Showing papers on "Bounded function published in 1983"
TL;DR: In this paper, an analytic inversion formula allowing the reconstruction of a 3D object from x-ray cone-beams is given, for the case where the source of the beams describes a bounded curve satisfying a set of weak conditions.
Abstract: An analytic inversion formula allowing the reconstruction of a three-dimensional object from x-ray cone-beams is given. The formula is valid for the case where the source of the beams describes a bounded curve satisfying a set of weak conditions.
978 citations
TL;DR: In this paper, a decision method for finding a continuous motion connecting two given positions and orientations of the whole collection of bodies is presented. But it is not shown that this problem can be solved in polynomial time.
909 citations
01 Dec 1983
TL;DR: All the apparently known lower bounds for linear decision trees are extended to bounded degree algebraic decision trees, thus answering the open questions raised by Steele and Yao [20].
Abstract: A topological method is given for obtaining lower bounds for the height of algebraic computation trees, and algebraic decision trees. Using this method we are able to generalize, and present in a uniform and easy way, almost all the known nonlinear lower bounds for algebraic computations. Applying the method to decision trees we extend all the apparently known lower bounds for linear decision trees to bounded degree algebraic decision trees, thus answering the open questions raised by Steele and Yao [20]. We also show how this new method can be used to establish lower bounds on the complexity of constructions with ruler and compass in plane Euclidean geometry.
584 citations
TL;DR: In this paper, a two-dimensional case of the problem is solved, where given a body B and a region bounded by a collection of "walls", either find a continuous motion connecting two given positions and orientations of B during which B avoids collision with the walls, or else establish that no such motion exists.
Abstract: We present an algorithm that solves a two-dimensional case of the following problem which arises in robotics: Given a body B, and a region bounded by a collection of “walls”, either find a continuous motion connecting two given positions and orientations of B during which B avoids collision with the walls, or else establish that no such motion exists. The algorithm is polynomial in the number of walls (O(n5) if n is the number of walls), but for typical wall configurations can run more efficiently. It is somewhat related to a technique outlined by Reif.
487 citations
TL;DR: For all vector fields ψ e L∞(Ω,Rn) whose divergence is in Ln(Φ) and for all vector measures Μ in Ω whose curl is a measure, a real valued measure (ψ, Μ) in Φ, that can be considered a suitable generalization of the scalar product of ψ and Μ was defined in this article.
Abstract: For all vectorfields ψ e L∞(Ω,R
n) whose divergence is in Ln(Ω) and for all vector measures Μ in Ω whose curl is a measure we define a real valued measure (ψ, Μ) in Ω, that can be considered a suitable generalization of the scalar product of ψ and Μ. Several properties of the pairing (ψ, Μ) are then obtained.
472 citations
01 Dec 1983
TL;DR: An algebraic approach to the problem of assigning canonical forms to graphs by computing canonical forms and the associated canonical labelings in polynomial time is announced.
Abstract: We announce an algebraic approach to the problem of assigning canonical forms to graphs. We compute canonical forms and the associated canonical labelings (or renumberings) in polynomial time for graphs of bounded valence, in moderately exponential, exp(n½ + o(1)),time for general graphs, in subexponential, nlog n, time for tournaments and for 2-(n,k,l) block designs with k,l bounded and nlog log n time for l-planes (symmetric designs) with l bounded. We prove some related problems NP-hard and indicate some open problems.
472 citations
TL;DR: In this paper, the authors investigated the large time behavior of the solutions of MHD equations for a viscous incompressible resistive fluid and established the regularity properties and bounds on the solutions to the equations which are valid for all time.
416 citations
TL;DR: In this article, an energy decay rate was obtained for solutions of wave type equations in a bounded region in Rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface.
332 citations
TL;DR: Some theorems relating K -density, cut finiteness, and discreteness are proved and the result that a place/transition net is bounded if and only if its processes are K -dense is obtained.
