Abstract: It has been known that the linear predictor coefficients (LPC) of speech signals can be transformed into a “pseudo” vocal‐tract area function whose boundary conditions are (a) a complete opening at the lips and (b) a matching resistance termination at the glottis. If the boundary condition at the glottis is replaced by a complete opening or a complete closure, all the poles of the resulting system function will move onto the unit circle in z plane. Using this fact it is possible to describe the original LPCs by two sets of pole frequencies corresponding to the two new boundary conditions at the glottis, or a set of frequency‐residue pairs corresponding to either set of poles. These representations have several important features: (1) If an original pole is narrow band, the new pole is close to the original pole; (2) the two sets of pole frequencies alternate and are ordered on the frequency axis; and (3) the problem of locating complex poles can be reduced to solving a polynomial with real roots whose order is one‐half that of the original all‐pole transfer function.

Abstract: A very primitive version of Gotlieb's timetable problem is shown to be NP-complete, and therefore all the common timetable problems are NP-complete. A polynomial time algorithm, in case all teachers are binary, is shown. The theorem that a meeting function always exists if all teachers and classes have no time constraints is proved. The multi-commodity integral flow problem is shown to be NP-complete even if the number of commodities is two. This is true both in the directed and undirected cases. Finally, the two commodity real flow problem in undirected graphs is shown to be solvable in polynomial time. The time bound is O(|v|2|E|).

Abstract: Many iterative algorithms for minimizing a function F (x) = F (x1, x2, …, xn) require first derivatives of F(x) to be calculated, but they maintain an approximation to the second derivative matrix automatically. In order that the approximation is useful, the change in x made by each iteration is subject to a bound that is also revised automatically. Some convergence theorems for a class of minimization algorithms of this type are presented, which apply to methods proposed by Powell (1970) and by Fletcher (1972). This theory has the following three valuable features which are rather uncommon. There is no need for the starting vector x(1) to be close to the solution. The function F(x) need not be convex. Superlinear convergence is proved even though the second derivative approximations may not converge to the true second derivatives at the solution.

Abstract: A simple procedure was developed to fit the first three moments of an actual phase function with a three parameter analytic phase function. The exact Legendre Polynomial decomposition of this function is, suitable for multiple scattering calculations. The use of this function is expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo omega sub 0 is greater than or equal to 0.9.

Abstract: When Fm in anova is significant, Scheffe's procedure provides no limit to the number of contrasts which can be declared significant. The new procedure described here provides a limit (r) to the number of significant contrasts which can be asserted. If assertions are made for v1 contrasts, which include r declarations of significance, the expectation of r/v1 will be a linearly decreasing function of v1 if traditional critical F values are used. A table is provided of new critical F values which set this expectation at a constant (0.05 or 0.01). The new critical F values are recommended for use whenever contrasts are sought, post hoc, for significance.

Abstract: In this paper, a discrete minimization problem arising from storage allocation considerations is studied. Owing to the complexity of finding an optimum solution, a heuristic is proposed and its performance is analyzed. The worst-case ratio of the cost by this algorithm to that by the optimum algorithm is shown to lie between 1.03 and 1.04, implying that this algorithm produces a solution within 4 per cent of the optimum. A generalization of this problem to a class of cost functions is also considered. The worst-case ratios for these functions tend, in the limit, to that of the cost function studied by Graham in his classical paper [1].

Abstract: An important component of mechanical theorem proving systems are unification algorithms which find most genaral substitutions which, when applied to two expresssions, maka them equivalent. Functions which are associative and commutative (such as the arithmetic addition and multiplication functions) are often the subject of mechanical theorem proving. An algorithm which unifies terms whose function is associativa and commutative is presented here The algorithm eliminates the need for axiomatizing the associativity and commutativity properties and returns a complete set of unifiers without recourse to the indefinite generation of vurianU and instances of the terms being unified required by previous solutions to the problem.

Abstract: Fault detecting test sets to detect multiple stuck-at-faults (s-a-faults) in certain networks, realizing Reed-Muller(RM) canonic expressions called RM canonic (RMC) networks, are given. It is shown that to detect t faults, t ≥ 1, in a network realizing an arbitrary n-variable logic function only tests need be applied ([x] is the integer part of x) and that these tests are independent of the function being realized.

Abstract: The question of controlling a linear retarded functional differential equation from an initial function to a terminal function, both functions belonging to the Sobolev space $W_2^{(1)} $, is considered. Necessary and sufficient conditions for full controllability in this function space are derived. These conditions result in computable algebraic criteria. Null controllability in function space is also investigated and conditions that are necessary and sufficient are obtained. In the absence of full controllability, methods for characterizing the attainable set in $W_2^{(1)} $ are discussed in detail along with a number of illustrative examples.

