Showing papers on "Monotone polygon published in 1982"
TL;DR: This correspondence analyzes the computational complexity of fault detection problems for combinational circuits and proposes an approach to design for testability, and shows that for k-level (k ≥ 3) monotone/unate circuits these problems are still NP-complete, but that these are solvable in polynomial time for 2-level monot one/ unate circuits.
Abstract: In this correspondence we analyze the computational complexity of fault detection problems for combinational circuits and propose an approach to design for testability. Although major fault detection problems have been known to be in general NP-complete, they were proven for rather complex circuits. In this correspondence we show that these are still NP-complete even for monotone circuits, and thus for unate circuits. We show that for k-level (k ≥ 3) monotone/unate circuits these problems are still NP-complete, but that these are solvable in polynomial time for 2-level monotone/unate circuits. A class of circuits for which these fault detection problems are solvable in polynomial time is presented. Ripple-carry adders, decoder circuits, linear circuits, etc., belong to this class. A design approach is also presented in which an arbitrary given circuit is changed to such an easily testable circuit by inserting a few additional test-points.
151 citations
TL;DR: In this paper, a decomposition theorem for multistate structure functions is proven and the result is applied to obtain bounds for the system performance function, which is then used to interpret the multistates structures of Barlow and Wu.
Abstract: A decomposition theorem for multistate structure functions is proven This result is applied to obtain bounds for the system performance function Another application is made to interpret the multistate structures of Barlow and Wu Various concepts of multistate importance and coherence are also discussed
98 citations
01 Jan 1982
TL;DR: The method of generalized cross validation for choosing the smoothing parameter in the presence of a family of linear inequality constraints is described, and appears to be quite successful in adding information, doing nearly the optimal amount of smoothing, and resolving distinct peaks in the solution which have been blurred by the convolution operation.
Abstract: : The relationship between certain regularization methods for solving ill posed linear operator equations and ridge methods in regression problems is described. The regularization estimates we describe may be viewed as ridge estimates in a (reproducing kernel) Hilbert space H. When the solution is known a priori to be in some closed, convex set in H, for example, the set of nonnegative functions, or the set of monotone functions, then one can propose regularized estimates subject to side conditions such as nonnegativity, monotonicity, etc. Some applications in medicine and meteorology are described. We describe the method of generalized cross validation for choosing the smoothing (or ridge) parameter in the presence of a family of linear inequality constraints. Some successful numerical examples, solving ill posed convolution equations with noisy data, subject to nonnegativity constraints, are presented. The technique appears to be quite successful in adding information, doing nearly the optimal amount of smoothing, and resolving distinct peaks in the solution which have been blurred by the convolution operation. (Author)
96 citations
TL;DR: In this article, it was shown that the sequence of approximate solutions is a Cauchy sequence, relatively compact so that one can appeal to Ascoli's theorem, and a monotone sequence in a cone.
68 citations
Book•
30 Apr 1982
TL;DR: In this article, the authors present a set of monotone functions and define Borel measurability, and integrate them into R to achieve Borel integration, and show that they are monotonous.
Abstract: 1. Monotone functions 2. Subsets of R 3. Continuity 4. Differentiation 5. Borel measurability 6. Integration.
64 citations
TL;DR: In this article, several situations involving survival data are examined, in which the nonparametric maximum likelihood estimator is not the Kaplan-Meier estimator, and the first two cases are nonstandard because survival and censoring are not independent, and thus form simple tractable variable-sum models.
Abstract: SUMMARY Several situations involving survival data are examined, in which the nonparametric maximum likelihood estimator is not the Kaplan-Meier estimator. Cases covered are inclusion of initial observations in field studies, estimation of the length distribution from convex window sampling of line segment processes in two dimensions, and estimation of a survival curve with monotone density. The first two cases are nonstandard because survival and censoring are not independent, and thus form simple tractable variable-sum models (Williams & Lagakos, 1977).
58 citations
TL;DR: In this paper, the authors consider numerical boundary value problems on nonuniform grids and show that the Engquist-Osher monotone scheme will reproduce essential properties of the true solution for any grid.
Abstract: We consider numerical solutions of the boundary value problem $\varepsilon y'' - (f(y))' - b(x,y) = 0$, $0 \leqq x \leqq 1$, $y(0) = A$, $y(1) = B$, $\varepsilon < 0$, $b_y \geqq \delta < 0$, with monotone difference schemes on nonuniform grids We prove general convergence results and show that the Engquist–Osher monotone scheme will reproduce essential properties of the true solution for any grid For the inversion of the nonlinear scheme, we suggest implicit time relaxation with variable time steps
58 citations
TL;DR: In this paper, a multidimensional, multiphase problem of Stefan type, involving quasilinear parabolic equations and nonlinear boundary conditions is considered, and the existence and uniqueness of a weak solution to the problem, as well as continuous and monotone dependence of the solution upon data are shown.
Abstract: A multidimensional, multiphase problem of Stefan type, involving quasilinear parabolic equations and nonlinear boundary conditions is considered. Regularization techniques and monotonicity methods are exploited. Existence and uniqueness of a weak solution to the problem, as well as continuous and monotone dependence of the solution upon data are shown.
