pinecone/core-2020-05-10-deduplication huggingface dataset:
Hydrodynamic Damping and Quasi-Coherent Structures at Large Strokes Numbers

The article of record as published may be located at http://dx.doi.org/10.1006/jfls.2001.0384Unsteady flow about solid and perforated cylinders at large Stokes numbers and very small Keulegan-Carpenter numbers has not been sufficiently understood to predict the hydroelastic response of compliant structures subjected to high frequency excitation. It is impossible to compute, difficult to quantify, and extremely difficult to visualize. Here, following a brief review of the previous research, new results for both forced and pluck-induced oscillations are presented. It is shown that: (a) the measured drag coefficients are larger (about double for
smooth cylinders) than those predicted from the Stokes-Wang analysis (in the region of its applicability); (b) there is an unstable #ow regime in which the oscillatory boundary layer develops quasicoherent structures (QCS) over a range of K values before giving rise to
Honji-type coherent structures (HTCS); (c) the drag coefficients for perforated cylinders are much larger than those for solid cylinders and do not follow the Stokes}Wang prediction even at small b. As expected, their inertia coefficients are considerably smaller than those for solid
cylinders
Continuity, authority and the place of heritage in the Medieval world

Copyright © 2000 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Historical Geography, Vol 25 (1), 2000, pp. 47-59. DOI:10.1006/jhge.1999.0190This essay supports the contention that knowledge of the past should be seen as a political resource. Furthermore, the interpretation of a particular version of the past is related to power differentiation and the legitimisation of authority. The subjective use of the past is not a recent phenomenon and in this paper, the use of the past is related to the construction of identity and ecclesiastical organisation during the Medieval period. Bourdieu's notion of habitus is used as a way of grounding the rhetoric of legitimisation, with particular reference to ecclesiastical authority. Hagiographical accounts and legends correspond to discourses of power and are related to the (re)production of a religious identity that legitimated Church authority. The essay pays special attention to west Cornwall where such institutional power is related to an identity that is generated via contemporary notions of heritage and a particular sense of past
Territoriality, parochial development, and the place of ‘community’ in later medieval Cornwall

Copyright © 2003 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Historical Geography, Vol 29 (2), 2003, pp. 151-165. DOI: 10.1006/jhge.2002.0411This paper explores the emerging territorial framework of west Cornwall in relation to community expression and power. It examines such issues as increasing administrative competence, territorial order and communal action. However, although such notions as emerging territoriality, secular political development and local communal cohesion are often associated with studies of modernisation and the emergence of distinctly modern systems and relations, this paper focuses on a peripheral region during the later medieval period (c. 1350–1550) and identifies such transitions as inherent within this pre-modern society. Evolving local ecclesiastical patterns in Cornwall during the fourteenth to sixteenth centuries saw numerous small chapels and sub-parochial foundations struggling for status and recognition amid an increasingly well-delineated territorial framework of parishes. By relating accounts of incidents and episodes of local ecclesiastical politics and discord to the territorial expressions of community organisation, combinations of local people are identified that were operating to control and order their local affairs. As well as questioning the implicit assumptions that some geographers and other scholars have about a medieval society that was supposedly dominated by a collage of lordly manorial and high ecclesiastical power, this paper also makes space for theories of territoriality and organisational complexity as a way of examining the developments of a period for which the written record is both sparse and partial
Optimal Control and Admissible Relaxation of Uncertain Nonlinear Elliptic Systems

AbstractIn this article we study the optimal control of uncertain systems monitored by nonlinear elliptic equations. First under convexity hypotheses, we show that the min–max problem has a solution. Then we drop the convexity assumptions and we pass to the larger relaxed system. We show that this always has a solution under very general hypotheses on the data. We also produce conditions that guarantee that the relaxation is admissible; i.e., the relaxed problem is the “closure” of the original one
On the Eigenfunction Expansions Associated with Fredholm Integral Equations of First Kind in the Presence of Noise

