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Additional Assumptions (additional + assumption)
Selected AbstractsMethods to Determine Storativity of Infinite Confined Aquifers from a Recovery TestGROUND WATER, Issue 4 2002Djaouida Chenaf Starting from the equations of Theis and Cooper-Jacob, two new mathematical methods are proposed for interpreting the residual drawdown data for an infinite confined aquifer. Under Theis' assumptions and using the Cooper-Jacob approximation, the principal aquifer characteristics of transmissivity, pumping storativity, and recovery storativity are expressed without any correction or additional assumption. An actual case is used for illustration and confirms the validity of proposed equations and methods. [source] Stability and linearization: discrete-time systemsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2002Irwin W. Sandberg Abstract A theorem by Hadamard gives a two-part condition under which a map from one Banach space to another is a homeomorphism. The theorem, while often very useful, is incomplete in the sense that it does not explicitly specify the family of maps for which the condition is met. Recently, under a typically weak additional assumption on the map, it was shown that Hadamard's condition is met if and only if the map is a homeomorphism with a Lipschitz continuous inverse. Here an application is given concerning the relation between the stability of a discrete-time non-linear system and the stability of related linear systems. Copyright © 2002 John Wiley & Sons, Ltd. [source] Design of the ATM-based interconnecting network of the access segment of future cellular systemsINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 2 2001P. P. Demestichas Abstract An important issue in future cellular communication systems is the design of the interconnecting network of their access segment. This problem aims at finding the minimum-cost configuration of cell site switches (CSSs) and local exchanges (LEs) given the base transceiver station (BTS) layout. An extended version of the problem may also comprise the deployment of mobility and service control points-access (MSCPs-A), based on the assumption that CSSs and LEs are not fully capable of handling the logic of the cellular system. In this paper we solve the extended problem, under the additional assumption that the communication among the network elements is based on the ATM technique. The problem is formally defined, optimally formulated, and solved by computationally efficient heuristics. Finally, results are provided and subsequent conclusions are drawn. Copyright © 2001 John Wiley & Sons, Ltd. [source] A Kharitonov-like theorem for robust stability independent of delay of interval quasipolynomialsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2010Onur Toker Abstract In this paper, a Kharitonov-like theorem is proved for testing robust stability independent of delay of interval quasipolynomials, p(s)+,eqk(s), where p and qk's are interval polynomials with uncertain coefficients. It is shown that the robust stability test of the quasipolynomial basically reduces to the stability test of a set of Kharitonov-like vertex quasipolynomials, where stability is interpreted as stability independent of delay. As discovered in (IEEE Trans. Autom. Control 2008; 53:1219,1234), the well-known vertex-type robust stability result reported in (IMA J. Math. Contr. Info. 1988; 5:117,123) (See also (IEEE Trans. Circ. Syst. 1990; 37(7):969,972; Proc. 34th IEEE Conf. Decision Contr., New Orleans, LA, December 1995; 392,394) does contain a flaw. An alternative approach is proposed in (IEEE Trans. Autom. Control 2008; 53:1219,1234), and both frequency sweeping and vertex type robust stability tests are developed for quasipolynomials with polytopic coefficient uncertainties. Under a specific assumption, it is shown in (IEEE Trans. Autom. Control 2008; 53:1219,1234) that robust stability independent of delay of an interval quasipolynomial can be reduced to stability independent of delay of a set of Kharitonov-like vertex quasipolynomials. In this paper, we show that the assumption made in (IEEE Trans. Autom. Control 2008; 53:1219,1234) is redundant, and the Kharitonov-like result reported in (IEEE Trans. Autom. Control 2008; 53:1219,1234) is true without any additional assumption, and can be applied to all quasipolynomials. The key idea used in (IEEE Trans. Autom. Control 2008; 53:1219,1234) was the equivalence of Hurwitz stability and , -o -stability for interval polynomials with constant term never equal to zero. This simple observation implies that the well-known Kharitonov theorem for Hurwitz stability can be applied for , -o -stability, provided that the constant term of the interval polynomial never vanishes. However, this line of approach is based on a specific assumption, which we call the CNF-assumption. In this paper, we follow a different approach: First, robust , -o -stability problem is studied in a more general framework, including the cases where degree drop is allowed, and the constant term as well as other higher-orders terms can vanish. Then, generalized Kharitonov-like theorems are proved for , -o -stability, and