Showing papers on "Function (mathematics) published in 1978"
NEC1
TL;DR: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition, in which the warping function slope is restricted so as to improve discrimination between words in different categories.
Abstract: This paper reports on an optimum dynamic progxamming (DP) based time-normalization algorithm for spoken word recognition. First, a general principle of time-normalization is given using time-warping function. Then, two time-normalized distance definitions, called symmetric and asymmetric forms, are derived from the principle. These two forms are compared with each other through theoretical discussions and experimental studies. The symmetric form algorithm superiority is established. A new technique, called slope constraint, is successfully introduced, in which the warping function slope is restricted so as to improve discrimination between words in different categories. The effective slope constraint characteristic is qualitatively analyzed, and the optimum slope constraint condition is determined through experiments. The optimized algorithm is then extensively subjected to experimental comparison with various DP-algorithms, previously applied to spoken word recognition by different research groups. The experiment shows that the present algorithm gives no more than about two-thirds errors, even compared to the best conventional algorithm.
6,712 citations
TL;DR: In this article, the root growth and function of the root systems of plants in the soil is divided into three parts : physiological background (5 chapters); response to soil conditions (4 chapters); and tillage of the soil (2 chapters).
Abstract: his book is concerned with the growth and function of the root systems of plants in the soil and is divided into 3 parts : physiological background (5 chapters); response to soil conditions (4 chapters); and tillage of the soil (2 chapters). The 1st part covers the physiological control of growth throughout the plant, the growth and form of roots, the absorption and transport of nutrients, water relations and root/rhizosphere flora interactions. The 2nd part covers the soil environment, mechanical impedance of root growth, effects of anaerobic soil conditions and the root/soil interface. The 3rd part covers traditional and modern methods of tillage and effects of reduced cultivation on soil conditions and crop growth. The book is aimed at 3rd yr undergraduates and research workers.ADDITIONAL ABSTRACT:The book is written for advanced students and research workers. Its first six chapters are concerned with root physiology (root/shoot relationships, growth substances, root growth and form, nutrient uptake and transport, water relations, and rhizosphere effects). The next four chapters deal with responses to soil conditions (physical and chemical environment, mechanical impedance, anaerobic conditions and the soil/root interface). The two concluding chapters are on tillage methods and reduced cultivation.ADDITIONAL ABSTRACT:The topics considered are: physiological relationships between roots and shoots; the growth and form of root systems; the absorption and transport of nutrients; the water relations of root systems; relationships between roots and the rhizosphere flora; the soil environment; mechanical impedance of root growth; effects of anaerobic soil conditions; the soil/root interface;traditional and modern methods of tillage; reduced cultivation, soil conditions and crop growth.
477 citations
TL;DR: In this paper, the theory of binary coherent systems is generalized for multi-state components, where the system state is defined to be the state of the worst component in the best min path, or equivalently, the best components in the worst min cut.
Abstract: The theory of binary coherent systems is generalized for multi-state components. The system state is defined to be the state of the “worst” component in the “best” min path, or equivalently, the state of the “best” component in the “worst” min cut. Many of the results for the binary case can be computed for multi-state systems using the binary structure and reliability function concepts. Monotonicity results are now valid with respect to stochastic ordering of component probability vectors.
424 citations
TL;DR: In this paper, an accurate model of the spectra of advected quantities, such as temperature, has been developed and is applied here to optical propagation, and the model is used to compute the temperature structure function, the variance of log intensity as a function of Fresnel-zone size, the covariance function of log amplitude, the structure function of phase, as well as the phase coherence length.
Abstract: Recent experiments reveal the high-wave-number form of the power spectrum of temperature fluctuations in turbulent flow. It is precisely this high-wave-number portion of the temperature spectrum that strongly affects optical propagation in the atmosphere. An accurate model of the spectra of advected quantities, such as temperature, has been developed and is applied here to optical propagation. An outstanding feature of the model and the observed temperature spectrum is a “bump” at high wave numbers. The accurate model of the temperature spectrum is used to compute the temperature structure function, the variance of log intensity as a function of Fresnel-zone size, the covariance function of log amplitude, the structure function of phase, as well as the phase coherence length. These results are compared with the predictions of Tatarskii’s spectrum. The bump in the temperature spectrum produces a corresponding bump in the temperature structure function, the variance of log intensity, and the structure function of phase. The accurate model is also used to determine the shape of the structure function of aerosol concentration fluctuations; it is found that this structure function varies as the logarithm of the separation distance for small separations.
272 citations
TL;DR: In this article, a review of existence theorems for critical points of real-valued functions on a real Banach space is presented and applied to elliptic and hyperbolic partial differential equations.
