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I ONE OF THE LIFELONG TASKS that Thomas Aquinas was faced with was to unite the recently rediscovered Greek scholarly literature with the existing Christian wisdom. All knowledge, whether deriving [...]

It was shown J. Phys. Soc. Jpn. 62,1418 (1993)) that Weber's force law predicts an influence upon the apparent inertial mass of electrically charged particles in relative motion. The quantity of this influence, called Weber's mass, depends on the relative motion (both speed and acceleration) and the relative spatial distribution of the particles. A special case was analytically solved, in which the motion of a single point charge was considered, surrounded by a static and fixed spherical surface with a homogeneous charge distribution. The first experimental test of the prediction showed positive results (Annal. Fond. Louis de Broglie, 24,161 (1999)). Two reproductions were carried out, in which null results were reported together with an explanation for the previous positive result. It was suggested that a possible reason for the null result in the experimental setup could be that the charges could freely move on the surface. We set out to reproduce all previous experiments to get detailed insight into the problem, after which we designed a setup that would exclude the possibility of the moving charges on the surface. In all situations we could confirm the null results with a statistical precision of up to 0.009% Key words: Weber's mass, intertial mass, potential dependent mass, charged particles, relative motion, spatial charge distribution. Il a ete demontre que la force de Weber prevoit influencer la masse inertielle de particules chargees en mouvement relatif J. Phys. Soc. Jpn. 62,1418 (1993)). La valeur quantifiee de cet effet, la masse de Weber, depend du mouvement relatif (vitesse et acceleration) et de la distribution spatiale relative des particules. Nous solutionnons analytiquement un cas special, dans lequel on envisage le mouvement d'une seule particule chargee entouree d'une surface spherique statique et fixe portant une distribution homogene de charges. La premiere verification experimentale de la prediction etait positive (Annal. Fond. Louis de Broglie, 24,161(1999)). Deuxautres essais ontete faits par la suite, avecdes resultats negatifs, mais suggerantune explication pour le resultat positif. Il a en effet ete suggere que le resultat nul peut resulter d'une liberte de mouvement des charges sur la surface. Nous nous sommes donnes comme mission de revoir le tout et avons construit un montage qui exclut que les charges puissent se deplacer sur la surface. Dans toutes les situations, nous pouvons confirmer un resultat nul, avec une precision statistique jusqu'a 0.009%. [Traduit par la Redaction] Mots-cles: masse de Weber, masse inertielle, masse dependante du potentiel, mouvement relatif, distribution spatiale de charges., 1. Introduction Weber [1] proposed an alternative mathematical formulation of the physics of electrodynamics that would combine all the equations of classical electrodynamics and the Maxwell equations together with the [...]

This paper studies the thermoelastic dynamic response of a simply supported beam under movable temporally non-Gaussian laser pulse. The heat conduction equation of the problem was solved by using the method of separation of variables. The Green's function for the forth-order partial differential equation was derived and was used to solve the vibration equation of a heated beam. The temperature, deflection, and strain of the beam were derived analytically and their variations with time and space were illustrated. The influences of moving speed and duration time of the laser pulse on the dynamic responses were also analyzed. It was interesting to observe the propagation of strain wave along the beam axis during the irradiation period of the laser pulse. Key words: beam, movable laser pulse, strain wave, thermoelastic, Green's function. Nous etudions ici la reponse dynamique thermo-elastique d'une poutre cantilever (a support simple) sous l'effet d'une impulsion laser deplacable temporellement non gaussienne. Nous solutionnons par separation des variables l'equation de conduction de la chaleur du probleme. Nous derivons la fonction de Green pour l'equation differentielle du quatrieme ordre et l'utilisons pour solutionner l'equation de vibration du cantilever chauffe. La temperature, la deflexion et la deformation du cantilever sont determinees analytiquement et nous illustrons leurs variations spatiale et temporelle. Nous analysons egalement l'influence de la vitesse de deplacement et de la duree de l'impulsion sur les reponses dynamiques de la poutre cantilever. Il est interessant d'observer la propagation de l'onde de deformation le long de l'axe de la poutre pendant l'irradiation par l'impulsion laser. [Traduit par la Redaction] Mots-cles: poutre, impulsion laser deplacable, onde de deformation, thermoelastique, fonction de Green., 1. Introduction Moving heat source problems are frequently encountered in numerous manufacturing processes, such as surface laser treatment, cutting, and welding, as well as in many tribological applications [1]. In [...]

In the R-Minkowski space-time, which we recently defined from an appropriate deformed Poisson brackets that reproduce the Fock coordinate transformation, we derive an extended form for Maxwell's equations by using a generalized version of Feynman's approach. Also, we establish in this context the Lorentz force. As in deformed special relativity, modifying the angular momentum in such a way as to restore the R-Lorentz algebra generates the magnetic Dirac monopole. Key words: Fock's transformation, R-Minkowski space-time, Maxwell's equations, R-Lorentz algebra, Dirac's monopole. Dans l'espace R-Minkowski, que nous avons recemment defini a partir d'un crochet de Poisson deforme approprie, qui reproduit la transformation de coordonnees de Fock, nous derivons une forme etendue des equations de Maxwell en utilisant une version generalisee de l'approche de Feynman. Dans ce meme contexte, nous etablissons la force de Lorentz. Comme dans la relativite speciale deformee, la modification du moment angulaire de facon a restaurer l'algebre R-Lorentz genere le monopole magnetique de Dirac. [Traduit par la Redaction] Mots-cles: transformation de Fock, espace-temps R-Mikowski, equations de Maxwell, algebre de R-Lorentz, monopole magnetique de Dirac., 1. Introduction Fock's nonlinear relativity is characterized by the following coordinate transformation [1]: [mathematical expression not reproducible] (1) where [gamma] = [(1 - [u.sup.2]/[c.sup.2]).sup.-1/2], [[alpha].sub.R] = 1 + [([gamma] - [...]

