is found that certain S-matrix elements (and thus the corresponding transition probabilities) for the general problem are exactly given by formulae of unexpected simplicity, suggesting that some kind of general analytic solution might exist. The full S-matrix is calculated for a solvable special case of the problem. The solution of another special case, previously discovered for systems with three states, is generalized to any number of states. The asymptotic behaviour of the system is discussed in general and given explicitly to lowest order in 1/t.

A high resolution fundamental frequency determination based on phase changes of the Fourier transform

Abstract: The constant Q transform described recently [J. C. Brown and M. S. Puckette, ‘‘An efficient algorithm for the calculation of a constant Q transform,’’ J. Acoust. Soc. Am. 92, 2698–2701 (1992)] has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages. For this purpose the calculation described previously has been modified so that it is constant frequency resolution rather than constant Q for lower frequency bins. This modified calculation serves as the input for a fundamental frequency tracker similar to that described by Brown [J. C. Brown, ‘‘Musical fundamental frequency tracking using a pattern recognition method,’’ J. Acoust. Soc. Am. 92, 1394–1402 (1992)]. Once the fast Fourier transform (FFT) bin corresponding to the fundamental frequency is chosen by the frequency tracker, an approximation is used for the phase change in the FFT for a time advance of one sample to obtain an extremely precise value for this frequency. Graphical examples are given for musical passages by a violin executing vibrato and glissando where the fundamental frequency changes are rapid and continuous.

Solving the two‐dimensional constant quantum Yang–Baxter equation

Abstract: A detailed analysis of the constant quantum Yang–Baxter equation Rk1k2j1j2 Rl1k3k1j3Rl2l3k2k3= Rk2k3j2j3 Rk1l3j1k3Rl1l2k1k2 in two dimensions is presented, leading to an exhaustive list of its solutions. The set of 64 equations for 16 unknowns was first reduced by hand to several subcases which were then solved by computer using the Grobner‐basis methods. Each solution was then transformed into a canonical form (based on the various trace matrices of R) for final elimination of duplicates and subcases. If we use homogeneous parametrization the solutions can be combined into 23 distinct cases, modulo the well‐known C, P, and T reflections, and rotations and scalings R=κ(Q⊗Q)R(Q⊗Q)−1.

Randomness fault detection system

Abstract: A method and apparatus are provided for detecting a fault on a power line carrying a line parameter such as a load current. The apparatus monitors and analyzes the load current to obtain an energy value. The energy value is compared to a threshold value stored in a buffer. If the energy value is greater than the threshold value a counter is incremented. If the energy value is greater than a high value threshold or less than a low value threshold then a second counter is incremented. If the difference between two subsequent energy values is greater than a constant then a third counter is incremented. A fault signal is issued if the counter is greater than a counter limit value and either the second counter is greater than a second limit value or the third counter is greater than a third limit value.

Thermally activated escape over fluctuating barriers

Abstract: We investigate the thermally activated escape of a Brownian particle over a potential barrier whose height fluctuates with a rate α between the values E + and E - . We are mainly interested in the low temperature behavior where E + /T>>E - /T. We calculate the mean exit time as a function of the rate of the barrier fluctuations for the piecewise linear and the piecewise constant barrier, τ=τ(α). For the piecewise constant potential we find three different regimes:τ∼τ + for α τ - -1 =exp(-E - /T), and τ∼α -1 for τ + -1 <α<τ - -1

A new approach to stability analysis of variable speed machining systems

Abstract: This paper presents a new method for the stability analysis of variable speed machining systems. By using spindle angular position as the independent variable, the system dynamics are modeled as a linear periodic time-varying system with fixed delay. This representation is proven much easier to analyze and to numerically simulate than the time-varying delay representation, which traditionally uses the real-time as the independent variable. With a finite difference scheme, the infinite dimensional periodic time-varying system is approximated by a finite dimensional periodic time-varying discrete system, which in turn is converted to a time-invariant system by multiplying the time-varying state transition matrix over one period of speed variation. System-relative stability becomes tractable by spectral radius analysis. This approach makes possible the quantitative characterization of system stability as a function of variable speed profiles as well as other system parameters such as stiffness and damping of the cutting process and the tool/workpiece structure. Verifications for the face milling process by numerical simulation and experiment for both constant and variable speed are given.

