Abstract: The problem of minimising a real scalar quantity (for example array output power, or mean square error) as a function of a complex vector (the set of weights) frequently arises in adaptive array theory. A complex gradient operator is defined in the paper for this purpose and its use justified. Three examples of its application to array theory problems are given.

Abstract: The configuration interaction CIPSI algorithm defines three classes of determinants of decreasing importance; the most important ones (∼ 100) are generators, the mean class (∼ 10 3 ) is treated variationally or to the fourth order, while the less important ones (∼ 10 5 ) are treated to the second order only. The accuracy of the result is studied as a function of the borders between the classes in the case of H 2 O (double-zeta basis set), where the exact solution is known, and for the nearly degenerate CN + problem.

Abstract: A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

Abstract: Coefficient bounds for functions with a positive real part are used in a rather novel way to find sharp bounds for the first six coefficients of a function which is inverse to a regular normalized univalent function whose derivative has a positive real part in the unit disk.

Abstract: A new class of methods for solving systems of nonlinear equations, called tensor methods, is introduced. Tensor methods are general purpose methods intended especially for problems where the Jacobian matrix at the solution is singular or ill-conditioned. They base each iteration on a quadratic model of the nonlinear function, the standard linear model augmented by a simple second order term. The second order term is selected so that the model interpolates function values from several previous iterations, as well as the current function value and Jacobian. The tensor method requires no more function and derivative information per iteration and hardly more storage or arithmetic per iteration, than a standard method based on Newton’s method. In extensive computational tests, a tensor algorithm is significantly more efficient than a similar algorithm based on the standard linear model, both on standard nonsingular test problems and on problems where the Jacobian at the solution is singular.

Abstract: Any continuous resistive nonlinear circuit can be approximated to any desired accuracy by a global piecewise-linear equation in the canonical form a + B x + \sum_{i=1}^{p}c_{i} |\langle \alpha_{i}, x \rangle - \beta_{i}|= 0 . All conventional circuit analysis methods (nodal, mesh, cut set, loop, hybrid, modified nodal, tableau) are shown to always yield an equation of this form, provided the only nonlinear elements are two-terminal resistors and controlled sources, each modeled by a one-dimensional piecewise-linear function. The well-known Katzenelson algorithm when applied to this equation yields an efficient algorithm which requires only a minimal computer storage. In the important special case when the canonical equation has a lattice structure (which always occur in the hybrid analysis), the algorithm is further refined to achieve a dramatic reduction in computation time.

Abstract: PASS transistors are used to reduce the layout complexity of logic circuits by using PASS transistors connected to pass a first and second input function to an output node in response to selected CONTROL signals, thereby to generate a selected output function on the output node. The PASS transistor comprises a transistor capable of passing an input function in response to a CONTROL signal applied to the transistor thereby to generate an output function related to the input function. In general, the input function comprises less than all of a set of input variables and the CONTROL function comprises one or more of the remainder of the set of input variables.

Abstract: Undergraduate students performed one of three levels of processing on each word (15, 30, or 45) presented during a 120-sec interval. Subjects were told in advance that they would be required to estimate the length of the presentation interval (prospective condition) or were presented with an unexpected estimation task (retrospective condition). In the prospective condition, interval estimates were an inverse function of list length when relatively deep levels of processing were required, but were an increasing function of list length when shallow processing was required. In the retrospective condition, estimates were an increasing function of list length and were unaffected by different levels of processing. The interval estimation model proposed by Hicks, Miller, and Kinsbourne (1976) provided a better account of the data than did the storage-size hypothesis of Ornstein (1969).

Abstract: There is no straightforward way to proceed from the continuous-time Wigner distribution to a discrete-time version of this time-frequency signal representation. A previously given definition of such a function turned out to yield a distribution that was periodic with period π instead of 2π and this caused aliasing to occur. Various alternative definitions are considered and compared with respect to aliasing and computational complexity. From this comparison it appears that no definition leads to a function that is optimum in all respects. This is illustrated by an example.

Abstract: Let It is proved that the function f reaches its maximum for n = 6 983 776 800, and that maxn≥2 f(n) = 1.5379. The proof deals with superior highly composite numbers introduced by Ramanujan.

Abstract: New dialogue is post-synchronised with guide track dialogue by using signal processing apparatus in which the analog guide track signal x, (t) undergoes speech parameter measurement processing in a processor 43 to provide a speech parameter measurement processing in a processor 43 to provide a speech parameter vector A (kT). The new dialogue signal x 2 (t') is processed to give waveform data which can be stored on disc 25 and a speech parameter vector B (jT) from a parameter extraction processor 42. The variables k and 1 are data frame numbers, and T is an analysis interval. Some parameters of the vector B are used in a process 48 to classify successive passages of the new dialogue signal into speech and silence, to produce classification data f (jT). The vectors A and B and the classification data are utilized in a time warp processor SBC2 to determine a timewarping function w (kT) giving the values of i in terms of the values of k associated with the corresponding speech features, and thereby, indicating the amount of expansion or compression of the waveform data of the new dialogue signal needed to align the time-dependent features of the new dialogue signal with the corresponding features of the guide track signal. Editing instructions are generated in signal editor computer SBCI from the w (kT) data, feature classification data, pitch data p (jT) and the data stream x 2 (nD) so that the editing of x 2 (nD) can be carried out by the computer SBCI in which periods of silence or speech are lengthened or shortened to give the desired alignment. The edited data x 2 (nD) is converted to analog by a converter unit 29. and low pass filtered to provide an audio output signal to be recorded as the synchronised new dialogue.

