This dissertation consists of three more or less independent projects. In the first project, we find the microstates free entropy dimension of a large class of L1[0; 1]{ circular operators, in the presence of a generator of the diagonal subalgebra. In the second one, for each sequence {cn}n in l1(N), we de fine an operator A in the hyper finite II1-factor R. We prove that these operators are quasinilpotent and they generate the whole hyper finite II1-factor. We show that they have non-trivial, closed, invariant subspaces affiliated to the von Neumann algebra, and we provide enough evidence to suggest that these operators are interesting for the hyperinvariant subspace problem. We also present some of their properties. In particular, we show that the real and imaginary part of A are equally distributed, and we find a combinatorial formula as well as an analytical way to compute their moments. We present a combinatorial way of computing the moments of A*A. Finally, let fTkg1k =1 be a family of *-free identically distributed operators in a finite von Neumann algebra. In this paper, we prove a multiplicative version of the Free Central Limit Theorem. More precisely, let Bn = T*1T*2...T*nTn...T2T1 then Bn is a positive operator and B1=2n n converges in distribution to an operator A. We completely determine the probability distribution v of A from the distribution u of jTj2. This gives us a natural map G : M M with u G(u) = v. We study how this map behaves with respect to additive and multiplicative free convolution. As an interesting consequence of our results, we illustrate the relation between the probability distribution v and the distribution of the Lyapunov exponents for the sequence fTkg1k=1 introduced by Vladismir Kargin.

1.Sn/Ag4.0/Cu0.5 solder with better performance by the improved reflow profile. 2.The Sn/Ag2.6/Cu0.6¡BSn/Ag4.0/Cu0.5 with similar reliability test performance.

ABSTRACT In package, it¡¦s easy to have defects in the solder joint, for the request of environment protection, lead-free solder research is one of the most important topics now. In soldering, the adhesion, diffusion barrier, and wettability of the interface between UBM and a lead-free solder, and the caused IMC structure that are important elements to influence long-term reliability tests. The thesis is aimed to investigate the combination of pure tin/Al-NiV-Cu UBM/STD Au substrate under reliability tests. The samples are bare dies in which the combination is pure tin/ Al-NiV-Cu UBM and packages of is pure tin/Al-NiV-Cu UBM/STD Au substrate. The goals are to realize the mechanical properties under multiple reflows and long term HTST tests with different temperatures and the operational life. We also uses SEM to observe the growth of IMC and the failure modes that help us to realize the connection between failure modes and IMC. The results of experiment can be concluded as follows. In a bare die, 260¢Jmultiple reflows test causes delamination between IMC and die, but doesn¡¦t affect the mechanical properties of it, and HTST test lowers the bump shear strength of it. In package, multiple reflows test and HTST test lower the mechanical properties significantly, the result also means that the adhesion between bump and die will drop significantly as tests go on. In HTOL test with the conditions of 150¢J and 320mA, the average stable service time of the package is 892 hours, and the average ultimate service time of the package is 1,053 hours, most probable failure site is in R1 joint.

Radial basis functions (RBFs) are probably best known for their applications to scattered data problems. Until the 1990s, RBF theory only involved functions that were scalar-valued. Matrix-valued RBFs were subsequently introduced by Narcowich and Ward in 1994, when they constructed divergence-free vector-valued functions that interpolate data at scattered points. In 2002, Lowitzsch gave the first error estimates for divergence-free interpolants. However, these estimates are only valid when the target function resides in the native space of the RBF. In this paper we develop Sobolev-type error estimates for cases where the target function is less smooth than functions in the native space. In the process of doing this, we give an alternate characterization of the native space, derive improved stability estimates for the interpolation matrix, and give divergence-free interpolation and approximation results for band-limited functions. Furthermore, we introduce a new class of matrix-valued RBFs that can be used to produce curl-free interpolants.

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Thesis (M.A.)--York University, 2008. Graduate Programme in Communication and Culture. / Typescript. Includes bibliographical references (leaves 107-114). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR38809

Inaug.-diss.--Göttingen. / Lebenslauf. "Literaturverzeichnis": p. 7-9.

Inaug.-diss.--Bonn. / Published in enlarged form in Renaissance und philosophie, hft. VII, 1914, with title: Die willensfreiheit bei Laurentius Valla und bei Petrus Pomponatius.

Thesis (M. Arch.)--University of Hong Kong, 1995. / Includes bibliographical references (leaves 29-30).

Thesis (M.S.)--Middle East Technical University, 2003. / Keywords: Ethyl methacrylate, atom transfer radical polymerization, gamma irradiation, free radical polymerization, viscosity.