Representation Theorem Research Papers - Academia.edu (original) (raw)

The first representation theorem establishes a correspondence between positive, self-adjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying... more

The first representation theorem establishes a correspondence between positive, self-adjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying space is a reflexive Banach space. In particular, the construction of the Friedrichs extension and the form sum of positive operators can be carried over to this case.

In this paper we introduce two general non-parametric first-order stationary time-series models for which marginal (invariant) and transition distributions are expressed as infinite-dimensional mixtures. That feature makes them the first... more

In this paper we introduce two general non-parametric first-order stationary time-series models for which marginal (invariant) and transition distributions are expressed as infinite-dimensional mixtures. That feature makes them the first Bayesian stationary fully non-parametric models developed so far. We draw on the discussion of using stationary models in practice, as a motivation, and advocate the view that flexible (non-parametric) stationary models might be a source for reliable inferences and predictions. It will be noticed that our models adequately fit in the Bayesian inference framework due to a suitable representation theorem. A stationary scale-mixture model is developed as a particular case along with a computational strategy for posterior inference and predictions. The usefulness of that model is illustrated with the analysis of Euro/USD exchange rate log-returns.

A constitutive model for anisotropic elastoplasticity at finite strains is developed together with its numerical implementation. An anisotropic elastic constitutive law is described in an invariant setting by use of structural tensors and... more

A constitutive model for anisotropic elastoplasticity at finite strains is developed together with its numerical implementation. An anisotropic elastic constitutive law is described in an invariant setting by use of structural tensors and the elastic strain measure Ce. The elastic strain tensor as well as the structural tensors are assumed to be invariant in relation to superimposed rigid body rotations. An anisotropic Hill-type yield criterion, described by a non-symmetric Eshelby-like stress tensor and further structural tensors, is developed, where use is made of representation theorems for functions with non-symmetric arguments. The model also considers non-linear isotropic hardening. Explicit results for the specific case of orthotropic anisotropy are given. The associative flow rule is employed and the features of the inelastic flow rule are discussed in full. It is shown that the classical definition of the plastic material spin is meaningless in conjunction with the present formulation. Instead, the study motivates an alternative definition, which is based on the demand that such a quantity must be dissipation-free, as the plastic material spin is in the case of isotropy. Equivalent spatial formulations are presented too. The full numerical treatment is considered in Part II.

Let f be a convex function defined on an interval I, 0⩽α⩽1 and A,Bn×n complex Hermitian matrices with spectrum in I. We prove that the eigenvalues of f(αA+(1−α)B) are weakly majorized by the eigenvalues of αf(A)+(1−α)f(B). Further if f is... more

Let f be a convex function defined on an interval I, 0⩽α⩽1 and A,Bn×n complex Hermitian matrices with spectrum in I. We prove that the eigenvalues of f(αA+(1−α)B) are weakly majorized by the eigenvalues of αf(A)+(1−α)f(B). Further if f is log convex we prove that the eigenvalues of f(αA+(1−α)B) are weakly majorized by the eigenvalues of f(A)αf(B)1−α. As applications we obtain generalizations of the famous Golden–Thomson trace inequality, a representation theorem and a harmonic–geometric mean inequality. Some related inequalities are discussed.

In this paper we construct a theory of stochastic integration of processes with values in calL(H,E)\calL(H,E)calL(H,E), where HHH is a separable Hilbert space and EEE is a UMD Banach space. The integrator is an HHH-cylindrical Brownian motion. Our... more

In this paper we construct a theory of stochastic integration of processes with values in calL(H,E)\calL(H,E)calL(H,E), where HHH is a separable Hilbert space and EEE is a UMD Banach space. The integrator is an HHH-cylindrical Brownian motion. Our approach is based on a two-sided LpL^pLp-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic

This paper gives a isomorphic representation of the subtheories RT − , RT − EC, and RT of Asher and Vieu’s first-order ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We... more

This paper gives a isomorphic representation of the subtheories RT − , RT − EC, and RT of Asher and Vieu’s first-order ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We develop the theory of p-ortholattices – lattices that are both orthocomplemented and pseudocomplemented – and show that the identity (x·y) ∗ = x ∗ +y ∗ defines the natural class of Stonian p-ortholattices. Equivalent conditions for a p-ortholattice to be Stonian are given. The main contribution of the paper consists of a representation theorem for RT − as Stonian p-ortholattices. Moreover, it is shown that the class of models of RT − EC is isomorphic to the non-distributive Stonian p-ortholattices and a representation of RT is given by a set of four algebras of which one need to be a subalgebra of the present model. As corollary we obtain that Axiom (A11) – existence of two externally connected regions – is in fact a theorem of the remaining axioms...

