On a Class of Self-Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite-Range Truncations

This paper investigates a class of self-adjoint compact operators in Hilbert spaces related to their truncated versions with finite-dimensional ranges. The comparisons are established in terms of worst-case norm errors of the composite operators generated from iterated computations. Some boundedness properties of the worst-case norms of the errors in their respective fixed points in which they exist are also given. The iterated sequences are expanded in separable Hilbert spaces through the use of numerable orthonormal bases.

The Relevance of Relative Position in Ultimatum Games

This paper investigates the effect of focal points and initial relative position in the outcome of a bargaining process. We conduct two on-line experiments. In the first experiment we attempt to replicate Güth, Huck and Müller's (2001) results about the relevance of equal splits. In our second experiment, we recover the choices of participants in forty mini-ultimatum games. This design allows us to test whether the equal split or any other distribution or set of distributions are salient. Our data provide no support for a focal-point explanation but we find support for an explanation based on relative position. Our results confirm that there is a norm against hyper-fair offers. Proposers are expected to behave selfishly when the unselfish distribution leads to a change in the initial relative position.

Bilingual Lexicography:Relevance of Corpora. The Example of German-Basque as Language Pair

Presentation for the 5th International Conference on Corpus Linguistics (CILC 2013), V Congreso Internacional de Lingüistica de Corpus.

Effects of rainfall infiltration on deep slope failure

With the finite element method and the limit equilibrium method, a numerical model has been estab-lished for examining the effects of rainfall infiltration on the stability of slopes. This model is able to reflect the variations in pore water pressure field in slopes, dead weight of the soil, and soil softening caused by rainfall infiltration. As a case study, an actual landslide located at the Nongji Jixiao in Chongqing was studied to analyze the effects of rainfall infiltration on the seepage field and slope sta-bility. The simulated results showed that a deep slope failure is prone to occur when rainfall infiltration leads to a remarkable variation in the seepage field, especially when the pore water pressure in slopes increases in a large range.

高桩码头不均匀沉降模型实验与数值模拟

以使用5年以上的高桩码头的大管桩为研究对象,采用模型实验的方法对大管桩的不均匀沉降进行了系统研究.首先通过量纲分析,确定模型实验的各个物理量和相关参数,以及模型材料(PVC管)等;然后利用电测技术,经过大量实验,获得大管桩的不均匀沉降量和变化规律;同时,利用数值模拟,分析了大管桩不均匀沉降变化规律,验证了模型实验结果的可靠性,说明了利用数值模拟方法分析大管桩不均匀沉降是可行的.

Language distance and non-native syntactic processing: Evidence from event-related potentials

[EN] In this study, we explore native and non-native syntactic processing, paying special attention to the language distance factor. To this end, we compared how native speakers of Basque and highly proficient non-native speakers of Basque who are native speakers of Spanish process certain core aspects of Basque syntax. Our results suggest that differences in native versus non-native language processing strongly correlate with language distance: native/non-native processing differences obtain if a syntactic parameter of the non-native grammar diverges from the native grammar. Otherwise, non-native processing will approximate native processing as levels of proficiency increase. We focus on three syntactic parameters: (i) the head parameter, (ii) argument alignment (ergative/accusative), and (iii) verb agreement. The first two diverge in Basque and Spanish, but the third is the same in both languages. Our results reveal that native and non-native processing differs for the diverging syntactic parameters, but not for the convergent one. These findings indicate that language distance has a significant impact in non-native language processing.

Topics in randomized numerical linear algebra

This thesis studies three classes of randomized numerical linear algebra algorithms, namely: (i) randomized matrix sparsification algorithms, (ii) low-rank approximation algorithms that use randomized unitary transformations, and (iii) low-rank approximation algorithms for positive-semidefinite (PSD) matrices.

Randomized matrix sparsification algorithms set randomly chosen entries of the input matrix to zero. When the approximant is substituted for the original matrix in computations, its sparsity allows one to employ faster sparsity-exploiting algorithms. This thesis contributes bounds on the approximation error of nonuniform randomized sparsification schemes, measured in the spectral norm and two NP-hard norms that are of interest in computational graph theory and subset selection applications.

Low-rank approximations based on randomized unitary transformations have several desirable properties: they have low communication costs, are amenable to parallel implementation, and exploit the existence of fast transform algorithms. This thesis investigates the tradeoff between the accuracy and cost of generating such approximations. State-of-the-art spectral and Frobenius-norm error bounds are provided.

The last class of algorithms considered are SPSD "sketching" algorithms. Such sketches can be computed faster than approximations based on projecting onto mixtures of the columns of the matrix. The performance of several such sketching schemes is empirically evaluated using a suite of canonical matrices drawn from machine learning and data analysis applications, and a framework is developed for establishing theoretical error bounds.

