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187
A path independent integral and the approximate analysis of strain concentration by notches and cracks
 Journal of Applied Mechanics
, 1968
"... An integral is exhibited which has the same value for all paths surrounding a class of notches in twodimensional deformation fields of linear or nonlinear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elasticplasti ..."
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Cited by 374 (11 self)
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An integral is exhibited which has the same value for all paths surrounding a class of notches in twodimensional deformation fields of linear or nonlinear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elasticplastic type (treated through a deformation rather than incremental formulation), with a linear response to small stresses followed by nonlinear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recorse to detailed nonlinear analyses. Such an approach is exploited here. Applications are made to: 1) Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elasticplastic materials, 2) A general solution for crack tip separation in the BarenblattDugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and 3) An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.2
ScaleSpace for Discrete Signals
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1990
"... We address the formulation of a scalespace theory for discrete signals. In one dimension it is possible to characterize the smoothing transformations completely and an exhaustive treatment is given, answering the following two main questions: 1. Which linear transformations remove structure in the ..."
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Cited by 132 (25 self)
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We address the formulation of a scalespace theory for discrete signals. In one dimension it is possible to characterize the smoothing transformations completely and an exhaustive treatment is given, answering the following two main questions: 1. Which linear transformations remove structure in the sense that the number of local extrema (or zerocrossings) in the output signal does not exceed the number of local extrema (or zerocrossings) in the original signal? 2. How should one create a multiresolution family of representations with the property that a signal at a coarser level of scale never contains more structure than a signal at a finer level of scale? We propose that there is only one reasonable way to define a scalespace for 1D discrete signals comprising a continuous scale parameter, namely by (discrete) convolution with the family of kernels T (n; t) = e I n (t), where I n are the modified Bessel functions of integer order. Similar arguments applied in the continuous case uniquely lead to the Gaussian kernel.
Stochastic Solutions for Fractional Cauchy Problems
 Calc. Appl. Anal
, 2001
"... Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the or ..."
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Cited by 69 (25 self)
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Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the original Cauchy problem. Fractional Cauchy problems are useful in physics to model anomalous di#usion.
Moving coframes. II. Regularization and theoretical foundations
 Acta Appl. Math
, 1999
"... Abstract. The primary goal of this paper is to provide a rigorous theoretical justification of Cartan’s method of moving frames for arbitrary finitedimensional Lie group actions on manifolds. The general theorems are based a new regularized version of the moving frame algorithm, which is of both th ..."
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Cited by 62 (6 self)
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Abstract. The primary goal of this paper is to provide a rigorous theoretical justification of Cartan’s method of moving frames for arbitrary finitedimensional Lie group actions on manifolds. The general theorems are based a new regularized version of the moving frame algorithm, which is of both theoretical and practical use. Applications include a new approach to the construction and classification of differential invariants and invariant differential operators on jet bundles, as well as equivalence, symmetry, and rigidity theorems for submanifolds under general transformation groups. The method also leads to complete classifications of generating systems of differential invariants, explicit commutation formulae for the associated invariant differential operators, and a general classification theorem for syzygies of the higher order differentiated differential invariants. A variety of illustrative examples demonstrate how the method can be directly applied to practical problems arising in geometry, invariant theory, and differential equations.
An Adaptive Multilevel Approach to Parabolic Equations in Two Space Dimensions
, 1991
"... A new adaptive multilevel approach, for linear parabolic partial differential equations is presented, which is able to handle complicated space geometries, discontinuous coefficients, inconsistent initial data. Discretization in time first (Rothe's method) with order and stepsize control is per ..."
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Cited by 61 (8 self)
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A new adaptive multilevel approach, for linear parabolic partial differential equations is presented, which is able to handle complicated space geometries, discontinuous coefficients, inconsistent initial data. Discretization in time first (Rothe's method) with order and stepsize control is perturbed by an adaptive finite element discretization of the elliptic subproblems, whose errors are controlled independently. Thus the high standards of solving adaptively ordinary differential equations and elliptic boundary value problems are combined. A theory of time discretization in Hilbert space is developed which yields to an optimal variable order method based on a multiplicative error correction. The problem of an efficient solution of the singularly perturbed elliptic subproblems and the problem of error estimation for them can be uniquely solved within the framework of preconditioning. A multilevel nodal basis preconditioner is derived, which allows
Integrated Semigroups and their Applications to the Abstract Cauchy Problem
 Pacific J. Math
, 1988
"... This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial v ..."
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Cited by 44 (0 self)
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This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A n). Investigating these operators we are led to the class of "integrated semigroups". Among others, this class contains the classes of strongly continuous semigroups and cosine families and the class of exponentially bounded distribution semigroups. The given characterizations of the generators of these integrated semigroups unify and generalize the classical characterizations of generators of strongly continuous semigroups, cosine families or exponentially bounded distribution semigroups. We indicate how integrated semigroups can be used studying second order Cauchy problems u"{t) — A\u'{t) Aiu(t) = 0, operator valued equations U'(t) = A { U(t) + U(t)A2 and nonautonomous equations u'{t) = A(t)u(t). 1. Introduction. We
Brownian subordinators and fractional Cauchy problems
, 2007
"... Abstract. A Brownian time process is a Markov process subordinated to the absolute value of an independent onedimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original Markov process. An apparently unrelated class of p ..."
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Cited by 36 (14 self)
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Abstract. A Brownian time process is a Markov process subordinated to the absolute value of an independent onedimensional Brownian motion. Its transition densities solve an initial value problem involving the square of the generator of the original Markov process. An apparently unrelated class of processes, emerging as the scaling limits of continuous time random walks, involve subordination to the inverse or hitting time process of a classical stable subordinator. The resulting densities solve fractional Cauchy problems, an extension that involves fractional derivatives in time. In this paper, we will show a close and unexpected connection between these two classes of processes, and consequently, an equivalence between these two families of partial differential equations. 1.
Triggers and Enablers of Sensegiving in Organizations
 Academy of Management Journal
, 2007
"... Drawing on a longitudinal study of sensegiving in organizations, we investigate the conditions associated with sensegiving by stakeholder and by leaders: for each group, we identify sets of conditions that trigger sensegiving and sets of conditions that enable sensegiving. We then integrate these an ..."
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Cited by 31 (0 self)
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Drawing on a longitudinal study of sensegiving in organizations, we investigate the conditions associated with sensegiving by stakeholder and by leaders: for each group, we identify sets of conditions that trigger sensegiving and sets of conditions that enable sensegiving. We then integrate these analyses across organizational actors to show that, more generally, sensegiving is triggered by the perception or anticipation of a gap in organizational sensemaking processes, and enabled by the possession of discursive ability, which allows leaders and stakeholders to construct and articulate persuasive accounts, and the presence of process facilitators, which are routines, practices and structures that provide the time and opportunity for organizational actors to engage in sensegiving. 3 Organizational life is full of attempts to affect how others perceive and understand the world. Gioia and Chittipeddi (1991: 442) coined the term “sensegiving ” to describe this “process of attempting to influence the sensemaking and meaning construction of others toward a preferred redefinition of organizational reality”. Sensegiving is an interpretive process (Bartunek, Krim, Necochea & Humphries, 1999; Gioia & Chittipeddi, 1991) in which actors influence each other through persuasive or evocative language (Dunford & Jones, 2000; Snell, 2002), and is used both by organizational leaders (Bartunek et al., 1999; Corley & Gioia, 2004; Gioia &