Infinite Input Research Articles

Reducing work-in-process inventory in certain classes of flexible manufacturing systems

In this paper, we establish that maintaining a balanced workload on each machine over time stochastically minimizes the work-in-process inventory in certain types of flexible manufacturing systems (FMSs) with finite or infinite common input buffer storage and an ample buffer et each machine. The results obtained here complement those obtained by Stecke and Morin (1985), in which it is established that balancing workloads maximizes expected production, again for the. same, particular types of FMSs. Stecke and Morin (1985) treats a static FMS loading problem, while this paper addresses a dynamic problem which considers three strategies to control the release of parts into the system.

Design of high-frequency amplifiers

Two novel active compensated noninverting and inverting finite gain amplifier circuits are reported. Compensation is achieved by using two extra operational amplifiers and four resistors. The proposed amplifiers have negligible phase and magnitude errors over a prescribed frequency range. The inverting amplifier has the attractive advantage of an infinite input impedance. The design equations are given.

Quadratic automata

In this paper the notion of a quadratic automaton transformation is defined and studied. The automata considered transform infinite input sequences of elements from a finite commutative ring with identity to infinite output sequences. Results extending the linear automaton transformation theory of A. Nerode are derived and two distinct approaches to machine realization arise depending upon whether 2 is invertible in the base ring or not. Such a naturally occurring quadratic map as the AND function of elementary switching theory is easily realized in this setting.

The feasibility of making spectral IP measurements in the time domain

The time-domain response of a published theoretical IP model has been explored, for single current pulses of infinite and finite duration and for a conventional repetitive pulse train. Because of the very slow increase of charging voltage on many natural outcrops it is impossible to produce a pulse of such a length that it behaves as an infinite input. A repetitive pulse train results in decay curves on which electromagnetic coupling, but not information on the nature of mineralisation, can be recognised. The response to a single finite pulse can be analysed by a rather inelegant curve-matching procedure. Field measurements using very simple equipment showed that black shales have a distinctive IP response but gave no other useful discriminatory information.

Novel two-o.a. three-resistor variable phase inverting amplifier

A new active phase-compensated inverting amplifier is proposed. The amplifier circuit employs two o.a.s and three resistors and has an infinite input impedance. The proposed amplifier is also suitable for phase correction in two-integrator loop filters.

The limiting distribution for the infinitely deep dam with a Markovian input

The paper outlines a case for taking greater interest in the bottomless, or infinitely deep, dam model in Hydrology. It then shows that for such a model with unit withdrawals and an ergodic Markov chain input process the limiting distribution of depletion, when this exists, is a zero modified geometric distribution. This result generalises the well known result for independent inputs. The technical conditions required for the proof are satisfied for finite state space input processes and are shown to be satisfied by certain infinite state space input processes. These include as special cases examples which have a negative binomial limiting input distribution.

Convergence theorems for stochastic automata and learning systems

It is shown that every stochastic automaton generates a semigroup of continuous linear operators in order to give conditions for the convergence of certain operators connected with infinite input sequences. The main results of this note are conditions for the infinitesimal stability of stochastic automata. Since under suitable conditions the behaviour of a learning system can be represented by a stochastic automaton, these results apply to the asymptotic stability of learning.

Realization of frequency-dependent negative resistance

A simple and elegant method to realize a Frequency-Dependent Negative Resistance (FDNR) with only one operational amplifier is presented. The input arid output admittances of the proposed amplifier configuration realize either a frequency-dependent negatives resistance or a combination of frequency-dependent negative resistance with series-parallel EC configuration. Infinite input impedance is realized by invoking certain constraints on the elements of the network. Input and output admittance/impedance sensitivity analysis is also presented.

On demand realization of a frequency-dependent negative resistance and an infinite input impedance

A simple configuration to realize an ideally infinite input impedance, both negative and positive, using an operational amplifier is presented. It is also shown that the same configuration results in a frequency-dependent, negative resistance at its output terminal.

ω-Computations on Turing machines

The paper develops the theory of Turing machines as recognizers of infinite (ω-type) input tapes. Various models of ω-type Turing acceptors are considered, varying mainly in their mechanism for recognizing ω-tapes. A comparative study of the models is made. It is shown that regardless of the ω-recognition model considered, non-deterministic ω-Turing acceptors are strictly more powerful than their deterministic counterparts. Canonical forms are obtained for each of the ω-Turing acceptor models. The corresponding families of ω-sets are studied; normal forms and algebraic characterizations are derived for each family.

