Abstract: When one integrates a function of two variables x,y - a point function f(P) in the plane - subject to suitable regularity conditions along an arbitrary straight line g then one obtains in the integral values F(g), a line function. In Part A of the present paper the problem which is solved is the inversion of this linear functional transformation, that is the following questions are answered: can every line function satisfying suitable regularity conditions be regarded as constructed in this way? If so, is f uniquely known from F and how can f be calculated? In Part B a solution of the dual problem of calculating a line function F(g) from its point mean values f(P) is solved in a certain sense. Finally, in Part C certain generalizations are discussed, prompted by consideration of non-Euclidean manifolds as well as higher dimensional spaces. The treatment of these problems, themselves of interest, gains enhanced importance through the numerous relationships that exist between this topic and the theory of logarithmic and Newtonian potentials. These are mentioned at appropriate places in the text.

Abstract: We propose a new mixed integral equation for the pair distribution function of classical fluids, which interpolates continuously between the soft core mean spherical closure at short distances, and the hypernetted chain closure at large distances. Thermodynamic consistency between the virial and compressibility equations of state is achieved by varying a single parameter in a suitably chosen switching function. The new integral equation generalizes a recent suggestion by Rogers and Young to the case of realistic pair potentials containing an attractive part. When compared to available computer simulation data, the new equation is found to yield excellent results for the thermodynamics and pair structure of a wide variety of potential models (including atomic and ionic fluids and mixtures) over an extensive range of temperatures and densities. The equation can also be used to invert structural data to extract effective pair potentials, with reasonable success.

Abstract: The hand apparatus has a plurality of module keys (101-105) by means of which the user can get access to a specific module, such as a TV-receiver, a teletext decoder, a videorecorder, a VLP-player, an audiosystem, an audiotuner, a compact disc player, an audiorecorder etc. In addition, a dot-matrix display element (300) is provided around which a plurality of multi-functional keys (301-312) are arranged. The control function of such a key depends on the module key operated and this function is shown on the display element for each of these keys.

Abstract: We consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right-hand-side vector. Among our results, we show that, for any optimal solution to a linear program max{wx: Ax≤b}, the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixA. Using this, we strengthen several integer programming ‘proximity’ results of Blair and Jeroslow; Graver; and Wolsey. We also show that the Chvatal rank of a polyhedron {x: Ax≤b} can be bounded above by a function of the matrixA, independent of the vectorb, a result which, as Blair observed, is equivalent to Blair and Jeroslow's theorem that ‘each integer programming value function is a Gomory function.’

Abstract: The results of three experiments demonstrated that the visual system calibrates motion parallax according to absolute-distance information in processing depth. The parallax was created by yoking the relative movement of random dots displayed on a cathode-ray tube to the movements of the head. In Experiment 1, at viewing distances of 40 cm and 80 cm, observers reported the apparent depth produced by motion parallax equivalent to a binocular disparity of 0.47 degree. The mean apparent depth at 80 cm was 2.6 times larger than at 40 cm. In Experiment 2, again at viewing distances of 40 cm and 80 cm, observers adjusted the extent of parallax so that the apparent depth was 7.0 cm. The mean extent of parallax at 80 cm was 31% of that at 40 cm. In Experiment 3, distances ranged from 40 cm to 320 cm, and a wide range of parallax was used. As distance and parallax increased, the perception of a rigid three-dimensional surface was accompanied by rocking motion; perception of depth was replaced by perception of motion in some trials at 320 cm. Moreover, the mean apparent depths were proportional to the viewing distance at 40 cm and 80 cm but not at 160 cm and 320 cm. Language: en

Abstract: We consider the mathematical programming problem: find $\inf \{ f(x)\mid x \in C\} $ where f is an arbitrary extended-real-valued function, and C a subset of a finite dimensional space. We give necessary and sufficient optimality conditions for this problem, generalizing previous results of A. Auslendex (this Journal, 22 (1984), pp. 239–254).

Abstract: Let F n be the set of all functions from n bits to n bits. Let f n specify for each key k of a given length a function f k n ∈ F n . We say f n is pseudorandom if the following two properties hold: (1) Given a key k and an input α of length n, the time to evaluate f k n (α) is polynomial in n. (2) If a random key k is chosen, f k n “looks like” a random function chosen from F n to any algorithm which is allowed to evaluate f k n at polynomial in n input values.