Algebraic techniques are employed to extend time in the complex plane. We then use the framework to examine the fundamental postulates of special relativity. Generalizing the notion of time introduces the reader to a unique perspective on the universality of light speed according to Einstein. In the context of complex time we will describe the mathematical conditions in which light speed universality arises. Using high level terminology we then develop a categorization scheme applicable to physical theories that assume light speed is universal. Key words: special relativity, logic, set theory, and algebra, mathematical physics, theoretical physics, high level categorization. Nous employons des techniques algebriques pour etendre le temps dans le plan complexe. Nous utilisons ce cadre de travail pour examiner les postulats fondamentaux de la relativite speciale. Generaliser la notion de temps introduit le lecteur a une perspective unique sur l'universalite de la vitesse de la lumiere d'Einstein. Dans le contexte du temps complexe, nous decrivons les conditions mathematiques dans lesquelles apparait l'universalite de la vitesse de la lumiere. Utilisant une terminologie de haut niveau, nous developpons alors un schema de caracterisation applicable aux theories physiques qui prennent comme hypothese que la vitesse de la lumiere est universelle. [Traduit par la Redaction] Mots-cles : relativite speciale, logique, theorie des ensembles, physique mathematique, physique theorique, categorisation de haut niveau., 1. Introduction If interpretation of the founding postulates of a physical theory has influence on the interpretation of experimental results, it is important to illustrate founding principles in the clearest [...]

Imperfect knowledge of the times at which 'snapshots' of a system are recorded degrades our ability to recover dynamical information, and can scramble the sequence of events. In X-ray free-electron lasers, for example, the uncertainty--the so-called timing jitter--between the arrival of an optical trigger ('pump') pulse and a probing X-ray pulse can exceed the length of the X-ray pulse by up to two orders of magnitude (1), marring the otherwise precise time-resolution capabilities of this class of instruments. The widespread notion that little dynamical information is available on timescales shorter than the timing uncertainty has led to various hardware schemes to reduce timing uncertainty (2-4). These schemes are expensive, tend to be specific to one experimental approach and cannot be used when the record was created under ill-defined or uncontrolled conditions such as during geological events. Here we present a data-analytical approach, based on singular-value decomposition and nonlinear Laplacian spectral analysis (5-7), that can recover the history and dynamics of a system from a dense collection of noisy snapshots spanning a sufficiently large multiple of the timing uncertainty. The power of the algorithm is demonstrated by extracting the underlying dynamics on the few-femtosecond timescale from noisy experimental X-ray free-electron laser data recorded with 300-femtosecond timing uncertainty (1). Using a noisy dataset from a pump-probe experiment on the Coulomb explosion of nitrogen molecules, our analysis reveals vibrational wave-packets consisting of components with periods as short as 15 femtoseconds, as well as more rapid changes, which have yet to be fully explored. Our approach can potentially be applied whenever dynamical or historical information is tainted by timing uncertainty., The fundamental premise of our approach is simple. A series of snapshots concatenated in the order of their inaccurate time stamps will contain some time-evolutionary information ('a weak arrow of [...]

The advent of digital computers in the 1950s and their rapid growth in the 1960s and 1970s has resulted in the neglect of analogue computers and analogue methods. Most analogue [...]

We give a simple proof of the [lambda] = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d [greater than or equal to] 3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation. Gagliardo-Nirenberg-Sobolev | gradient flow doi/ 10.1073/pnas.1008323107

Problem statement: Modified Gauss-Seidel (MGS) was developed in order to improve the convergence rate of classical iterative method in solving linear system. In solving linear system iteratively, it takes longer time when many computational points involved. It is known that by applying quarter-sweep iteration scheme, it can decrease the computational operations without altering the accuracy. In this study, we investigated the effectiveness of the new Quarter-Sweep Projected Modified Gauss-Seidel (QSPMGS) iterative method in solving a Linear Complementarity Problem (LCP). Approach: The LCP we looked into is the LCP arise in American option pricing problem. Actually, American option is a Partial Differential Complementarity Problem (PDCP). By using full-, half- and quarter-sweep Crank-Nicolson finite difference schemes, the problem was reduced to Linear Complementarity Problem (LCP). Results: Several numerical experiments were carried out to test the effectiveness of QSPMGS method in terms of number of iterations, computational time and root mean square error (RMSE). Comparisons were made with full-, half- and quarter-sweep algorithm based on Projected Gauss-Seidel (PGS) and Projected Modified Gauss-Seidel (PMGS) methods. Thus, the experimental results showed that the QSPMGS iterative method has the least number of iterations and shortest computational time. The RMSE of all tested methods are in good agreement. Conclusion: QSPMGS is the most effective among the tested iterative methods in solving LCP whereby it is fastest and the accuracy remains the same. Key words: Projected modified gauss-seidel, quarter-sweep iteration, linear complementarity problem, Crank-Nicolson scheme, INTRODUCTION The Linear Complementarity Problem (LCP) is normally applied in the area of computational mechanics, financial engineering and other disciplines in engineering, science and economics. The widely applications of LCP [...]