Abstract: Publisher Summary This chapter reviews some existence theorems for critical points of a real-valued function on a real Banach space and to apply these results to elliptic and hyperbolic partial differential equations The abstract results on critical points are obtained using minimax arguments Applications to elliptic equations are thereafter provided for the same A new proof is given for a recent result of Ahmad et al , as well as some variants of their result The work on abstract results on critical points is applied to hyperbolic problems
189 citations
TL;DR: In this article, the friction between two juxtaposed leptodermous systems in relative motion arising from the exchange of particles between them was studied and a universal key function related to the flux between two parallel surfaces as a function of their separation was derived.
158 citations
TL;DR: Under various noise conditions, it is shown that the estimates are strongly uniformly consistent and can be exploited to design a simple random search algorithm for the global minimization of the regression function.
Abstract: A class of nonparametric regression function estimates generalizing the nearest neighbor estimate of Cover [ 12] is presented. Under various noise conditions, it is shown that the estimates are strongly uniformly consistent. The uniform convergence of the estimates can be exploited to design a simple random search algorithm for the global minimization of the regression function.
147 citations
TL;DR: A simple technique for reasoning about equalities that is fast and complete for ground formulas with function symbols and equality is presented.
Abstract: A simple technique for reasoning about equalities that is fast and complete for ground formulas with function symbols and equality is presented. A proof of correctness is given as well.
146 citations
TL;DR: The point-area method for deconvolution derives a "staircase" input function which, when convolved onto the characteristic function, gives an output function coincidental with the given output data points.
131 citations
TL;DR: In this article, three different Green's function methods are synthesized, showing that the final equations in the different cases are identical and using the transverse transmission line theory, using an N-layer dielectric structure.
Abstract: To find the characteristic parameters of the wave propagation in microstrip structures, several Green's function methods have already been developed, corresponding to particular geometric configurations In this paper, three of these methods are synthesized, showing that the final equations in the different cases are identical Moreover, using the transverse transmission line theory, the Green's function is solved numerically for an N-layer dielectric structure
1 Feb 1978
TL;DR: This paper presents precise versions of some "laws" that must be satisfied by computations involving communicating parallel processes, intended to be applied to the design and analysis of systems consisting of large numbers of physical processors.
Abstract: This paper presents precise versions of some "laws" that must be satisfied by computations involving communicating parallel processes. The laws take the form of stating plausible restrictions on the histories of computations that are physically realizable. The laws are very general in that they are obeyed by parallel processes executing on a time varying number of distributed physical processors. For example, some of the processors might be in orbiting satellites. The laws are justified by appeal to physical intuition and are to be regarded as falsifiable assertions about the kinds of computations that occur in nature rather than as proved theorems in mathematics. The laws are intended to be used to analyze the mechanisms by which multiple processes can communicate to work effectively together to solve difficult problems. The laws presented in this paper are intended to be applied to the design and analysis of systems consisting of large numbers of physical processors. The development of such systems is becoming economical because of rapid progress in the development of large scale integrated circuits. We generalize the usual notion of the history of a computation as a sequence for events for the notion of a partial order of events. Partial orders of events seem better suited to expressing the causality involved in parallel computations than totally ordered sequences of events obtained by "considering all shuffles" of the elementary steps of the various parallel processes [2l, 22]. The utility of partial orders is demonstrated by using them to express our laws for distributed computation. These laws in turn can be used to prove the usual induction rules for proving properties of procedures. They can also be used to derive the continuity criterion for graphs of functions studied in the Scott-Strachey model of computation. The graph of a function is simply the set of all input output pairs for the function. We can prove that the graph of any physically realizable procedure p that behaves like a mathematical function is the limit of a continuous functional F such that: i graph(p) = F ({}) i N In other words the graph of p is the limit of the n-fold compositions of F with itself beginning with the empty graph.
IBM1
TL;DR: In this paper, the temperature dependence of the homogeneous width and frequency of the S 1 − S 0 − 0 transition of free-base porphin as a guest in an n-octane matrix was investigated.
TL;DR: It is demonstrated by means of simple examples that the equilibrium total flow vector and origin to destination travel cost functions are not differentiable at certain possibly difficult to predict points in the set of feasible input flow vectors and that the cost functions do not in general possess such other potentially useful properties as convexity or concavity.
Abstract: The Wardrop equilibrium problem for urban road networks is considered. It is shown that the unique equilibrium total flow vector is a continuous function of the input traffic flows. Under fairly weak conditions it is proven that the total origin to destination travel costs are also continuous functions of the input traffic flows. It is then shown that each origin to destination cost is a monotonically nondecreasing function of its own input flow when other inputs are held fixed. Finally, it is demonstrated by means of simple examples that the equilibrium total flow vector and origin to destination travel cost functions are not differentiable at certain possibly difficult to predict points in the set of feasible input flow vectors and that the cost functions do not in general possess such other potentially useful properties as convexity or concavity. These results are important to an understanding of the sensitivity of the equilibrium state to variations in input data.