Abstract: Objective analyses using the so-called method of optimum interpolation incorporates statistical information on the variable(s) by means of the covariance or correlation functions. The concern in this contribution is with some properties of the analytic forms of the correlation functions that are used to model the statistical structure. First, some attention is directed to the question of fitting the various analytic forms (containing adjustable constants) to samples of actual correlations. All but one of the candidate forms were indistinguishable on the basis of the residuals of the statistical fitting procedure. Second, the criterion of positive-definiteness of the correlation function is extended to stipulate that the transform (or spectrum) of the function should possess some features of the spectra of actual variables—the most important one being the spectral decay rate at high wavenumber. Again, all but one of the candidate forms (the same one as above) had transforms that were acceptable. T...

Abstract: An algorithm has been described by S. Burris [3] which decides if a finite set of identities, whose function symbols are of rank at most 1, has a finite, nontrivial model. (By “nontrivial” it is meant that the universe of the model has at least two elements.) As a consequence of some results announced in the abstracts [2] and [8], it is clear that if the restriction on the ranks of function symbols is relaxed somewhat, then this finite model problem is no longer solvable by an algorithm, or at least not by a “recursive algorithm” as the term is used today.In this paper we prove a sharp form of this negative result; showing, by the way, that Burris' result is in a sense the best possible result in the positive direction. Our main result is that in a first order language whose only function or relation symbol is a 2-place function symbol (the language of groupoids), the set of identities that have no nontrivial model, is recursively inseparable from the set of identities such that the sentence has a finite model. As a corollary, we have that each of the following problems, restricted to sentences defined in the language of groupoids, is algorithmically unsolvable: (1) to decide if an identity has a finite nontrivial model; (2) to decide if an identity has a nontrivial model; (3) to decide if a universal sentence has a finite model; (4) to decide if a universal sentence has a model. We note that the undecidability of (2) was proved earlier by McNulty [13, Theorem 3.6(i)], improving results obtained by Murskiǐ [14] and by Perkins [17]. The other parts of the corollary seem to be new.

Abstract: We report measurements of the solvent proton spin–lattice relaxation rate 1/T1 in a water solution of GdCl3, pH 5.5, at 5, 15, and 25 °C. The data were obtained as a function of magnetic field, from 5 Oe to 12 kOe, corresponding to proton Larmor frequencies in the range 20 kHz to 50 MHz. The data are compared with theory, and it is shown that a satisfactory fit may be obtained for a range of values of the parameters of the theory. We give the results of a least squares fit of the theory to the data for two extremes of the range, one limit corresponding to the condition that the residence lifetime τM of a proton in the first hydration shell of the Gd3+ aquoion be comparable to the spin–lattice relaxation time T1M of the proton on the ion, the other limit corresponding to τM≪T1M. It is shown that knowledge of the temperature dependence of 1/T1 cannot distinguish between the two limits, and indeed, that unless a value for τM is obtained from independent experiments, the ambiguous results cannot be resolved. The source of the ambiguities is discussed in some detail since it is particularly clear in the present system, but considerably less so in systems containing complexes of macromolecules with paramagnetic ions, to which the present experiment is pertinent. It is also pointed out that, while there are many references to values for τM in the published literature, no experiments have been published that report values of τM for protons on the Gd3+ ion.

Abstract: Three different approaches to the problem of defining a location parameter in the case of asymmetry are considered First, the distribution F is approximated as closely as possible from above and below by two symmetric distribu- tion functions, and the points 0 and 0 of symmetry of these two distributions are called lower and upper points of sym- metry, respectively The interval (O, V is now a set of location points for F Next, the class of location parameters that are location- and scale-invariant and preserve order is considered This class forms a location set which turns out to coincide with (0, 01 Finally, it is shown that by allowing parameters to be function valued, it is possible to find a parameter 0F(0) that has the defining property of the point of symmetry for general, continuous F OF(-) is essentially unique Its minimum value is 0 and its maximum value is 0 Estimates, confidence regions and tests for OF(- ), and 0 are considered Extensions to the case where one is interested only in the location of the central part of F are given Applications to the measurement model with asymmetric errors, measures of asymmetry (skew- ness), and tests of symmetry, are treated

Abstract: The expectation value of the electronic energy of a n-electron system may be written as the ratio of two integrals, $$E = / $$ integration being taken over the 3n spatial and n spin coordinates of the electrons. Procedures for integration over the spin variables are not the concern of the present work, and we proceed under the assumption that the spin integrations of the energy expectation value have been completed. We are thus left with the evaluation of two integrals over the 3n spatial coordinates. A rather widely used procedure is to construct the trial form of the many electron wavefunction, Ψ, from a set of functions of the coordinates of one electron. We will denote the basis set of one electron functions by {Φ}. Notice that each basis function defines a set of n building blocks to be used in the construction of the wavefunction, since each function may be written in the coordinates of any of the n electrons.