The trap-loaded cylindrical antenna

The trap-loaded cylindrical antenna is a cylindrical antenna having one or more traps located in its arms. The traps are either parallel inductor-capacitor circuits or short-circuited transmission line stubs that are designed to be antiresonant (having essentially an infinite input impedance) at some particular frequency. The location and the antiresonant frequency of the traps are selected to enhance the radiation pattern or input impedance of the antenna. This study is confined to the properties of trap-loaded cylindrical antennas that contain only one trap in each arm. The effect of the length of the outer section, length of the inner section, diameter of the cylinder and characteristic impedance or inductance-capacitance ratio of the trap on the input impedance, radiation pattern, and current distribution were studied both experimentally and with the aid of two numerical solutions of an integral equation for the current distribution. The conclusions drawn from this study are that the design procedure for the multiband trap antenna described by Greenberg [1], adjusting the antiresonant frequency of the trap to control the upper resonant frequency, is indeed valid. Graphs suitable for designing trap antennas using this procedure are available in this paper. Furthermore, it is shown that the characteristic impedance or inductance-capacitance ratio of the trap can also be adjusted to vary the lower resonant frequency of the antenna. Design graphs using this procedure are also available in this paper. This study also showed that a relatively wide range of upper to lower antenna resonant frequency ratios can be obtained while still maintaining radiation patterns and input impedances close to those of a half-wave dipole at both frequencies. Graphs are available showing the tradeoff in pattern shape and input impedance that must be made to obtain resonant frequency ratios other than 2 to 1. It was discovered that the trap antenna, sometimes called a Franklin array, must be operated somewhat below the nominal design frequency or have the spacing between traps shortened somewhat, for it to have a radiation pattern similar to a collinear array of half-wave dipoles. Furthermore, the thicker the antenna, the more pronounced this effect is. While the nominal design was discovered to give an input impedance nearly resistive and near 70\Omega (for a dipole), any of the aforementioned modifications resulted in a nonresonant highly capacitive input impedance.

Π10 classes and Boolean combinations of recursively enumerable sets

Let be the collection of all sets which are finite Boolean combinations of recursively enumerable (r.e.) sets of numbers. Dale Myers asked [private correspondence] whether there exists a nonempty class of sets containing no member of . In this note we construct such a class. The motivation for Myers' question was his observation (reported in [1]) that the existence of such a class is equivalent to the assertion that there is a finite consistent set of tiles which has no m-trial tiling of the plane for any m (obeying the “origin constraint”). (For explanations of these terms and further results on tilings of the plane, cf. [1] and [5].) In addition to the application to tilings, the proof of our results gives some information on bi-immune sets and on complete extensions of first-order Peano arithmetic.A class of sets may be roughly described as the class of infinite binary input tapes for which a fixed Turing machine fails to halt, or alternatively as the class of infinite branches of a recursive tree of finite binary sequences. (In these definitions, sets of numbers are identified with the corresponding binary sequences.) Precise definitions, as well as many results concerning such classes, may be found in [3] and [4].

Realization of an on demand capacitive reactance

Abstract A configuration has been proposed by which an ideally infinite input impedance can be realized at all frequencies. The advantage of this configuration is that both positive and negative capacitive reactance can be realized just be controlling the gain of the amplifier, the realized capacitance being independent of frequency.

Noise performance of RC-active quadratic filter sections

A method for calculating the noise voltage at the output of quadratic filter sections is developed. Multiple-feedback low-pass, bandpass, and high-pass quadratic filter sections realized using differential-input single-ended output operational amplifiers are analyzed. The amplifiers are assumed to have infinite input impedance, infinite gain, and zero output impedance. The noise sources associated with the amplifiers are assumed to be statistically independent, but can have both white and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l/f</tex> noise components. A noise analysis of a fourthorder maximally flat low-pass filter realized by cascading two quadratic filter sections is included.

Input Resistance of a Short Dipole Antenna in a Warm Uniaxial Plasma

The input resistance of a short dipole antenna immersed in a warm magnetoplasma is calculated on the basis of the kinetic theory (Boltzmann equation). The plasma is uniaxial; i.e., the cyclotron frequency is much larger than the operating frequency of the antenna and the plasma frequency. The plasma is homogeneous, and collisions are included although the sheath is neglected. The dipole is assumed to be infinitesimally thin (producing an infinite input reactance( except for the case in which the dipole axis is parallel to the static magnetic field when we allow the dipole to have a nonzero radius and calculate the input impedance. It is found that at frequencies much less than the plasma frequency the input resistance differs markedly from the hydrodynamic and cold‐plasma results because of collisionless absorption processes. The input resistance is generally smaller when the dipole axis is inside the resonance cone than when it is outside. The resonance cone anomaly in the input resistance is reduced in magnitude from that of the cold‐plasma theory and is shifted to a higher frequency.

Statistics of laser Doppler velocimeter signals: frequency measurement

The statistical properties of laser Doppler velocimeter signals are derived and used to obtain the signal zero crossing statistics for steady flows and high scattering particle concentrations. The results are applied to a model of a zero crossing counter, and expressions for the power spectrum and autocorrelation of the output signal are given in terms of the input signal autocorrelation. The RMS value of the fluctuations in the zero crossing counter output is calculated as a function of the optical system bandwidth and the counting time for infinite and finite input signal-to-noise ratios, and simple asymptotic expressions are found for large counting times and infinite signal-to-noise ratio. For finite input signal-to-noise ratios and large counting times bounds are derived for the output of a zero crossing counter preceded by a tracking filter, and the effects of the tracking filter are discussed.