Abstract: The idea of representing non-sequential processes as partially ordered sets (occurrence nets) is applied to place/transition nets (Petri nets), based on the well known notion of process for condition/event-systems. For occurrence nets some theorems relating K -density, cut finiteness, and discreteness are proved. With these theorems the result that a place/transition net is bounded if and only if its processes are K -dense is obtained.
320 citations
TL;DR: In this article, it is conjectured that the mass of the Higgs particle in the minimal model is bounded by an amount that can be estimated without the knowledge of the physics at shorter distances.
Abstract: In view of the almost established triviality of ϕ 4 in four dimensions it is conjectured that the mass of the Higgs particle in the minimal model is bounded by an amount that can be estimated without the knowledge of the physics at shorter distances. A possible numerical experiment which could give a nonperturbative estimate for the bound is proposed. PACS numbers: 14.80.Gt, 11.15.Ex, 11.15.Ha, 12.10.En
246 citations
TL;DR: In this article, it was shown that general second order elliptic boundary value problems on bounded domains generate analytic semigroups on L.............. p, 1≦p < ∞.
Abstract: It is shown that general second order elliptic boundary value problems on bounded domains generate analytic semigroups onL
1. The proof is based on Phillips’ theory of dual semigroups. Several sharp estimates for the corresponding semigroups inL
p, 1≦p<∞, are given.
TL;DR: The problem of determining both the existence and regularity properties of the solution u of au = a, where u is orthogonal to the null space of a on (p, q l)-forms, is known as the a-Neumann problem as discussed by the authors.
Abstract: Let a be a a-closed form of type (p, q) with L2-coefficients on a smoothly bounded domain Q in C'. The problem of determining both the existence and regularity properties of the solution u of au = a, where u is orthogonal to the null space of a on (p, q l)-forms, is known as the a-Neumann problem. One of the principal methods used in the investigation of this problem is the proof of certain a priori subelliptic estimates. Let U be a neighborhood of a point z0 in the boundary of Q. A subelliptic estimate is said to hold in U if the estimate
TL;DR: In this paper, the problem of analysis of a parabolic divergence equation in the form (0.2) has been studied, where the problem is not bounded or bounded away from zero.
Abstract: which is of parabolic divergence form since $’ 3 0 a.e. However it is the solution u of (0.1) which will be continuous, while the solution u of (0.2) need not be. In certain physical applications u corresponds to temperature while u is the enthalpy. The difficulty in the analysis of this equation, written in the form (0.2), stems from the fact that c#+ need not be bounded or bounded away from zero. Thus the equation may be of degenerate or singular parabolic type. As particular cases of the equations covered by our results we mention the three model problems
TL;DR: An approach for studying stability of adaptively controlled systems subject to bounded disturbances with unknown statistics is given and uniform boundedness of all signals is proven under a condition that is discussed.
TL;DR: These bounds, which are given in terms of polynomials in p, the common arc failure probability, are based on recent bounding results developed by the authors for the class of shellable independence systems.
Abstract: In this article, computational procedures are presented for generating bounds on measures of network reliability. The two measures considered, reachability and connectedness, are the probability that there is an operating path from a node to all other nodes in a directed (respectively undirected) stochastic network. Our bounds, which are given in terms of polynomials in p, the common arc failure probability, are based on recent bounding results developed by the authors for the class of shellable independence systems. Two pairs of bounds are given: weaker bounds whose computation time is bounded by a polynomial in the size of the network and tighter bounds whose computation time is bounded by a polynomial in the size of the network and the number of minimum-cardinality network cuts. Computational results are also given which evaluate the quality of the bounds. The generation of the bounds involves several interesting path and cut counting problems.
TL;DR: In this paper, a generalization of a virial theorem for a bounded system is given, and a detailed discussion starting from a Virial theorem of the derivation of a microscopic expression of the stress tensor is presented.
Abstract: A generalization of a virial theorem for a bounded system is given. Also a detailed discussion starting from a virial theorem of the derivation of a microscopic expression of the stress tensor is presented. Two applications are briefly indicated.
TL;DR: In this paper, the authors considered the problem of finding a non-selfadjoint representation of a C*-algebra A on a Hilbert space similar to a unitary representation.
