Showing papers on "Constant (mathematics) published in 1986"

Renormalization-group analysis of turbulence.

Abstract: Using renormalization-group methods and the postulated equivalence between the inertial-range structures of turbulent flows satisfying initial and boundary conditions and of flows driven by a random force, we evaluate the Kolmogorov constant (1.617) and Batchelor constant (1.161), skewness factor (0.4878), power-law exponent (1.3307) for the decay of homogeneous turbulence, turbulent Prandtl number (0.7179), and von K\'arm\'an constant (0.372). This renormalization-group technique has also been used to derive turbulent transport models.

Upper and lower time bounds for parallel random access machines without simultaneous writes

Abstract: One of the frequently used models for a synchronous parallel computer is that of a parallel random access machine, where each processor can read from and write into a common random access memory. Different processors may read the same memory location at the same time, but simultaneous writing is disallowed. We show that even if we allow nonuniform algorithms, an arbitrary number of processors, and arbitrary instruction sets, $\Omega (\log n)$ is a lower bound on the time required to compute various simple functions, including sorting n keys and finding the logical “or” of n bits. We also prove a surprising time upper bound of $.72\log _2 n$ steps for these functions, which beats the obvious algorithms requiring $\log _2 n$ steps.If simultaneous writes are allowed, there are simple algorithms to compute these functions in a constant number of steps.

Finding a shortest solution for the N x N extension of the 15- Puzzle is intractable

Abstract: The 8-puzzle and the 15-puzzle have been used for many years as a domain for testing heuristic search techniques. From experience it is known that these puzzles are "difficult" and therefore useful for testing search techniques. In this paper we give strong evidence that these puzzles are indeed good test problems. We extend the 8-puzzle and the 15-puzzle to a nxn board and show that finding a shortest solution for the extended puzzle is NP-hard and thus computationally infeasible. We also present an approximation algorithm for transforming boards that is guaranteed to use no more than c L (SP) moves, where L (SP) is the length of the shortest solution and c is a constant which is independent of the given boards and their size n.

A uniqueness theorem for an inverse boundary value problem in electrical prospection

Abstract: We show that a near constant conductivity of a two-dimensional body can be uniquely determined by steady state direct current measurements at the boundary. Mathematically, we show that the coefficient γ in the operator ∇.γ∇ is uniquely determined by its Dirichlet integrals.

The least-squares CMA: A new technique for rapid correction of constant modulus signals

Abstract: A new rapidly-converging constant modulus algorithm is presented, analyzed, and demonstrated for a two-sensor array. The algorithm is shown to be globally stable and convergent for any linearly-independent set of input data. The algorithm is also shown to converge significantly (10 to 100 times) faster than the conventional CMA, with negligible (< 1 dB.) convergent misadjustment, in the presence of moderate and severe co-channel interference.

Distributions of sources and normal dipoles over a quadrilateral panel

Abstract: The potential due to a distribution of sources or normal dipoles on a flat quadrilateral panel is evaluated for the cases where the density of the singularities is constant, linear, bilinear, or of arbitrary polynomial form. The results in the first two cases are consistent with those derived previously, but the present derivation is considered to be simplified. In particular, the constant dipole distribution is derived from a geometric argument which avoids direct integration; this derivation applies more generally on a curvilinear panel bounded by straight edges. Also presented are multipole expansions for the same potentials, suitable for use when the distance to the field point is substantially larger than the panel dimensions. Algorithms are derived to evaluate the coefficients in these expansions to an arbitrary order.

Multiplication by Integer constants

Abstract: Methods are given for finding a sequence of ‘add’, ‘subtract’ and ‘shift’ instructions to multiply the contents of a register by an integer constant. Each method generalizes the previous one and requires only a few intermediate or scratch registers. A variation of the last method is used in the PL.8 compiler and uses an unnoticeable amount of the overall compile time. Some statistics roughly indicating the effectiveness of the methods are presented.

Reconstruction of propagated electrical activity with a two-dimensional model of anisotropic heart muscle.