Abstract: The global minimization of a large-scale linearly constrained concave quadratic problem is considered. The concave quadratic part of the objective function is given in terms of the nonlinear variablesx ∈R n , while the linear part is in terms ofy ∈R k. For large-scale problems we may havek much larger thann. The original problem is reduced to an equivalent separable problem by solving a multiple-cost-row linear program with 2n cost rows. The solution of one additional linear program gives an incumbent vertex which is a candidate for the global minimum, and also gives a bound on the relative error in the function value of this incumbent. Ana priori bound on this relative error is obtained, which is shown to be ≤ 0.25, in important cases. If the incumbent is not a satisfactory approximation to the global minimum, a guaranteede-approximate solution is obtained by solving a single liner zero–one mixed integer programming problem. This integer problem is formulated by a simple piecewise-linear underestimation of the separable problem.

Abstract: We give a substitute for the Whitney decomposition of an arbitrary open set in R2 where squares are replaced by rectangles. Then we deduce the LOO-BMO boundedness of certain singular integral operators defined on product spaces. In [2] it is shown that BMO(R x R), the dual of H1 (R x R), can be characterized in terms of Carleson measures on R+ x R+ [1]. Let 9 be a bounded open set in R2 and S(Q) be the shadow region over Q, that is, the set of (xl,x2,tl,t2) such that [xi t1,xl + t1] x [x2 t2, x2 + t2] C Q. Let ?/ E Co (R) be supported on [-1, 1], such that fV0dx = 0, and let Qt = Qtl 0 Qt2 be the convolution with (1/t1t2)>0(x1/t1)0V(x2/t2). Then a function b c L2c (R2) is in BMO(R x R) if and only if there exists a constant Cb such that (1) | |QtbI2 dxl dX2 d dt2 < C2|j tl t2 and then Cb jlblIBMO. The problem in proving (1) for a given function b is that one has to consider all possible bounded open sets and not simply rectangles. However, (1) can still be checked in special cases, using the following proposition. PROPOSITION 1. Let Q be a bounded open subset of R2, let {Rk, k c K} be the collection of maximal dyadic rectangles contained in Q, and let Rk = Ik X Jk for all k c K. There exist dyadic intervals {Ik, k c K} such that Ik C Ik for all k c K and such that for all increasing functions : {2-j, j E N} [0, +xo) (2) U Ik x Jk < 219 kEK

Abstract: A function is said to be strict in one of its formal parameters if, in all calls to the function, either the corresponding actual parameter is evaluated, or the call does not terminate. Detecting which arguments a function will surely evaluate is a problem that arises often in program transformation and compiler optimization. We present a strategy that allows one to infer strictness properties of functions expressed in the lambda calculus. Our analysis improves on previous work in that (1) a set-theoretic characterization of strictness is used that permits treatment of free variables, which in turn permits a broader range of interpretations, and (2) the analysis provides an effective treatment of higher-order functions. We also prove a result due to Meyer [15]: the problem of first-order strictness analysis is complete in deterministic exponential time. However, because the size of most functions is small, the complexity seems to be tractable in practice.This research was supported in part by NSF Grant MCS-8302018, and a Faculty Development Award from IBM.

Abstract: We consider two setsA andB to be close to each other if the census of their symmetric difference,A ▵B, is a slowly increasing function (e.g. a polynomial.) The classes of sets which are polynomially close to some set in a complexity classC (likeP) are studied and characterized. We investigate the question whether complete sets forNP or EXPTIME can be polynomially close to a set inP. Some of the obtained results strengthen or generalize results by Yesha [24], e.g. it is shown that no EXPTIME-hard set can be polynomially close to any set inP.

Abstract: Most distortion theorems for K-quasiconformal mappings in Rn, n > 2, depend on both n and K in an essential way, with bounds that become infinite as n tends to oo. The present authors obtain dimension-free versions of four well-known distortion theorems for quasiconformal mappings-namely, bounds for the linear dilatation, the Schwarz lemma, the e-distortion theorem, and the r1-quasisymmetry property of these mappings. They show that the upper estimates they have obtained in each of these four main results remain bounded as n tends to oo with K fixed. The proofs are based on a "dimensioncancellation" property of the function t H-* r-1(r(t)/K), t > 0, K > 0, where r(t) is the capacity of a Teichmiiller extremal ring in Rn. The authors also prove a dimension-free distortion theorem for the absolute (cross) ratio under K-quasiconformal mappings of n, from which several other distortion theorems follow as special cases.

