Un metodo per la costruzione di smoothing splines naturali mono e bidimensionali

Sommario In questa nota vengono dapprima presentati i teoremi di esistenza ed unicità (in opportuni spazi) delle smoothing splines naturali mono e bidimensionali, soluzioni rispettivamente dei problemi (1,5)–(1,6) e (4,5)–(4,6). Viene quindi indicato un procedimento, basato sulla costruzione di basi locali di splines naturali, per la costruzione di tali soluzioni. Infine viene presentato un metodo generale per la costruzione di tali basi.

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In this paper, we shall present the theorems of existence and uniqueness (in proper spaces) of the natural smoothing splines which are the solutions of the problems (1,5)–(1,6) for the one dimension case, and of the problems (4,5)–(4,6) for the two dimension case. We shall then suggest a method, based on construction of local bases of the natural splines, to determine these solutions. Finally, we shall indicate a general method to construct these bases.

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Lavoro eseguito nell’ambito del gruppo di ricerca GNAFA del CNR e dei programmi di ricerca dell’Istituto per le Applicazioni del Calcolo del CNR in Roma     

Sull’approssimazione di funzioni continue mediante operatori lineari

Sommario Si introduce un operatore lineare, definito su un insieme di funzioni reali, continue e limitate, definite in una parte diR ⁿ e si propongono alcune formule generali di approssimazione. Successivamente si stabilisce un procedimento che consente di estendere a funzioni di più variabili ogni trasformazione lineare di funzioni di una variabile. Si ottengono, così, formule di approssimazione che contengono un termine residuo, di facile costruzione. Si trovano criteri di convergenza uniforme e formule di maggiorazione del resto. Come applicazione si ottengono in modo semplice ed uniforme risultati già noti, peraltro conseguiti con procedimenti diversi, ed altri nuovi. In particolare si migliora un risultato di Quilghini, riguardante i polinomi di Hermite-Fejer in due variabili ed un teorema di Merli relativo alla convergenza dei polinomi interpolanti di Lagrange.

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We introduce a linear operator defined on a set of real continuous and bounded functions, defined on a subset ofR ⁿ , and suggest some approximation formulae. Moreover we establish a method which extends any linear transformation of functions of one real variable to functions of many variables. Thus we obtain approximation formulae with remainder of easy construction. We find criteria of uniform convergence and evaluations of errors. As application we obtain well known results differently and some else new. We improve a theorem of Quilghini, about polynomials of Herminte-Fejer in two variables, and a theorem of Merli concerning the convergence of Lagrange’s interpolating polynomials.

     

Diramazioni di soluzioni di equazioni differenziali ordinarie non lineari

Sommario In questa nota vengono studiate proprietà delle soluzioni non banaliw(x) (0≤x≤1) del problema non linearew″+λw=g(w) w′ ²,w(0)=w(1)=0, dove λ è reale eg(w) è intera; sono studiati in dettaglio alcuni casi corrispondenti a scelte particolari dig.

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Properties are obtained of the non trrivial solutionsw (x) (0≤x≤1) of the non linear boundary problemw″+λw=g(w)w′ ²,w(0)=w(1)=0, where λ is real andg(w) is entire. Some special cases (corresponding to special choices ofg) are studied in detail.

     

Interpolazione,rappresentazione e analisi di funzioni sperimentali

The present paper deals with the numerical problems which arise when spatially sampled data on a spherical surface are to be displayed and rotated around an arbitrary axis. We describe also a set of programs which implement these algorithms.     

Un chiarimento e qualche complemento ad una precedente nota

Some statements obtained in a previous paper, concerning an estimate of the error in the quadrature formulas of Newton-Cotes, are here considered in more detail.      

Formule di runge-kutta di ordine elevato per i sistemi differenziali lineari del 1o ordine con applicazione al calcolo delle radici delle equazioni algebriche

Simple formulae of the Runge-Kutta type and order greater than four are established for linear differential systems of the first order. They can also be used to solve numerically algebraic equations with real coefficients.      

