Existence and multiplicity of periodic solutions for the ordinary p-Laplacian systems

Some existence and multiplicity results are obtained for periodic solutions of the ordinary p-Laplacian systems: $$\left\{\begin{array}{@{}l@{\quad{}}l}(|u'(t)|^{p-2}u'(t))'=\nabla F(t,u(t)),&\mbox{a.e. }t\in[0,T],\\[4pt]u(0)-u(T)=u'(0)-u'(T)=0\end{array}\right.$$ by using the Saddle Point Theorem, the least action principle and the Three-critical-point Theorem.     

The onset of positive periodic solutions for a biochemical pest management model

In this paper, the bifurcation of nontrivial periodic solutions for an impulsively perturbed system of ordinary differential equations which models an integrated pest management strategy is studied by means of a fixed point approach. A biological control, consisting in the periodic release of infective pests, and a chemical control, consisting in pesticide spraying, are employed to maintain susceptible pests below an acceptable level. It is assumed that the biological and chemical control act with the same periodicity, but not in the same time. It is then shown that if the constant amount of infective pests released each time reaches a certain threshold value, then the trivial susceptible pest-eradication periodic solution loses its stability, which is transferred to a newly emerging nontrivial periodic solution.     

Existence and global stability of periodic solution for impulsive predator-prey model with diffusion and distributed delay

In this paper, the nonlinear nonautonomous predator-prey model with impulsive effect is considered. By using the method of coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solution, and by the means of a suitable Lyapunov function, the uniqueness and global attractivity of positive periodic solution are presented. An example shows the feasibility of our main results.     

Analysis of global exponential stability and periodic solutions of FCNNs with constant delays and time-varying delays

In this paper, we investigate a class of fuzzy cellular neural networks with constant delays and time-varying delays. By constructing suitable Lyapunov functional and employing Young inequality, we find sufficient conditions for the existence, uniqueness, global exponential stability of equilibrium, and the existence of periodic solutions of fuzzy cellular neural networks with time-varying delays. The results of this paper are new and they extend previously known results.     

Strong Normalizability of Typed Lambda-Calculi for Substructural Logics

The strong normalization theorem is uniformly proved for typed λ-calculi for a wide range of substructural logics with or without strong negation. We would like to thank the referees for their valuable comments and suggestions. This research was supported by the Alexander von Humboldt Foundation. The second author is grateful to the Foundation for providing excellent working conditions and generous support of this research. This work was also supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Young Scientists (B) 20700015, 2008.     

Time periodic traveling wave solutions for periodic advection–reaction–diffusion systems

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection–reaction–diffusion systems. Under certain conditions, we prove that there exists a maximal wave speed c^?$c^{?}$ such that for each wave speed c≤c^?$c\le c^{?}$, there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c≤c^?$c\le c^{?}$ are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves with speed c>c^?$c>c^{?}$.     

Magnetically-Induced Buckling of a Whirling Conducting Rod with Applications to Electrodynamic Space Tethers

We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure, motivated by stability problems of electrodynamic space tethers. Both static (buckling) and dynamic (whirling) instability are considered and we also compute post-buckling configurations. The equations used are the geometrically exact Kirchhoff equations. Magnetic buckling of a welded rod is found to be described by a surprisingly degenerate bifurcation, which is unfolded when both transverse anisotropy of the rod and angular velocity are considered. By solving the linearised equations about the (quasi-) stationary solutions, we find various secondary instabilities. Our results are relevant for current designs of electrodynamic space tethers and potentially for future applications in nano- and molecular wires.     

Combinatorial Integer Labeling Theorems on Finite Sets with Applications

Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1,±2,…,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1,±2,…,±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0,1} ⁿ +q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations under certain natural conditions. An economic application is provided.     

Inexact Josephy–Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization

We propose and analyze a perturbed version of the classical Josephy–Newton method for solving generalized equations. This perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version, sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly constrained Lagrangian methods, in particular, we obtain superlinear convergence under the second-order sufficient optimality condition and the strict Mangasarian–Fromovitz constraint qualification, while previous results in the literature assume (in addition to second-order sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity condition. For the sequential quadratically constrained quadratic programming methods, we prove primal-dual superlinear/quadratic convergence under the same assumptions as above, which also gives a new result.     