Abstract: The general distance problem that arises in H∞ optimal control theory is considered. Transformations that reduce the general H∞ problem to the general distance problem are reviewed, and an iterative scheme called γ-iteration is considered, in which the general distance problem is reduced to a standard best approximation problem. The γ-iteration is viewed as a problem of finding the zero crossing of a function, This function is shown to be continuous, monotonically decreasing, convex and bounded by some very simple functions. These properties make it possible to obtain very rapid convergence of the iterative process. The issues of model-reduction and approximation in H∞-synthesis will also be addressed.

Abstract: Optimum design of complex engineering systems needs a globally and superlinearly convergent (robust and efficient) algorithm using active set strategy. Such an algorithm based on extensions of Pshenichny's linearization method is derived in the paper. In the original method, a linearized subproblem with a quadratic step-size constraint is used to compute a direction of design change. No second-order information is computed or approximated for use in the direction finding problem. Therefore, the rate of convergence is only linear. In the paper, we propose to incorporate a variable metric W which is a positive-definite approximation to the Hessian of the Lagrange function. This gives local superlinear rate of convergence to the algorithm. Some other computational improvements are discussed and incorporated. The proposed improvements appear to be quite simple. They are, however, quite significant for applications to engineering design problems. This is explained and several small-scale problems are solved using a program based on the modified algorithm. Results are compared to Pshenichny's original algorithm. The modified algorithm is considerably more efficient compared to the previous algorithm. It also appears to be quite robust, though more extensive testing is needed on a wider range of problems.

Abstract: This paper analyzes the performance of the two efficient algorithms (presented by Stein and Cabot) for time delay of arrival estimation (TDE) between two signals. It is shown that these estimators are unbiased, and explicit expressions for the TDE mean-square error (MSE) are presented. It is also shown how to improve the performance of these algorithms by combining them with generalized cross-correlation (GCC) methods. In the analysis, we only assume stationary signals which are not necessarily Gaussian. The first algorithm (Stein) is indirect and uses the symmetry of the cross-correlation function between the two signals. It is shown here that the TDE-MSE depends on the unknown delay. The performance of this algorithm can be improved by combining it with the GCC method, and the pertinent TDE-MSE expressions are presented. The second algorithm (Cabot) is based on finding the zero of the cross-correlation function between one signal and the Hilbert transform of the other signal. Here, too, the pertinent TDE-MSE expressions are presented. This algorithm is also combined with the GCC method, and the optimal weight function for which the TDE-MSE expression coincides with the Cramer-Rao lower bound is found.

Abstract: One method of model-based compensator design for linear multivariate systems consists of state-feedback design and observer design (Athans 1971). A key step in recent work in multivariate synthesis involves selecting an observer gain so the final loop-transfer function is the same as the state-feedback loop transfer function (Doyle and Stein 1979, Goodman 1984). This is called loop transfer recovery (LTR). This paper shows how identification of the eigenstructure of the compensators that achieve LTR makes possible a design procedure for observer gain (Luenberger 1971). This procedure is based on the eigenstructure assignment of the observers. The sufficient condition for LTR and the stability of the closed-loop system is that the plant be minimum-phase. The limitation of this method might arise when the plant has multiple transmission zeros.

Abstract: We consider weakly-coupled elliptic systems of the typewith each fi being either an increasing or a decreasing function of each uj. Assuming the existence of coupled super- and subsolutions, we prove the existence of solutions, and provide a constructive iteration scheme to approximate the solutions. We then apply our results to study the steady-states of two-species interaction in the Volterra–Lotka model with diffusion.

Abstract: Consider a fluid which has free energy1 ψ(u) a prescribed function of density u, and which occupies a fixed container Ω, with Ω a bounded, open region in ℝ N .

Abstract: The present state of the minimum assumption multivariate component resolution theory is outlined. Some new developments are presented: limiting function domains; the analytical expression for the limiting function; efficient algorithms for defining the FIRPOL and INNPOL hyperpolyhedrons. A very low resolution data set is analyzed.