Identification of chaos in a regenerative cutting process by the 0-1 test

We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test for chaos. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. We are able to show that regular or chaotic motion occur in the investigated model depending on the delay time. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

0–1 laws for maps

A class of finite structures has a 0–1 law with respect to a logic if every property expressible in the logic has a probability approaching a limit of 0 or 1 as the structure size grows. To formulate 0–1 laws for maps (i.e., embeddings of graphs in a surface), it is necessary to represent maps as logical structures. Three such representations are given, the most general being the full cross representation based on Tutte's theory of combinatorial maps. The main result says that if a class of maps has two properties, richness and large representativity, then the corresponding class of full cross representations has a 0–1 law with respect to first‐order logic. As a corollary the following classes of maps on a surface of fixed type have a first‐order 0–1 law: all maps, smooth maps, 2‐connected maps, 3‐connected maps, triangular maps, 2‐connected triangular maps, and 3‐connected triangular maps. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 215–237, 1999     

Heuristics for the 0–1 multidimensional knapsack problem

Two heuristics for the 0–1 multidimensional knapsack problem (MKP) are presented. The first one uses surrogate relaxation, and the relaxed problem is solved via a modified dynamic-programming algorithm. The heuristics provides a feasible solution for (MKP). The second one combines a limited-branch-and-cut-procedure with the previous approach, and tries to improve the bound obtained by exploring some nodes that have been rejected by the modified dynamic-programming algorithm. Computational experiences show that our approaches give better results than the existing heuristics, and thus permit one to obtain a smaller gap between the solution provided and an optimal solution.     

The 0–1 inverse maximum stable set problem

In this paper we study the 0–1 inverse maximum stable set problem, denoted by IS_{0,1}. Given a graph and a fixed stable set, it is to delete the minimum number of vertices to make this stable set maximum in the new graph. We also consider IS_{0,1} against a specific algorithm such as Greedy and 2opt, aiming to delete the minimum number of vertices so that the algorithm selects the given stable set in the new graph; we denote them by IS_{0,1},greedy and IS_{0,1},2opt, respectively. Firstly, we show that they are NP-hard, even if the fixed stable set contains only one vertex. Secondly, we achieve an approximation ratio of for IS_{0,1},2opt. Thirdly, we study the tractability of IS_{0,1} for some classes of perfect graphs such as comparability, co-comparability and chordal graphs. Finally, we compare the hardness of IS_{0,1} and IS_{0,1},2opt for some other classes of graphs.     

A pseudo-Boolean consensus approach to nonlinear 0–1 optimization

It is proved that any pseudo-Boolean function f can be represented as , where z is the minimum of f and φ is a polynomial with positive coefficients in the original variables x_i and in their complements . A non-constructive proof and a constructive one are given. The latter, which is based on a generalization to pseudo-Boolean functions of the well-known Boolean-theoretical operation of consensus, provides a new algorithm for the minimization of pseudo-Boolean functions.     

On the maximum density of 0–1 matrices with no forbidden rectangles

This note provides bounds for the maximal number of ones allowed in an N × N 0–1 matrix, N=2ⁿ, in which there are no ‘forbidden rectangles’ of a special type.     

A Simplified Proof of the 0–1 Law for Existential Second-Order Ackermann Sentences

Recently we gave a finitistic proof of the 0–1 law for ∑₁¹ (Ackermann) sentences, which relied as much as possible on the original argument of Kolaitis and Vardi. Here we present another version of our proof which, on the contrary, is self-contained. Finitism allows us to use the beautiful probabilistic argument of Kolaitis and Vardi in a simple and intuitive way. Consequently, we obtain a shorter proof.     

Using rank-1 lift-and-project closures to generate cuts for 0–1 MIPs, a computational investigation

Various techniques for building relaxations and generating valid inequalities for pure or mixed integer programming problems without special structure are reviewed and compared computationally. Besides classical techniques such as Gomory cuts, Mixed Integer Rounding cuts, lift-and-project and reformulation–linearization techniques, a new variant is also investigated: the use of the relaxation corresponding to the intersection of simple disjunction polyhedra (i.e. the so-called elementary closure of lift-and-project cuts). Systematic comparative computational results are reported on series of test problems including multidimensional knapsack problems (MKP) and MIPLIB test problems. From the results obtained, the relaxation based on the elementary closure of lift-and-project cuts appears to be one of the most promising.     

Smooth perturbations the self–adjoint operators defined by the ℋ︁–2–construction

The existence of the wave operators for the self–adjoint operator constructed by ??_–2–construction is discussed in the abstract theory by using Kato's smooth perturbation method. Moreover, the s–matrix is calculated explicitly.     