Problem statement: This research purposely brought up to solve complicated equations such as partial differential equations, integral equations, Integro-Differential Equations (IDE), stochastic equations and others. Many physical phenomena contain mathematical formulations such integro-differential equations which are arise in fluid dynamics, biological models and chemical kinetics. In fact, several formulations and numerical solutions of the linear Fredholm integro-differential equation of second order currently have been proposed. This study presented the numerical solution of the linear Fredholm integro-differential equation of second order discretized by using finite difference and trapezoidal methods. Approach: The linear Fredholm integro-differential equation of second order will be discretized by using finite difference and trapezoidal methods in order to derive an approximation equation. Later this approximation equation will be used to generate a dense linear system and solved by using the Generalized Minimal Residual (GMRES) method. Results: Several numerical experiments were conducted to examine the efficiency of GMRES method for solving linear system generated from the discretization of linear Fredholm integro-differential equation. For the comparison purpose, there are three parameters such as number of iterations, computational time and absolute error will be considered. Based on observation of numerical results, it can be seen that the number of iterations and computational time of GMRES have declined much faster than Gauss-Seidel (GS) method. Conclusion: The efficiency of GMRES based on the proposed discretization is superior as compared to GS iterative method. Key words: Fredholm integro-differential, finite difference, quadrature, generalized minimal residual, INTRODUCTION Integro-Differential Equation (IDE) is an important branch of modern mathematics and arises frequently in many applied areas which include engineering, mechanics, physics, chemistry, astronomy, biology, economics, potential theory and [...]

Given a function f : E [right arrow] R with E [subset] [R.sup.n], we explain how to decide whether f extends to a [C.sup.m] function F on [R.sup.n]. If E is finite, then one can efficiently compute an F as above, whose [C.sup.m] norm has the least possible order of magnitude (joint work with B. Klartag).

The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once nonlinear effects are taken into account, solitary wave or soliton solutions can be created, which can be stable enough to persist indefinitely. The construction of such solutions can be relatively straightforward, but the fact that they are stable requires some significant amounts of analysis to establish, in part due to symmetries in the equation (such as translation invariance) which create degeneracy in the stability analysis. The theory is particularly difficult in the critical case in which the nonlinearity is at exactly the right power to potentially allow for a self-similar blowup. In this article we survey some of the highlights of this theory, from the more classical orbital stability analysis of Weinstein and Grillakis-Shatah-Strauss, to the more recent asymptotic stability and blowup analysis of Martel-Merle and Merle-Raphael, as well as current developments in using this theory to rigorously demonstrate controlled blowup for several key equations.

We propose a generalized T-matrix definition that facilitates the conversion between the S-parameter and T-parameter for multiport networks based on the well understood and mathematically simple two-port relations. This approach generalizes all multiport networks into two cases: balanced and unbalanced. Balanced networks have the same number of entrance and exit ports and are symmetric to the two-port network. Unbalanced networks generate a nonsquare T-matrix and do not have the same number of entrance and exit ports. Through careful selection of the T-matrix, this method extends two-port symmetry to multiport networks and provides an engineering implementable relationship between the S-parameter and T-parameter for multiport networks. This symmetry extension allows a practical means to cascade and deembed such networks. Index Terms--Deembedding, multiport networks, scattering parameter, transmission parameter.

This paper proposes a one-to-one mapping between the coefficients of continuous-time (s-domain) and discrete-time (z-domain) IIR transfer functions such that the s-domain numerator/denominator coefficients can be uniquely mapped to the z-domain numerator/denominator coefficients. The one-to-one mapping provides a firm basis for proving the inverses of the so-called generalized Pascal matrices from various first-order s-z transformations. We also derive recurrence formulas for recursively determining the inner elements of the generalized Pascal matrices from their boundary ones. Consequently, all the elements of the whole generalized Pascal matrix can be easily generated through utilizing their neighbourhood, which can be exploited for further simplifying the Pascal matrix generations. Finally, we reveal and prove some interesting properties of the generalized Pascal matrices. Index Terms--Generalized Pascal matrix, inverse Pascal matrix, continuous-time (CT) filter, discrete-time (DT) filter, first-order s-z transformation, one-to-one coefficient mapping.

In block matching, the matching criterion plays a pivotal role in both matching accuracy and computational complexity. Mean squared error (MSE) is one most widely accepted benchmark for matching accuracy. To avoid multiplication operations for simpler implementation, the sum of absolute difference (SAD) is normally taken as a substitute to approximate MSE. In this paper, we first examine statistically the quantitative deviation of SAD from MSE in terms of maximum and average deviations. To minimize the average deviation, a new measure, namely, weighted sum of absolute difference (WSAD), is proposed in a two-element case first, for which an optimal weight is obtained theoretically. The weight is approximately adapted to 1/2 so that the weighting operation can be simplified to a shift operation, and the resulting multiplication-free WSAD also shows better matching accuracy with a smaller deviation from MSE than SAD. The two-element WSAD is further extended to a multi-element case in a multilevel pyramid structure. The proposed WSAD is experimentally validated by applying it in block motion estimation for video coding, showing better rate-distortion performance than SAD. Index Terms--Block matching, matching criterion, mean square error (MSE), sum of absolute difference (SAD), video coding, weighted SAD (WSAD).

