Triangulating a simple polygon in linear time

We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm. The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8700917.     

Rectifiable oscillations in second-order linear differential equations

We study the linear differential equation , on I=(0,1), where the coefficient f(x) is strictly positive and continuous on I, and satisfies the Hartman-Wintner condition at x=0. The four main results of the paper are: (i) a criterion for rectifiable oscillations of (P), characterized by the integrability of on I; (ii) a stability result for rectifiable and unrectifiable oscillations of (P), in terms of a perturbation on f(x); (iii) the s-dimensional fractal oscillations (for which we assume also f(x)∼cx−α when x→0, α>2, and s=max{1,3/2−2/α}); and (iv) the co-existence of rectifiable and unrectifiable oscillations in the absence of the Hartman-Wintner condition on f(x). Explicit examples related to the above results are given.     

Local chaos induced by spatial oscillations of a perturbation

We study motion of an one-dimensional Hamiltonian oscillator driven by an external force which is periodic in time and in coordinate as well. It is shown that dynamics of the oscillator is strongly affected by the resonance between spatial and temporal oscillations of the perturbation imposed. In particular, this resonance can induce strong but bounded chaotic diffusion in certain areas of phase space. The model of the Duffing oscillator is used as an example for the numerical simulation.     

Time scales in linear delayed differential equations

The aim of this paper is to apply and justify the so-called aggregation of variables method for reduction of a complex system of linear delayed differential equations with two time scales: slow and fast. The difference between these time scales makes a parameter ε>0 to appear in the formulation, being a mathematical problem of singular perturbations. The main result of this work consists of demonstrating that, under some hypotheses, the solution to the perturbed problem converges when ε→0 to the solution of an aggregated system whose construction is proposed.     

Quasi-periodic and chaotic relaxation oscillations in a laser model with variable delayed optoelectronic feedback

Doklady Mathematics - We derive asymptotically discrete mappings which determine the dynamics of relaxation spikes in a model of laser with optoelectronic feedback in the pump circuit. The time...     

Limiting the oscillations in queues with delayed information through a novel type of delay announcement

Queueing Systems - Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the...     

Control of linear stochastic time delayed systems

The linear-quadratic control problem of stochastic time-delayed systems has been solved using function space method. The solution demonstrates directly that the “separation theorem” holds for such systems.     

Time optimal boundary controllability of a simple linear viscoelastic liquid

A viscoelastic liquid confined between two parallel plates is considered under the action of L₂ (O, T)-boundary controls. Applying Laplace-Transform-techniques it is shown that L₂ (O, l)-states are exactly controllable in finite time, depending on the speed of propagation of singularities. Finally the existence of time-optimal controls respecting a given norm bound is shown.     

Oscillations of a simple valve connected to a pipe. Part III,lateral oscillations

Summary Oscillations of a valve connected to a pipe are treated along the lines given in [1]. In the present case, lateral oscillations of the valve are considered. It is shown that for realistic parameters, amplified oscillations are predicted for a large range of the eigenfrequency of the valve, and that the amplification increases with increasing pressure difference across the valve. The most efficient way to eliminate oscillations seems to be to decrease the parameterA and to increaseB, both defined by Eqn. (22). A practical way to decreaseA is indicated.

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Zusammenfassung Querschwingungen von einem Ventil, das mit einem Rohr verbunden ist, werden untersucht. Dabei wird wie in [1] vorgegangen. Für realistische Ventil- und Rohrparameter werden für einen grossen Bereich der Ventileigenfrequenz angefachte Schwingungen vorausgesagt. Die Anfachung nimmt zu mit zunehmendem Druckfall über dem Ventil. Die Schwingungen scheinen sich am besten eliminieren zu lassen, indem manA verkleinert undB erhöht. Beide sind durch Gl. (22) gegeben. Es wird gezeigt, durch welche FormgebungA verkleinert werden kann.

     

Stabilization of the second-order linear time-invariant control systems by a delayed feedback

We consider a static stabilization problem for a two-dimensional linear time-invariant control system with a delayed feedback. We obtain the necessary and sufficient conditions for the stabilizability of the system under consideration. The theorems proved in this paper show that such a delayed feedback approach is efficient in stabilizing the second-order linear systems.     

Nonintegral criterion for oscillations of linear Hamiltonian matrix systems

In this paper we present nonintegral criteria for oscillation of linear Hamiltonian matrix system U^′=A(x)U+B(x)V, V^′=C(x)U−A^*(x)V under the hypothesis (H): A(x), B(x)=B^*(x)>0, and C(x)=C^*(x) are 2×2 matrices of real valued continuous functions on the interval I=[a,∞),(−∞<a). These criteria are conditions of algebraic type only. Our results are also useful for the detection of the oscillation of particular matrix differential systems.     

Space of orbits of a three-dimensional simple compact linear Lie group

An upper estimate for the codimension of the subspace of points with finite orbits for a representation of a three-dimensional simple compact Lie group whose quotient is a manifold is obtained.     

On trend estimation of time-series: a simple linear programming approach

This paper presents a simple linear programme for the solution of the trend-estimation problem in time-series. We studied the trade-off between two important properties of the trend component: smoothness and fidelity (closeness to the data). The linear programming solution is a monotone sequence optimizing some (weighted) combination of both properties. A single coefficient in the objective function is user-dependent and represents the user’s preference with respect to the two properties. The method is illustrated on several empirical series.     

A linear time algorithm to remove winding of a simple polygon

In this paper, we present a linear time algorithm to remove winding of a simple polygon P with respect to a given point q inside P. The algorithm removes winding by locating a subset of Jordan sequence that is in the proper order and uses only one stack.     

Fractal oscillations for a class of second order linear differential equations of Euler type

The s-dimensional fractal oscillations for continuous and smooth functions defined on an open bounded interval are introduced and studied. The main purpose of the paper is to establish this kind of oscillations for solutions of a class of second order linear differential equations of Euler type. Next, it will be shown that the dimensional number s only depends on a positive real parameter α appearing in a singular term of the main equation. It continues some recent results on the rectifiable and unrectifiable oscillations given in Paši? [M. Paši?, Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type, J. Math. Anal. Appl. 335 (2007) 724-738] and Wong [J.S.W. Wong, On rectifiable oscillation of Euler type second order linear differential equations, Electron. J. Qual. Theory Differ. Equ. 20 (2007) 1-12].