Abstract: The propagated electrical activity in normal anisotropic cardiac muscle is characterized by directionally dependent variations in the rising phase of the action potential. An important question concerns the relation between such variations and the propagation velocity and extracellular potentials. This problem was studied here in a sheet of cells, under conditions of uniform intracellular anisotropic resistivity and constant electrical membrane properties, through a numerical solution of the two-dimensional propagation equation. The numerical solution implies a lumping of the cytoplasmic and intercellular resistances into an equivalent junctional resistance to form a distributed resistive network representing the intracellular domain. The interstitial space is assumed isotropic and unbounded, with a resistivity of 100 omega X cm. The electrical properties of the cell membrane are represented by a Beeler-Reuter model. The stimulus current is applied to a small area of the sheet, and attention is focussed on the stable propagated events occurring some 5 or 6 length constants away from the stimulation site. The numerical solution is a good approximation of a continuous uniform structure when the cell size is less than 10% of the length constant along both major axes. Conditions of non-uniform propagation, with directionally dependent variations in the maximum rate of rise and time constant of the foot of the action potential were simulated by increasing the cell size to 30% of the length constant in the transverse direction of the sheet. Our results indicate that the directional changes in the maximum rate of rise correspond to small modifications of the extracellular potentials, while the directional changes in time constant of the foot are associated with the propagation velocity. The maximum effects are observed along the transverse direction as follows: a 19% increase in maximum rate of rise corresponds to a decrease of about 6% in the peak-to-peak amplitude of the extracellular potential, and a 24% increase in time constant of the foot is associated with a decrease of about 7% in the propagation velocity. Under the conditions of the present study, however, the simulated directional changes in maximum rate of rise are smaller than those experimentally observed so the corresponding changes in the extracellular potentials are probably underestimated.

An existence theorem for the flow of a non-newtonian fluid past an infinite porous plate

Abstract: Non-Newtonian fluid mechanics affords an excellent opportunity for studying many of the mathematical methods which have been developed to analyse non-linear problems in mechanics. The flow of an incompressible fluid of grade three past an infinite porous flat plate, subject to suction at the plate, is governed by a non-linear differential equation that is particularly well suited to demonstrate the power and usefulness of three such techniques. We establish an existence theorem using shooting methods. Next, we investigate the problem using a perturbation analysis. It is not clear that the perturbation solution converges and thus may not be the appropriate solution for a certain range of a material constant (which is not the perturbation parameter). Finally, we employ a numerical method which is particularly suited to the problem in question.

Constant time generation of free trees

Abstract: An algorithm of Beyer and Hedetniemi [SIAM J. Comput., 9 (1980), pp. 706–712] for generating rooted unlabeled trees is extended to generate unlabeled free trees. All the nonisomorphic trees of a given size are generated, without repetition, in time proportional to the number of trees.

Variable-G cosmology and creation

Abstract: It has recently been asserted that a universe with a time-varying gravitational “constant”G necessarily implies creation if the rest mass of matter particles is constant. It is shown that this is not necessarily true. An example of a cosmological model with variableG and Λ is presented, in which there is no creation and in which the rest mass of matter particles is constant.

Energy levels of a neutral hydrogen-like system in a constant magnetic field of arbitrary strength

Abstract: The variational method is employed to calculate the energy levels of a hydrogenlike system in a constant magnetic field of arbitrary strength. The general approach is similar to that of Aldrich and Greene (1979), but uses a different set of basis functions, enabling smaller matrices to be used. Results are obtained for energy levels up to n=4, and are of high accuracy judged by comparison with other published data.

A comparison of rule-based and positionally constant arrangements of computer menu items

Abstract: An experiment was conducted to evaluate user performance under four different menu item arrangements: alphabetic, probability of selection (most popular choices are positioned near the beginning of the list), random, and positionally constant (consistent assignment of individual items to screen positions). During the initial stages of practice, the rule-based approaches produced faster mean search times, but after moderate amounts of practice, the positionally constant arrangement appeared to be most efficient. People seem to remember quite easily the location of items on a display, indicating that positional constancy can be an important factor in increasing the efficiency of the search of computer menus and other displays.

Method for providing variable output gas-fired furnace with a constant temperature rise and efficiency

Abstract: A furnace is operated such that the air-fuel ratio and the temperature rise are maintained constant so that the efficiency remains constant over the range of operation.

Constant-parameter capture-recapture models.