Abstract: In a paper from 1955 [13] Kadison considered the following problem: Is any bounded, non-selfadjoint representation 77 of a C*-algebra A on a Hilbert space H similar to a *-representation?; i.e. does there exist an invertible operator T E B(H), such that ThT( )T-' is a *-representation of A? This problem is a natural counterpart to a problem considered by Dixmier in 1950 [9]: Is any bounded representation of a group G on a Hilbert space similar to a unitary representation? The group question was solved in the negative by Kunze and Stein in 1960 [14], which in turn was based on previous work of Ehrenpreis and Mautner [21]. The similarity problem for representations of C*-algebras is still open, although a number of partial results have been obtained. Using the deep results of Connes on infective von Neumann algebras [7] and the characterization of nuclear C*-algebras given in [3], one gets the result fairly easily that every bounded representation of a nuclear C*-algebra is similar to a *-representation (cf. [2, Th. 3.5] and [5, Th. 4.1]). The similarity problem for bounded cyclic representations of arbitrary C*-algebras was first considered by Barnes in [1]. He proved that when 77 is a bounded representation of a C*-algebra A on a Hilbert space H. such that 7V(A) and v((A)* have a common cyclic vector I, then there exists a closed, infective operator T on H. such that T and T' are densely defined, and such that x -> ThT(x)T-' is a *-representation of A. Bunce sharpened this in [2] by proving that T can be chosen bounded, but not necessarily with bounded inverse. He also removed the condition that ( is cyclic for 7v(A)*. Finally, Christensen proved in [5] that every irreducible bounded representation of a C*-algebra is similar to a *-representation. These two results of Bunce and Christensen rely on an inequality due to Pisier [16, Cor. 2.3] stating that, when S is a bounded linear map from a C*-algebra A into a C*-algebra B. then for all n E N and a. an E A:
TL;DR: An algorithm for assigning the secondary structure of alpha/beta proteins is described, which successfully divides protein sequences into two classes: alpha/ beta and non-alpha/beta.
Abstract: We describe an algorithm for assigning the secondary structure of alpha/beta proteins. Turns are identified very accurately (98%) by simultaneously considering hydrophilicity and the ideal spacing of turns throughout the sequence. The segments bounded by these turns are labeled by a pattern-recognition scheme based on the physical properties of alpha-helices and beta-strands, in this class of proteins. Long-range, as well as local, information is incorporated to enhance the quality of the assignments. Although the assignment for any one sequence is not unique, at least one of the assignments bears a close resemblance to the native structure. The algorithm successfully divides protein sequences into two classes: alpha/beta and non-alpha/beta. The accuracy of the secondary-structure assignments in the alpha/beta class is sufficient to provide useful input for tertiary-structure assignments.
TL;DR: In this article, the problem of task allocation in fault-tolerant distributed systems is formulated as a constrained sum-of-squares minimization problem and an efficient approximation algorithm is proposed.
Abstract: This paper examines task allocation in fault-tolerant distributed systems. The problem is formulated as a constrained sum of squares minimization problem. The computational complexity of this problem prompts us to consider an efficient approximation algorithm. We show that the ratio of the performance of the approximation algorithm to that of the optimal solution is bounded by 9m/(8m?r+1)), wherem is the number of processors to be allocated andr is the number of times each task is to be replicated. Experience with the algorithm suggests that even better performance ratios can be expected.
TL;DR: In this article, a theorem based on the circle criterion is developed, which gives sufficient conditions for the stability of a saturating linear control for a linear system with bounded states, and can be applied to determine a range of gains for the linear control which ensures stability.
Abstract: A theorem is developed, based on the circle criterion, which gives sufficient conditions for the stability of a saturating linear control for a linear system with bounded states. This theorem can be applied to determine a range of gains for the linear control which ensures stability. It is shown by example that this approach results in an increased speed of response over that obtained by previous methods which do not account for state bounds.