AbstractIn this paper we consider the eigenfunction expansions associated with Fredholm integral equations of first kind when the data are perturbed by noise. We prove that these expansions are asymptotically convergent, in the sense ofL2-norm, when the bound of the noise tends to zero. This result allows us to construct a continuous mapping from the data space to the solution space, without using any constraint ora prioribound. We can also show a probabilistic version of this result, which is based on the order–disorder transition in the Fourier coefficients of the noisy data. From these results one can derive algorithms and in particular statistical methods able to furnish approximations of the solution without any use of prior knowledge
Linear Optimal Control Problems with Piecewise Analytic Solutions

AbstractThis paper is concerned with the existence of piecewise analytic optimal solutions for various linear optimal control problems with piecewise analytic problem data. Some results of this form may be found in the literature but their proofs are generally based on the maximum principle and require certain normality conditions before they can be applied. Also the control constraints are required to be polyhedral and fixed in time. Using the recent theory developed for a class of problems known as separated continuous linear programs we are able to remove the normality conditions completely and allow time varying control constraints of both polyhedral and integral form. In particular, we prove theorems on the existence of piecewise analytic optimal solutions for the linear time-optimal control problem and the linear optimal control problem with or without end point constraints
Solutions of the Strong Hamburger Moment Problem

AbstractThe strong Hamburger moment problem for a bi-infinite sequence {cn:n=0,±1,±2,…} can be described as follows: (1) Find conditions for the existence of a (positive) measure μ on (−∞,∞) such thatcn=∫−∞∞tndμ(t) for alln. (2) When there is a solution, find conditions for uniqueness of the solution. (3) When there is more than one solution, describe the family of all solutions. In this paper a theory concerning question (3) is developed. In particular, an analog to the Nevanlinna parametrization describing the solutions of the classical Hamburger moment problem is given
An Inversion Formula for the Distributional Generalised Laplace Transformation

AbstractA unification and generalisation of several extensions of the classical Laplace transform was given by Professor H. M. Srivastava in 1968. S. K. Sinha gave complex inversion and Tauberian theorems for this general integral transformation. A. K. Tiwari and A. Ko gave several further properties in the distributional sense. S. K. Akhaury extended the generalisation to distributions and derived the Abelian theorems of the initial and final value types. In the present paper we give the inversion formula for the distributional generalised Laplace transformation
A Spectral Analysis for Self-Adjoint Operators Generated by a Class of Second Order Difference Equations

AbstractA qualitative spectral analysis for a class of second order difference equations is given. Central to the analysis of equations in this class is the observation that real-valued solutions exhibit a type of stable asymptotic behavior for certain real values of the spectral parameter. This asymptotic behavior leads to the characterization of the limit point and limit circle nature of these equations, and is used to show that a strong nonsubordinacy criterion is satisfied on subintervals ofRfor equations of limit point type. These subintervals are part of the absolutely continuous spectrum of the self-adjoint realization of these equations. By other means, the nature of the discrete spectrum for these self-adjoint realizations is also discussed
Permanence and Positive Periodic Solutions ofn-Species Competition Reaction–Diffusion Systems with Spatial Inhomogeneity

AbstractThis paper is mainly devoted to the study of permanence and existence of positive periodic solutions ofn-species competition reaction–diffusion systems with spatial inhomogeneity, which are defined on a bounded domain and subjected to Neumann boundary conditions. We first discuss in detail the single-species periodic reaction–diffusion equations. Then by using comparison and maximum principle arguments, we get the sufficient conditions in terms of the principal eigenvalue of periodic-parabolic problem for then-species competition reaction–diffusion systems to be permanent. We further show by using the Schauder fixed point theorem that under the same condition the system admits at least one positive periodic solution. The special case of Lotka–Volterra systems with diffusion and periodic coefficients is also discussed
On Statistical Limit Points and the Consistency of Statistical Convergence

AbstractThis article extends the concept of a statistical limit (cluster) point of a sequencex(as introduced by Fridy) to aT-statistical limit (cluster) point, whereTis a nonnegative regular matrix summability method. These definitions are reformulated in the setting of βN\N. It is shown that for a bounded sequencex, the set ofT-statistical cluster points ofxforms a compact subset of R. It is also shown that, ifTandRare two nonnegative regular summability matrices, thenT-statistical convergence andR-statistical convergence are consistent if and only if the support sets ofTandRhave nonempty intersection
Hankel Matrices and Their Applications to the Numerical Factorization of Polynomials