Meter to submeter resolution satellite images have generated new interests in extracting man-made structures in the urban area. However, classification accuracies for such purposes are far from satisfactory. Spectral characteristics of urban land cover classes are so similar that they cannot be separated using only spectral information. As a result, there is an increased interest in incorporating geometrical information. One possible approach is the use of morphological profiles (MPs). In this paper, we introduce two improvements on the use of MPs. Current approaches use disk-shaped structuring elements (SEs) to derive an ME This profile contains information about the minimum dimension of objects. In this paper, we extend this approach by using linear SEs. This results in a profile containing information about the maximum object dimension. We show that the addition of the line-based MP gives a substantial improvement of the classification result. A second improvement is achieved by using 'partial morphological reconstruction' instead of the normal morphological reconstruction. Morphological reconstruction is commonly used to better preserve the shape of objects. However, we show that this leads to 'over-reconstruction' in typical remote sensing images and a decreased classification performance. With 'partial reconstruction,' we are able to overcome this problem and still preserve the shape of objects. Index Terms--Classification, high-resolution imagery, mathematical morphology, urban areas.

Both nonlinear and fractal properties of beat-to-beat R-R interval variability signal (RRV) of freely moving lizards (Gallotia galloti) were studied in baseline and under autonomic nervous system blockade. Nonlinear techniques allowed us to study the complexity, chaotic behavior, nonlinearity, stationarity, and regularity over time of RRV. Scaling behavior of RRV was studied by means of fractal techniques. The autonomic nervous system blockers used were atropine, propranolol, prazosin, and yohimbine. The nature of RRV was linear in baseline and under [beta]-, [[alpha].sub.1]- and [[alpha].sub.2]-adrenoceptor blockades. Atropine changed the linear nature of RRV to nonlinear and increased its stationarity, regularity and fractality. Propranolol increased the complexity and chaotic behavior, and decreased the stationarity, regularity, and fractality of RRV. Both prazosin and yohimbine did not change any of the nonlinear and fractal properties of RRV. It is suggested that 1) the use of both nonlinear and fractal analysis is an appropriate approach for studying cardiac period variability in reptiles; 2) the cholinergic activity, which seems to make the [[alpha].sub.1]-, [[alpha].sub.2]- and [beta]-adrenergic activity interaction unnecessary, determines the linear behavior in basal RRV; 3) fractality, as well as both RRV regularity and stationarity over time, may result from the balance between cholinergic and [beta]-adrenergic activities opposing actions; 4) [beta]-adrenergic activity may buffer both the complexity and chaotic behavior of RRV, and 5) neither the [[alpha].sub.1]-nor the [[alpha].sub.2]-adrenergic activity seem to be involved in the mediation of either nonlinear or fractal components of RRV. autonomic nervous system; fractal analysis; nonlinear analysis; recurrence plot; telemetry

The joint velocity jump for redundant robots in the presence of locked-joint failures is discussed in this paper. First, the analytical formula of the optimal joint velocity with minimum jump is derived, and its specific expressions for both all joint failure and certain single joint failure are presented. Then, the jump difference between the minimum jump solution and the least-norm velocity solution is mathematically analyzed, and the influence factors on this difference are also discussed. Based on this formula, a new fault tolerant algorithm with the minimum jump is proposed. Finally, simulation examples are implemented with a planar 3R robot and a 4R spatial robot, and an experimental study is also done. Study results indicate that the new algorithm proposed in this paper is well suited for real time implementation, and can further reduce the joint velocity jump thereby improving the motion stability of redundant robots in fault tolerant operations. Also, the fewer the possible failed joints are, the more obvious the effect of this new algorithm becomes. [DOI: 10.1115/1.2943302]

This paper describes methods and issues related to interfacing electromagnetic transient simulation programs with general mathematical algorithms, which are either custom-developed by the user or are available through other mathematical analysis platforms. Various interfacing types and techniques are described along with potential areas of application. Implementation methods are detailed for each type of interface as well. This paper presents several interfacing examples from a wide variety of applications, including advanced switching schemes for power converters and controller implementation. Index Terms--Electromagnetic transient simulation, interfacing, mathematical algorithms.

A traditional distance protection relay uses a lumped parameter model of the transmission line. For a long 1000-kV UHV line with large distributed capacitance, such a simplified line model is inadequate and can cause malfunction of the relay due to large errors in the impedance measurement. This paper presents a new fine model for a distance relay and the procedure of reliable fault impedance measurement and relay setting. It describes the proposed application of the relay developed to a 645-km 1000-kV UHV transmission line including shunt reactor compensation, which is currently being constructed in China. Tests are carried out on an RTDS (real time dynamic system) to evaluate the relay performance, showing significant improvement compared to a more traditional distance relay. The new distance relay is shown to satisfy the requirement of 1000-kV UHV transmission line protection. Index Terms--Distance relay, protection, transmission line equations, 1000-kV UHV transmission line.