57 citations
TL;DR: In this paper, a monotone sequence of functions which satisfy scalar equations is constructed so that they will converge to upper and lower bounds for the solutions of the systems, in case a related system has a unique positive solution.
Abstract: Semilinear elliptic systems of partial differential equations related to ecology are studied, with Dirichlet boundary conditions. Monotone sequences of functions which satisfy scalar equations are constructed so that they will converge to upper and lower bounds for the solutions of the systems. In case a related system has a unique positive solution, then these sequences will converge to the solution of the original system. Applications of the monotone sequences to uniqueness and stability are also given.
53 citations
TL;DR: In this paper, Schoenberg and Cavaretta proved inequalities about various clases of monotone functions which yield, as special cases, pointwise inequalities of the form (1) where the norm is as in (2).
52 citations
TL;DR: In this article, the proximal point algorithm for the minimization of non-convex functions with maximal strictly hypomonotone subdifferentials is extended to lower-C2 functions.
Abstract: The proximal point algorithm for solving 0 e T(x) with T maximal monotone is extended to mappings T satisfying the weaker property of maximal strict hypomonotonicity. The algorithm is applied to the minimization of a certain class of nondifferentiable nonconvex functions, the lower-C2 functions., whose subdifferentials are maximal strictly hypomonotone. For functions in this class, each step of the algorithm consists in minimizing a convex function.
TL;DR: In this article, a system of semilinear elliptic partial differential equations is studied, which determines the equilibria of the Volterra-Lotka equations describing prey-predator interactions with diffusion.
TL;DR: In this paper, a conservative extension of ID α (W) c is presented, where the first theory expresses the iteration α times of inductive definitions by successive monotonic operators and where α is an effectively presented ordinal and c indicates that the logic is classical.
Abstract: Publisher Summary This chapter explains that ID α mon,c is a conservative extension of ID α (W) c , where the first of these theories expresses the iteration α times of inductive definitions by successive monotonic operators and where α is an effectively presented ordinal and c indicates that the logic is classical. The language of the theory T o provides a flexible broad framework within which to consider general constructive operations on classes. The theory includes all constructive formulations of iteration of monotone-inductive definition, while T o is based squarely on the general iteration of accessibility-inductive definitions. Thus, it would be of great interest for the present subject to settle the relationship between these theories. The proof-theoretic reductions obtained show that ID α mon,i is justified indirectly by much more restricted evidence. However, the status of monotone-inductive definition in a more general constructive setting is still open.
TL;DR: In this paper, a monotone rule is introduced to sum up individual declarations in a multi-variate stopping problem and the existence of an equilibrium stopping strategy and the associated gain are discussed for the tlnite and infinite horizon cases.
Abstract: A monotone rule is introduced to sum up individual declarations in a multi-variate stopping problem. The rule is defined by a monotone logical function and is equivalent to the winning class of Kadane. This paper generalizes the previous works on a majority rule. The existence of an equilibrium stopping strategy and the associated gain are discussed for the tlnite and infinite horizon cases. n be p -dimentional random vectors on a probability space ( ~ ,J3, p). The process {X } can be interpreted as a sequence of payoffs to n a group of p players. Each of p players observes sequentially the values of Its distribution is assumed to be known to all of the p players. A player must make a declaration to either "stop" or "continue" on the basis of the observed value at each stage. A group decision whether to stop the process or not is determined by summing up from the individual declarations.
TL;DR: In this paper, the authors obtained Jackson type estimates for the approximation of increasing or convex functions by splines with the same property, when the knots are not uniformly spaced, and they used this method to obtain an algorithm for fitting a curve to data with local convexity preservation.
Abstract: We obtain Jackson type estimates for the approximation of increasing or convex functions by splines with the same property. These estimates are new when the knots are not uniformly spaced. The method of proof motivates an algorithm for fitting a curve to data with local convexity preservation. The properties of this algorithm are developed and some examples are given.
TL;DR: In this paper, an iterative method for the solution of systems of nonlinear equations having at leastR-order 1+ $$\sqrt 2 $$ for simple roots has been investigated; this method uses as many function evaluations per step as the classical Newton method.
Abstract: Recently an iterative method for the solution of systems of nonlinear equations having at leastR-order 1+ $$\sqrt 2 $$ for simple roots has been investigated by the author [7]; this method uses as many function evaluations per step as the classical Newton method. In the present note we deal with several properties of the method such as monotone convergence, asymptotic inclusion of the solution and convergence in the case of multiple roots.
TL;DR: In this paper, the exact meaning of what is meant by an initial condition to such an equation is defined, and the collection of possible initial values is characterized as being the domain of the square root of a certain operator.