In addition to studying these algorithms, this thesis extends the Matrix Laplace Transform framework to derive Chernoff and Bernstein inequalities that apply to all the eigenvalues of certain classes of random matrices. These inequalities are used to investigate the behavior of the singular values of a matrix under random sampling, and to derive convergence rates for each individual eigenvalue of a sample covariance matrix.

Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.

The variations and climatic significance of D/H ratios in the carbon-bound hydrogen of cellulose in trees

The σD values of nitrated cellulose from a variety of trees covering a wide geographic range have been measured. These measurements have been used to ascertain which factors are likely to cause σD variations in cellulose C-H hydrogen.

It is found that a primary source of tree σD variation is the σD variation of the environmental precipitation. Superimposed on this are isotopic variations caused by the transpiration of the leaf water incorporated by the tree. The magnitude of this transpiration effect appears to be related to relative humidity.

Within a single tree, it is found that the hydrogen isotope variations which occur for a ring sequence in one radial direction may not be exactly the same as those which occur in a different direction. Such heterogeneities appear most likely to occur in trees with asymmetric ring patterns that contain reaction wood. In the absence of reaction wood such heterogeneities do not seem to occur. Thus, hydrogen isotope analyses of tree ring sequences should be performed on trees which do not contain reaction wood.

Comparisons of tree σD variations with variations in local climate are performed on two levels: spatial and temporal. It is found that the σD values of 20 North American trees from a wide geographic range are reasonably well-correlated with the corresponding average annual temperature. The correlation is similar to that observed for a comparison of the σD values of annual precipitation of 11 North American sites with annual temperature. However, it appears that this correlation is significantly disrupted by trees which grew on poorly drained sites such as those in stagnant marshes. Therefore, site selection may be important in choosing trees for climatic interpretation of σD values, although proper sites do not seem to be uncommon.

The measurement of σD values in 5-year samples from the tree ring sequences of 13 trees from 11 North American sites reveals a variety of relationships with local climate. As it was for the spatial σD vs climate comparison, site selection is also apparently important for temporal tree σD vs climate comparisons. Again, it seems that poorly-drained sites are to be avoided. For nine trees from different "well-behaved" sites, it was found that the local climatic variable best related to the σD variations was not the same for all sites.

Two of these trees showed a strong negative correlation with the amount of local summer precipitation. Consideration of factors likely to influence the isotopic composition of summer rain suggests that rainfall intensity may be important. The higher the intensity, the lower the σD value. Such an effect might explain the negative correlation of σD vs summer precipitation amount for these two trees. A third tree also exhibited a strong correlation with summer climate, but in this instance it was a positive correlation of σD with summer temperature.

The remaining six trees exhibited the best correlation between σD values and local annual climate. However, in none of these six cases was it annual temperature that was the most important variable. In fact annual temperature commonly showed no relationship at all with tree σD values. Instead, it was found that a simple mass balance model incorporating two basic assumptions yielded parameters which produced the best relationships with tree σD values. First, it was assumed that the σD values of these six trees reflected the σD values of annual precipitation incorporated by these trees. Second, it was assumed that the σD value of the annual precipitation was a weighted average of two seasonal isotopic components: summer and winter. Mass balance equations derived from these assumptions yielded combinations of variables that commonly showed a relationship with tree σD values where none had previously been discerned.

It was found for these "well-behaved" trees that not all sample intervals in a σD vs local climate plot fell along a well-defined trend. These departures from the local σD VS climate norm were defined as "anomalous". Some of these anomalous intervals were common to trees from different locales. When such widespread commonalty of an anomalous interval occurred, it was observed that the interval corresponded to an interval in which drought had existed in the North American Great Plains.

Consequently, there appears to be a combination of both local and large scale climatic information in the σD variations of tree cellulose C-H hydrogen.

