An abstract Nyquist criterion containing old and new results

We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.     

An affirmative answer to a question of Ciliberto

We give an example of a nondegeneraten-dimensional smooth projective varietyX inP ²ⁿ⁺¹ with the canonical bundle ample a varietyX whose tangent variety TanX has dimension less than 2n over an algebraically closed field of any characteristic whenn≥9. This varietyX is not ruled by lines and the embedded tangent space at a general point ofX intersectsX at some other points, so that this yields an affirmative answer to a question of Ciliberto.     

An answer to a question by J. Milnor

We consider two commuting automorphismsT ₁,T ₂ of the Lebesque space (M, M, μ) such thath _m,n=h(T ₁ ^m T ₂ ⁿ )<∞ whereh is the measure-theoretic entropy. Under additional assumptions we show the existence of the limits lim (1/m)h _m,n wherem→∞,n→∞,m/n→ω and ω is an irrational number.     

Interior-point methods: An old and new approach to nonlinear programming

In this paper we discuss the main concepts of structural optimization, a field of nonlinear programming, which was formed by the intensive development of modern interior-point schemes.     

An answer to a question on the convolution of functions

Let G be a locally compact group. Recently, G?a¸b and Strobin [2] asked when f*g exists for all \({f, g \in L^p(G)}\) , and also: is the set \({\{(f,g)\in L^p(G) \times L^p(G): f\ast g \in L^p(G)\}}\) σ-c-lower porous (in particular, meager) for \({p\in(1,2]}\) ? In this paper, we answer these questions. In particular, we prove that if 1 <  p <  ∞, 1 ≤  q < ∞, and G is a non-unimodular locally compact group, then the set \({\{(f, g) \in L^p(G) \times L^q(G): f * g}\) is not λ -a.e. finite on G} is a residual set in L ^p (G) ×  L ^q (G).     

Long strange segments in a long-range-dependent moving average

We establish the rate of growth of the length of long strange intervals in an infinite moving average process whose coefficients are regularly varying at infinity. We compute the limiting distribution of the appropriately normalized length of such intervals. The rate of growth of the length of long strange intervals turns out to change dramatically once the exponent of regular variation of the coefficients becomes smaller than 1, and then the rate of growth is determined both by the exponent of regular variation of the coefficients and by the heaviness of the tail distribution of the noise variables.     

An answer to a question of Isaacs on character degree graphs

Let N be a normal subgroup of a finite group G. We consider the graph Γ(G|N) whose vertices are the prime divisors of the degrees of the irreducible characters of G whose kernel does not contain N and two vertices are joined by an edge if the product of the two primes divides the degree of some of the characters of G whose kernel does not contain N. We prove that if Γ(G|N) is disconnected then G/N is solvable. This proves a strong form of a conjecture of Isaacs.     

An answer to a question of Cao, Reilly and Xiong

We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.     

Benchmarking in a multiple criteria performance context: An application and a conceptual framework

This article presents a conceptual benchmarking framework which applies a multiple criteria approach to assess performance. In the process, a multiple criteria procedure is used to assess the performance of three hundred and ninety two (392) Portuguese firms. Based on the results of this procedure, a conceptual framework is devised to facilitate addressing relevant benchmarking implications. The framework is designed to provide a conceptual linkage between the performance measurement methodology and the organizational benchmarking system.     

An answer to a question by Herings et al.

We answer an open question by Herings et al. [J.J. Herings, G. van der Laan, D. Talman, Z. Yang, A fixed point theorem for discontinuous functions, Operations Research Letters 36 (1) (2008) 89–93], by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of , and not only polytopes. This rests on a fixed point result of Toussaint [S. Toussaint, On the existence of equilibria in economies with infinitely many commodities and without ordered preferences, Journal of Economic Theory 33 (1) (1984) 98–115].     

Autonomous strange nonchaotic oscillations in a system of mechanical rotators

We investigate strange nonchaotic self-oscillations in a dissipative system consisting of three mechanical rotators driven by a constant torque applied to one of them. The external driving is nonoscillatory; the incommensurable frequency ratio in vibrational-rotational dynamics arises due to an irrational ratio of diameters of the rotating elements involved. It is shown that, when losing stable equilibrium, the system can demonstrate two- or three-frequency quasi-periodic, chaotic and strange nonchaotic self-oscillations. The conclusions of the work are confirmed by numerical calculations of Lyapunov exponents, fractal dimensions, spectral analysis, and by special methods of detection of a strange nonchaotic attractor (SNA): phase sensitivity and analysis using rational approximation for the frequency ratio. In particular, SNA possesses a zero value of the largest Lyapunov exponent (and negative values of the other exponents), a capacitive dimension close to 2 and a singular continuous power spectrum. In general, the results of this work shed a new light on the occurrence of strange nonchaotic dynamics.     

Convolution kernels in Clifford analysis: old and new

New singular integral operators are constructed involving the so‐called spherical monogenics of Clifford analysis, as special cases of broad families of specific Clifford distributions. They constitute refinements of the classical singular integral operators involving spherical harmonics and give rise to generalized Hilbert transforms. Copyright © 2005 John Wiley & Sons, Ltd.     

An answer to a question of Schmidt on (α, β) games

Schmidt has defined (α, β) games and has found applications for them in diophantine approximation. The following question has been asked: If S is (α, β)-winning and 0 < α′ ≤ α < 1 and 0 < β ≤ β′ < 1, does it follow that S is (α′, β′)-winning? Here I give a counterexample which answers this in the negative.