Abstract: The Combinatorial Grouping Problem is defined as the general problem of computing a set of boolean bounds (GLB, LUB) for an incomplete power set P(U)so that a system of lattice-theoretic filter-ideal intersections (GLB, LUB) results which optimizes a cost function defined on the parent set U. The problem arises as a mathematical formulation of the Group-Technology Problem of Industry. A system of independent Production Cells is required which provides the manufacturing capacity for the commercial life of an industrial product. A group of components is matched with a group of facilities so that there is a maximal degree of scheduling flexibility and a minimal cost of manufacture. A Set-Partitioning Algorithm has been developed which may be adapted to solve a wide class of related combinatorial problems.

Abstract: A solution of the laser fields, both inside and outside the laser, is given in terms of the mode-conversion coefficients and an integral equation for the radiation pattern. It is shown how very accurate analytic solutions can be obtained by what, at first sight, appear to be extremely crude approximations. The reason is that mode conversion is taken implicitly into account by using a multiplier, whose exact form does not appear to be very critical, as a weighting function to average two different formulas for the function representing the radiation; and with the correct form for it, all the mode-conversion and reflection coefficients can be legitimately ignored. A plane-wave formula for this multiplier is a good first approximation, and a number of existing expressions occurring in the literature are obtained in this way. It is also shown rigorously that the results of an earlier obliquity-factor analysis apply. Further refinements are introduced to allow for higher order discrete modes, and good approximate analytic forms for the mode-reflection and conversion coefficients are obtained. A check with a rather extreme example shows excellent agreement with Ikegami's numerical computation for the dominant-mode reflection at the laser-air interface. The methods of this paper are applicable to general laser structures of cylindrical geometry with either continuous or discontinuous variations in refractive index. Very accurate numerical solutions should be obtainable after only one iteration of the integral equation, starting with the reflection-modified form of Hockham's formula as initiating function.

Abstract: This specification describes a set of arrays for performing logic function in various subsets of the original set. The array structure is characterized by a plurality of arrays joined together with a bidirectional bussing system. This bussing system comprises addressing lines of the arrays joined together by switching circuitry used to regroup the set into subsets as necessary to perform the logic functions.

Abstract: A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. The major characteristics of this approach are: (i) it does not require any grid refinement; (ii) the entire process of computation quickly converges to the acceptable level of accuracy, and (iii) the method employs specific sets of mesh points for specific variables, whereby it reduces the number of variables for the separable programming technique. Numerical examples were provided to illustrate the procedure.

Abstract: A response surface criterion for design selection is developed in this paper for the case of estimation of a set of parametric functions rather than a single response. A specific application is emphasized, that in which interest, centers on the partial derivat. ives of the response function. Both bias and variance of the parametric functions are taken into consideration. For the case of the slope of the response function two situations are given special emphasis; the fitting of a first order model in the presence of a true second order structure, and the fitting of a second order function in the presence of a third order alternative. The traditional response surface bias and variance criteria arise as a special case for the situation in which a single parametric function is merely the ordinary response surface.

Abstract: An algorithm is presented for solving nonlinear ordinary differential equations that generates a broad class of implicit linear differentiation formulas. Specific interest is concerned in one type of formula which for constant timestep reduces to the well-known Gear formulas. Although these formulas are mathematically fully equivalent to the BDF formulas as presented by Brayton et al. [1], their construction is quite different. Instead of using previously calculated function values, we employ predictions extrapolated from these values to set up and evaluate the differentiation formula. A recursive relation for these predictions is derived in order to simplify their calculation in the next timestep. As predictions are needed for order and error control, our algorithm appears to be more efficient as to the number of arithmetic operations than Brayton's algorithm, as well as more general and systematic. Moreover, a change of the order can be accomplished without extra work. Due to the available predictions, an interpolation to determine function values at intermediate time instants, as for instance required in plotting procedures, can be performed in a fast way.

Abstract: Simple inequalities are obtained for the Green's function G(t, s) of a two-point boundary value problem for a kth order linear ordinary differential equation. The constants appearing in the inequalities are best possible. Each estimate has right side a product of a function of t and a function of s. Illustrations are given for k—2,3,4 and certain kih order constant coefficient operators.