Non-Walker Self-Dual Neutral Einstein Four-Manifolds of Petrov Type III

The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Díaz-Ramos, García-Río and Vázquez-Lorenzo (J. Geom. Anal. 16, 39–52, 2006). Work begun during the author’s visit to the University of Santiago de Compostela, supported by Grant MTM2006-01432 (Spain).     

A Mathematica package for q-holonomic sequences and power series

We describe a Mathematica package for dealing with q-holonomic sequences and power series. The package is intended as a q-analogue of the Maple package gfun and the Mathematica package GeneratingFunctions. It provides commands for addition, multiplication, and substitution of these objects, for converting between various representations (q-differential equations, q-recurrence equations, q-shift equations), for computing sequence terms and power series coefficients, and for guessing recurrence equations given initial terms of a sequence. C. Koutschan partially supported by the Austrian Science Foundation (FWF) grants SFB F1305.     

Four positive periodic solutions to a periodic Lotka–Volterra predatory–prey system with harvesting terms

By using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of four positive periodic solutions for two species periodic Lotka–Volterra predatory–prey system with harvesting terms. An example is given to illustrate the effectiveness of our results.     

Do we self-regulate actions or perceptions? A test of two computational models

Self-regulation theories in applied psychology disagree about whether action or perceptions are the focus of regulation. Computational models based on the two conceptualizations were constructed and simulated. In one scenario, they performed identically and in conjunction with participants in a study of the goal-level effect (Vancouver et al., Organ Res Methods 8:100–127, 2005). In another scenario they created differentiating predictions and only the computational model based on the self-regulation of perceptions matched the data of participants. Implications for research and practice are discussed.

Tate–Hochschild cohomology for periodic algebras

This paper is devoted to studying the Tate–Hochschild cohomology for periodic algebras. We will prove that the Tate–Hochschild cohomology ring of a periodic algebra can be written as the localization of the non-negative part of the Tate–Hochschild cohomology ring.

     

Stability of periodic Kuramoto–Sivashinsky waves

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized Kuramoto–Sivashinsky equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of decay. The approach extends readily to other second- and higher-order parabolic equations, for example, the Cahn Hilliard equation or more general thin film models.     

Poincaré-Hopf inequalities for periodic orbits

The interplay between the dynamics of a nonsingular Morse-Smale flow on a smooth, closed, n-dimensional manifold, M, and the topology of M, was exhibited in Franks (Comment Math Helv 53(2):279?C294, 1978), Smale (Bull Am Math Soc 66:43?C49, 1960), by means of a collection of inequalities, which we refer to as Morse-Smale inequalities. These inequalities relate the number of closed orbits of each index to the Betti numbers of M. These well-known inequalities provide the necessary conditions for a given dynamical data in the form of a specified number of closed orbits of a given index to be realized as a nonsingular Morse-Smale flow on M. In this article we provide two inequalities, hereby referred to as Poincaré-Hopf inequalities for periodic orbits, which imposes constraints on the dynamics of periodic orbits without reference to the Betti numbers of the manifold M. The main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse-Smale inequalities to hold.     

Limit Property for Regular and Weak Generalized Convolution

We denote by ? \((\mathcal{P_{+}})\) the set of all probability measures defined on the Borel subsets of the real line (the positive half-line [0,∞)). K. Urbanik defined the generalized convolution as a commutative and associative ?₊-valued binary operation ? on ? ₊ ² which is continuous in each variable separately. This convolution is distributive with respect to convex combinations and scale changes T _a (a>0) with δ ₀ as the unit element. The key axiom of a generalized convolution is the following: there exist norming constants c _n and a measure ν other than δ ₀ such that \(T_{c_{n}}\delta_{1}^{\bullet n}\to\nu\).In Sect. 2 we discuss basic properties of the generalized convolution on ? which hold for the convolutions without the key axiom. This rather technical discussion is important for the weak generalized convolution where the key axiom is not a natural assumption. In Sect. 4 we show that if the weak generalized convolution defined by a weakly stable measure μ has this property, then μ is a factor of strictly stable distribution.     

Units of ℤ(Cp × C2) and ℤ(Cp × C2 × C2)

The goal of this article is to describe a multiplicatively independent set, which generates the group of units of the integral group ring ?G, where G is either the cyclic group of order 2p or C₂ × C₂ × C_p, for a prime number p that satisfies some suitable conditions that will be specified later.