inspired by the techniques used in (IEEE Trans. Autom. Control 2008; 53:1219,1234), it is shown that robust stability independent of delay of an interval quasipolynomial can be reduced to stability independent of delay of a set of Kharitonov-like vertex quasipolynomials, even if the assumption adopted in (IEEE Trans. Autom. Control 2008; 53:1219,1234) is not satisfied. Copyright © 2009 John Wiley & Sons, Ltd. [source] On the properties of the periodogram of a stationary long-memory process over different epochs with applicationsJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2010Valdério A. Reisen Primary 60G10; 60K35; Secondary 60G18 This article studies the asymptotic properties of the discrete Fourier transforms (DFT) and the periodogram of a stationary long-memory time series over different epochs. The main theoretical result is a novel bound for the covariance of the DFT ordinates evaluated on two distinct epochs, which depends explicitly on the Fourier frequencies and the gap between the epochs. This result is then applied to obtain the limiting distribution of some nonlinear functions of the periodogram over different epochs, under the additional assumption of gaussianity. We then apply this result to construct an estimator of the memory parameter based on the regression in a neighbourhood of the zero-frequency of the logarithm of the averaged periodogram, obtained by computing the empirical mean of the periodogram over adjacent epochs. It is shown that replacing the periodogram by its average has an effect similar to the frequency domain pooling to reduce the variance of the estimate. We also propose a simple procedure to test the stationarity of the memory coefficient. A limited Monte Carlo experiment is presented to support our findings. [source] Boundedness and exponential stabilization in a signal transduction model with diffusionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2008Michael Winkler Abstract The influence of diffusion in a model arising in the description of signal transduction pathways in living cells is investigated. It is proved that all solutions of the corresponding semilinear parabolic system, consisting of four equations, are global in time and bounded. Under the additional assumption that certain two of the diffusion coefficients are equal, it is furthermore demonstrated that all solutions approach a spatially homogeneous steady state as t,,,,. This equilibrium is uniquely determined by the initial data, and the rate of convergence is shown to be at least exponential. Copyright © 2008 John Wiley & Sons, Ltd. [source] Residuated lattices arising from equivalence relations on Boolean and Brouwerian algebrasMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 4 2008Thomas Vetterlein Abstract Logics designed to deal with vague statements typically allow algebraic semantics such that propositions are interpreted by elements of residuated lattices. The structure of these algebras is in general still unknown, and in the cases that a detailed description is available, to understand its significance for logics can be difficult. So the question seems interesting under which circumstances residuated lattices arise from simpler algebras in some natural way. A possible construction is described in this paper. Namely, we consider pairs consisting of a Brouwerian algebra (i. e. a dual Heyting algebra) and an equivalence relation. The latter is assumed to be in a certain sense compatible with the partial order, with the formation of differences, and with the formation of suprema of pseudoorthogonal elements; we then call it an s-equivalence relation. We consider operations which, under a suitable additional assumption, naturally arise on the quotient set. The result is that the quotient set bears the structure of a residuated lattice. Further postulates lead to dual BL-algebras. In the case that we begin with Boolean algebras instead, we arrive at dual MV-algebras. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] The star formation law in a multifractal ISMMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2007Konstantinos Tassis ABSTRACT The surface density of the star formation rate in different galaxies, as well as in different parts of a single galaxy, scales non-linearly with the surface density of the total gas. This observationally established relation is known as the Kennicutt,Schmidt star formation law. The slope of the star formation law has been shown to change with the density of the gas against which the star formation rate is plotted. This dependence implies a non-linear scaling between the dense gas and the total gas surface densities within galaxies. Here, we explore a possible interpretation of this scaling as a property of the geometry of the interstellar medium (ISM), and we find that it arises naturally if the topology of the ISM is multifractal. Under the additional assumption that, at very high densities, the star formation time-scale is roughly constant, the star formation law itself can also be recovered as a consequence of the multifractal geometry of the ISM. The slope of the scaling depends on the width of the global probability density function (PDF), and is between 