162,589 research outputs found
Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error
We consider a cointegrating regression in which the integrated regressors are
messy in the sense that they contain data that may be mismeasured, missing,
observed at mixed frequencies, or have other irregularities that cause the econometrician
to observe them with mildly nonstationary noise. Least squares estimation
of the cointegrating vector is consistent. Existing prototypical variancebased
estimation techniques, such as canonical cointegrating regression (CCR),
are both consistent and asymptotically mixed normal. This result is robust to
weakly dependent but possibly nonstationary disturbances.cointegration, canonical cointegrating regression, near-epoch dependence,
messy data, missing data, mixed-frequency data, measurement error, interpolation
Singular Higher-Order Complete Vector Bases for Finite Methods
This paper presents new singular curl- and divergence- conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems
The Effect of Quadrature Errors in the Computation of L^2 Piecewise Polynomial Approximations
In this paper we investigate the L^2 piecewise polynomial approximation problem. L^2 bounds for the derivatives of the error in approximating sufficiently smooth functions by polynomial splines follow immediately from the analogous results for polynomial spline interpolation. We derive L^2 bounds for the errors introduced by the use of two types of quadrature rules for the numerical computation of L^2 piecewise polynomial approximations. These bounds enable us to present some asymptotic results and to examine the consistent convergence of appropriately chosen sequences of such approximations. Some numerical results are also included
Thermodynamically consistent equilibrium properties of normal-liquid Helium-3
The high-precision data for the specific heat C_{V}(T,V) of normal-liquid
Helium-3 obtained by Greywall, taken together with the molar volume V(T_0,P) at
one temperature T_0, are shown to contain the complete thermodynamic
information about this phase in zero magnetic field. This enables us to
calculate the T and P dependence of all equilibrium properties of normal-liquid
Helium-3 in a thermodynamically consistent way for a wide range of parameters.
The results for the entropy S(T,P), specific heat at constant pressure
C_P(T,P), molar volume V(T,P), compressibility kappa(T,P), and thermal
expansion coefficient alpha(T,P) are collected in the form of figures and
tables. This provides the first complete set of thermodynamically consistent
values of the equilibrium quantities of normal-liquid Helium-3. We find, for
example, that alpha(T,P) has a surprisingly intricate pressure dependence at
low temperatures, and that the curves alpha(T,P) vs T do not cross at one
single temperature for all pressures, in contrast to the curves presented in
the comprehensive survey of helium by Wilks.
Corrected in cond-mat/9906222v3: The sign of the coefficient d_0 was
misprinted in Table I of cond-mat/9906222v1 and v2. It now correctly reads
d_0=-7.1613436. All results in the paper were obtained with the correct value
of d_0. (We would like to thank for E. Collin, H. Godfrin, and Y. Bunkov for
finding this misprint.)Comment: 19 pages, 19 figures, 9 tables; published version; note added in
proof; v3: misprint correcte
Advancing In Situ Modeling of ICMEs: New Techniques for New Observations
It is generally known that multi-spacecraft observations of interplanetary
coronal mass ejections (ICMEs) more clearly reveal their three-dimensional
structure than do observations made by a single spacecraft. The launch of the
STEREO twin observatories in October 2006 has greatly increased the number of
multipoint studies of ICMEs in the literature, but this field is still in its
infancy. To date, most studies continue to use on flux rope models that rely on
single track observations through a vast, multi-faceted structure, which
oversimplifies the problem and often hinders interpretation of the large-scale
geometry, especially for cases in which one spacecraft observes a flux rope,
while another does not. In order to tackle these complex problems, new modeling
techniques are required. We describe these new techniques and analyze two ICMEs
observed at the twin STEREO spacecraft on 22-23 May 2007, when the spacecraft
were separated by ~8 degrees. We find a combination of non-force-free flux rope
multi-spacecraft modeling, together with a new non-flux rope ICME plasma flow
deflection model, better constrains the large-scale structure of these ICMEs.
We also introduce a new spatial mapping technique that allows us to put
multispacecraft observations and the new ICME model results in context with the
convecting solar wind. What is distinctly different about this analysis is that
it reveals aspects of ICME geometry and dynamics in a far more visually
intuitive way than previously accomplished. In the case of the 22-23 May ICMEs,
the analysis facilitates a more physical understanding of ICME large-scale
structure, the location and geometry of flux rope sub-structures within these
ICMEs, and their dynamic interaction with the ambient solar wind
Constitutive modeling of two phase materials using the Mean Field method for homogenization
A Mean-Field homogenization framework for constitutive modeling of materials involving two distinct elastic-plastic phases is presented. With this approach it is possible to compute the macroscopic mechanical behavior of this type of materials based on the constitutive models of the constituent phases. Different homogenization schemes that exist in the literature are implemented in efficient algorithms to be used in full-scale FE simulations. These schemes are compared with each other in terms of efficiency. Additionally two new schemes are proposed which are both computationally efficient and compare in accuracy with the more physically based approaches. Finally the algorithms are demonstrated on FE simulations of sheet metal forming operations and compared with experimental results
Quantifier-Free Interpolation of a Theory of Arrays
The use of interpolants in model checking is becoming an enabling technology
to allow fast and robust verification of hardware and software. The application
of encodings based on the theory of arrays, however, is limited by the
impossibility of deriving quantifier- free interpolants in general. In this
paper, we show that it is possible to obtain quantifier-free interpolants for a
Skolemized version of the extensional theory of arrays. We prove this in two
ways: (1) non-constructively, by using the model theoretic notion of
amalgamation, which is known to be equivalent to admit quantifier-free
interpolation for universal theories; and (2) constructively, by designing an
interpolating procedure, based on solving equations between array updates.
(Interestingly, rewriting techniques are used in the key steps of the solver
and its proof of correctness.) To the best of our knowledge, this is the first
successful attempt of computing quantifier- free interpolants for a variant of
the theory of arrays with extensionality
Singular Higher Order Divergence-Conforming Bases of Additive Kind and Moments Method Applications to 3D Sharp-Wedge Structures
We present new subsectional, singular divergence conforming vector bases that incorporate the edge conditions for conducting wedges. The bases are of additive kind because obtained by incrementing the regular polynomial vector bases with other subsectional basis sets that model the singular behavior of the unknown vector field in the wedge neighborhood. Singular bases of this kind, complete to arbitrarily high order, are described in a unified and consistent manner for curved quadrilateral and triangular elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. Our singular bases guarantee normal continuity along the edges of the elements allowing for the discontinuity of tangential components, adequate modelling of the divergence, and removal of spurious solutions. These singular high-order bases provide more accurate and efficient numerical solutions of surface integral problems. Several test-case problems are considered in the paper, thereby obtaining highly accurate numerical results for the current and charge density induced on 3D sharp-wedge structures. The results are compared with other solutions when available and confirm the faster convergence of these bases on wedge problem
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