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension on the space B 1 of ideal sets. We show that... more

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension on the space B 1 of ideal sets. We show that if the extension is concave then the core of the game v is non-empty iff is homogeneous of degree one along the diagonal of B 1. We use this result to obtain representation theorems for the core of a non-atomic game of the form v=f^μ where μ is a finite dimensional vector of measures and f is a concave function. We also apply our results to some non-atomic games which occur in economic applications.

... discussed in the general review Makinson (to appear). However, we shall group the ... However, as shown in Makinson and Gärdenfors (1990), if the set Δ of expectations is assumed, as in what follows, to be closed under logical... more

... discussed in the general review Makinson (to appear). However, we shall group the ... However, as shown in Makinson and Gärdenfors (1990), if the set Δ of expectations is assumed, as in what follows, to be closed under logical consequence, then the special case ...

This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about... more

This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about the hypothesis set: it is a vectorial space, it is a set of pointwise defined functions, and the evaluation functional on this set is a continuous mapping. Based on these principles an original theory is developed generalizing the notion of reproduction kernel Hilbert space to non hilbertian sets. Then it is shown that the hypothesis set of any learning machine has to be a generalized reproducing set. Therefore, thanks to a general “representer theorem”, the solution of the learning problem is still a linear combination of a kernel. Furthermore, a way to design these kernels is given. To illustrate this framework some examples of such reproducing sets and kernels are given.

For a coisotropic (or first-class) submanifold C of a Poisson manifold X we consider star-products for which the vanishing ideal I of C becomes a left ideal in the deformed algebra thus defining a left module structure on the space of... more

For a coisotropic (or first-class) submanifold C of a Poisson manifold X we consider star-products for which the vanishing ideal I of C becomes a left ideal in the deformed algebra thus defining a left module structure on the space of smooth functions on C. We show how this can be deduced from a formality conjecture a la Tamarkin generalized

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gärdenfors developed... more

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gärdenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourrón and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of its axiomatic bases), that fails to imply the proposition being eliminated.In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate “partial meet contraction functions”, which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular...

We define quasi--locally presentable categories as big unions of coreflective subcategories which are locally presentable. Under appropriate hypotheses we prove a representability theorem for exact contravariant functors defined on a... more

We define quasi--locally presentable categories as big unions of coreflective subcategories which are locally presentable. Under appropriate hypotheses we prove a representability theorem for exact contravariant functors defined on a quasi--locally presentable category taking values in abelian groups. We show that the abelianization of a well generated triangulated category is quasi--locally presentable and we obtain a new proof of Brown representability theorem. Examples of functors which are not representable are also given.

The polar representation theorem for the n-dimensional time-dependent linear Hamiltonian system with continuous coefficients, states that, given two isotropic solutions (Q1, P1) and (Q2, P2), with the identity matrix as Wronskian,the... more

The polar representation theorem for the n-dimensional time-dependent linear Hamiltonian system with continuous coefficients, states that, given two isotropic solutions (Q1, P1) and (Q2, P2), with the identity matrix as Wronskian,the formula Q2 = rcos(f), Q1 = rsin(f), holds, where r and f are continuous matrices, r is non-singular and f is symmetric. In this article we use the monotonicity properties of the matrix f eigenvalues in order to obtain results on the Sturm-Liouville problem.

Common kinematic strong motion modeling techniques can be divided into integral and composite according to the source representation. In the integral approach, we usually consider the rupture propagating in the form of a slip pulse,... more

Common kinematic strong motion modeling techniques can be divided into integral and composite according to the source representation. In the integral approach, we usually consider the rupture propagating in the form of a slip pulse, creating the k-squared final slip distribution. Such a model is acceptable on large scales where the faulting process is assumed to be deterministic, which is

The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and su cient for the vanishing of tetrad di erences in a linear correlation structure. This note simpli es their proof... more

The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and su cient for the vanishing of tetrad di erences in a linear correlation structure. This note simpli es their proof and generalizes the ...