Bounds and positivity conditions for operator valued functions in a Hilbert lattice

In this paper we investigate regular functions of a bounded operator A acting in a Hilbert lattice and having the form A=D + T, where T is a positive operator and D is a selfadjoint operator whose resolution of the identity P(t) $(a\le s \le b)$ has the property $P(s_2)-P(s_1)\;\;(s_1<s_2)$ are non-negative in the sense of the order. Upper and lower bounds and positivity conditions for the considered operator valued functions are derived. Applications of the obtained estimates to functions of integral operators, partial integral operators, infinite matrices and differential equations are also discussed.     

Weakly hyperbolic equations with non-analytic coefficients and lower order terms

In this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey well-posedness of the Cauchy problem under $C^k$ -regularity of coefficients of the principal part and natural Levi conditions on lower order terms which may be only continuous. In the case of analytic coefficients in the principal part we establish the $C^\infty $ well-posedness. The proofs are based on using the quasi-symmetriser for the corresponding companion system and inductions on the order of equation and on the frequency regions. The main novelty compared to the existing literature is the possibility to include lower order terms to the equation (which have been untreatable until now in these problems) as well as considering any space dimensions. We also give results on the ultradistributional and distributional well-posedness of the problem, and we look at new effects for equations with discontinuous lower order terms.     

Equivariant Universal Coefficient and Kunneth Spectral Sequences

This paper constructs hyper-homology spectral sequences of Z-gradedand RO_G-graded Mackey functors that compute Ext and Tor overG-equivariant S-algebras A ring spectra) for finite groups G.These specialize to universal coefficient and Künneth spectralsequences. 2000 Mathematics Subject Classification 55N91 (primary),55P43, 55U20, 55U25 (secondary).     

Analysis of Basis Pursuit via Capacity Sets

Finding the sparsest solution α for an under-determined linear system of equations D α=s is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of α that allow its recovery using ? ₁-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of D called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given D, called the capacity sets. We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of D α=s.     

Fracture Mechanics of Rubber Material

This contribution presents an approach based on the material force method which allows to evaluate the fracture sensitivity of rubber material. In order to account for the rate–independent dissipation of filled elastomers subjected to low rates, an endochronic plasticity formulation is introduced. It is shown how configurational forces under consideration of material body forces correspond with the elastic and dissipative energy and how they can be related to energy release rates measured in test configurations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lower Bounds on the Size of Maximum Independent Sets and Matchings in Hypergraphs of Rank Three

In this paper, we study lower bounds on the size of a maximum independent set and a maximum matching in a hypergraph of rank three. The rank in a hypergraph is the size of a maximum edge in the hypergraph. A hypergraph is simple if no two edges contain exactly the same vertices. Let H be a hypergraph and let and be the size of a maximum independent set and a maximum matching, respectively, in H, where a set of vertices in H is independent (also called strongly independent in the literature) if no two vertices in the set belong to a common edge. Let H be a hypergraph of rank at most three and maximum degree at most three. We show that with equality if and only if H is the Fano plane. In fact, we show that if H is connected and different from the Fano plane, then and we characterize the hypergraphs achieving equality in this bound. Using this result, we show that that if H is a simple connected 3‐uniform hypergraph of order at least 8 and with maximum degree at most three, then and there is a connected 3‐uniform hypergraph H of order 19 achieving this lower bound. Finally, we show that if H is a connected hypergraph of rank at most three that is not a complete hypergraph on vertices, where denotes the maximum degree in H, then and this bound is asymptotically best possible. © 2012 Wiley Periodicals, Inc. J. Graph Theory     

Efficiency of electrostatic air moving devices

An ion-driven gas flow is characterized by the breakdown of a gas into ions in the presence of a high electric potential. Ions flow due to the potential gradient. Mass transfer motivates bulk airflow. In the current study, an ionic air moving device was constructed using needles as ion sources, and a ring as collector. Airflow and efficiency were evaluated at various ring widths and with various numbers of ionization sites. Efficiency was seen to increase with ring width if airflow and distance was held constant and also increased with the number of ionization sites when airflow was held constant.     

Resonance splitting in gyrotropic ring resonators

We present the theoretical concept of an optical isolator based on resonance splitting in a silicon ring resonator covered with a magneto-optical polymer cladding. For this task, a perturbation method is derived for the modes in the cylindrical coordinate system. A polymer magneto-optical cladding causing a 0.01 amplitude of the off-diagonal element of the dielectric tensor is assumed. It is shown that the derived resonance splitting of the clockwise and counterclockwise modes increases for smaller ring radii. For the ring with a radius of approximately 1.5μm, a 29GHz splitting is demonstrated. An integrated optical isolator with a 10μm geometrical footprint is proposed based on a critically coupled ring resonator.     

Scattering of plane guided waves obliquely incident on a straight feature with uniform cross-section

A frequency-domain finite element (FE) method is presented for modeling the scattering of plane guided waves incident on an infinitely-long, straight feature with uniform cross-section in a planar host waveguide. The method utilizes a mesh of 2-dimensional finite elements with harmonic shape functions in the perpendicular direction. The model domain comprises a cross-section through the feature and short lengths of the adjoining host waveguide. A spatial frequency equal to the wavenumber of the desired incident mode multiplied by the sine of the desired incidence angle is prescribed for the element shape functions. An integral representation of the incident mode is used to determine a suitable system of harmonic forces to uniquely excite that mode. These are applied at nodes through the thickness of the host waveguide on one side of the feature. The displacement field is measured at nodes through the thickness of the host waveguide on either side of the feature and decomposed into reflected and transmitted modes. The cases of guided wave transmission in a featureless waveguide and the reflection of guided waves from a free-edge are examined as validation cases. Finally, the results for transmission at an adhesively-bonded stiffener are presented and compared with experimental measurements.     

Adaptive flocking with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity

This paper investigates adaptive flocking of multi-agent systems (MASs) with a virtual leader. All agents and the virtual leader share the same intrinsic nonlinear dynamics, which satisfies a locally Lipschitz condition and depends on both position and velocity information for the agent itself. Under the assumption that the initial network is connected, an approach to preserving the connectivity of the network is proposed. On the basis of the Lyapunov stability theory, an adaptive flocking control law is derived, for making the MASs track the virtual leader without collision. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.