Experimental study of controlling chaos in a DC–DC boost converter

This paper presents a delayed feedback control scheme for eliminating chaotic behaviour in a peak current-mode controlled DC–DC boost converter operating in the continuous current conduction mode. Experimental results and FORTRAN simulations show the effectiveness and robustness of the scheme.     

On the Π11‐separation principle

We study the proof‐theoretic strength of the Π₁¹‐separation axiom scheme, and we show that Π₁¹‐separation lies strictly in between the Δ₁¹‐comprehension and Σ₁¹‐choice axiom schemes over RCA₀. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Eigenvalues of a λ – Rational Sturm– Liouville Problem

The Sturm – Liouville problem (1.1), (1.2) is considered, which depends rationally on the eigenvalue parameter. Estimates for the eigenvalues and especially for the embedded eigenvalues are proved. Moreover, conditions for the non – existence of embedded eigenvalues are given.     

Π11‐Martin‐Löf randomness and Π11‐Solovay completeness

Developing an analogue of Solovay reducibility in the higher recursion setting, we show that results from the classical computably enumerable case can be extended to the new context.     

Quotient Fields of a Model of IΔ0 + Ω1

In [4] the authors studied the residue field of a model M of IΔ₀ + Ω₁ for the principal ideal generated by a prime p. One of the main results is that M/<p> has a unique extension of each finite degree. In this paper we are interested in understanding the structure of any quotient field of M, i.e. we will study the quotient M/I for I a maximal ideal of M. We prove that any quotient field of M satisfies the property of having a unique extension of each finite degree. We will use some of Cherlin's ideas from [3], where he studies the ideal theory of non standard algebraic integers.     

A note on parameter free Π1‐induction and restricted exponentiation

We characterize the sets of all Π₂ and all $\mathcal {B}(\Sigma _{1})We characterize the sets of all Π₂ and all $\mathcal {B}(\Sigma _{1})$ (= Boolean combinations of Σ₁) theorems of IΠ^?₁ in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ^?_{n + 1} is conservative over IΣ^?_n with respect to $\mathcal {B}(\Sigma _{n+1})$ sentences cannot be extended to Π_{n + 2} sentences. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Chaotic vibrations in a regenerative cutting process

We have analysed vibrations generated in an orthogonal cutting process. Using a simple one degree of freedom model of the regenerative cutting, we have observed the complex behaviour of the system. In presence of a shaped cutting surface, the nonlinear interaction between the tool and a workpiece leads the to chatter vibrations of periodic, quasi-periodic or chaotic type depending on system parameters. To describe the profile of the surface machined by the first pass we used a harmonic function. We analysed the impact phenomenon between the tool and a workpiece after their contact loss.     

Asymptotic Behaviour of C0–Semigroups with Bounded Local Resolvents

Let {T(t)}_t≥0 be a C₀–semigroup on a Banach space X with generator A, and let H^∞_T be the space of all x ∈ X such that the local resolvent λ ↦ R(λ, A)x has a bounded holomorphic extension to the right half–plane. For the class of integrable functions ϕ on [0, ∞) whose Fourier transforms are integrable, we construct a functional calculus ϕ ↦ T_ϕ, as operators on H^∞_T. Weshow that each orbit T(·)T_ϕx is bounded and uniformly continuous, and T(t)T_ϕx → 0 weakly as t → ∞, and we give a new proof that ∥T(t)R(μ, A)x∥ = O(t). We also show that ∥T(t)T_ϕx∥ → 0 when T is sun –reflexive, and that ∥T(t)R(μ, A)x∥ = O(ln t) when T is a positive semigroup on a normal ordered space X and x is a positive vector in H^∞_T.     

Nonlinear analysis of RED––a comparative study

Random Early Detection (RED) is an active queue management (AQM) mechanism for routers on the Internet. In this paper, performance of RED and Adaptive RED are compared from the viewpoint of nonlinear dynamics. In particular, we reveal the relationship between the performance of the network and its nonlinear dynamical behavior. We measure the maximal Lyapunov exponent and Hurst parameter of the average queue length of RED and Adaptive RED, as well as the throughput and packet loss rate of the aggregate traffic on the bottleneck link. Our simulation scenarios include FTP flows and Web flows, one-way and two-way traffic. In most situations, Adaptive RED has smaller maximal Lyapunov exponents, lower Hurst parameters, higher throughput and lower packet loss rate than that of RED. This confirms that Adaptive RED has better performance than RED.     

Devaney’s chaos implies distributional chaos in a sequence

Let X be a complete metric space without isolated points, and let f:X→X be a continuous map. In this paper we prove that if f is transitive and has a periodic point of period p, then f is distributionally chaotic in a sequence. Particularly, chaos in the sense of Devaney is stronger than distributional chaos in a sequence.