1 Oct 1978
TL;DR: In this paper, a generalised Wiener-Hopf equation is derived for systems under Gaussian excitation that can be described by a model consisting of a linear system in cascade with a static nonlinear element, followed by another linear system.
Abstract: By considering the class of separable random processes, a generalised Wiener-Hopf equation is derived for systems under Gaussian excitation that can be described by a model consisting of a linear system in cascade with a static nonlinear element, followed by another linear system. This result, together with a similar relationship for the 2nd-order crosscorrelation function, is used to formulate an identification and structure testing algorithm for this class of nonlinear system. The results of a simulation study are included to illustrate the validity of the algorithm.
TL;DR: This extended interval Newton method will isolate and bound all the real roots of a continuously differentiable function in a given interval and it is proved that the method never fails to converge.
Abstract: In this paper, we extend the interval Newton method to the case where the interval derivative may contain zero. This extended method will isolate and bound all the real roots of a continuously differentiable function in a given interval. In particular, it will bound multiple roots. We prove that the method never fails to converge.
TL;DR: A special class of methods that needs only 17 function evaluations per step to calculate a Runge-Kutta method of order 10, which has to solve a non-linear algebraic system of 1205 equations.
Abstract: In order to calculate a Runge-Kutta method of order 10, one has to solve a non-linear algebraic system of 1205 equations. We give here a special class of methods that needs only 17 function evaluations per step.
TL;DR: In this paper, the parameters of several families of distributions are estimated by means of minimum χ2; use is made of random samples taken from Dutch income-earning groups in 1973.
TL;DR: In this article, the cyclic behavior of points under repeated application of a function yields insights into population patterns, and points' cyclic behaviour can be used to predict population patterns.
Abstract: Analysis of the cyclic behavior of points under repeated application of a function yields insights into population patterns.
TL;DR: Compared with Walsh function approaches, the proposed method is simpler to compute, is more suitable for computer programming, and provides the same accuracy.
Abstract: A recursive algorithm is developed for the piecewise-constant solution of dynamic equations via block-pulse functions φj(t),where j=1,2,...,m. For 1≤j≤m (where j and m are integers) and final timeT, each block-pulse function φj(t) is defined by φj(t)=1 for (j−1)T/m≤t
TL;DR: Weitzman as mentioned in this paper argued that the amount of uncertainty in marginal cost is sufficient to justify a second-order approximation of total cost and benefit functions, where 4 is the quantity level chosen to maximize the expected benefits over costs when quantity controls are used.
Abstract: It seems to have become fashionable in economics to assume that some function has a particular form, such as quadratic, to derive some results on the basis of that form, and then to present those results as being approximate results for any case in which the original function can be approximated reasonably well by the particular form chosen. This is essentially the procedure used by Weitzman [2] in an interesting article in this Review discussing the question of whether it is better to use quantity control or control by price to regulate the output of some good. It is a procedure that has also been used by others. Weitzman justified it by asserting that it can be defended rigorously along the lines developed by Samuelson [1], although Samuelson is there concerned with a somewhat different problem. This procedure is not, however, a rigorous one and its use can, as I will show, give rise to misleading conclusions. At a heuristic level, it is not difficult to see where the problem may lie. The fact that an error in the representation of a function is small in relation to the values of that function does not necessarily imply that, after a number of manipulations, the resulting error is small in relation to the results that are derived. The point is a general one. The force of it can, I hope, be brought across by an example applied to the problem considered by Weitzman. Weitzman's argument is set out in terms of cost and benefit functions C(q, 0) and B(q, il), where q is the output produced and 0 and il are independent random variables reflecting the uncertainty involved in the functions. Weitzman assumes that " the amount of uncertainty in marginal cost is ... sufficiently small to justify a second-order approximation of total cost and benefit functions ... around 4 ", where 4 is the quantity level chosen to maximize the excess of expected benefits over costs when quantity controls are used. Hence he treats the marginal cost and benefit functions Cl(q, 0) and Bl(q, '1) as represented by the linear functions
TL;DR: A new method for numerical deconvolution is described, based on the least-squares criterion and approximates the input rate by a polynomial function, for use in calculating drug input rates.
Abstract: A new method for numerical deconvolution is described, for use in calculating drug input rates. The method is based on the least-squares criterion and approximates the input rate by a polynomial function. Ill-conditioning of the normal equations is avoided by using orthogonal functions. The use of the method is illustrated by means of examples, using simulated data.