1.5 and 1.6 for wide PDFs relevant to high-mass systems, while it is higher for narrower PDFs appropriate for lower mass dwarf galaxies, in agreement with observations. [source] Octahedral tilting in cation-ordered Jahn,Teller distorted perovskites , a group-theoretical analysisACTA CRYSTALLOGRAPHICA SECTION B, Issue 1 2010Christopher J. Howard Computer-based group-theoretical methods are used to enumerate structures arising in A2BB,X6 perovskites, with either rock-salt or checkerboard ordering of the B and B, cations, under the additional assumption that one of these two cations is Jahn,Teller active and thereby induces a distortion of the BX6 (or B,X6) octahedron. The requirement to match the pattern of Jahn,Teller distortions to the cation ordering implies that the corresponding irreducible representations should be associated with the same point in the Brillouin zone. Effects of BX6 (and B,X6) octahedral tilting are included in the usual way. Finally, an analysis is presented of more complex models of ordering and distortion as might lead to the doubling of the long axis of the common Pnma perovskite, observed in systems such as Pr1,,,xCaxMnO3 (x, 0.5). The structural hierarchies derived in this work should prove useful in interpreting experimental results. [source] Atomvolumen, Packungsdichte der Atome und chemische Bindung in nichtmetallischen ElementenACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2007M. Trömel The atomic volume of crystalline elements is largely determined by the packing density of atoms in the respective modification. The determination of packing density is improved by assuming that the atomic distances depend on bond valences according to Pauling's equation. With the additional assumption of equal valence in different modifications, the experimental atomic volume of an element in any given structure is reduced to its volume in close-packed structures, e.g. f.c.c. The ratio of this reduced atomic volume and the experimental atomic volume is a measure of packing density. Reduced atomic volumes of C, Si, Ge, P, As, S and Se, as calculated from different modifications, correspond in most cases to within less than ±1% for each element, even if calculated from extremely different structures like diamond and buckminsterfullerene in the case of carbon, or from numerous modifications of sulfur with annular molecules of different sizes. Exceptions (graphite, white phosphorus, tin and selenium) indicate deviating valences. [source] An Overview of the Anatomy of Crystal Plasticity ModelsADVANCED ENGINEERING MATERIALS, Issue 9 2009Georges Cailletaud Abstract Single crystals, polycrystals, and DS alloys can be modeled in the same framework by means of crystal plasticity. This paper wants to show the common features of the different approaches on the grain level, and the additional assumptions that are needed to derive polycrystal or DS models. Phenomenological rules are introduced for representing the hardening in the single crystal constitutive equations. Series of examples are given to illustrate the capabilities of the various approaches that are mainly related to the crystallographic character, and to the fact that the macroscopic yield locus is not predefined, but built from a collection of linear yield conditions. [source] A comparison of no-take zones and traditional fishery management tools for managing site-attached species with a mixed larval poolFISH AND FISHERIES, Issue 3 2007William J F Le Quesne Abstract No-take zones (NTZs) can generate higher larval production by sessile, sedentary and site-attached species per unit area than in exploited areas, and may increase recruitment and yield compared to status quo management. Whilst NTZs may be considered an essential part of optimal management, few studies have specifically compared the effects of NTZs with those of correctly applied gear and effort controls. A yield-per-recruit (YPR) population model, based on the sedentary abalone Haliotis laevigata, was used to compare the effects of management by minimum landing size (MLS), effort limitation and NTZs, either singularly or in combination. Initially, a minimum basic YPR model was used. Three additional assumptions were sequentially added to the model to see if they affected conclusions drawn from the model. The additional assumptions were the inclusion of: (i) a length,fecundity relationship; (ii) an age-dependent natural mortality function; and (iii) mortality of undersized individuals due to fishery operations. In the absence of undersized mortality caused by fishing, under virtually all conditions the population is best managed with a combination of MLS and effort control, without any NTZs. For simulations that included mortality of undersized individuals in the fished area, under nearly all circumstances NTZs were considered an essential part of optimal fishery management, and management incorporating NTZs greatly increased the sustainable yield that could be taken. [source] Self-similar solution of a plane-strain fracture driven by a power-law fluidINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2002J. I. Adachi Abstract This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power-law