This paper presents a practical and effective novel approach to solve the coordination problem caused by the curve intersection of overcurrent relays in subtransmission systems. Based on the IEEE and IEC standard characteristic curve equations of digital overcurrent relays, as well as the simulation curve equation for electromagnetic overcurrent relays, lever setting adjustment equations for a selected point on the characteristic curve is derived. Then, centered on the derived equations, a dedicated software program is developed to compute the corresponding relay lever setting with different tap value in order that, passing through the selected point, another curve with the new lever setting is chosen. Finally, assisting with the graphical capability of the commercial ASPEN OneLiner, the proposed fixed-point coordination curve adjustment procedure can completely eliminate the coordination curve intersections. In addition, an actual case of a subtransmission network in Taiwan Power Company is simulated to validate the feasibility of the technique proposed. Index Terms--Overcurrent relay, protection coordination, subtransmission system, sympathy trip.

A calculation method for the electric field over the ground surface under double-circuit HVDC transmission lines is proposed to satisfy the engineering design requirement. A comparison of the calculation results with the experimental measurement results finds that the maximal values and lateral distributions of the electric field over the ground surface under this type of line are obviously affected by different pole arrangement schemes and unequal corona onset electric fields of the positive and negative poles, and the maximal values and lateral distributions of the electric field over the ground surface under this type of line with diversified pole arrangement schemes can be predicted by using this method. Index Terms--Calculation, corona, double-circuit HVDC transmission lines on the same tower, electric field, lateral distribution, maximal values, measurement, pole arrangement schemes.

This paper shows that exact maximum singular value of a complex interval matrix can be found from a set of selected matrices. The results include both square interval matrix and generalized non-square interval matrix. Three illustrative examples are presented to verify the validity and utility of the proposed method. Index Terms--Complex interval matrix, maximum singular value.

Characterization and control of stability of switched dynamical systems and differential inclusions have attracted significant attention in the recent past. The most of the current results for this problem are obtained by application of the Lyapunov function method which provides sufficient but frequently over conservative stability conditions. For planar systems, practically verifiable necessary and sufficient conditions are found only for switched systems with two subsystems. This paper provides explicit necessary and sufficient conditions for asymptotic stability of switched systems and differential inclusions with arbitrary number of subsystems; these conditions turned out to be identical for the both classes of systems. A precise upper bound for the number of switching points in a periodic solution, corresponding to the break of stability, is found. It is shown that, for a switched system, the break of stability may also occur on a solution with infinitely fast switching (chattering) between some two subsystems. Index Terms--Asymptotic stability, differential inclusion, necessary and sufficient conditions, switched plane system.

For general finite-dimensional time-varying nonlinear systems, we derive sufficient conditions for closed-loop asymptotic controllability and asymptotic stabilization by means of a smooth ordinary time-varying feedback integrator. The main hypotheses are based on the existence of an almost smooth time-varying control Lyapunov function. The corresponding results generalize earlier works in the literature concerning dynamic stabilization for autonomous systems. Index Terms--Control Lyapunov functions, dynamic closed-loop asymptotic controllability, stabilization.

We give a necessary and sufficient condition on a radially symmetric potential V on a bounded domain [OMEGA] of [R.sup.n] that makes it an admissible candidate for an improved Hardy inequality of the following type. For every u [member of] [H.sup.1.sub.0]([OMEGA]) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] A characterization of the best possible constant c(V) is also given. This result yields easily the improved Hardy's inequalities of Brezis-Vazquez [Brezis H, Vazquez JL (1997) Blow up solutions of some nonlinear elliptic problems. Revista Mat Univ Complutense Madrid 10:443-469], Adimurthi et al. [Adimurthi, Chaudhuri N, Ramaswamy N (2002) An improved Hardy Sobolev inequality and its applications. Proc Am Math Soc 130:489-505], and Filippas-Tertikas [Filippas S, Tertikas A (2002) Optimizing improved Hardy inequalities. J Funct Anal 192:186-233] as well as the corresponding best constants. Our approach clarifies the issue behind the lack of an optimal improvement while yielding the following sharpening of known integrability criteria: If a positive radial function V satisfies lim [inf.sub.r[right arrow]0] ln(r) [[integral].sup.r.sub.0] sV(s)ds > -[infinity], then there exists [rho] := [rho]([OMEGA]) > 0 such that the above inequality holds for the scaled potential [V.sub.[rho]](x) = V([absolute value of x]/[rho]). On the other hand, if [lim.sub.r[right arrow]0] ln(r) [[integral].sub.0.sup.r] sV(s)ds = -[infinity], then there is no [rho] > 0 for which the inequality holds for [V.sub.[rho]. improved Hardy inequality | oscillatory behavior of ordinary differential equations

Two types of uncertainty exist in engineering. Aleatory uncertainty comes from inherent variations while epistemic uncertainty derives from ignorance or incomplete information. The former is usually modeled by the probability theory and has been widely researched. The latter can be modeled by the probability theory or nonprobability theories and is much more difficult to deal with. In this work, the effects of both types of uncertainty are quantified with belief and plausibility measures (lower and upper probabilities) in the context of the evidence theory. Input parameters with aleatory uncertainty are modeled with probability distributions by the probability theory. Input parameters with epistemic uncertainty are modeled with basic probability assignments by the evidence theory. A computational method is developed to compute belief and plausibility measures for blackbox performance functions. The proposed method involves the nested probabilistic analysis and interval analysis. To handle black-box functions, we employ the first order reliability method for probabilistic analysis and nonlinear optimization for interval analysis. Two example problems are presented to demonstrate the proposed, method. [DOI: 10.1115/1.2943295]