DOI•
01 Jan 1983TL;DR: In the efforts to seek optimum solutions to the single machine weighted tardiness problem, a hybrid dynamic programming procedure is developed which provides lower and upper bounds when it becomes impractical to find the optimum solution.
Abstract: : It is well known that the single machine weighted tardiness problem is NP-complete Hence, it is unlikely that there exist polynomially bounded algorithms to solve this problem Further, the problem is of great practical significance We develop myopic heuristics for this problem; these heuristics have been tested against competing heuristics, against a tight lower bound, and where practical, against the optimum, with uniformly good results Also, these heuristics can be used as dispatching rules in practical situations In our efforts to seek optimum solutions we develop a hybrid dynamic programming procedure (a modified version of Baker's procedure) which provides lower and upper bounds when it becomes impractical to find the optimum solution Further, stopping rules are developed for identifying optimal first job/jobs (Author)
TL;DR: In this paper, an existence result for optimal control problems of Lagrange type with unbounded time domain is derived very directly from a corresponding result for problems with bounded time domain, which subsumes the main existence result of R. F. Baum and M. P. Magill.
TL;DR: It is shown that a class of ultimate boundedness problems which have been solved to date via nonlinear control, can in point of fact be solved via linear control and some of the so-called matching assumptions can be weakened somewhat.
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TL;DR: In this article, the authors present a direct approach to finite-order compensator design for distributed parameter systems, i.e., one that is not based on reduced order modelling, and use a parametrization around an initial compensator which displays both controller order and closed-loop stability in a convenient way.
Abstract: We present a direct approach to finite-order compensator design for distributed parameter systems, i.e., one that is not based on reduced order modelling. Instead, we use a parametrization around an initial compensator which displays both controller order and closed-loop stability in a convenient way. The main result is an existence theorem which holds for a wide class of linear time-invariant systems (parabolic, delay, damped hyperbolic). The most important assumptions are: bounded inputs and outputs, finitely many unstable modes, completeness of eigenvectors. An example is included to illustrate the feasibility of our method for purposes of design.
TL;DR: In this article, the influence of position of very high leverage points (i.e., points where the diagonal element of the hat matrix H = X(XTX)−1 XT exceeds a certain bound) was examined from the point of view of finite-sample minimax robust estimation theory.
Abstract: Bounded-influence regression (in the sense of Hampel-Mallows-Krasker-Welsch) is examined critically from the point of view of finite-sample minimax robust estimation theory. The main conclusion is that the influence of position of very high leverage points—that is, of points where the diagonal element of the hat matrix H = X(XTX)−1 XT exceeds a certain bound—should be cut down selectively. This bound should be chosen roughly between .2 and .5; for the upper of these values, the resulting estimate can be approximated very simply by scaling the residuals by their own estimated standard deviation. A conflict between decision theoretic (estimation) and data analytic (diagnostic) viewpoints is pointed out and briefly discussed.
TL;DR: The main result is an existence theorem which holds for a wide class of linear time-invariant systems (parabolic, delay, damped hyperbolic) and bounded inputs and outputs, finitely many unstable modes, completeness of eigenvectors.
Abstract: We present a direct approach to finite-order compensator design for distributed parameter systems, i.e., one that is not based on reduced order modelling. Instead, we use a parametrization around an initial compensator which displays both controller order and closed-loop stability in a convenient way. The main result is an existence theorem which holds for a wide class of linear time-invariant systems (parabolic, delay, damped hyperbolic). The most important assumptions are: bounded inputs and outputs, finitely many unstable modes, completeness of eigenvectors. An example is included to illustrate the feasibility of our method for purposes of design.
TL;DR: In this article, it was shown that the result EX = E(E(X | Y)) is true for bounded X, when the usual concept of conditional expectation or prevision is replaced by an alternative definition reflecting an individual's actual beliefs concerning X after observing Y.
Abstract: We prove that the result EX = E(E(X | Y)) is true, for bounded X, when the usual concept of conditional expectation or prevision is replaced by an alternative definition reflecting an individual's actual beliefs concerning X after observing Y. We discuss the importance of this result to subjectivist theory.