Stability results for Mountain Pass and Linking type solutions of semilinear problems involving Dirichlet forms

Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also given.     

Semigroups Generated by Ordinary Differential Operators in L 1(I)*

In this paper we give necessary and sufficient conditions for the existence of a C> ₀-semigroup in L ¹(I) (I real interval) generated by a second-order differential operator when suitable boundary conditions at the endpoints are imposed.     

Stable determination of an inhomogeneous inclusion by local boundary measurements

We deal with the problem of determining an inclusion within an electrostatic conductor from boundary measurements. Under mild a priori assumptions we establish optimal stability estimates. Measurements are performed on a portion of the boundary of the conductor.     

On the impact of physical layer awareness on scheduling and resource allocation in broadband multicellular IEEE 802.16 systems [Radio Resource Management and Protocol Engineering for IEEE 802.16]

Multicellular networks based on the IEEE 802.16 standard appear to be very promising candidates to provide end users with broadband wireless access. However, they also pose interesting challenges in terms of radio resource management, where several design choices are not specified in the standard, intentionally left open to implementors. For this reason, we focus in this article on scheduling and resource allocation, and investigate how they could operate in a cross-layer fashion. In particular, we describe the principles of joint scheduling and resource allocation for IEEE 802.16 operating in AMC mode, and discuss the critical role played by physical layer considerations, especially intercell interference estimation and channel state awareness, in the obtained performance. This leads to identifying key open issues and possible general solutions     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

A remark on Serrin’s Theorem

An approximation theorem for families of weakly coercive convex functions by means of countably many smooth families of convex functions is proved. As a consequence, the classical “three-fold” lower semicontinuity theorem for integral functionals of the Calculus of Variations by James Serrin is unified in one single statement.     

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H ₅ ⁺ .     

Stability analysis of an adaptive packet access scheme for mobile communication systems with high propagation delays

In this paper, we investigate a packet access scheme that is able to support mixed traffics in the presence of high propagation delays. Referring to a Time‐Code Division Multiple Access air interface, we propose a Medium Access Control (MAC) protocol based on a random access scheme. A successful attempt grants the use of a slot‐code resource. This protocol is named Adaptive Time Code‐Packet Reservation Multiple Access (ATC‐PRMA), since the access parameters are changed, depending on the traffic load conditions, so as to fulfil Quality of Service requirements. Numerical examples are carried out for the Low Earth Orbit (LEO)‐Mobile Satellite System (MSS) scenario, but all these considerations could be applied to High‐Altitude Platform Stations (HAPSs) as well. In both cases, high propagation delays prevent an immediate feedback to users. An analytical approach is proposed to study the stability of our MAC scheme. Accordingly, we define a criterion for optimizing system performance. The predicted ATC‐PRMA behaviour is supported by simulation results. Finally, we show the performance improvement of ATC‐PRMA with respect to a MAC protocol not employing adaptive parameters. Copyright © 2003 John Wiley & Sons, Ltd.