Given a data set P, a [kappa]-means query returns [kappa] points in space (called centers), such that the average squared distance between each point in P and its nearest center is minimized. Since this problem is NP-hard, several approximate algorithms have been proposed and used in practice. In this paper, we study continuous [kappa]-means computation at a server that monitors a set of moving objects. Reevaluating [kappa]-memos every time there is an object update imposes a heavy burden on the server (for computing the centers from scratch) and the clients (for continuously sending location updates). We overcome these problems with a novel approach that significantly reduces the computation and communication costs, white guaranteeing that the quality of the solution, with respect to the reevaluation approach, is bounded by a user-defined tolerance. The proposed method assigns each moving object a threshold (i.e., range) such that the object sends a location update only when it crosses the range boundary. First, we develop an efficient technique for maintaining the k-means. Then, we present mathematical formulas and algorithms for deriving the individual thresholds. Finally, we justify our performance claims with extensive experiments. Index Terms--[kappa]-Means, continuous monitoring, query processing.

Byline: Jose I. Suarez (Industrial Engineering School, University of Extremadura, Avda. de Elvas, s/n. 06071 Badajoz, Spain, jmarcelo@unex.es); Blas M. Vinagre (Industrial Engineering School, University of Extremadura, Avda. de Elvas, [...]

This paper presents a mathematical framework to properly account for uncertainty in wind resource assessment and wind energy production estimation. A meteorological tower based wind measurement campaign is considered exclusively, in which measurecorrelate-predict is used to estimate the long-term wind resource. The evaluation of a wind resource and the subsequent estimation of the annual energy production (AEP) is a highly uncertain process. Uncertainty arises at all points in the process, from measuring the wind speed to the uncertainty in a power curve. A proper assessment of uncertainty is critical for judging the feasibility and risk of a potential wind energy development. The approach in this paper provides a framework for an accurate and objective accounting of uncertainty and, therefore, better decision making when assessing a potential wind energy site. It does not investigate the values of individual uncertainty sources. Three major aspects of site assessment uncertainty are presented here. First, a method is presented for combining uncertainty that arises in assessing the wind resource. Second, methods for handling uncertainty sources in wind turbine power output and energy losses are presented. Third, a new method for estimating the overall AEP uncertainty when using a Weibull distribution is presented. While it is commonly assumed that the uncertainty in the wind resource should be scaled by a factor between 2 and 3 to yield the uncertainty in the AEP, this work demonstrates that this assumption is an oversimplification and also presents a closed form solution for the sensitivity factors of the Weibull parameters. [DOI: 10.1115/1.2931499]

We present analytical formulations, based on a coulombian approach, of the magnetic field created by permanent-magnet rings. For axially magnetized magnets, we establish the expressions for the three components. We also give the analytical 3-D formulation of the created magnetic field for radially magnetized rings. We compare the results determined by a 2-D analytical approximation to those for the 3-D analytical formulation, in order to determine the range of validity of the 2-D approximation. Index Terms--Analytical calculation, axiai magnetization, magnetic fie|d, permanent-magnet rings, radial magnetization.

Layout of temporary construction facilities (objects) is an important activity during the planning process of construction projects. The construction area layout is a complex problem whose solution requires the use of analytical models. Existing popular models employ genetic algorithms that have proven to be useful tools in generating near optimal site layouts. This paper presents an alternative approach based on mathematical optimization that offers several important features and generates a global optimal solution. The construction area consists of an unavailable area that includes existing facilities (sites) and available area in which the objects can be located. The available area is divided into regions that are formulated using binary variables. The locations of the objects are determined by optimizing an objective function subject to a variety of physical and functional constraints. The objective function minimizes the total weighted distance between the objects and the sites as well as among the objects (if desired). The distance can be expressed as Euclidean or Manhattan distance. Constraints that ensure objects do not overlap are developed. The new approach, which considers a continuous space in locating the objects simultaneously, offers such capabilities as accommodating object adjacency constraints, facility proximity constraints, object--region constraints, flexible orientation of objects, visibility constraints, and nonrectangular objects, regions, and construction areas. Application of the model is illustrated using two examples involving single and multiple objects. The proposed model is efficient and easy to apply, and as such should be of interest to construction engineers and practitioners. DOI: 10.1061/(ASCE)0733-9364(2008)134:8(653) CE Database subject headings: Construction sites; Construction management; Optimization models.

This paper addresses the optimal control problem of timed continuous Petri nets under infinite servers semantics. In particular, our goal is to find a control input optimizing a certain cost function that permits the evolution from an initial marking (state) to a desired steady-state. The solution we propose is based on a particular discrete-time representation of the controlled continuous Petri net system, as a certain linear constrained system. An upper bound on the sample period is given in order to preserve important information of the timed continuous net, in particular the positiveness of the markings. The reachability space of the sampled system in relation to autonomous continuous Petri nets is also studied. Based on the resulting linear constrained model, the optimal control problem is studied through model predictive control (MPC). Implicit and explicit procedures are presented together with a comparison between the two schemes. Stability of the closed-loop system is also studied. Index Terms--Continuous-time systems, discrete-time systems, model predictive control, Petri-nets.