Mismatch Oriented Circuit Design and Its Application to Nuclear Electronics

Consistent application of mismatch between source and load is shown to lead to the design of feedback amplifiers, whose characteristics closely approach those of idealized black boxes exhibiting zero or infinite input and output impedance levels. The resulting configurations are shown to employ enhancing combinations between four kinds of basic amplifiers and series or shunt feedback applied to their input and output, respectively. Depending upon the signal parameter employed, the input and output terminals of the black boxes will operate in the voltage or in the current mode, each emerging in its own rights as the preferable technique if employed under proper conditions. Enhancing combinations result in greater flexibility of usable gain values and functions, and in reduced noise contribution to the preceding stage. Further extension of mismatch to active circuit design makes it possible to employ a greatly simplified transistor model, and restricts the dominant poles to those which are unavoidably introduced by the active elements. The resulting circuits are readily reproducible by conventional manufacturing methods, and further improvement of their performance is predicted through the application of microcircuit techniques. The design of a high resolution spectrometer is described, which employs enhancing combinations of such standard circuits. The choice of the most suitable circuit for each stage depends on the preferred signal parameter, noise considerations, and gain requirements.

Sensitivities of six R-C active circuits

The R-C active filters investigated use operational amplifiers as the active element and are capable of realizing second-order network functions with no finite transmission zeros. One of the networks uses positive feedback; another uses negative feedback (from an amplifier of nominally infinite gain); two use both positive and negative feedback (from a paraphase amplifier of nominally infinite gain); the fifth uses a combination of three amplifiers all of nominally infinite gain; the sixth uses a four-amplifier realization of a gyrator, again all of nominally infinite gain.Expressions are given for the sensitivity of the (Q-factor and frequency of location of the ‘peak’ to variations in the ratios of the passive elements and to gain. Also the effects on the Q-factor of finite gain and phase shift in the amplifier are observed.The operational amplifiers are assumed to be of infinite input impedance and zero output impedance and to have a gain which is approximated to a first-order lag.

Rejoinder to Professor Mckenzie

PROFESSOR MCKENZIE objects to my contention that every cost function can be extended on the grounds that in some cases the set of input vectors producing unit output may not be bounded. In particular he quotes the where we may wish to consider disposal processes. Later the Cobb-Douglas production function is instanced as a simple case which does not fall within the scope of my theorem. Consider first the Cobb-Douglas function, since this will serve to illustrate very well the way I would deal with disposal processes. Notice first that, however realistic an approximation the Cobb-Douglas function may be to production functions of the real world over part of its range, it cannot possibly continue to be a good approximation to anything likely to be observed in a region where any factor price approaches zero. This is because in this region the number of units of input of at least one factor will begin to exceed the number of elementary particles in the universe. This absurdity is, of course, precisely why I thought it reasonable to assume the boundedness of the set of input vectors. But let us suppose (impossibly) that the laws of physics are truly reflected by the Cobb-Douglas function over the whole range and that no marginal product can ever be zero for a finite input of the factor. What we should then observe is not an infinite input of a factor but that the factor price could never attain the value zero. There would be a natural bound, different from zero, on the economically significant domain of factor prices and a corresponding natural bound on the quantity of input, both determined by the maximum quantity of the factor in existence in any one country. Suppose now we consider the reduced domain of definition of factor prices which will in this be contained in the positive orthant. Let S1 be the corresponding reduced set of minimum cost techniques. Now extend the cost function as required by defining it as the support function of the reduced set Si. If an inverse exists to the extended cost function, there must also be an inverse to the cost function thought of as defined only over the economically significant range. Disposal processes of any kind can be treated the same way. This leads to the following proposition.

Active RC filters employing a single operational amplifier to obtain biquadratic responses

In this paper, networks are presented in tabular form to simplify the design of RC active filters having magnitude responses characterised by pass-band attenuation ripples and stop-band transmission zeros. The responses of these networks may be described by biquadratic rational functions. In all, the form and element values for 11 different networks are tabulated.The basic network discussed in the paper is an operational amplifier with multiloop feedback in cascade with a passive RC circuit and having a second-order response. Higher-order responses than the second may be obtained by cascading second-order stages of the tabulated networks, with suitable isolating stages when necessary.Two different forms of passive circuit are given, together with their design formulas. Both low-pass and high-pass filters are considered; these can be cascaded to give band-pass or band-stop characteristics.The operational amplifier is assumed to have infinite input and zero output impedance; the effects of departure from these ideal conditions on the filter response is considered.