Projetos de cuidado em Fisioterapia

As práticas de cuidado em fisioterapia, em muitas situações, resgatam a função do fisioterapeuta de executor de técnicas que lhe era atribuída nos primórdios da profissão. Ao exercer essa função meramente técnica, muitas vezes deixando-se substituir pelo equipamento nas suas ações, o profissional compromete o estabelecimento do vínculo terapeuta-paciente, contribuindo para o esvaziamento do encontro em saúde. Nessas situações, predomina o êxito técnico (a eficiência na realização do procedimento) sobre o sucesso prático (os benefícios trazidos para vida das pessoas). Para que o sucesso prático seja atingido, é fundamental que haja o questionamento sobre o que sonham as pessoas, profissionais e pacientes, para as suas vidas e para a saúde, quais são suas perspectivas e projetos de vida, seus projetos de felicidade. Nesse sentido, é imprescindível considerar, também, os projetos de felicidade dos profissionais da saúde enquanto sujeitos desse encontro. Afinal, é a partir deles que o profissional elabora o seu projeto de cuidado para cada paciente. Assim, esse trabalho buscou compreender os elementos que configuram a construção de projetos de cuidado em fisioterapia a partir da reflexão dos próprios fisioterapeutas. Para tanto, utilizou-se a metodologia qualitativa de pesquisa por meio de entrevistas semi-estruturadas para que fossem produzidas narrativas da história de vida do trabalho. Os discursos foram analisados integralmente e a categorização foi feita em três sub-temas: exercício profissional, relação com os pacientes e reflexões. Foi possível perceber que muitos dos arranjos de trabalho estabelecidos visam coibir o vínculo profissional-paciente, transformando-o em valor de troca e mercantilizando a relação terapêutica. Expropriada do vínculo, a prática se resume à realização de procedimentos independentes de sua finalidade, minando as possibilidades de sucesso prático. Nesse caso, não é a tecnologia que gera o afastamento e a mecanização, mas são as estratégias de mercantilização do cuidado fisioterápico. Essa situação só pode ocorrer por um processo de subordinação do profissional e seu saber, o que está fortemente associado a condições de trabalho exploratórias. Podemos dizer que a mercantilização do cuidado facilita a restrição sobre as condições de trabalho e também é fruto dela. O problema é que essa restrição é vista pelos profissionais como não definitiva, mas como um caminho para se alcançar reconhecimento na busca pelo exercício liberal da fisioterapia. A intenção desse estudo não foi traçar um plano normativo de conduta para a profissão, mas imaginamos que o equacionamento dessas questões passa necessariamente pelo reconhecimento, pelas inquietações e indignações com o problema. O que se espera, portanto, é facilitar esse processo de desconforto por meio da proximidade dessas questões trazidas pelas narrativas.

Paranormal operator on a Hilbert space

In this thesis an extensive study is made of the set P of all paranormal operators in B(H), the set of all bounded endomorphisms on the complex Hilbert space H. T ϵ B(H) is paranormal if for each z contained in the resolvent set of T, d(z, σ(T))//(T-zI)^-1 = 1 where d(z, σ(T)) is the distance from z to σ(T), the spectrum of T. P contains the set N of normal operators and P contains the set of hyponormal operators. However, P is contained in L, the set of all T ϵ B(H) such that the convex hull of the spectrum of T is equal to the closure of the numerical range of T. Thus, N≤P≤L.

If the uniform operator (norm) topology is placed on B(H), then the relative topological properties of N, P, L can be discussed. In Section IV, it is shown that: 1) N P and L are arc-wise connected and closed, 2) N, P, and L are nowhere dense subsets of B(H) when dim H ≥ 2, 3) N = P when dimH ˂ ∞ , 4) N is a nowhere dense subset of P when dimH ˂ ∞ , 5) P is not a nowhere dense subset of L when dimH ˂ ∞ , and 6) it is not known if P is a nowhere dense subset of L when dimH ˂ ∞.

The spectral properties of paranormal operators are of current interest in the literature. Putnam [22, 23] has shown that certain points on the boundary of the spectrum of a paranormal operator are either normal eigenvalues or normal approximate eigenvalues. Stampfli [26] has shown that a hyponormal operator with countable spectrum is normal. However, in Theorem 3.3, it is shown that a paranormal operator T with countable spectrum can be written as the direct sum, N ⊕ A, of a normal operator N with σ(N) = σ(T) and of an operator A with σ(A) a subset of the derived set of σ(T). It is then shown that A need not be normal. If we restrict the countable spectrum of T ϵ P to lie on a C²-smooth rectifiable Jordan curve G_o, then T must be normal [see Theorem 3.5 and its Corollary]. If T is a scalar paranormal operator with countable spectrum, then in order to conclude that T is normal the condition of σ(T) ≤ G_o can be relaxed [see Theorem 3.6]. In Theorem 3.7 it is then shown that the above result is not true when T is not assumed to be scalar. It was then conjectured that if T ϵ P with σ(T) ≤ G_o, then T is normal. The proof of Theorem 3.5 relies heavily on the assumption that T has countable spectrum and cannot be generalized. However, the corollary to Theorem 3.9 states that if T ϵ P with σ(T) ≤ G_o, then T has a non-trivial lattice of invariant subspaces. After the completion of most of the work on this thesis, Stampfli [30, 31] published a proof that a paranormal operator T with σ(T) ≤ G_o is normal. His proof uses some rather deep results concerning numerical ranges whereas the proof of Theorem 3.5 uses relatively elementary methods.