rheology and behaviour index n,0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self-similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self-similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd. [source] A reduced integration solid-shell finite element based on the EAS and the ANS concept,Geometrically linear problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2009Marco Schwarze Abstract In this paper a new reduced integration eight-node solid-shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu,Washizu variational principle requires only one EAS degree-of-freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight-node solid-shell elements in the literature. Owing to the three-dimensional modeling of the structure, fully three-dimensional material models can be implemented without additional assumptions. Copyright © 2009 John Wiley & Sons, Ltd. [source] From mixed finite elements to finite volumes for elliptic PDEs in two and three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Anis Younes Abstract The link between Mixed Finite Element (MFE) and Finite Volume (FV) methods applied to elliptic partial differential equations has been investigated by many authors. Recently, a FV formulation of the mixed approach has been developed. This approach was restricted to 2D problems with a scalar for the parameter used to calculate fluxes from the state variable gradient. This new approach is extended to 2D problems with a full parameter tensor and to 3D problems. The objective of this new formulation is to reduce the total number of unknowns while keeping the same accuracy. This is achieved by defining one new variable per element. For the 2D case with full parameter tensor, this new formulation exists for any kind of triangulation. It allows the reduction of the number of unknowns to the number of elements instead of the number of edges. No additional assumptions are required concerning the averaging of the parameter in hetero- geneous domains. For 3D problems, we demonstrate that the new formulation cannot exist for a general 3D tetrahedral discretization, unlike in the 2D problem. However, it does exist when the tetrahedrons are regular, or deduced from rectangular parallelepipeds, and allows reduction of the number of unknowns. Numerical experiments and comparisons between both formulations in 2D show the efficiency of the new formulation. Copyright © 2003 John Wiley & Sons, Ltd. [source] Robust adaptive output-feedback control for nonlinear systems with output unmodeled dynamicsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 11 2008Zhaojing Wu Abstract In this paper, for a class of uncertain nonlinear systems in the presence of inverse dynamics, output unmodeled dynamics and nonlinear uncertainties, a robust adaptive output-feedback controller design is proposed by combining small-gain theorem, changing supply function techniques with backstepping methods. It is shown that all the signals of the closed-loop system are uniformly bounded in biased case, and the output can be regulated to a small neighborhood of the origin in unbiased case. Furthermore, under some additional assumptions, an asymptotical result is obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source] Global existence for a contact problem with adhesionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2008Elena Bonetti Abstract In this paper, we analyze a contact problem with irreversible adhesion between a viscoelastic body and a rigid support. On the basis of Frémond's theory, we detail the derivation of the model and of the resulting partial differential equation system. Hence, we prove the existence of global in time solutions (to a suitable variational formulation) of the related Cauchy problem by means of an approximation procedure, combined with monotonicity and compactness tools, and with a prolongation argument. In fact the approximate problem (for which we prove a local well-posedness result) models a contact phenomenon in which the occurrence of repulsive dynamics is allowed for. We also show local uniqueness of the solutions, and a continuous dependence result under some additional assumptions. Copyright © 2007 John Wiley & Sons, Ltd. [source] Scepticism and its SourcesPHILOSOPHY AND PHENOMENOLOGICAL RESEARCH, Issue 3 2003SAMIR OKASHA A number of recent philosophers, including Michael Williams, Barry Stroud and Donald Davidson, have argued that scepticism about the external world stems from the founda-tionalist assumption that sensory experience supplies the data for our beliefs about the world. In order to assess this thesis, I offer a brief characterisation of the logical form of sceptical arguments. I suggest that sceptical arguments rely on the idea that many of our beliefs about the world are,underdetermined'by the evidence on which they are based. Drawing on this characterisation of scepticism, I argue that Williams, Stroud and Davidson are right to see the foundationalist assumption as essential to the sceptic's argument, but wrong to think that scepticism is inevitable once that assumption is in place. By pursuing an analogy with some recent debates in the philosophy of science, I try to locate