Abstract: In this paper, we generalize the well-known notions of minimax, maximin, and saddle point to vector-valued functions. Conditions for a vector-valued function to have a generalized saddle point are given. An example is used to illustrate the generalized concepts of minimax, maximin, and saddle point.

Abstract: Detection of edges and lines in multidimensional data is an important operation in a number of image processing applications. The multidimensional picture function is a sampling of the underlying reflectance function of the objects in the scene with the noise added to the true function values. Edges and lines refer to places in the image where there are jumps in the values of the function or its derivatives. The multidimensional greytone surface is expanded as a weighted sum of basis functions. Using multidimensional orthogonal polynomial basis functions, expressions are developed for the coefficients of the fitted quadrautic and cubic surfaces. The parameters of the fitted surfaces are obtained when there is a rotation in the coordinate system. Assuming the noise is Gaussian, statistical tests are devised for the detection of significant edges and lines. Direction isotropic properties of the fitted surfaces are described. For computational efficiency, recursive relations are obtained between the parameters of the fitted surfaces of successive neighborhoods. Furthermore, experimental results are presented by applying the developed theory to multiband Landsat-Imagery Data.

Abstract: Edge effect is an inherent problem when using live-trapping grids to census animals in populations. The relationship between grid size and home range size, shape, and dispersion pattern was investi...

Abstract: Unique phase recovery from a single two-dimensional intensity data set depends on the complex function's being represented by a globally irreducible entire function. Functions of two complex variables, in general, are likely to be irreducible, but no conditions have been stated to ensure this except for objects consisting of specific arrays of points. A condition based on Eisenstein's criterion for irreducibility is given here that requires two reference points in the object plane.

Abstract: We consider an optimal control problem with end-constraints formulated in terms of a differential inclusion. A sufficient condition for local optimality of a trajectory is given, involving a Lipschitzian function $\phi $ which is a generalized solution to the Hamilton–Jacobi equation. It is shown that the weakest hypothesis under which the condition is also necessary is that the problem be locally calm. It is further proved that local calmness is implied by strong normality. We thereby establish that the Caratheodory approach, modified to permit Lipschitzian functions $\phi $, is applicable in principle when the first order optimality conditions yield nontrivial information.

Abstract: An integral representation for the Green's function of the one-dimensional Morse potential is obtained by solving path integrals. To test the method employed, the correct bound-state energy spectrum and the wave functions are derived.

Abstract: Let be a connected, analytic (in general, not closed) subset of the complex space and let be a compact set which is not pluri-polar in . In this article it is proved that the extremal function is locally bounded on if and only if belongs to some algebraic set of the same dimension as . Moreover, it is shown that for an algebraic set in a neighborhood of any ordinary point the function can be represented as the limit of an increasing sequence of maximal functions. Bibliography: 10 titles.

Abstract: Robust estimates for the parameters in the general linear model are proposed which are based on weighted rank statistics. The method is based on the minimization of a dispersion function defined by a weighted Gini's mean difference. The asymptotic distribution of the estimate is derived with an asymptotic linearity result. An influence function is determined to measure how the weights can reduce the influence of high-leverage points. The weights can also be used to base the ranking on a restricted set of comparisons. This is illustrated in several examples with stratified samples, treatment vs control groups and ordered alternatives.

Abstract: A problem of considerable interest in the design of a database is the selection of indexes. In this paper, we present a probabilistic model of transactions (queries, updates, insertions, and deletions) to a file. An evaluation function, which is based on the cost saving (in terms of the number of page accesses) attributable to the use of an index set, is then developed. The maximization of this function would yield an optimal set of indexes. Unfortunately, algorithms known to solve this maximization problem require an order of time exponential in the total number of attributes in the file. Consequently, we develop the theoretical basis which leads to an algorithm that obtains a near optimal solution to the index selection problem in polynomial time. The theoretical result consists of showing that the index selection problem can be solved by solving a properly chosen instance of the knapsack problem. A theoretical bound for the amount by which the solution obtained by this algorithm deviates from the true optimum is provided. This result is then interpreted in the light of evidence gathered through experiments.

Abstract: In nondifferentiable optimization an important role is performed by a sub-differential — a set of linear functionals — which, in one sense or another, locally approximate a given function. For a convex function the subdifferential enables one to describe necessary conditions for a minimum, to compute directional derivative, to find steepest descent directions. That's why in any attempts have been made to extend the concept of subdifferential to nonconvex nonsmooth functions. It has been shown by the authors that for a rather large family of functions it is useful and natural to consider as an approximating tool not a single set (the subdifferential), but a pair of sets (the quasidifferential). The family of quasidifferential functions is a linear space closed with respect to all algebraic operations as well as the operations of taking pointwise maximum and minimum. In this paper a short survey of some properties of quasidifferentiable functions is presented. The notion of quasidifferentiable mappings is i...

Abstract: Branching programs for the computation of Boolean functions were first studied in the Master's thesis of Masek.7 In a rather straightforward manner they generalize the concept of a decision tree to a decision graph. Let P be a branching program with edges labelled by the Boolean variables, x1,...,xn and their complements. Given an input a=(a1,...,an) e {0,1}n, program P computes a function value fp(a) in the following way. The nodes of P play the role of states or configurations. In particular, sinks play the role of final states or stopping configurations. The length of program P is the length of the longest path in P. Following Cobham,2capacity of the program is defined to be the logarithm to the base 2 of the number of nodes in P. Length and capacity are lower bounds on time and space requirements for any reasonable model of sequential computation. Clearly, any n-variable Boolean function can be computed by a branching program of length n if the capacity is not constrained. Since space lower bounds in excess of log n remain a fundamental challenge, we consider restricted branching programs in the hope of gaining insight into this problem and the closely related problem of time-space trade-offs.