A Direct Approach to Robustness Optimization

This dissertation reformulates and streamlines the core tools of robustness analysis for linear time invariant systems using now-standard methods in convex optimization. In particular, robust performance analysis can be formulated as a primal convex optimization in the form of a semidefinite program using a semidefinite representation of a set of Gramians. The same approach with semidefinite programming duality is applied to develop a linear matrix inequality test for well-connectedness analysis, and many existing results such as the Kalman-Yakubovich--Popov lemma and various scaled small gain tests are derived in an elegant fashion. More importantly, unlike the classical approach, a decision variable in this novel optimization framework contains all inner products of signals in a system, and an algorithm for constructing an input and state pair of a system corresponding to the optimal solution of robustness optimization is presented based on this information. This insight may open up new research directions, and as one such example, this dissertation proposes a semidefinite programming relaxation of a cardinality constrained variant of the H ∞ norm, which we term sparse H ∞ analysis, where an adversarial disturbance can use only a limited number of channels. Finally, sparse H ∞ analysis is applied to the linearized swing dynamics in order to detect potential vulnerable spots in power networks.

Range of validity of the method of averaging

Sufficient conditions are derived for the validity of approximate periodic solutions of a class of second order ordinary nonlinear differential equations. An approximate solution is defined to be valid if an exact solution exists in a neighborhood of the approximation.

Two classes of validity criteria are developed. Existence is obtained using the contraction mapping principle in one case, and the Schauder-Leray fixed point theorem in the other. Both classes of validity criteria make use of symmetry properties of periodic functions, and both classes yield an upper bound on a norm of the difference between the approximate and exact solution. This bound is used in a procedure which establishes sufficient stability conditions for the approximated solution.

Application to a system with piecewise linear restoring force (bilinear system) reveals that the approximate solution obtained by the method of averaging is valid away from regions where the response exhibits vertical tangents. A narrow instability region is obtained near one-half the natural frequency of the equivalent linear system. Sufficient conditions for the validity of resonant solutions are also derived, and two term harmonic balance approximate solutions which exhibit ultraharmonic and subharmonic resonances are studied.

On certain discrete inequalities and their continous analogues

In a 1955 paper, Ky Fan, Olga Taussky, and John Todd presented discrete analogues of inequalities of Wirtinger type, and by taking limits they were able to recover the continuous inequalities. We generalize their techniques to mixed and higher derivatives and inequalities with weight functions in the integrals. We have also considered analogues of inequalities of Müller and Redheffer and have used these inequalities to derive a necessary and sufficient condition on ordered pairs of numbers so that the first number is the square norm of the k^th derivative of some periodic function and the second number is the square norm of the m^th derivative of the same periodic function.

Smooth Banach spaces and approximations

If E and F are real Banach spaces let C^p,q(E, F) O ≤ q ≤ p ≤ ∞, denote those maps from E to F which have p continuous Frechet derivatives of which the first q derivatives are bounded. A Banach space E is defined to be C^p,q smooth if C^p,q(E,R) contains a nonzero function with bounded support. This generalizes the standard C^p smoothness classification.

If an L^p space, p ≥ 1, is C^q smooth then it is also C^q,q smooth so that in particular L^p for p an even integer is C^∞,∞ smooth and L^p for p an odd integer is C^p-1,p-1 smooth. In general, however, a C^p smooth B-space need not be C^p,p smooth. C_o is shown to be a non-C^2,2 smooth B-space although it is known to be C^∞ smooth. It is proved that if E is C^p,1 smooth then C_o(E) is C^p,1 smooth and if E has an equivalent C^p norm then c_o(E) has an equivalent C^p norm.

Various consequences of C^p,q smoothness are studied. If f ϵ C^p,q(E,F), if F is C^p,q smooth and if E is non-C^p,q smooth, then the image under f of the boundary of any bounded open subset U of E is dense in the image of U. If E is separable then E is C^p,q smooth if and only if E admits C^p,q partitions of unity; E is C^p,psmooth, p ˂∞, if and only if every closed subset of E is the zero set of some C^P function.

f ϵ C^q(E,F), 0 ≤ q ≤ p ≤ ∞, is said to be C_p,q approximable on a subset U of E if for any ϵ ˃ 0 there exists a g ϵ C^p(E,F) satisfying

sup/xϵU, O≤k≤q ‖ D^k f(x) - D^k g(x) ‖ ≤ ϵ.

It is shown that if E is separable and C^p,q smooth and if f ϵ C^q(E,F) is C_p,q approximable on some neighborhood of every point of E, then F is C_p,q approximable on all of E.

In general it is unknown whether an arbitrary function in C¹(l², R) is C_2,1 approximable and an example of a function in C¹(l², R) which may not be C_2,1 approximable is given. A weak form of C_∞,q, q≥1, to functions in C^q(l², R) is proved: Let {U_α} be a locally finite cover of l² and let {T_α} be a corresponding collection of Hilbert-Schmidt operators on l². Then for any f ϵ C^q(l²,F) such that for all α

sup ‖ D^k(f(x)-g(x))[T_αh]‖ ≤ 1.

xϵU_α,‖h‖≤1, 0≤k≤q