TL;DR: This paper considers the problem of identifying the parameters of dynamic systems from input-output records, both lumped-parameter and distributed-parameters systems, deterministic and stochastic, and a feature of the method permits the identification of unknown initial conditions simultaneously with the parameter identification.
Abstract: This paper considers the problem of identifying the parameters of dynamic systems from input-output records Both lumped-parameter and distributed-parameter systems, deterministic and stochastic, are studied The approach adopted is that of expanding the system variables in Walsh series The key point is an operational matrix P which relates the coefficient matrix Г of the Walsh series of a given function with the coefficient matrix of its first derivative Using this operational matrix P one overcomes the necessity to use differentiated data, a fact that usually is avoided either by integration of the data or by using discrete-time models Actually, the original differential input-output model is converted to a linear algebraic (or regression) model convenient for a direct (or a least squares) solution A feature of the method is that it permits the identification of unknown initial conditions simultaneously with the parameter identification The results are first derived for single-input single-output systems and then are extended to multi-input multi-output systems The case of non-constant parameters is treated by assuming polynomial forms Some results are also included concerning the identification of state-space and integral equation models The theory is supported by two examples, which give an idea of how effective the method is expected to be in the real practice
1 Jan 1978
TL;DR: In this article, the authors studied the free boundary problem of the PDE in nuclear fusion and obtained at least two distinct non-trivial free boundaries for the case where the constrained functional is continuously convex and nondifferentiable.
Abstract: We study the EVP of the PDE: Lu=λφ(x, u(x)), where L is a second order elliptic differential operator, and φ(x, t) is a function in x and t, which may be discontinuous in t. Under certain conditions of φ, the structure of the positive spectrum and the existence of at least three distinct solutions of this equation are treated. These results are applied to a class of free boundary problems of the equilibrium equations in nuclear fusion. We obtain at least two distinct non-trivial free boundaries. In addition, the Lagrangian multiplier theorem in a Hilbert space covers the case where the constrained functional is continuously convex and nondifferentiable.
TL;DR: A perturbation theory for molecular fluids due to Smith, and Perram and White is analyzed and equations are presented in a computationally convenient form for determining the full angular-dependent pair correlation function as discussed by the authors.
Abstract: A perturbation theory for molecular fluids due to Smith, and Perram and White is analysed and equations are presented in a computationally convenient form for determining the full angular-dependent pair correlation function. The discussion centres on the most appropriate choice of reference system and we use the Mayer function as expansion functional. The implications of the resulting RAM (reference system average Mayer-function expansion) theory are discussed.
TL;DR: In this article, the authors obtained the Bayes estimator for the Dirichlet process under the loss function (L(F, \hat{F}) = \int (F(u) - \hat {F}(u))^2 dw(u), where L(F) is a loss function.
Abstract: Let $X_1, \cdots, X_n$ be i.i.d. $F_0$ and let $Y_1, \cdots, Y_n$ be independent (and independent also of $X_1, \cdots, X_n$) random variables. Then assuming that $F$ is distributed according to a Dirichlet process with parameter $\alpha,$ the authors obtained the Bayes estimator $\hat{F}_\alpha$ of $F$ under the loss function $L(F, \hat{F}) = \int (F(u) - \hat{F}(u))^2 dw(u)$ when $X_1, \cdots, X_n$ are censored on the right by $Y_1, \cdots, Y_n,$ respectively, and when it is known whether there is censoring or not. Assuming $X_1, \cdots, X_n$ are i.i.d. $F_0$ and $Y_1, \cdots, Y_n$ are i.i.d. $G,$ this paper shows that $\hat{F}_\alpha$ is mean square consistent with rate $O(n^{-1}),$ almost sure consistent with rate $O(\log n/n^\frac{1}{2}),$ and that $\{\hat{F}_\alpha(u) \mid 0 u\rbrack P\lbrack Y_1 > u\rbrack > 0.$
TL;DR: In this article, the set of all e-periods for f is denoted by J ( f e), where f is almost periodic, written a.a.p, if for every e > 0, the set J(J~e) is relatively dense in,I1.
Abstract: The set of all e-periods for f is denoted by J ( f e). We say that f is almost periodic, written a.p., if for every e >0, the set J(J~e) is relatively dense in ,I1. A subset V of $ is called relatively dense (in $) if there exists an l > 0 such that every subinterval of $ of length I meets V. We call f weakly almost periodic, written w.a.p., if for each x' in the conjugate space X', the function x' of, mapping $ into the complex plane ~, is almost periodic. Continuous a.p. and continuous w.a.p, functions are treated in [1]. Let ~ be a family of functions mapping $ into X. We say that ~ is uniformly