We stabilize the unstable "shock-like" equilibrium profiles of the viscous Burgers equation using control at the boundaries. These equilibria are not stabilizable (even locally) using the standard "radiation feedback boundary conditions." Using a nonlinear spatially-scaled transformation (that employs three ingredients, of which one is the Hopf--Cole non-linear integral transformation) and linear backstepping, we design an explicit nonlinear full-state control law that achieves exponential stability, with a region of attraction for which we give an estimate. The region of attraction is not the entire state space since the Burgers PDE is known not to be globally controllable. Index Terms--Burgers PDE.

In this correspondence, we show that a function in the Bernstein class [B.sup.p.sub.[pi]] (1 [less than or equal to] p [less than or equal to] [infinity]) can be reconstructed in the Lagrange interpolation form with sampling points {[t.sub.n]} satisfying [absolute value of [t.sub.n] - n] [less than or equal to] d and [4d] additional points, where d is any nonnegative real number that is not necessarily less than 1/4. Here, [x] denotes the integer part of x. Index Terms--Bandlimited function, Kadec's constant 1/4, Lagrange interpolation, nonuniform sampling series expansion, uniform convergence.

The hash function design strategy SMASH was recently proposed as an alternative to the MD4 family of hash functions. It can be shown that the strategy leads to designs that are vulnerable to efficient collision and (second) preimage attacks. The mathematical structure of the SMASH description facilitates the description of the weakness and the resulting attacks, but also functions with less mathematical elegance may show similar weaknesses. Index Terms--Collisions, cryptanalysis, cryptography, hash functions, (second) preimages.

Reliable estimates of reference evapotranspiration ([ET.sub.0]) are key elements for efficient water resource management, and estimating [ET.sub.0], based on 'Class 'A' pan evaporation' data is common in arid climates. A pan coefficient ([K.sub.p]), which depends on the distance (or fetch) of green vegetation or fallow soil around the pan (F), wind run (U), and relative humidity (RH), is used to convert from pan evaporation to [ET.sub.0]. Several researchers have developed models for estimating [K.sub.p] values for pans surrounded by green vegetated fetch, but there is only one equation to estimate [K.sub.p], values for dry fetch conditions. The equation is complex, so the objective of this research was to develop a new simple equation to estimate [K.sub.p] under fallow soil fetch conditions. The new [K.sub.p] equation and the more complex equation were compared with tabular values published by the United Nations Food and Agriculture Organization. The new equation performed slightly better at matching the tabular [K.sub.p] values than the complex equation. The equation derivation and evaluation are presented. DOI: 10.1061/(ASCE)0733-9437(2008)134:4(425) CE Database subject headings: Coefficients; Evaporation; Evapotranspiration; Water resources; Water management.

A series of detailed laboratory measurements were made under steady-state flow conditions through a 0.914-m (3-ft) Cutthroat flume in an attempt to more accurately define transition submergence for four standard throat widths. It was found that the change from free to submerged flow, and vice versa, is gradual and that there is no easily observable transition point. The gradual transition between the flow regimes suggested a new calibration approach in which a single equation could more elegantly and more accurately fit the laboratory measurements, eschewing the need for separate tree- and submerged-flow equations, and obviating the need to define transition submergence. Such an equation was found, providing greater calibration accuracy up to 95% submergence in 0.914-In Cutthroat flumes. DOI: 10.1061/(ASCE)0733-9437(2008)134:4(521) CE Database subject headings: Flumes; Calibration; Measurement; Submerged flow; Steady flow.

Although the Darcy-Weisbach equation combined with the Colebrook-White semitheoretical formula for calculating the friction coefficient is a highly accurate generalized pipe-water flow resistance equation, most users prefer the use of simple, explicit power law form formulas. Because of their simplicity (despite their limitations) the purely empirical power formulas of Hazen-Williams and Manning remain the most popular pipe flow resistance equations used in routine hydraulic engineering applications. In this paper, a new simple power law form formula is derived to approximate the generalized Darcy-Weisbach combined with the Colebrook-White equation. The two main pipe flow parameters, such as the discharge (or velocity) and the diameter, appeared explicitly in the proposed formula. The suggested power-form formula compared with the Darcy-Weisbach and Coolbrook-White equation yields a maximum relative error of about [+ or -] 4.5%. The power-form suggested formula is dimensionally homogeneous and its accuracy is sufficient for practical engineering applications. A correction factor is introduced for the variation of kinematic viscosity with temperature. The usefulness of the formula is demonstrated in an application concerning the optimal design of a delivery pipeline with pumping. The power form of the friction formula facilitates the formulation of the problem leading to the derivation of a simple equation from which the economic diameter is explicitly calculated. DOI: 10.1061/(ASCE)0733-9437(2008)134:4(454) CE Database subject headings: Friction: Turbulent flow; Hydraulic roughness; Pipe networks; Pipe flow.

This paper considers the effect of time-dependent lower boundary wave forcing on the internal variability found to appear spontaneously in a stratosphere-only model when the forcing is perfectly steady. While the time-dependent forcing is found to modulate the internal variability, leading in some cases to frequency locking of the upper-stratospheric response to the forcing, the temporal and spatial structure of the variability remains similar to the case when the forcing is time independent. Experiments with a time-periodic modulation of the forcing amplitude indicate that the wave flux through the lower boundary is only partially related to the instantaneous forcing, but is more significantly influenced by the condition of the polar vortex itself. In cases of purely random wave forcing with zero time mean, the stratospheric response is similar to that obtained with steady forcing of magnitude equal to the root-mean-square of the time-varying forcing.