AbstractGlobally convergent algorithms for the numerical factorization of polynomials are presented. When the zeros of a polynomial are all simple and of different modulus, these procedures are useful in the simultaneous determination of all zeros. These methods are derived based on the algebraic properties of sums of powers of complex numbers and Hankel matrices. The remainder and quotient polynomials which arise from applying the Euclidean and a version of Householder's algorithms are investigated in terms of their convergence properties which turn out to be useful in the splitting of a polynomial into a product of two factors
A New Unconstrained Optimization Method for Imprecise Function and Gradient Values

AbstractA new algorithm for unconstrained optimization is presented which is based on a modified one-dimensional bisection method. The algorithm actually uses only the signs of function and gradient values. Thus it can be applied to problems with imprecise function and gradient values. It converges in one iteration on quadratic functions ofnvariables, it rapidly minimizes general functions and it does not require evaluation or estimation of the matrix of second partial derivatives. The algorithm has been implemented and tested. Performance information for well-known test functions is reported
A Projective Description of the Nachbin-Ported Topology

AbstractIn this article we give a projective description of the Nachbin-ported topology τωin H(U,X), the space of holomorphic mappings on a balanced open subsetUof a Fréchet spaceE(which satisfies certain general conditions) with values in a Banach spaceXwhich is complemented in its bidual. To do this we use the topology τbintroduced by Dineen [Math. Scand.,74(1994) 215–236]. As a consequence we characterize when the compact open topology τ0and τωcoincide on H(U,X′) for every Banach spaceX, in terms of a condition onE. Among the techniques we use to obtain these results are the BB-property, the density condition, a version of quasinormability, and Taylor series expansions
Bifurcation Analysis for Singularities on a Tangent Space for Quadratic Penalty-Barrier and Multipliers Methods for Solving Constrained Optimization Problems, Part I

AbstractThe structure and persistence of critical point solutions obtained from solving constrained optimization problem by the quadratic penalty, the logarithmic-barrier functions, and the multiplier methods are analyzed. This analysis is mainly concerned with singularities due to the Hessian of the Lagrangian being singular on a tangent space. Formulation of the first order conditions of optimality into an algebraic system of equations is first established. The singularities of this system are then classified and solutions are investigated at singularities of codimensions zero and one in terms of the bifurcation behavior and persistence of the curve of critical points
Optimal Error Bounds for Convergents of a Family of Continued Fractions

AbstractLet F be the family of continued fractionsK(ap/1), wherea1=−g1,ap=(1−gp−1)gpxp,p=2,3,…, with 0≤gp≤1,gpfixed, and |xp|≤1,p=2,3,…. In this work, we derive upper bounds on the errors in the convergents ofK(ap/1) that are uniform for F, and optimal in the sense that they are attained by some continued fraction in F. For the special casegi=g<1/2,i=1,2,…, this bound turns out to be especially simple, and forgi=g=1/2,i=1,2,…, the known best form of the theorem of Worpitzki is obtained as an immediate corollary
Length Biasing and Laws Equivalent to the Log-Normal

AbstractLetX>0 denote a generic lifetime of a renewal process having unit mean lifetime, let \hat X denote the stationary total lifetime and letq∈(0,1) be a fixed constant. We consider anew the scale invariance problem: For which laws does q\hat X have the same distribution asX? Our setting is more probabilistic than those presented hitherto, and we explore connections with the log-normal moment problem. In particular it is shown that all explicitly known laws which have log-normal moments solve our problem. The notion of remaining lifetime is generalized and its scaling invariance is investigated using the notion of total lifetime. Two (moment) equivalent laws of Askey are shown to have a simple representation in terms of laws equivalent to the log-normal. The representation involves aq-gamma law, which we explore in its own right. An affine extension of our basic scale invariance relation, arising in the theory of orthogonal polynomials, is shown to be equivalent to the latter
Iterative Parametric Minimax Method for a Class of Composite Optimization Problems