Abstract: Jolly (1982, Biometrics 38, 301-321) presented modifications of the Jolly-Seber model for capture-recapture data, which assume constant survival and/or capture rates Where appropriate, because of the reduced number of parameters, these models lead to more efficient estimators than the Jolly-Seber model The tests to compare models given by Jolly do not make complete use of the data, and we present here the appropriate modifications, and also indicate how to carry out goodness-of-fit tests which utilize individual capture history information We also describe analogous models for the case where young and adult animals are tagged The availability of computer programs to perform the analysis is noted, and examples are given using output from these programs

Some remarks on the Rayleigh process

Abstract: The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.

Approximation Formulations for the Single-Product Capacitated Lot Size Problem

Abstract: We consider two approximation formulations for the single-product capacitated lot size problem. One formulation restricts the number of production policies and the other rounds demands up to multiples of a constant. After briefly reviewing the literature within a new framework, we discuss the relations between these approximation formulations. Next, we provide relative error bounds and algorithms for solving the approximation problems. We demonstrate that these approximation formulations require a significantly smaller number of calculations than the original formulation, and that the relative error bounds are satisfactory for practical purposes.

Explicit solutions of the viscous model vorticity equation

Abstract: Explicit solutions are found for the viscous version of the model vorticity equation recently proposed by P. Constantin, P. D. Lax, and A. Majda: where H(w) is the Hilbert transform of w, and v is a positive constant. Various properties of these solutions, including the fact that they blow up after a finite time, are discussed.

A Theory for Steady and Variable Wind-and Wave-Induced Currents

Abstract: A theory is presented for time-dependent currents induced by a variable wind stress and wave field in deep water away from coastal boundaries. It is based on a second-order perturbation expansion of the Navier-Stokes equations in Lagrangian coordinates. The effects of rotation and of a constant eddy viscosity are included. Partial differential equations are derived for the vertical and time variation of the mass transport velocity, together with boundary conditions at the sea surface. Some simple analytical solutions are presented. For small viscosities, a near-zero mean mass transport is obtained, in agreement with Ursell. Inertial oscillation are superimposed on the above mean solution, in agreement with Hasselmann and Pollard. In the case of a constant wind stress and a constant, horizontally homogeneous wave field, the steady-state results of Weber are reproduced (a surface drift current of about 3% of the wind speed, 23–30 deg to the right of the wind direction).

Stochastic minimization with constant step-size: asymptotic laws

Abstract: The behavior of the stationary distribution of a Markovian process of the form \[( * )\qquad X_{n + 1}^a = \pi _S (X_n^a - aY_n^a )\] as a tends to zero is studied. The process $( * )$ is a constant step-size (constant gain) constrained stochastic approximation process, with $\pi _S $ being the projection onto the convex set of constraints S. If the gains a are held constant, the process $\{ X_n^a \} $ does not converge to the point of solution but the stationary distribution of $\{ X_n^a \} $ converges to the unit mass at the solution, if $a \to 0$. Properly normalized the stationary distribution converges to a nondegenerated limit. This limit depends on the smoothness of the feasible set S in the neighborhood of the solution (in particular on the dimension of the largest linear subspace contained in the tangential cone).

Small-Signal Frequency Response Theory for piecewise-constant two-switched-network dc-to-dc converter systems

Abstract: Small-Signal Frequency Response Theory is a theory for calculating the output spectrum of ideal dc-to-dc converter systems, i.e. systems with system coefficients piecewise constant in time, for a given spectrum of the signal injected into the control-input, in the small-signal limit. This theory, unlike other methods, can be applied to both resonant and PWM converters, and gives analytic results in closed form for ideal converters. This paper discusses the special case of ideal two-switched-network converter systems in PWM, programmed, and bang-bang operation. For the examples under study, theoretical prediction and experimental results are found to differ by at most 2dB in amplitude and 10 degrees in phase at most frequencies up to three times the switching frequency. Examples are given in this paper for which the theory gives the correct prediction, while other methods fail.

System for generating substantially constant fluid pressure

Abstract: A system for generating substantially constant fluid pressure is provided for forcing fluid from a variable volume container. The system includes a roller that rotates in response to a constant applied torque to force fluid from the flexible container under a substantially constant pressure. Two spaced apart parallel rollers can exert force on both sides of the container.

The Hurwitz Constant and Diophantine Approximation on Hecke Groups

Abstract: Etude de l'approximation d'un nombre G-irrationnel x par des nombres G-rationnels appartenant a l'orbite de ∞