the additional assumptions which the sceptic must make, in order to derive her conclusion. [source] The effective-site percolation approach in two dimensionsPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 7 2007G. Paw, owski Abstract A new Monte Carlo cluster approach to describe the order,order and order,disorder transitions in two-dimensional (2D) correlated systems is presented. It is shown that a phase transition of a physical system can be correctly described in terms of the percolation language of the effective-site approach. In contrast to the well-known bond approaches, the method proposed does not require additional assumptions as to the acceptance of the bonds. The new idea is based on the site approach to elementary ordered plaquettes, leading to the accurate coincidence of percolation and the phase transitions in 2D. Here I present the analysis of the spin-system in the Blume,Capel model and the charged-system in the atomic limit of the extended Hubbard model. In both cases the interpretation of the phase transition is made in terms of the percolation of different types of order. The new method allows precise identification of the pure and mixed phases. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Suspense: Dynamic Incentives in Sports Contests,THE ECONOMIC JOURNAL, Issue 534 2009William Chan In a dynamic model of sports competition, if spectators care only about contestants' efforts, incentive schemes depending linearly on the final score difference dominate rank order schemes based only on who wins. If spectators also care about suspense, defined as valuing more contestants' efforts when the game is closer, rank order schemes can dominate linear score difference schemes, and this will be the case when the demand for suspense is sufficiently high. Under additional assumptions, we show that the optimal rank order scheme dominates a broad class of incentive schemes. [source] A Bayesian Approach to Surrogacy Assessment Using Principal Stratification in Clinical TrialsBIOMETRICS, Issue 2 2010Yun Li Summary A surrogate marker (S) is a variable that can be measured earlier and often more easily than the true endpoint (T) in a clinical trial. Most previous research has been devoted to developing surrogacy measures to quantify how well,S,can replace,T,or examining the use of,S,in predicting the effect of a treatment (Z). However, the research often requires one to fit models for the distribution of,T,given,S,and,Z. It is well known that such models do not have causal interpretations because the models condition on a postrandomization variable,S. In this article, we directly model the relationship among,T,,S, and,Z,using a potential outcomes framework introduced by Frangakis and Rubin (2002,,Biometrics,58, 21,29). We propose a Bayesian estimation method to evaluate the causal probabilities associated with the cross-classification of the potential outcomes of,S,and,T,when,S,and,T,are both binary. We use a log-linear model to directly model the association between the potential outcomes of,S,and,T,through the odds ratios. The quantities derived from this approach always have causal interpretations. However, this causal model is not identifiable from the data without additional assumptions. To reduce the nonidentifiability problem and increase the precision of statistical inferences, we assume monotonicity and incorporate prior belief that is plausible in the surrogate context by using prior distributions. We also explore the relationship among the surrogacy measures based on traditional models and this counterfactual model. The method is applied to the data from a glaucoma treatment study. [source] Regularized Estimation for the Accelerated Failure Time ModelBIOMETRICS, Issue 2 2009T. Cai Summary In the presence of high-dimensional predictors, it is challenging to develop reliable regression models that can be used to accurately predict future outcomes. Further complications arise when the outcome of interest is an event time, which is often not fully observed due to censoring. In this article, we develop robust prediction models for event time outcomes by regularizing the Gehan's estimator for the accelerated failure time (AFT) model (Tsiatis, 1996, Annals of Statistics18, 305,328) with least absolute shrinkage and selection operator (LASSO) penalty. Unlike existing methods based on the inverse probability weighting and the Buckley and James estimator (Buckley and James, 1979, Biometrika66, 429,436), the proposed approach does not require additional assumptions about the censoring and always yields a solution that is convergent. Furthermore, the proposed estimator leads to a stable regression model for prediction even if the AFT model fails to hold. To facilitate the adaptive selection of the tuning parameter, we detail an efficient numerical algorithm for obtaining the entire regularization path. The proposed procedures are applied to a breast cancer dataset to derive a reliable regression model for predicting patient survival based on a set of clinical prognostic factors and gene signatures. Finite sample performances of the procedures are evaluated through a simulation study. [source] | |||||||||||||||||||