AbstractThis paper considers a class of composite optimization problems that are often difficult to solve directly due to large dimension, nonlinearity, nonseparability, and/or nonconvexity of the problem. An iterative parametric minimax method is proposed in which the original optimization problem is embedded into a weighted minimax formulation. The resulting auxiliary parametric optimization problems at the lower level often have simple structures that are readily tackled by efficient solution strategies, such as the decomposition scheme in dynamic programming and in the primal-dual method. The analytical expression of the partial derivatives of systems performance indices with respect to the weighting vector in the parametric minimax formulation is derived. The gradient method can be thus adopted at the upper level to adjust the value of the weighting vector. The solution of the weighted minimax formulation converges to the optimal solution of the original problem in a multilevel iteration process. An application of the proposed iterative parametric minimax method is demonstrated in constrained reliability optimization problems
On the Equivalence of Ramanujan's Partition Identities and a Connection with the Rogers–Ramanujan Continued Fraction

AbstractA famous identity of Ramanujan connected with partitions modulo 5 is shown to be equivalent to another identity of Ramanujan. The latter identity is used to establish a differential equation for the Rogers–Ramanujan continued fraction found in Ramanujan's lost notebook. We also prove that two other identities of Ramanujan are equivalent, one of which is associated with Ramanujan's partition congruence modulo 7. Last, we give a new proof of the transformation formula for the Dedekind eta-function, which is used in our proofs of equivalence
AnN-Dimensional Analogue of Szegö's Limit Theorem

AbstractLet T denote the unit circle in the complex plane, let φ∈L∞(TN), and for (a1,…,aN)∈(Z+\0)Nlet Λ be the rectangular lattice: Λ={(m1,…,mN)∈ZN:mi∈[0,ai)}. For each positive integerpdefine Λp={(m1,…mN)∈ZN:mi∈[0,pai)}. The Toeplitz matrixTp(φ):l2(Λp)→l2(Λp) with symbol φ is defined by[formula]where[formula]denotes the Fourier coefficients of φ. Assuming appropriate conditions on φ and on a functionFwe findN+1 terms of the asymptotic expansion of the trace ofF(Tp(φ)) asp→∞. This expansion takes the form[formula]where the coefficientscJ,F=cJ,F(φ) depend on theN−Jdimensional faces of Λ. We also find an expansion for the case when the edges of Λ expand at different rates and we apply this generalization to compute an example
A Lévy–Khinchine Formula for Semigroups and Related Problems: An Adapted Spaces Approach

AbstractIn this paper we use a Choquet type theorem on adapted spaces to obtain or reobtain some results in harmonic analysis on semigroups. Thus we give a Lévy–Khinchine formula for some negative definite functions defined on a commutative semigroup with neutral element, we prove that completely monotonic (resp. alternating) functions are completely positive (resp. negative) definite, we characterize the completely monotonic and the completely alternating functions defined on N*≔{1,2,3,…}, and we consider a Stieltjes' moment problem
Convergence and Extraction of Bounded Sequences inL1(R)

AbstractWe present several applications of H. P. Rosenthal's subsequence splitting lemma: Each bounded sequence inL1(R) admits a subsequence satisfying the conclusion of a generalized Fatou's lemma and presenting a concentration of mass phenomenon. We show that the modulus of uniform integrability of a bounded sequence inL1(R) plays a capital role in the convergence in measure of such a sequence. A Cauchy type theorem for the convergence in measure is established. Finally we study the existence of minima of theL1-norm on closed convex subsets ofL1(R+)
Dynamics of Nonlinear Parabolic Systems with Time Delays