Providing MAC QoS for multimedia traffic in 802.11e based multi-hop ad hoc wireless networks

Ad hoc wireless networks with their widespread deployment, now need to support applications that generate multimedia and real-time traffic. Video, audio, real-time voice over IP, and other multimedia applications require the network to provide guarantees on the Quality of Service (QoS) of the connection. The 802.11e Medium Access Control (MAC) protocol was proposed with the aim of providing QoS support at the MAC layer. The 802.11e performs well in wireless LANs due to the presence of Access Points (APs), but in ad hoc networks, especially multi-hop ones, it is still incapable of supporting multimedia traffic.One of the most important QoS parameters for multimedia and real-time traffic is delay. Our primary goal is to reduce the end-to-end delay, thereby improving the Packet Delivery Ratio of multimedia traffic, that is, the proportion of packets that reach the destination within the deadline, in 802.11e based multi-hop ad hoc wireless networks.Our contribution is threefold: first we propose dynamic ReAllocative Priority (ReAP) scheme, wherein the priorities of packets in the MAC queues are not fixed, but keep changing dynamically. We use the laxity and the hop length information to decide the priority of the packet. ReAP improves the PDR by over 28% in comparison with 802.11e, especially under heavy loads. Second, we introduce Adaptive-TXOP (A-TXOP), where transmission opportunity (TXOP) is the time interval during which a node has the right to initiate transmissions. This scheme reduces the delay of video traffic by reducing the number of channel accesses required to transmit large video frames. It involves modifying the TXOP interval dynamically based on the packets in the queue, so that fragments of the same packet are sent in the same TXOP interval. A-TXOP is implemented over ReAP to further improve the performance of video traffic. ReAP with A-TXOP helps in reducing the delay of video traffic by over 27% and further improves the quality of video in comparison with ReAP without A-TXOP. Finally, we have TXOP-sharing, which is aimed at reducing the delay of voice traffic. It involves using the TXOP to transmit to multiple receivers, in order to utilize the TXOP interval fully. It reduces the number of contentions to the channel and thereby reduces the delay of voice traffic by over 14%. A-TXOP is implemented over ReAP to further improve the performance of voice traffic. The three schemes (ReAP, A-TXOP, and TXOP-sharing) work together to improve the performance of multimedia traffic in 802.11e based multi-hop ad hoc wireless networks.     

Filtering and smoothing in an H∞ setting

The problems of filtering and smoothing are considered for linear systems in an H^∞ setting, i.e. the plant and measurement noises have bounded energies (are in L₂), but are otherwise arbitrary. Two distinct situations for the initial condition of the system are considered; the initial condition is assumed known in one case, while in the other the initial condition is not known but the initial condition, the plant, and measurement noise are in some weighted ball of RⁿXL₂. Finite-horizon and infinite-horizon cases are considered. Necessary and sufficient conditions are presented for the existence of estimators (both filters and smoothers) that achieve a prescribed performance bound, and algorithms that result in performance within the bounds are developed. In case of smoothers, the optimal smoother is also presented. The approach uses basic quadratic optimization theory in a time-domain setting, as a consequence of which both linear time-varying and time-invariant systems can be considered with equal ease. (In the smoothing problem, for linear time-varying systems, one considers only the finite-horizon case)     

A simple recursive scheme for adjusting the contention window size in IEEE 802.11e wireless ad hoc networks

The IEEE 802.11e standard has been introduced recently for providing Quality of Service (QoS) capabilities in the emerging wireless local area networks. This standard introduces a contention window based Enhanced Distributed Channel Access (EDCA) technique that provides a prioritized traffic to guarantee the minimum bandwidth needed for time critical applications. However, the EDCA technique resets the Contention Window (CW) of the mobile station statically after each successful transmission. This static behavior does not adapt to the network state since it reduces the network usage and results in bad performance and poor link utilization whenever the demand for link utilization increases. This paper proposes a new adaptive differentiation technique for IEEE 802.11e Wireless Local Area Networks that takes into account the network state before resetting the contention window. In the new technique, the congestion level of the network is sensed by using previous CW values. Three other enhancement techniques that focus on network adaptation are also discussed. Their main limitations are the high complexity of the implemented algorithms and their slow adaptation to the network state when the channel experiences bursty traffic. The proposed technique is compared to the original differentiation techniques of IEEE 802.11a and IEEE 802.11e standards, as well as to the enhancement schemes. Results show that the proposed adaptive technique outperforms IEEE 802.11e and is comparable to the other enhancement schemes while maintaining relatively low complexity requirements.