Abstract: Many initial boundary value problems can be put in the form: where is either a pseudo monotone or Type M operator, and V is a reflexive Banach space B(t) is a linear continuous mapping of V to V' which may vanish Conditions are given on the operators :(t) and A(t, ) that insure the existence of a solution to the Cauchy problem Also, the exact meaning of what is meant by an initial condition to such an equation is made precise, and the collection of possible initial values is characterized as being the domain of the square root of a certain operator These results generalize earlier results in which the operators B(t) do not depend on t
TL;DR: For monotone functions, this article showed that any function that satisfies a certain strong monotonicity condition, and approximate intermediate values, is pointwise continuous, and that any point-wise continuous function is uniformly continuous.
Abstract: Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here. Functions which satisfy a certain strong monotonicity condition, and approximate intermediate values, are pointwise continuous. Any monotone pointwise continuous function is uniformly continuous. Continuous inverse functions are also obtained. The methods used are in accord with the principles of Bishop's Foundations of Constructive Analysis, 1967.
TL;DR: In this paper, the authors consider the monotone cubic spline interpolating g at the knots of s n and show that 1.2 dt = 0, 2.
TL;DR: It is shown that Pavlidis's method for decomposing a polygon into (possibly overlapping) convex pieces can be viewed as simplifying a Boolean switching function expressed in disjunctive normal form, suggesting that the search for a minimal polygon decomposition can be organized along the same lines used to find a minimal prime implicant cover for a Boolean expression.
TL;DR: In this paper, a pseudo-monotone operator was introduced to take into account the difference of the properties of the highest order functions A, in their top order variables from the lower order derivatives.
01 Jan 1982
TL;DR: In this paper, it was shown that the solution mapf→u is continuous, even if the f′s are topologized much more weakly than usual, and as a corollary the existence of solutions ofu′(t)+Au(t)∋B(u (t)), whereB is a compact mapping in a Hilbert space.
Abstract: We consideru′(t)+Au(t)∋f(t), whereA is maximal monotone in a Hilbert spaceH. AssumeA is continuous or A=ϱφ or intD(A)≠∅ or dimH<∞. For suitably boundedf′s, it is shown that the solution mapf→u is continuous, even if thef′s are topologized much more weakly than usual. As a corollary we obtain the existence of solutions ofu′(t)+Au(t)∋B(u(t)), whereB is a compact mapping inH.
TL;DR: In this paper, it was shown that a symmetric positive semidefinite matrix is monotone on its range if and only if it is monotonous on its length.
TL;DR: This article obtained Jackson type estimates for the approximation of monotone nondecreasing functions f by monotonically nonsmooth splines with equally spaced knots in the L_p [0, 1]-norm.
Abstract: We obtain Jackson type estimates for the approximation of monotone nondecreasing functions f by monotonically nondecreasing splines with equally spaced knots in the $L_p [0,1]$-norm $1 \leq p \leq \infty $. The estimates involve high order moduli of smoothness of some derivatives of f and are obtained for functions f with a continuous derivative in case $p = \infty $ and for functions f that are the second primitive of $f'' \in L_p [0,1]$ if $1 \leq p < \infty $.
TL;DR: In this paper, a steady-state, one-phase, Stefan problem corresponding to the solidification process of an ingot of pure metal by continuous casting with nonlinear lateral cooling is considered via the weak formulation introduced by H. Brezis et al.
Abstract: A steady-state, one-phase, Stefan problem corresponding to the solidification process of an ingot of pure metal by continuous casting with nonlinear lateral cooling is considered via the weak formulation introduced by H. Brezis et al . [C. R. Acad. Sci. Paris Ser. A 287 (1978), no. 9, 711--714] for the dam problem. Two existence results are obtained, for a general nonlinear flux and for a maximal monotone flux. Comparison results and the regularity of the free boundary are discussed. A uniqueness theorem is given for the monotone case.
TL;DR: In this paper, it was proved that a topological space is necessarily paracompact if it is monotonically normal and any one of the following: screenable, paralindelof, has a Gδ-diagonal or a quasi-Gδ -diagonal, or has a σ-locally-countable base.
TL;DR: In this paper, the complete system of the quasi-linear Maxwell equations with monotone characteristic in a bounded domain is studied, and the existence and uniqueness of a local regular solution is established.
Abstract: The complete system of the quasi- linear Maxwell equations with monotone characteristic in a bounded domain is studied. Following Kato's theory in [14] for quasilinear hyperbolic systems, existence and uniqueness of a local regular solution is established.
TL;DR: Benilan et al. as mentioned in this paper studied the semilinear perturbation of Poisson's equation (E): −Δu+β(u)∋f, where β is a maximal monotone graph in R and β takes only positive values and N≧3, and gave necessary and sufficient conditions on β and f to be solvable in a natural sense.
Abstract: The semilinear perturbation of Poisson’s equation (E): −Δu+β(u)∋f, where β is a maximal monotone graph inR, has been investigated by Ph. Benilan, H. Brezis and M. Crandall forf∈L
1(R
N
),N≧1, under the assumptions 0∈β(0) ifN≧3 and 0∈β(0) ∩ Int β(R) ifN=1,2. We discuss in this paper the solvability and well-posedness of (E) in terms of any maximal monotone graph β. In particular, if β takes only positive values andN≧3 we prove that no solution exists; ifN=2 we give necessary and sufficient conditions on β andf for (E) to be solvable in a natural sense.