AbstractThe dynamics of a coupled system of semilinear parabolic equations with discrete time delays is investigated using the method of upper and lower solutions. It is shown that if the reaction function in the system possesses a mixed quasimonotone property and the corresponding elliptic system has a pair of coupled upper and lower solutions then there is a monotone iteration process which yields a pair of quasisolutions of the elliptic system and the sector between the quasisolutions is an attractor of the delayed parabolic system. Under some additional conditions this sector is a global attractor and the solution of the parabolic system converges to a true solution of the elliptic system. The same conclusions are obtained for a coupled system of parabolic-ordinary equations with time delays. Applications are given to three model problems arising from ecology and nuclear engineering. These model problems possess multiple steady-state solutions and sufficient conditions are given to ensure the stability and instability of these solutions
Persistent Unstable Periodic Motions, I

AbstractWe study the initial value problems of the two dimensional system:[formula]whereI(t)=Ii+ϵtis a slowly varying parameter,f(u,t,I) is analytic on all variables and periodic ontwith period 2π/ω, andu0(t,I) are periodic solutions of the system[formula]whereIis a constant parameter. We assume that the variational equations of (0.2),wt=fv(u0(t,I),t,I)w, have the corresponding characteristic exponents λ1(I),λ2(I)=λ1(I) which move across the imaginary axis from the left half complex plane to the right half complex plane asIincreases pastI−. We show that under the nonresonant conditions H4 and H5 that ω≠(2/n)|Imλ1(I−)| forn∈N (in Section 4), along with other generic conditions such as H1–H3 below, the separations ofu(I(t)) fromu0(t1+t,I(t)) do not occur at the critical point whereI(t)=I−, rather, the bifurcations are substantially delayed untilI(t)=Ii+ϵtreachesIq>I−which is independent of ϵ, as ϵ→0+. In other words, |u(t)−u0(t1+t,I(t))|=0(ϵ) fort∈{t:Ii≤I(t)≤Iq} for someIq=Iq(Ii)>I−independent of ϵ, when ϵ→0+. An exact formula forIqis given for general situations. In near resonance cases, a sharp estimate ofIqis also derived
Generalized Lorenz-Type Systems

AbstractExact general solutions of the Lorenz system of differential equations with arbitrary parameters are unknown. We first present exact particular solutions of this system for special values of the parameters, in terms of Jacobian elliptic functions, but no sensitive dependence on the initial conditions (leading to chaotic behavior) is exhibited by these solutions. We next consider two generalizations of the Lorenz system involving quadratic and cubic terms and obtain their exact general solutions in terms of Bessel and modified Bessel functions, exhibiting sensitive dependence on initial conditions for certain parameter ranges. Finally, a generalized system involving arbitrary powers is reduced to the general Duffing equation with damping, which can be solved exactly when some of the parameters are interconnected. The exact solutions presented, showing precisely how chaotic behavior occurs, are useful for testing conjectures about such differential systems, as well as testing the validity and accuracy of approximate computer solutions, for which numerical errors may grow exponentially fast
Persistent Unstable Periodic Motions, II

AbstractWe study the initial value problems of the two dimensional system:[formula]whereI(t)=Ii+ϵtis a slowly varying parameter,f(u,t,I) is analytic on all variables and periodic ontwith period 2π/ω, andu0(t,I) are periodic solutions of the system[formula]whereIis a constant parameter. We assume that the variational equations of (0.2),wt=fv(u0(t,I),t,I)w, have the corresponding characteristic exponents λ1(I),λ2(I)=λ1(I) which move across the imaginary axis from the left half complex plane to the right half complex plane asIincreases pastI−. We show that under the nonresonant conditions H4 and H5 that ω≠(2/n)|Imλ1(I−)| for anyn∈N in [24], along with other generic conditions H1–H3, the bifurcations ofu(I(t)) fromu0(t1+t,I(t)) would not occur at the critical point whereI(t)=I−, rather, the bifurcations are substantially delayed untilI(t)=Ii+ϵtreachesIq>I−which is independent of ϵ, as ϵ→0+. In other words, |u(t)−u0(t1+t,I(t))|=O(ϵ) fort∈{t:Ii⩽I(t)⩽Iq} for someIq=Iq(Ii)>I−independent of ϵ, when ϵ→0+. We continue from [24] to study the structure of the delayed bifurcations, the exact formula forIqand the effects of the resonance. A counterexample is given to show no delay at resonance