The stochastic kinetic equation is solved analytically for precipitating particles that can be identified as rain, snow, and graupel. The general solution for the size spectra of the large-size particles is represented by the product of an exponential term and a term that is an algebraic function of radius. The slope of the exponent consists of the Marshall-Palmer slope and an additional integral that is a function of the radius. Both the integral and algebraic terms depend on the condensation and accretion rates, vertical velocity, turbulence coefficient, terminal velocity of the particles, and the vertical gradient of the liquid (ice) water content. At sufficiently large radii, the radius dependence of the algebraic term is a power law, and the spectra have the form of gamma distributions. Simple analytical expressions are derived for the slopes and indices of the size distributions. These solutions provide explanations of the observed dependencies of the cloud particle spectra in different phases and size regimes on temperature, height, turbulence, vertical velocities, liquid or ice water content, and other cloud properties. These analytical solutions and expressions for the slopes and shape parameters can be used for parameterization of the spectra of precipitating particles and related quantities (e.g., optical properties, radar reflectivities) in bulk cloud microphysical parameterizations and in remote sensing techniques.

A rigorous mathematical analysis is given of spherical stacked-patch arrays with emphasis on the physical interpretation of mutual coupling mechanisms present in doubly- curved convex structures. The analysis method is based on electromagnetic field representation in terms of spherical harmonics where each harmonic has the same angular variation as the spectral source component. To obtain the spectral representation the vector-Legendre transformation is applied to currents and fields. A novel approach to the mutual coupling calculation within the method of moments analysis of spherical arrays is applied. By expressing the patch current in terms of two suitable potential-like auxiliary functions, it is possible to avoid the use of Euler's formulas for coordinate system rotation and the related lengthy integrations. Instead, the rotation of antenna elements and corresponding current distributions can be done in closed form with the help of Vilenkin's addition theorem for associated Legendre functions. It is shown that the new approach results in significant acceleration and improved accuracy of the analysis of spherical patch antenna arrays. The algorithm is successfully tested against a commercially available electromagnetic software and measurements performed on the developed laboratory model, confirming its accuracy for both input impedance and mutual coupling calculation and with only a small difference between the predicted and measured resonant frequencies, due to limitations in the experimental model. The influence of the structure parameters on mutual coupling level is extensively investigated, including all coupling mechanisms and leakage of energy due to curvature of the structure. It is shown that stacked-patch antennas can have reduced coupling level comparing to single patch antennas with possible deep nulls above the antenna resonant frequency. Index Terms--Conformal antennas, method of moments (MoM), microstrip arrays, mutual coupling, spherical antennas.

We derive an optimum power and rate adaptation for maximizing the spectral efficiency based on an imperfect channel estimate and subject to average power and instantaneous bit error rate (BER) constraints for multilevel quadrature amplitude modulation (MQAM) over Rayleigh flat-fading channels. The optimal solution is derived for continuous- and discrete-rate adaptation and is expressed in terms of a specific bounded function that is the solution of a nonlinear equation and cannot be expressed in a closed mathematical form. The optimum power adaptation for the continuous rate is shown to be a generalization of water pouring for that function. It is also shown that the conventional water-pouring (with bias) strategy for power adaptation in the continuous-rate condition is a suboptimum solution of the general optimization problem, and it tends to the optimal solution as the correlation coefficient between the true channel gain and its estimate tends to one. We also show that less than 1dB power is lost by using discrete-rate MQAM with only six different signal constellations compared to the continuous-rate adaptation with an unconstrained constellation size. Index Terms--Channel estimation, flat fading, power and rate adaptation, spectral efficiency.

The object-based analysis of remotely sensed imagery provides valuable spatial and structural information that is complementary to pixel-based spectral information in classification. In this paper, we present novel methods for automatic object detection in high-resolution images by combining spectral information with structural information exploited by using image segmentation. The proposed segmentation algorithm uses morphological operations applied to individual spectral bands using structuring elements in increasing sizes. These operations produce a set of connected components forming a hierarchy of segments for each band. A generic algorithm is designed to select meaningful segments that maximize a measure consisting of spectral homogeneity and neighborhood connectivity. Given the observation that different structures appear more clearly at different scales in different spectral bands, we describe a new algorithm for unsupervised grouping of candidate segments belonging to multiple hierarchical segmentations to find coherent sets of segments that correspond to actual objects. The segments are modeled by using their spectral and textural content, and the grouping problem is solved by using the probabilistic latent semantic analysis algorithm that builds object models by learning the object-conditional probability distributions. The automatic labeling of a segment is done by computing the similarity of its feature distribution to the distribution of the learned object models using the Kullback--Leibler divergence. The performances of the unsupervised segmentation and object detection algorithms are evaluated qualitatively and quantitatively using three different data sets with comparative experiments, and the results show that the proposed methods are able to automatically detect, group, and label segments belonging to the same object classes. Index Terms--Hierarchical segmentation, image segmentation, mathematical morphology, object-based analysis, unsupervised object detection.