Chemostats used for studying natural selection and adaptive evolution.

Abstract: Publisher Summary Chemostats are open systems in which nutrients are continually added at a constant rate and spent medium plus cells removed at the same rate, such that a constant volume is maintained. Thus, they are designed to provide a constant, homogeneous environment in which the cells grow at a constant rate. Chemostats are used in two ways to study evolution. The first approach attempts to characterize natural selection in terms of how selection coefficients change as either the genetics or the environment is changed. Two strains are mixed and the initial selective difference between the strains is measured over the first 50 generations. The second approach follows the course of adaptive evolution of a population in a particular environment. A single initial strain is monitored over hundreds to thousands of generations to determine the evolutionary changes. The advantage of the first approach is that the genetic differences are known and the effects of these differences in various environments can be explored. The advantage of the second approach is that the actual evolutionary trajectory of fitness changes is followed.

Static and Dynamic Algorithms for k-Point Clustering Problems

Abstract: Let S be a set of n points in d-space, where d ≥ 2 is a constant, and let 1 ≤ k ≤ n be an integer. A unified approach is given for solving the problem of finding a subset of S of size k that minimizes some closeness measure, such as the diameter, perimeter or the circumradius. Moreover, data structures are given that maintain such a subset under insertions and deletions of points.

New bounds for lower envelopes in three dimensions, with applications to visibility in terrains

Abstract: We consider the problem of bounding the complexity of the lower envelope of n surface patches in 3-space, all algebraic of constant maximum degree, and bounded by algebraic arcs of constant maximum degree, with the additional property that the interiors of any triple of these surfaces intersect in at most two points. We show that the number of vertices on the lower envelope of n such surface patches is O(n2d2c√log n), for some constant c depending on the shape and degree of the surface patches. We apply this result to obtain an upper bound on the combinatorial complexity of the “lower envelope” of the space of all rays in 3-space that lie above a given polyhedral terrain K with n edges. This envelope consists of all rays that touch the terrain (but otherwise lie above it). We show that the combinatorial complexity of this ray-envelope is O(n2d2c√log n) for some constant c; in particular, there are at most that many rays that pass above the terrain and touch it in 4 edges. This bound, combined with the analysis of de Berg et al. [2], gives an upper bound (which is almost tight in the worst case) on the number of topologically-different orthographic views of such a terrain.

On quasi-linear stochastic partial differential equations

Abstract: We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.

Hardness and Softness in Density Functional Theory

Abstract: The fundamental equations to describe the change from one ground-state to another, in the framework of density functional theory, are used to analyze a set of hardness and softness functions that are hierarchized as non-local, local and global quantities. Through these definitions it is shown that under conditions of constant chemical potential, the interaction between two chemical systems evolves towards a state of maximum hardness, and that soft-soft, and hard-hard interactions are energetically favored. It is also shown that to a good approximation, the ground-state energy of a system decreases when its hardness increases. Possible applications of these principles are briefly discussed.

Interprocedural constant propagation: a study of jump function implementation

Abstract: An implementation of interprocedural constant propagation must model the transmission of values through each procedure. In the framework proposed by Callahan, Cooper, Kennedy, and Torczon in 1986, this intraprocedural propagation is modeled with a jump function. While Callahan et al. propose several kinds of jump functions, they give no data to help choose between them. This paper reports on a comparative study of jump function implementations. It shows that different jump functions produce different numbers of useful constants; it suggests a particular function, called the pass-through parameter jump function, as the most cost-effective in practice.